Minimum Wage and Individual Worker

Productivity: Evidence from a Large US

Retailer∗

Decio Coviello

HEC Montréal

Erika Deserranno

Northwestern

Nicola Persico

Northwestern

June 5, 2020

Abstract

We study how individual worker productivity responds to the minimum wage. Our

workers are employed by a large US retailer, work in di�erent store locations, and

are paid based on performance. By means of a border-discontinuity analysis we

document that workers whose average pay is very close to minimum wage become

more productive, and they are terminated less often after a minimum wage increase.

Workers whose average wage exceeds minimum wage also become more productive

and are terminated less, but this e�ect is more muted. We interpret these �ndings

using a new model where incentives to exert e�ort come from two channels: pay for

performance (where the minimum wage is expected to de-motivate e�ort provision),

and e�ciency wages (where the minimum wage is expected to motivate it). A pure

pay-for-performance model is rejected in favor of a hybrid model where the e�ciency

wage channel predominantly shapes the worker's productivity response.

Keywords: minimum wage, worker productivity, termination, e�ciency-wage, pay-

for-performance. JEL Classi�cation: J24, J38, J63, J88, M52

∗Thanks to �ve anonymous referees, David Card, Luis Garicano, Mitch Ho�man, Daniel Parent,Daniele Paserman, Oskar Nordstrom Skans, Chris Stranton and seminar participants at NBER-OE,SIOE2018, Barcelona GSE forum, Syracuse University, UCLA Anderson, Uppsala University, Univer-sity of Miami, University of Toronto, Bank of Canada, McGill University, the Productivity PartnershipLabor Workshop (HEC Montreal) and the Wages and Labor Market Workshop (Helsinki). This researchwas conducted in collaboration with Workforce Science Project of the Searle Center for Law, Regulationand Economic Growth at Northwestern University, and was undertaken, in part, thanks to funding fromthe Canada Research Chairs program. We thank Suhail Amiri, Vincent Chartray, Margaux Jutant, An-dre Cazor Katz, Athanasse Za�rov for excellent research assistance. The authors declare they have norelevant or material �nancial interests that relate to the research described in this paper. This paper hasbeen screened to ensure no con�dential information is revealed. Data and institutional background willbe provided such that we do not disclose information that may allow the �rm to be identi�ed. E-mails:decio.coviello@hec.ca; erika.deserranno@kellogg.northwestern.edu; nicola@nicolapersico.com.

1 Introduction

We study the e�ect of the minimum wage on individual worker productivity. Our workers

are salespeople, whose individual productivity is measured by sales per hour and whose

pay is based on individual performance. They are employed by a large US retailer that

operates more than 2,000 stores across all �fty states and employs more than 10% of

department store employees nationwide, or roughly 1-2% of employment in the entire US

retail sector.

Using a border-discontinuity research design, we show that increasing the minimum

wage causes an increase in individual worker productivity. This e�ect is strongest for

workers whose average pay is very close to the minimum wage. These workers are also

terminated less often after a minimum wage increase. We interpret these �ndings through

the lens of an e�ciency wage model, where the threat of losing one's now-higher paying job

incentivizes the worker to exert more e�ort. In our context, e�ort consists of meeting and

greeting the customer, explaining product features, up-selling to higher-margin products,

and cross-selling (warranties, loans, credit cards, etc.).

Workers whose average pay exceeds the minimum wage are shown to exhibit the same

response, only less pronounced. This is interesting because all our workers are compen-

sated based on performance, and economic logic suggests that the minimum wage should

disincentivize e�ort by reducing the steepness of the incentive schedule. This disincentive

e�ect works against the other incentive e�ect of the minimum wage, which comes through

the e�ciency wage channel.

To keep track of these opposing incentives we introduce a new model where e�ort is

incentivized in two ways: by the variable component of pay, and by the threat of termi-

nation. Termination is based on monitoring of e�ort, which is carried out by supervisors.

In this model incentives come from two channels: pay for performance (where the mini-

mum wage is expected to de-motivate e�ort provision), and e�ciency wages (where the

minimum wage is expected to motivate it). Depending on parameter values, the model

specializes to a �pure pay for performance� case, to a �pure e�ciency wage� case, or to

�hybrid� case where workers are incentivized by both e�ects but the e�ciency wage ef-

1

fect dominates. The key parameter that determines which case obtains is the parameter

capturing monitoring accuracy.

Depending on the value of the monitoring parameter, workers response to the mini-

mum wage �ips sign. We show evidence of this sign �ip in the data, by comparing worker

response to the minimum wage across stores with di�erent supervisor/worker ratios. By

means of this and other comparative statics, we prove that our empirical setting resem-

bles the �hybrid� case. This means that the e�ciency wage motive predominates over

performance pay as the source of incentives.

Our results on individual productivity are not confounded by worker selection, cross

border migration, price changes, nor by other organizational changes as far as we could

measure. Demand shifts are ruled out as confounders by means of a novel demand proxy:

parking-lot occupancy measured by satellite pictures. Our core �ndings are robust to a

�state-panel� research design or to using alternative samples.

Moving to store-level outcomes, we document that termination, hiring, and turnover

rates all decrease with the minimum wage, and that the e�ect is increasing in the fraction

of workers with low average pay. This is as predicted by the model. This evidence agrees

with the minimum wage literature's �ndings on aggregate �ows of low-paid workers (e.g.,

Brochu and Green 2013, Dube et al. 2016). Finally, the model has some speci�c predictions

regarding employment and pro�ts. Because HQ sets wages and prices uniformly across

stores, average pro�ts across all stores are expected to decrease with the minimum wage,

and this is what we �nd in the data. Employment is expected to co-move with pro�ts at

the store level, and we document this too.

The paper proceeds as follows. Next, we discuss the small literature on minimum wage

and individual worker productivity. Section 2 presents the model. Section 3 describes the

data, the institutional context, and the identi�cation strategy. Section 4 discusses our core

results: the e�ect of minimum wage on worker productivity. Section 5 tests additional

comparative statics predictions by means of heterogeneous e�ects analyses. The point

is to reinforce the reader's trust in the model. Section 6 presents store-level results on

turnover, employment, and pro�ts. These results have independent interest but, more

importantly, the results on termination and turnover for low types (they decrease after a

2

minimum wage increase) are an integral part of the e�ciency wage channel that we say

is operative. Section 7 rules out two alternative channels: demand and organizational

adjustment. Section 8 discusses the external validity of our �ndings and how they connect

to the vast minimum wage literature on employment and pro�ts. Section 9 concludes.

Literature on Minimum Wage and Worker Productivity

This section focuses speci�cally on the small literature on minimum wage and worker

productivity, which is where our core contribution lies. Our connection with the vast

literature on the minimum wage, employment, and pro�ts is discussed in Section 8.

To our knowledge, the literature on the individual productivity e�ects of the minimum

wage only consists of Ku (2018) and Hill (2018). They study tomato and strawberry

pickers, respectively, in a single farm around one or two minimum wage events. Because

they use relatively more productive workers as the control group, their research designs

only a�ord relative estimates (low vs. high types) of the productivity gain. We are able to

estimate absolute productivity gains because we observe workers in nearby establishments

experiencing no minimum wage increase. This is our most important contribution to the

literature.

Our second contribution is that our model reconciles Ku's (2018) and Hill's (2018)

apparently con�icting results. If one is willing to interpret their estimates as absolute,

and not relative to other types, then it can be said that individual productivity increases

in Ku (2018), and decreases in Hill (2018), after a minimum wage increase. In our model,

this ��ipped� response arises naturally if the e�ciency wage logic operates in one setting,

and the pay-for-performance logic in the other. And, indeed, Ku (2018) appeals implicitly

to termination as the source of incentives, whereas Hill (2018, page 6) remarks that her

workers are rarely terminated, suggesting that incentive must come from performance pay.

Our third contribution to the literature is that we observe many homogeneous work-

places across space (local stores) and time (70 minimum wage events). This richness

a�ords a rich set of covariates, such as local economic conditions and store-level mon-

itoring, which we use to shed light on the underlying mechanisms. Finally, being able

3

to observe store-level pro�ts and employment allows us to more closely connect with the

empirical labor literature. With that being said, our analysis is complementary and not

substitute with Ku (2018) and Hill (2018) because of di�erent sectors (retail vs. agricul-

ture), and because their dependent variable, the weight of fruit picked, is a more direct

measure of productivity than sales per hour.

2 Model

The model generalizes the e�ciency wage model of Rebitzer and Taylor (1995, henceforth

RT) by allowing pay to depend on performance. In addition, workers di�er by type, i.e.,

by productivity and cost of e�ort. Ours, then, is a �dual model� where e�ort provision

follows either an e�ciency wage logic or as a pay-for-performance logic, depending on

parameter values and on worker type. All the proofs are presented in Appendix B.1.

Each worker has a �rm-speci�c type x ≥ 0 and chooses an e�ort level e ∈ {0, 1}.1 We

say that the worker �exerts e�ort� if e = 1. Worker productivity (i.e., value of output: in

our case, sales revenue per hour) is a non-negative random variable Y (x, e) such that:

Y (x′, e) % Y (x, e) for x′ > x

Y (x, 1) % Y (x, 0) ,

where the relation % denotes �rst-order stochastic dominance. Thus higher types have

a lower cost of e�ort and higher productivity. Exerting e�ort improves productivity for

every type x. The cost of exerting e�ort is c (x) > 0, a decreasing function of x such that

c(0) =∞.

Consider any non-decreasing compensation scheme w (·) that transforms sales revenue

into pay. (For example, w (Y ) = b + cY where b represents the base salary and c the

1 The binary e�ort assumption is carried over from RT. We interpret it as a crude approximation of acontinuous e�ort model with a cost function that has moderate slope for e ∈ [0, 1] and becomes extremelysteep for e > 1. We work out a continuous-e�ort extension in Appendix B.2, and show that our main Eq.(4) generalizes with few changes.

4

commission rate.) Denote a worker's expected wage by:

w (x, e) = E (w (Y (x, e))) .

As in RT, we denote by q the exogenous probability that the worker quits, by r the

discount rate, by D the probability that shirking is detected, and by s the probability

of exiting unemployment. The workers' value from not shirking, shirking, and being

unemployed, solves:

V N (x) = w (x, 1)− c (x) +(1− q)(1 + r)

V N (x) +q

(1 + r)V A (1)

V S (x) = w (x, 0) +(1− q)(1 + r)

(1−D)V S (x) +[1− (1− q) (1−D)]

(1 + r)V A (2)

V A =sV + (1− s)V A

(1 + r)(3)

These equations are directly comparable with equations (2-4) of RT, except that expected

wages are conditional on e�ort. Eq. (3) stipulates that an unemployed worker receives a

�ow utility of zero, and transitions with probability s to a job in the local economy that

yields value V independent of type. We discuss richer speci�cations of V on page 7. The

parameter D captures the managers' e�ectiveness in monitoring workers.

The no-shirking condition for type x is V N (x) ≥ V S (x) . In Appendix B.1 we show

that this condition boils down to:

w (x, 1)︷ ︸︸ ︷e�ciency-wage

incentive channel

(from RT)

+

[q + r

D (1− q)

][w (x, 1)− w (x, 0)]︷ ︸︸ ︷

pay-for-performance

incentive channel

(new)

≥ ω + c (x)

[1 +

q + r

D (1− q)

], (4)

where:

ω =rs

(1 + r) (r + s)V ,

is the discounted value of being unemployed. Eq. (4) reveals the model's dual nature: a

worker is motivated by a static incentive (pay for performance) and, in addition, by the

5

dynamic consideration of losing one's income if found shirking (e�ciency wage).

Linking the Model to Our Empirical Setting

We study a single �rm with many store locations across the U.S., and the above model

describes the problem of a worker operating in a speci�c store.

Compensation scheme Since in our �rm all workers nation-wide are subject to the

same compensation scheme, the compensation scheme cannot be optimally adapted to the

local conditions of most stores. At best, it is optimal on average. Hence, in our model,

we cannot assume that the compensation scheme w (·) is optimally adapted to the local

parameters M,D, q, s, ω, Y (x, e). We assume, instead, that when a locality increases M ,

w does not change. (This assumption is validated empirically in Table 2.2) Thus, in a

store that is subject to a local minimum wage M , the expected wage is:

w (x, e;M) = E (max [M,w (Y (x, e))]) . (5)

The function w (x, e;M) is bounded below byM and is nondecreasing in all its arguments.3

We assume that a store o�ering wages w (x, e;M) makes nonnegative pro�ts.

Henceforth w (x, e;M) will replace w (x, e).

Low types Next, we de�ne �low types� within the model as types whose performance

is never su�cient to earn above minimum wage.

De�nition 1. (MMW, or low type) Type x is MMW (i.e., �motivated by the minimum

wage�) or a �low type� if w (x, 1;M) = M . The largest among MMW-types is denoted by

xM .

For MMW types, any incentive to exert e�ort comes from the fear of losing the min-2There we show empirically that when a locality increases M, base pay and commission rates in the

store do not change.3It is obviously nondecreasing in M. It is nondecreasing in x and e by stochastic dominance, because

the function max [M,w (Y )] is nondecreasing in Y .

6

imum wage. Indeed, for such a type w (x, 1;M) = w (x, 0;M) = M and, plugging into

condition (4), one sees that no incentives come from performance pay. MMW types, in

other words, behave exactly as in the RT model. The set of MMW types has the form

[0, xM ], so it is appropriate to refer to them as �low types.� Empirically, we will de�ne a

�low type� as a worker whose pay is often determined by the minimum wage and, therefore,

has incentives similar to the MMW types in the theory.

Three cases nested by the model The model nests two polar cases and a �hybrid�

one.

Special Cases Nested by the Model

Polar case: pure e�ciency wages If w (x, 1;M) = w (x, 0;M), as is the case

for MMW types, the second addend in condition (4) vanishes, and the condition is

essentially identical to condition (5) in RT. This is the pure e�ciency-wage model.

Polar case: pure pay-for-performance If D ≈ 0, i.e., no-one is ever �red for

lack of e�ort, condition (4) converges to the familiar pay-for-performance condition:

w (x, 1;M)− w (x, 0;M) ≥ c (x) , (6)

which means that every type's incentives come entirely from performance pay, and

the e�ciency-wage channel vanishes.

Hybrid case: (our preferred model) When D > 0 and M is not too high, our

model is a hybrid of pure e�ciency wages and pure pay-for-performance, meaning

that some types (MMW types) will be motivated by e�ciency-wages only, and others

(higher types) will additionally be motivated by performance pay.

The pure e�ciency wage case may be disregarded for empirical purposes: the great

majority of our workers receive a substantial amount of variable pay. Therefore, only two

cases could possibly match our setting: pure pay-for-performance, and the hybrid case.

7

Value of outside option We allow the value of a job in the local economy V = V (M)

to depend on the minimum wage, so that:

ω (M) =rs

(1 + r) (r + s)V (M) .

If increasing, the function V (·) is assumed to have slope no greater than 1, meaning that

local-economy wages do not increase more than 1-to-1 with the minimum wage. This

ensures that the function ω (·) has slope less than 1. All results go through if ω is a

decreasing function of M , as would be the case if we let s be a decreasing function of

M . Also, the results go through if the local economy is composed of �rms that motivate

type-less workers by paying e�ciency wages, as in RT: see Appendix B.3 for this extension.

Core Theoretical Results: E�ect of Minimum Wage on Individual

Productivity

To assess the incentive e�ects of increasing the minimum wage, plug w (x, e;M) into

condition (4). If D ≈ 0 condition (4) reduces to Eq. (6), in which no MMW type has

any incentive to exert e�ort and, furthermore, the higher types' incentives to exert e�ort

are compressed as M increases (this is shown in Lemma 8). This observation proves the

following result.

Lemma 2. (Increasing the minimum wage reduces productivity in the pure pay-

for-performance case) Suppose D ≈ 0. Then increasing M does not change the e�ort

of any MMW type and decreases (weakly) every other type's e�ort level.

This prediction will be rejected in our setting: see Section 4.1 below.

The opposite theoretical prediction holds true in the hybrid case. The following as-

sumption formally de�nes the hybrid case.

Assumption 1. (Hybrid case) There is at least one MMW type who �nds it optimal to

exert e�ort.

This assumption says that the probability of monitoring D is high enough, relative to

8

the minimum wage and the cost of e�ort, that the pure e�ciency wage motive is su�cient

to incentivize at least one type. This assumption fails if D ≈ 0 (refer to Eq. 6), so

Assumption 1 excludes the pure pay-for-performance case.

Lemma 3. (Core result: increasing the minimum wage increases productivity

in the hybrid case) Fix M, and suppose Assumption 1 holds. Then:

1. There is an MMW type xM > 0 that solves:

M = ω (M) + c (xM)

[1 +

q + r

D (1− q)

]. (7)

2. All types greater than or equal to xM exert e�ort and all types below it shirk.

3. For any M ′ > M there is a type xM ′ < xM with the same properties.

Parts 1 and 2 of the lemma identify the �marginal type� with regards to e�ort provision.

Importantly, this marginal type xM is an MMW type, meaning that this type's e�ort

provision responds to an e�ciency-wage logic. This observation explains why in the hybrid

case e�ort response to the minimum wage follows an e�ciency-wage logic, and not a pay-

for-performance logic.

Part 3 is our core result: an increase in the minimum wage M causes an interval of

types below xM to start exerting e�ort. This prediction is veri�ed in Section 4, where we

show that low types in the average store exert more e�ort after a minimum wage increase.

For this reason, Lemma 3 is titled �Core result.�

Lemma 3 partitions the type space into three intervals: types below xM do not exert

e�ort, and are paid the minimum wage; types between xM and the highest MMW type

xM exert e�ort, and are paid the minimum wage; types above xM exert e�ort and are paid

more than the minimum wage, in expectation.

The simplifying assumption that e�ort is binary has a stark implication in the hybrid

case: types higher than MMW do not change their e�ort provision as M increases. In

Appendix B.2 we work out an extension where e�ort is a continuous variable e. In this

extension, under some intuitive conditions, optimal continuous e�ort is increasing for types

9

higher than MMW.4 The continuous model's predictions for other types and other cases

(pure pay-for-performance, pure e�ciency wages) are the same as in the discrete model.

Refer to Eq. (4′) on page 43 for an intuitive explanation of the comparative statics in the

continuous case.

Heterogeneous E�ect by Labor Market Conditions

In a pure pay-for-performance case, labor market conditions are not expected to matter

in the worker's e�ort choice (indeed, the parameter s is absent in Eq. 6). In our hybrid

case, they do. To see this, consider two stores with the same local primitives except that

in one location unemployed workers take longer to �nd a job, that is, the parameter s is

lower. Consider the marginal type who, in either location, switches to exerting e�ort due

to an increase in M. Is the productivity boost greater or smaller in this location? The

answer depends on the following assumption.

Assumption 2. (�Innate� di�erences between types are reduced by e�ort exer-

tion.) The di�erence E [Y (x, 1)− Y (x, 0)] is decreasing in x.

This assumption says that the higher the type, the smaller the impact of e�ort on

productivity. In other words, di�erences in �innate talent� are not magni�ed but rather

attenuated by e�ort. We cannot test Assumption 2 directly, but we can test it indirectly

in the presence of a minimum wage increase. This is shown in the next lemma.

Lemma 4. (Impact of minimum wage on individual productivity, as a function

of labor market conditions) Fix M .

1. (Pure pay-for-performance) Suppose D ≈ 0. Then the probability s of exiting

unemployment does not a�ect how e�ort choices respond to an increase in M .

2. (Hybrid model) Suppose D > 0 and Assumption 1 holds. Then the individual

productivity gain of the marginal type xM who switches to exerting e�ort due to

4These conditions are that the dynamic motivation provided by the future bene�ts of a higher minimumwage (e�ciency wage motive) must prevail over its static disincentive e�ect (pay for performance).

10

a marginal increase in M , depends on s. If, moreover, Assumption 2 holds, that

productivity gain is smaller if the probability of exiting unemployment is larger.

Part 1 is a falsi�cation test for the pure pay-for-performance model. The intuition

for part 2 is that when labor market conditions are worse, the marginal type who is

�barely unwilling� to exert e�ort is lower. The lower this marginal type, the bigger the

productivity increases when this type starts exerting e�ort (by Assumption 2). In Section

5.1 we present evidence that falsi�es the pure pay-for-performance model, and is consistent

with Assumption 2 holding.

Heterogeneous E�ect by Monitoring; and Endogenous Monitoring

We now extend the above model such that a fraction (1− µ) of workers, chosen at random

independently of their type, is �not monitored,� that is, a shirking worker is detected with

probability D ≈ 0.5 The remaining fraction µ of workers is �monitored,� meaning that

shirking workers are detected with probability D > 0. We think of µ as a continuous

measure of monitoring coverage. For now, we take µ as given.6

It helps to think of the �rm as being partitioned into two divisions. In the non-

monitored division, workers e�ectively operate on a �pure pay-for-performance� basis:

they are never terminated for lack of e�ort, and their no-shirking condition equals Eq.

(6). Workers in the monitored division behave as in the previous sections. Next, we

characterize how e�ort, and therefore individual productivity, changes in either division.

Denote by E (D,M) the set of types who exert e�ort for given M,D ∈ {0, D}.

Lemma 5. (Heterogeneous e�ect of the minimum wage on individual produc-

tivity, by monitoring) Suppose Assumption 1 holds for given M,D. For any M ′ > M

we have:5To be able to rely on Eq. (7) without change, formally we make D arbitrarily close to zero and write

D ≈ 0 in the proofs.6In the context of optimal monitoring, it may seem ad-hoc to split the workers into only two groups

who are monitored with di�erent probabilities. It is not. In a general monitoring game, only two strategiescan ever attain maximal deterrence. One is to monitor all agents with the same probability; the otheris to create exactly two groups of agents (and never more than two) who are monitored with di�erentintensities. See Lazear (2006), Eeckhout et al. (2010).

11

1.

E (0,M ′) ⊆ E (0,M) ⊂ E(D,M

)⊆ E

(D,M ′) .

2. When D ≈ 0, increasing M to M ′ does not change the e�ort of any type below xM .

Types above xM weakly decrease their e�ort.

3. When D = D, increasing M to M ′ does not change the e�ort of any type above xM .

Types below xM weakly increase their e�ort.

Part 1 is both intuitive and instructive. It is intuitive because it con�rms that mon-

itoring increases the set of types who provide e�ort, relative to no monitoring (middle

inclusion). It is instructive because of the contrast between the right- and left-most in-

clusions. Increasing the minimum wage promotes e�ort among the monitored (right-most

inclusion); however, it promotes shirking among the non-monitored (left-most inclusion).

The instructive results have already been established in Lemmas 2 and 3.

Parts 2 and 3 yield testable predictions by type. Among the non-monitored workers,

the low types do not change their e�ort (because non-monitored types below xM shirk

regardless of the minimum wage level). Instead, the high types decrease their e�ort as the

minimum wage increases, due to the attenuated pay-for-performance incentive. Among

the monitored workers, an increase in M causes some low types to start exerting e�ort,

and no high type to start shirking. Both predictions were obtained in Lemmas 2 and 3,

and both are found to hold in the data (see Section 5.2). Taken together, they are a strong

empirical test of the dual nature (e�ciency wage and pay-for-performance) of the model.

So far we have assumed that the monitoring coverage µ is not endogenous to M . In

Appendix B.4 we work out a theory where µ is endogenous, and can be purchased by the

�rm at a cost K (µ). Roughly speaking, the theory predicts that µ should increase with

M, but the increase could be small depending on the shape of the function K (µ) . This

premise is tested empirically in Section 5.2. The coe�cient on M has the expected sign,

but its magnitude is small and statistical signi�cance is lacking. Overall, we believe that

the evidence is consistent with the theory of endogenous coverage µ, but points to a degree

of endogeneity small enough that it can be ignored for practical purposes. Therefore, we

proceed under the assumption that µ is exogenous.

12

This section has shown that the individual e�ort response to the minimum wage �ips

sign, depending on whether they are monitored with intensity 0 or D. The empirical

analysis of e�ort response will suggest that workers in the average store behave as if

D = D, meaning that monitoring is relatively high in the average store.

E�ect of Minimum Wage on Turnover and Tenure in a Store's

Steady State

In this section, we characterize the distribution fM of worker types who are employed in a

store in steady state. Steady state means that, given M and the termination policy baked

into Eq. (1, 2), replacement workers are randomly drawn from the pool of the unemployed

such that the fraction of employees terminated and hired are equal, and in the next period

the distribution fM is reproduced identically. Note that the absolute size of the labor force

in the store is left unspeci�ed in this de�nition.

Denote by H the c.d.f. of the type distribution that our �rm can expect upon hiring

a random worker from the unemployment pool, and let h be its density. Since types are

�rm-speci�c, unemployed workers are not negatively (or positively) selected from a hiring

�rm's perspective, hence H is not a function of any of the model's parameters.

We show in Appendix B.1 that the steady-state type distribution is:

fM (x) = µf (x) + (1− µ)h (x) ,

where:

f (x) =

{λq′h (x) for x < xM

λqh (x) for x ≥ xM

,

q′ = q + D (1− q) is the probability that a monitored employee with type below xM

separates from the �rm, and:

λ = q

[1−H (xM)

(q′ − qq′

)]−1,

is the average turnover rate among the monitored workers. The average turnover rate in

13

steady state is:

λM = µλ+ (1− µ) q.

Since λ is increasing in xM , the following result obtains.

Lemma 6. (Impact of minimum wage on steady-state turnover and tenure in a

store) In steady-state, the average turnover rate in a store is decreasing, and the average

tenure is increasing, in the level of the minimum wage. Both e�ects are driven by low

types.

The decrease in turnover comes from those marginal MMW types who, after an increase

in the minimum wage, start exerting e�ort and thus are terminated less frequently.

E�ect of Minimum Wage on Store Output, Pro�ts and Employ-

ment

Store-level output is determined by two factors: the individual productivity of each worker

type, and the type distribution fM in the store (what fraction of the workforce is low,

medium, and high types). In the hybrid case, which most closely approximates the data,

both change as M increases. Individual worker productivity increases with the minimum

wage, and this is good for output. However, fM also changes: as low types stick around

longer, the type distribution will get worse, so the change in fM is expected to be bad

for store-level output. The adverse change in fM represents a �hidden� cost attached to

incentivizing the low types through retention: a �reverse labor-labor substitution� e�ect

speci�c to the e�ciency wage channel.

Let us now turn to pro�ts. In our empirical setting, the compensation scheme w is

set uniformly for all workers nationally, not adapted to local store conditions. Therefore,

increasing the local minimum wage may well cause pro�ts to increase in some stores, and

to decrease in others.7 However, the average e�ect across all stores could never be positive

if w is set to maximize aggregate pro�ts at the national level.7Increasing the minimum wage may increase pro�ts in a store if the compensation scheme w is not

pro�t-maximizing given local store conditions. Here is an example. Suppose w (Y ) < M , so that allworkers are paid the minimum wage. Suppose all workers have the same type x = xM − ε, with xMsolving Eq. (7) and ε an arbitrarily small number. Then no worker exerts e�ort. Increasing M by a �nite

14

Let us now turn to store size, which we denote by L. Given a certain M , L is set to

solve:

maxL

L · Π (FM ,M)− κ (L) , (8)

where Π (FM ,M) denotes gross store pro�ts per worker,8 and the convex function κ (·)captures the amortization or capital cost of operating at a given size. The solution to

problem (8) depends on the value of the term Π (FM ,M) , with higher values yielding a

larger optimal store size in steady state.

The above discussion is summarized in the following result.

Lemma 7. (Impact of minimum wage on store-level pro�ts and employment) If

w is set to maximize nationwide pro�ts, increasing M cannot increase nationwide pro�ts.

Optimal store size co-moves with store pro�ts per worker.

This lemma says on average across all stores, pro�ts must decrease with the minimum

wage. However, for certain types of stores that are not representative of the average store,

pro�ts could increase. Lemma 7 additionally says that variation in per-worker pro�ts

should cause employment to co-move at the store level, regardless of where the variation

in pro�ts comes from. These predictions are shown to hold in Section 6.2.

3 Data and Empirical Strategy

3.1 Data and Institutional Background

We match bi-weekly worker-level payroll data with monthly personnel records of a nation-

wide American retail store chain. Restricting attention to salespeople who are paid for

performance creates our �total sample� of more than 40,000 hourly salespeople. Further

restricting the sample to border stores as required by our research design (Section 3.2)

leaves us with more than 200 stores with over 10,000 salespeople. Table 1 reports the

summary statistics of this �border� sample.but small amount causes all workers to switch to exerting e�ort, and the wage bill increases only a little.Hence pro�ts increase with M .

8This is the level attained by expression (31); empirically, it is proxied by Ebitda per hour.

15

Workers and Compensation Our workers are consultative sales associates. A worker

will answer a walk-in customer's questions, demonstrate product features, and record

the customer's purchases as her own sales. Pay is based on individual performance: it

consists of a base salary plus a commission on individual sales. �Exerting e�ort� consists

of meeting and greeting the customer, taking the time to explain and persuade, up-selling

(to higher-margin products) and cross-selling (warranties, loans, credit cards, etc.).9

For every salesperson we aggregate at the monthly level: hours worked (avg. 107), sales

(avg. 2, units shrouded for con�dentiality),10 and pay (avg $1,361; base $6.12/h, variable

$5.95/h).11 We compute the commission rate (avg. 3.5%) by dividing �variable pay� by

the value of sales. We compute �sales per hour,� corresponding to �productivity� in our

model, as the value of sales divided by the number of hours worked. Tenure averages 49

months, as measured from the hiring date in the HR records.

Stores and Employment There are on average 16.64 sales associates in a store. As is

typical in retail, store-level turnover is high: 3.4% per month (being the average of 4.8%

termination rate and 2.1% hiring rate).12 Within a store there are several departments

with somewhat di�erent conditions for workers: we control for this heterogeneity by adding

department �xed e�ects in all our speci�cations.13 Every store has a store manager and,

sometimes, one or more assistant store managers, which we classify not as �workers� but

as �supervisors.� We use the ratio of supervisors to workers as a proxy for monitoring

coverage in a store (µ in the model). Pro�ts per store are positive on average (units

shrouded).

9A job description posted on the company's website may be paraphrased as: �our salespeople arecharged with making customers happy, providing them with information, increasing sales, helping keepup the sales �oor appearance, help process customer transactions as needed, and generally cooperate withother employees.� Some of these are �common value� activities, but in Section 7.1 we show empiricallythat e�ort spillovers among employees do not play a large role in our �ndings.

10The number is re-scaled by a factor between 1/50 and 1/150 relative to its value in dollars.11The �eld �total monthly variable pay� is an aggregate of several corporate incentive programs tied to

sales.12The termination (hiring) rate is de�ned as the percent of sales associates in the store who are termi-

nated (hired) in a given month. We do not distinguish between voluntary and involuntary terminationsbecause we believe that this distinction, as coded by HR, is subjective. The turnover rate is de�ned asthe percent of sales associates in the store who are terminated or hired in a given month divided by two.

13Pay is base plus commission in all departments, but base and commission rates vary somewhat acrossdepartments.

16

Minimum Wage Variation States, counties, and even cities can set minimum wage

requirements, with the highest requirement being the applicable one. The mean minimum

wage in our sample is $7.87 per hour. From February 2012 to June 2015, stores in our

sample are a�ected by 70 minimum wage increases: 49 at the state level, and 21 at the

county or city level.14 The average minimum wage increase is $0.54.

If a worker's average hourly pay in a week (base plus variable) falls below the minimum

wage, the employer is required to make up the di�erence as prescribed by the Fair Labor

Standards Act (FLSA).15 In an average month, 5% of our workers are paid no more than

the minimum wage and 42% receive an adjustment in at least one of the four weeks. We

create a variable called �minimum wage adjustment� which equals the amount paid by the

employer to comply with the minimum wage (this variable is often zero and averages $0.23

per hour). A $1 increase in the minimum wage raises the �minimum wage adjustments�

by $0.25 per hour (Table 2, Col. 3).16 In addition, variable pay per hour increases by

$0.44 per hour (Table 2, Col. 4), re�ecting the endogenous increase in productivity that

is the subject of this paper. Overall, a $1 increase in the minimum wage raises average

total pay per hour by $0.65 per hour (Col. 5), which corresponds to a 5% increase and an

elasticity of 0.38.

We divide workers into three �types.� In the spirit of Aaronson et al. (2012) and

Clemens and Wither (2019), and following De�nition 1 in the theory, low types are those

paid at the minimum wage (about 4% of our observations); the rest are split into medium

and high types, with the threshold between the latter two types being the 3rd quartile of

the pay distribution.17 As expected, higher types sell more per hour, they take advantage

of the �minimum wage adjustment� less often, and they are terminated less often: see

Table 3.18

14Refer to Appendix C for a full list of the minimum wage changes.15 The minimum wage law does have an exception: commissioned workers can occasionally be deemed

�exempt� and the top-up can be zero for exempt workers. Based on administrative records, all our workersare non-exempt.

16A 1$ increase in the minimum wage increases the share of workers who are topped up every singleweek of the month by 4.5pp (144%), while the share of workers who are topped up at least one week permonth increases by 16pp (38.5%). Results available upon request.

17The technical de�nition of �type� is spelled out the end of Section 3.2.18Low types (4% of our observations) receive a minimum wage adjustment roughly once every two

weeks and their termination rate is 7%. Medium types (72% of our observations) receive a minimum

17

HQ vs. Store-Level Decisions Headquarters set the nationwide compensation scheme

(base and commission rates, not adjusted for minimum wage) uniformly across stores and

jurisdictions. Accordingly, when a local minimum wage changes, the base and commission

rates do not change in that location: we show this in Table 2 (Col. 1 and 2). This wage

stickiness makes sense in the presence of menu costs. The theory re�ects these institutional

features in the assumption that the compensation scheme w does not vary with M , and

by avoiding the assumption that w is optimized at the local level.19

Personnel decisions are made by the store managers in coordination with central HR.

Local managers have relative freedom of deciding whether to terminate a worker and

whether to hire a new worker, subject to keeping the number of workers close to a level

agreed upon with HR. In the model, the total number of workers L in a store is chosen to

maximize expression (8), store by store.

Pricing for our company is nationwide, as in most national retail chains (Della Vigna

and Gentzkow 2019). In Section 7.2 we compute a store-level price index for our company

and con�rm that it does not vary with the local minimum wage.

In summary, besides personnel decisions, stores have limited autonomy vis à vis HQ.

This feature must be kept in mind when evaluating the external validity of our analysis,

and we will return to it in Section 8.

3.2 Identi�cation Strategy

Sample Selection and Border Discontinuity Design Our main empirical speci�ca-

tion implements a border discontinuity design in the spirit of Card and Krueger (2000),

and follows Dube et al. (2010) and Allegretto et al. (2011) closely. In this speci�cation,

workers on the side of the border where the minimum wage increased (treatment group)

are compared to workers on the other side where the minimum wage did not increase

(control group). This research design aims to ensure that treated and control groups are

wage adjustment roughly once every �ve weeks and their termination rate is 5%. High types (24% of ourobservations) receive the adjustment roughly once every 10 weeks only and their termination rate is 3%.

19We would expect w to vary with the federal, as opposed to state or local minimum wage. We do nothave federal wage increases in our sample. Recent literature on the minimum wage (Flinn and Mullins2018) analyzes the e�ect of wage renegotiation between �rm and employee as the minimum wage changes.

18

similarly situated but for the minimum wage change; the pre-trend analysis in Section 4.3

supports this presumption.

An alternative research design is the traditional �state-panel� approach used by Neu-

mark and Wascher (1992, 2007) among others, and recently summarized by Neumark

(2019). This approach uses the entire sample of stores, regardless of their distance from

the border. In Section 4.3, we show that our core estimates are similar in this alternative

research design.

Our sample includes minimum wage increases enacted by states, counties, and cities.

Appendix C describes how the sample is constructed and presents a map of these minimum

wage increases. After restricting to stores located in counties whose centroids are less

than 75 km apart,20 we are left with more than 200 stores and over 10,000 salespeople,

approximately half of which experienced variations in minimum wage in our sample period.

Deriving the Testable Implications from the Model Letting e∗ (x,M) denote type

x's optimal e�ort at minimum wage M , type x's equilibrium productivity is given by:

Y ∗ (x;M) = Y (x, e∗ (x,M)) .

Linearizing around M yields the following estimating equation:

Y ∗ (x;M ′) = Y ∗ (x;M) + (M ′ −M) · β. (9)

When β is estimated across all worker types, β̂ = E [∆Y ∗ (x,M)/∆M ] represents the

e�ect of minimum wage on average worker's productivity across all worker types. The

theory predicts β ≤ 0 in the pure pay for performance case, and β > 0 in the hybrid case

(Lemmas 2 and 3, respectively).

The analog of Eq. (9) by worker type is:

Y ∗ (x;M ′) = Y ∗ (x;M) + (M ′ −M) · [βL1L (x) + βM1M (x) + βH1H (x)] , (10)

20In doing so, we follow the existing literature (see Appendix C for more details). Section 4.3 showsthat the analysis is robust to using di�erent distance thresholds (i.e., 37.5km or 18.75km).

19

where each βi represents the within-category productivity e�ect of the minimum wage.

Our testable predictions are as follows. In the pure pay for performance case, Lemma 2

predicts βM , βH ≤ 0, and βL = 0. In the hybrid case, Lemma 3 predicts βL > 0, and,

when e�ort is continuous and under plausible conditions βM , βH ≥ 0 (these predictions

are discussed on page 9 in the context of the continuous e�ort model). We will use these

predictions to reject one case or the other. Recall that the pure e�ciency wage case may

be disregarded because the great majority of our workers receive a substantial amount of

variable pay.

Empirical Speci�cation We translate Eq. (9) into the following regression speci�ca-

tion:

Yijpt = α + βMinWjt +Xit · ζ + ηZjt + δi + φpt + εijpt. (11)

Yijpt is the productivity (sales per hour) of worker i in store j of county-pair p in month

t. MinWjt is the prevailing minimum wage in store j 's jurisdiction in month t.21 Xit is a

vector of time-varying worker characteristics that are likely to predict worker productivity,

speci�cally: the worker's tenure and the department in which she works. Including worker

�xed e�ects δi means that we leverage within-worker variation in minimum wage and our

estimates hold selection constant.22

To account for time-varying local economic conditions and local demand shocks, as in

Lemieux et al. (2012), Zjt includes the monthly county unemployment rate. In addition,

Eq. (11) includes county-pair × month �xed e�ects φpt that interact 113 unique county-

pair identi�ers with 41 month dummies. These �xed e�ects restrict the comparison to

�treated� and �control� stores/workers on either side of the same border. We estimate this

equation by �stacking� our data as in Dube et al. (2010, 2016), meaning that stores/workers

located in a county sharing a border with n other counties appear n times in the �nal

sample. In Section 4.3 we show that our core results are similar without stacking. The

standard errors are two-way clustered at the state level and at the border-segment level.23

21This is the highest among state, county, and city minimum wages.22Store �xed e�ects are redundant because less than 1% of the workers moved across stores.23As explained in Dube et al. (2010), the presence of a single county in multiple pairs along a border

segment induces a mechanical correlation across county-pairs, and potentially along an entire bordersegment. This requires standard errors to be clustered both at the state level and at the border-segment

20

To study the heterogeneous e�ects of minimum wage on worker productivity by worker

type, we translate Eq. (10) into the following regression speci�cation:

Yijpt = β0 + β1MinWjt + β2MediumTypeijt + β3HighTypeijt + (12)

β4MinWjt ·MediumTypeijt + β5MinWjt ·HighTypeijt +

Xit · ζ + ηZjt + δi + φpt + εijpt,

where MediumTypeijt and HighTypeijt are indicators for whether worker i is a medium

or a high type. The e�ect of minimum wage on low, medium and high types � i.e, the

coe�cients βL, βM , βH in Eq. (10) � corresponds here to β1, β1+β4, β1+β5, respectively.24

Low, medium and high types are de�ned based on their pay in t− 1: low types earn the

minimum wage, medium types earn between the minimum wage and 180% × minimum

wage, high types earn more than 180% of the minimum wage.25

4 Core Empirical Results: E�ect of Minimum Wage on

Individual Worker Productivity

This section uses the testable predictions from Section 3.2 to test the pure pay-for-

performance case against the hybrid case. Recall that the pure e�ciency wage case may

be disregarded because the great majority of our workers receive a substantial amount of

variable pay.

level (32 states and 44 border segments).24This speci�cation resembles the triple di�erence approach used by Clemens and Wither (2019) and

discussed in Neumark (2019).25 We de�ne low types at time t as those whose total pay in month t-1 is below 1.02*minimum wage.

The 0.02 accounts for rounding errors because the �total pay� �eld is sometimes o� by a few cents: theresults are robust to de�ning workers �at minimum wage� as those who earn exactly the minimum wage.The 180% threshold was picked so that the top category of workers represents one quarter of the overallworkforce. In Section 4.3 we show that our results are robust to using alternative thresholds (120%, 140%,160%) or various alternative classi�cations.

21

4.1 Core Findings

Figure 1 presents the e�ect of a $1 in increase minimum wage on the percent change

in the productivity of low, medium, and high types (see Table 4 Col. 2 for the exact

point estimates from Eq. 12). We �nd that a $1 increase in minimum wage increases

productivity � sales per hour � strongly among low types, i.e., by 0.244 (shrouded units)

or 22.6%. In the notation from Section 3.2 this means that β̂L > 0, which rejects the pure

pay-for-performance case, and is consistent with the hybrid case.

Figure 1: Minimum Wage Increases Productivity for Low Types and not for High Types

Notes: E�ects of a $1 increase in minimum wage on the percent change in productivity (Y:Sales/Hrs) for low, medium, and high types. Vertical bars represent 95% con�dence intervalscomputed using the estimated coe�cients (β̂1, β̂1 + β̂4 and β̂1 + β̂5) from Eq. (12) and theassociated standard errors.

The e�ect is weaker, but still positive, for medium types (β̂M = 0.156, or 8.2%). Again

the pure pay-for-performance case is rejected and the hybrid case is not. According to the

theory, this �productivity ripple e�ect� obtains because our medium types earn minimum

wage occasionally,26 so their response aligns somewhat with the low types'.26Our medium types receive the minimum wage adjustment 18% of the weeks, on average, compared

to 47% for low types (Table 3).

22

The e�ect vanishes for high types (β̂H = 0.062, or 2.3%, statistically indistinguishable

from zero). These workers' pay is least a�ected by the minimum wage, and so they barely

respond to it.

Next, we study the e�ect of the minimum wage on average worker productivity. We

expect average worker productivity to increase, but not by much because the e�ect is

mostly driven by low types who are less than 5% of the workforce. This is con�rmed in

Table 4, Col. 1: a $1 increase in the minimum wage raises average individual productivity

by 0.094 (shrouded units), or 4.5%. This individual productivity gain is economically large

and statistically signi�cant at the 5% level. The overall implied elasticity is 0.35.27

We conclude with a sanity check: as expected, worker pay increases with the minimum

wage (Table A.1). This increase is not due to a change in the compensation scheme

(recall: we do not �nd one), but rather to the mechanical e�ect of the minimum wage

increase (more �minimum wage adjustments�) combined with the endogenous e�ort boost

(more variable pay). Interestingly, the e�ect on pay is sizable for both low and medium

types, suggesting that both worker types bene�t from the increase in the minimum wage

adjustment and, also, from becoming more productive. The pay increase on medium types

could be viewed as an instance of the �wage ripple e�ect� which been documented in the

labor literature:28 in our case, it is associated with a �productivity ripple e�ect.�27A $1 increase in the minimum wage is equivalent to a 12.7% increase relative to the mean, and

4.5/12.7 = 0.35.28See, e.g., Flinn (2006), Dube et al. (2019), Cengiz et al. (2019). For a review of the earlier literature

on the �wage ripple e�ect,� see Neumark and Wascher (2008).

23

4.2 Dynamic E�ects

We explore pre-trends and also the time pattern of the treatment e�ect. We estimate the

following dynamic equation:

Yijpt = α +2∑

m=−2

βi3mMinWj,t−3m +2∑

m=−2

βii3mMinWj,t−3m ·MediumTypeijt

+2∑

m=−2

βiii3mMinWj,t−3m ·HighTypeijt + γ1MediumTypeijt

+γ2HighTypeijt +Xit · ζ + ηZjt + δi + φpt + εijpt, (13)

where Yijpt is worker productivity. The two leading coe�cients (β−6, β−3) quantify the

pre-treatment e�ects of the minimum wage six and three months before a time-t change,

respectively. Their estimates are not statistically signi�cant for any worker type, con�rm-

ing that there is no pre-trend within worker type and no di�erential pre-trend across types

(Figure 2 and Table A.2).

The lag coe�cients (β3, β6) quantify post-treatment e�ects. Low types display a

20.3% (statistically signi�cant) cumulative increase in productivity at the six-month mark,

suggesting that the productivity e�ect is persistent. The e�ect sets in immediately after

the minimum wage increase, which may be an indication that individual worker reaction

and not organizational change is at play.29 High types, in contrast, do not experience a

statistically signi�cant response at the six-month mark. Overall, we �nd no pre-treatment

e�ect and the treatment e�ect is immediate and persistently heterogeneous across types.30

4.3 Threats to Identi�cation and Robustness Checks

This section explores two potential threats to identi�cation: lack of pre-trends, and cross-

border movements. It also shows that our core �ndings (a minimum wage increase causes

29We thank an anonymous referee for this observation.30The coe�cients displayed in Figure 2 are estimated in the sub-sample of 102k observations who remain

employed throughout a 12-month window centered at the minimum wage event. The same patterns persistif we extend the window to 24 months (12 prior to, and 12 following the minimum wage event), butstatistical signi�cance is lost because the sample shrinks to only 52k observations pertaining to workerswho are continuously employed during the 24-months window. Results available upon request.

24

Figure 2: The Dynamic E�ect of Minimum Wage on Worker Productivity

Notes: E�ects of a $1 increase in minimum wage on the percent change in productivity (Y:Sales/Hrs) for low, medium, and high types. Vertical bars represent 95% con�dence intervals.

an increase in individual worker productivity especially among low types) are robust across

many alternative implementations of our research design. All tables are presented in

Appendix D.

Pre-Trends Figure 2 displays the dynamic e�ects of the minimum wage. It shows no

pre-trends in our core outcome (individual productivity by type) in the sample of workers

who remain employed throughout a 12 month window around the minimum wage event.

In the larger sample of workers who are continuously employed for six months before

the minimum wage event, Table D.1 shows no pre-trends too (Panel A, Col. 1-3). The

fact that �gure and table agree is encouraging because the di�erence in numerosity is

nonnegligible (102k in the �gure vs. 144k in the table) and may partly re�ect selection.

25

Cross-border Worker Movements Border-discontinuity research designs are subject

to the criticism that workers may move across borders (Neumark et al. 2014). Our

core results on individual productivity (Section 4.1) shouldn't be subject to this concern

because we include worker �xed e�ects, thus e�ectively comparing the �same worker� at

two minimum wage levels. We corroborate this by showing that a minimum wage increase

does not correlate with the home-to-work distance of new hires (Table D.2, Col. 1), which

rules out changes in our workforce's commuting patterns after a minimum wage hike. One

might worry that cross-county migrants, rather than commuters, may confound store-level

estimates. Zhang (2018, page 18) �nds that after a minimum wage hike, migrants �ow

toward the same counties as commuters. Then, the null e�ect in Table D.2 Col. 1 implies

that migration patterns, also, do not change in our workforce after a minimum wage

hike. Furthermore, migration is likely more costly across state lines than across county

or city lines.31 Yet our estimates are the same in the sample including only county-city

minimum wage increases, as in the sample including only state-level increases (see page

27). Finally, Table D.2 shows that the minimum wage does not a�ect the home-to-work

distance proportionally more for low, medium, or high types (Table D.2, Col. 3). In sum,

we believe it's unlikely that cross-border movement of workers play a signi�cant role in

our estimates.32

Worker Selection Worker �xed e�ects control for selection in our main productivity

results. If, after controlling for worker �xed e�ects, any residual selection remains, the

disproportionate retention of low types (which we will document in Section 6.1) would

presumably bias our individual productivity estimates downward. Here, we probe selection

further by restricting the sample to a balanced panel of workers who are employed during

the entire sample period.33 The sample drops in size, but its pre-trends are the same, and

the results are similar to the main sample (Tables D.3 and D.4).

31Moving one's residence across state lines requires, for example, applying for a new driver license andcar insurance, and registering one's vehicle in the new state. if migration exists it should be more frequentwhen the minimum wage changes at the county/city level.

32We thank an anonymous referee for helping us improve the analysis cross-border movements.33This test follows Lazear et al. (2016).

26

Alternative Research Designs Our border-discontinuity approach discards a large

portion of the sample. We now show that our results are robust to a state-level approach

à la Neumark and Wascher (1992) that uses the entire sample of stores, regardless of

their distance from a border. What controls should be included in this speci�cation?

Adding more controls is thought to produce estimates closer to the border-discontinuity

speci�cation (Dube et al. 2010, 2016). Accordingly, in the spirit of showing the robustness

of our results, we opt for minimally controlled state-level speci�cations because they are

expected to produce the most-di�erent results from ours. We present the estimated e�ects

with a minimal two-way �xed e�ects model (worker and month �xed e�ects) and, in

addition, a variant with linear state-trends and another variant with census-division ×month �xed e�ects.34 Regardless of the speci�cation, we �nd that the minimum wage

increases the productivity of low types and does not a�ect the productivity of high types

(see Table D.5 for all three speci�cations and Figure 3, Panel A).

State vs. Local Variation in the Minimum Wage Restricting the analysis to state-

level minimum wage changes only, or to county and city changes only (Figure 3, Panels

B-C and Table D.6), does not change our �ndings. This is reassuring as one could worry

that the cross-state variation is contaminated by other state-level policy changes.

Alternative De�nitions of �Bordering Stores� We explore de�nitions of �bordering�

based on the exact location of the store rather than its county's centroid; or, where distance

from the border is set to �less than 37.5 km,� or �less than 18.75 km,� which are both shorter

than in the main de�nition. Reassuringly, our results are consistent across these samples.

See Figure 3, Panels D-E and Table D.7.

Robustness to �Unstacking� The results are also robust to using the same county-

level border discontinuity design as in our main estimates but without stacking the ob-

servations, with border-segment × month �xed e�ects and clustering standard errors at34Including state-level linear trends or census-division × month �xed e�ects have both been proposed

as a solution to the parallel trend problem. Table D.1 Col. 2-4 show that, in our context, the variantwith division × month �xed e�ects is the only one that eliminates pre-trends in worker productivity. Weacknowledge that the inclusion of division × month �xed e�ects has been criticized by Neumark, Salas,Wascher (2014) because �the identifying information about minimum wage e�ects comes from within-division variation in minimum wages and removes a good deal of valid identifying information.�

27

Figure 3: Minimum Wage Has a Robust Positive E�ect on Productivity of Low Types andno E�ect on High Types

Notes: E�ects of a $1 increase in minimum wage on the percent change in productivity (Y:Sales/Hrs) for low, medium, and high types. Panel A includes all stores, regardless of theirdistance from the border, in a speci�cation with division·month �xed e�ects (and standard errorsclustered at the state level). Panel B (C) considers our main sample (stores located in countieswhose centroids are less than 75 km apart) but only for state (within-state) variations in minimumwage. Panel D (E) considers the sample of stores that are located less than 37.5 km (18.75 km)from the border. Panel F considers our main sample but with no stacked data and with border-segment-month �xed e�ects. Vertical bars represent 95% con�dence intervals computed usingthe estimated coe�cients (β̂1, β̂1 + β̂4 and β̂1 + β̂5) from Eq. (12) and the associated standarderrors.

the border-segment level (Figure 3, Panel F and Table D.8). This speci�cation is closer

in spirit to an experimental event approach. See Appendix D for more details.

Alternative Classi�cations of Low, Medium, and High Types We explore al-

ternative ways of de�ning types, as follows. Exploring other thresholds between medium

and high types. Classifying types based on average pay in the previous three months, as

opposed to the previous month. Constructing time-invariant types based on pay in their

�rst month of employment; or productivity in their �rst quarter of employment. Reas-

suringly, the �ndings paint the same picture regardless of the classi�cation method: the

low types become signi�cantly more productive, while the high types do not become more

productive when minimum wage increases. See Appendix D and Tables D.9 - D.10 for

details.

Alternative Controls Our results are similar if we further control for department ×store time-trends and take into account potential di�erential trends across departments of

a given store, or if we run our speci�cations by department. The results are also similar if

we remove potential �bad controls� (worker tenure and county-level unemployment). See

Appendix D and Tables D.11 - D.12 for more details.

5 Testing Additional Model Predictions About Individ-

ual Worker Productivity

Beyond the �core implications,� the model delivers other testable predictions about indi-

vidual productivity. In this section, we test two salient ones, and �nd support for them.

We interpret this section as �testing the model.�

5.1 Heterogeneous Productivity Gain by Labor Market Condi-

tions Rejects Pure Pay-for-Performance Model

The pure pay-for-performance case should be rejected if the productivity improvement

due to a minimum wage increase depends on s (refer to Lemma 4). This is because the

29

fear of becoming unemployed has no incentive value in a pure pay-for-performance model.

We proxy for s, the probability of exiting the unemployment state, with the hiring

rate in the county in which the store is located.35 We estimate the heterogeneous e�ect

of the minimum wage on individual productivity by quartile of the county's empirical

distribution of hiring rates.

Figure 4 (Panel A) and the corresponding Table A.3 (Col. 1) show that the individual

productivity improvement due to a minimum wage increase depends on the hiring rate

in the local economy. This �nding rejects the pure pay-for-performance model (Lemma

4 part 1). Furthermore, the dependence is negative, consistent with the �hybrid� model

under Assumption 2 (Lemma 4 part 2).

Figure 4 (Panel B) presents the estimates by worker type in a pooled regression. Reas-

suringly, all the action comes from low types, as predicted by Lemma 4 part 2. See Table

A.3, Col. 2 for the regression coe�cients.36

5.2 Heterogeneous E�ect by Monitoring Illuminates Dual Nature

of Model

Aggregating across all stores in our border sample, the no-monitoring, pure pay-for-

performance case has been rejected in favor of the hybrid case (Section 4). In this section

we check whether employees in stores with less monitoring deviate from average behav-

ior, and behave as in the no-monitoring, pure-pay-for-performance parameterization of

the model. We view this exercise as a test of the dual nature of our model, which can

��ip� between a pure pay-for-performance and a hybrid version, depending on monitoring

intensity.

The theory (Lemma 5) makes two kinds of predictions. First, subjecting a worker to

�monitoring� weakly increases her individual productivity, relative to �no monitoring� (part35The hiring rate is the number of new hires in the �department stores� industry divided by the number

of workers employed in that same industry; computation based on the Quarterly Workforce Indicators(QWI) series. The data vary at the quarterly level.

36As a robustness check we repeated this analysis using county-level monthly unemployment rates asa proxy for s. The evidence is comparable to the one using hiring rates. See estimates in Coviello et al.(2018).

30

Figure 4: Minimum Wage Increases Productivity of Low Types Only with Bad LaborMarket Conditions (Low Hiring Rate)

Notes: E�ects of a $1 increase in minimum wage on the percent change in productivity (Y:

Sales/Hrs) when county-level hiring rate is in the 1st, 2nd, 3rd, or 4th quartile of the within-

county distribution. Panel A presents the average e�ect across all workers. Panel B presents the

e�ect for low, medium, and high types separately. The shaded areas represent 95% con�dence

intervals.

1, middle inclusion). This is reasonable. Second, and more interesting, the productivity

e�ect of the minimum wage is heterogeneous by monitoring. Among the �non-monitored

workers,� the low types should not change their e�ort, however, high types should decrease

their e�ort (part 2). Among the �monitored� workers, low types should become more pro-

ductive and no high type should start shirking (part 3). This duality re�ects the marginal

worker's di�erent incentives: if monitored, the marginal worker is a low type whose re-

sponse follows an e�ciency wage logic, meaning that the minimum wage motivates such a

worker. If not monitored, the marginal worker is a high type who has pay-for-performance

incentives; such a worker is demotivated by the minimum wage. This bifurcated prediction

is a strong test of the dual nature of the theoretical model.

31

These predictions are tested using store-level variation in monitoring coverage µ. In

the model, µ represents the fraction of workers (independent of type) who behave as if

�monitored.� We proxy for µ using the supervisors-to-workers ratio in a store-month. We

classify a store as �low coverage� if its supervisors-to-workers ratio is in the �rst quartile

of the store-month distribution (proxying for the parameterization D ≈ 0), else as �high

coverage� (proxying for the parameterization D = D > 0).

Consistent with Lemma 5 part 1 (middle inclusion), we do �nd that high coverage

positively correlates with average worker productivity (Table 5, Col. 1). This is reassur-

ing, but is not a very strong test of the dual nature of our model because the presence

of supervisors could also improve productivity through channels other than monitoring.

Accordingly, we now test the predictions most revealing of our model's dual nature.

Figure 5: MinimumWage Increases Productivity of Low Types when Monitoring Coverageis High and Reduces Productivity of High Types when Monitoring Coverage is Low

Notes: E�ects of a $1 increase in minimum wage on the percent change in productivity (Y:Sales/Hrs) for low, medium, or high types for high/low monitoring coverage. Monitoring coverageis measured as the ratio of supervisors to workers. �Low coverage� is an indicator for whetherthe store is in the bottom quartile of the monitoring coverage distribution. Vertical bars (solidfor �Low coverage,� dashed otherwise) represent 95% con�dence intervals.

Consistent with the distinctive predictions in Lemma 5 parts 2 and 3, Figure 5 and the

32

corresponding Table 5 (Col. 2-5) show that in high-coverage stores, low types become more

productive as the minimum wage increases, and no high type becomes less productive. In

low-coverage stores, the low types do not change their e�ort, however, high types decrease

their e�ort (though the p-value of the latter e�ect is only 0.11). This bifurcated pattern

is strong evidence in favor of the dual nature of our model.

Our assumption so far has been that coverage µ is not endogenous to the minimum

wage M . If µ were endogenous, the theory in Section 2 predicts that it should increase

with M. Table A.4 (Col. 1) estimates the following store-level equation:

Yjpt = α + βMinWjt + ηZjt + δj + φpt + εjpt, (14)

where Yjt is the outcome of interest (supervisors-to-workers ratio) in store j of county-pair

p in month t, δj are store �xed e�ects and all the other variables are de�ned as in eq.

(11). Our estimate of β is positive, but small and non-signi�cant e�ect. This suggests

that store-level variation in the supervisor-worker ratio re�ects circumstances that are

largely uncorrelated with the minimum wage level. We believe that this evidence may be

suggestive that µ is endogenous, but points to a degree of endogeneity small enough that

it can be neglected for the purpose of computing the heterogeneous e�ects of the minimum

wage.

6 E�ect of Minimum Wage on Store-level Outcomes

6.1 Testing the Predicted Decrease in Turnover

The theory (Lemma 6) predicts that termination rates should decrease after a minimum

wage increase, because the marginal types start exerting e�ort and therefore separate less

often. In steady state, fewer separations imply less hiring, and so less turnover and longer

worker tenure.37 Because the e�ect is driven by the marginal types who are also low types,

we expect these e�ects to be stronger in stores with relatively many low types.37Table A.4 Col. 2 supports the assumption that store-level employment is in steady state conditional

on store �xed e�ects and county-level unemployment.

33

In the spirit of Draca et al. (2011) and Harasztosi and Lindner (2019), we estimate

the following store-level model:

Yjpt = α + βMinWjt + γ%LowTypesjt + δMinWjt ·%LowTypesjt + ηZjt + δj + φpt + εjpt

where Yjpt is the outcome of interest in store j of county-pair p in month t, %LowTypesjt

is the fraction of workers in store j in month t who are low types, δj are store �xed e�ects.

Figure 6 (Panels A-D) plots the e�ect of minimum wage for the range of %LowTypes

we observe in our stores (0 to 40%).38 As predicted, an increase in the minimum wage

reduces store-level termination, hiring, turnover, and increases tenure in stores with a high

enough fraction of low types. The slope δ̂ is negative for termination, hiring, turnover,

and positive for tenure. It is statistically signi�cant at the 5% level for hiring and at the

10% level for turnover and tenure (see Table 6 for the regression coe�cients).39

In sum, the heterogeneous e�ects have the predicted direction (larger on low types).

We read this evidence as supportive, on the whole, of the theoretical proposition that

turnover should decrease as the minimum wage increases, especially among low types.

We conclude the analysis on employment �ows with a deep dive on terminations.

A worker-level speci�cation, as opposed to store-level, allows us to measure individual

outcomes by type.40 We go back to Eq. (12), with a dummy as dependent variable that

takes value one on the month of termination, and zero during employment; we control

for worker tenure; and we remove worker �xed e�ects to capture store-level, rather than

within-worker, variation. Because a terminated worker is dropped from the sample, this

speci�cation acts like a discrete time hazard model.41 Figure 7 and Table 7 Col. 2 con�rm38The variable %LowTypes has mean 3.9% and standard deviation 7.5%.39According to the theory, the turnover e�ect should only a�ect a small fraction of the workforce, i.e.,

the low types. As such it is not surprising to see that the average e�ect of minimum wage on turnoveris negative and sizable but not statistically signi�cant. Another, not mutually exclusive culprit, maybe that a store's turnover, being a store-level decision, may adjust more slowly than individual workerproductivity. In line with this, Figure A.1 shows that the e�ect on hiring and turnover is statisticallysigni�cant, and in the expected direction, three months after the change in minimum wage.

40This individual-level analysis can only be carried out for terminations, and not for hiring and turnover,because the individual termination rate is de�ned as a fraction of the pool of employees, which we observe,whereas individual hiring rates are de�ned as a fraction of the hiring pool, which we do not observe.

41This approach to duration data has been illustrated in Frederiksen et al. (2007) and Arellano (2008),and variants of it have been used by, among others, Ho�man and Tadelis (2019), and Sandvik et al.

34

Figure 6: Minimum Wage Reduces Turnover and Increases Tenure in Stores with a HighFraction of Low Types

Notes: This �gure plots β̂ + δ̂ ·%LowTypes. Y is the termination rate (Panel A), hiring (PanelB), turnover rate (Panel C), average worker tenure (Panel D) and number of sales associates(Panel E). Vertical bars represent 95% con�dence intervals. We report the e�ects in percentagepoints in Panels A-C and in percent in Panel D-E.

that low types are signi�cantly less likely to be terminated after a minimum wage increase

(-19%, statistically signi�cant at the 10% level). These results reinforce those in Figure 6.

Medium types are also less likely to be terminated (-7%) but the e�ect is not statistically

signi�cant. Finally, no e�ect is found among high types.

While the theory does not have speci�c predictions about employment levels in the

border sample (the next section discusses this issue in depth), it is descriptively interesting

(2019).

35

Figure 7: Minimum Wage Reduces Termination of Low Types but not of High Types(Individual Level, Without Worker Fixed E�ects)

Notes: E�ects of a $1 increase in minimum wage on the percent change in termination (Y:Terminated) for low, medium, and high types. Vertical bars represent 95% con�dence intervalscomputed using the estimated coe�cients (β̂1, β̂1+ β̂4 and β̂1+ β̂5) from Eq. (12) but with storerather than worker �xed e�ects.

to know how employment responds to the minimum wage in this sample. Figure 6 Panel

E and the corresponding Table 6 Col. 9-10 show that the minimum wage has no e�ect on

employment on average, and that there is no heterogeneous e�ect by the fraction of low

types in the store.

6.2 Testing the Predicted Decrease in Pro�ts

The hypothesis that headquarters choose w to maximize nationwide pro�ts may not be

tested in the border-store sample, but only in the nationwide sample. This is because

the nationwide compensation scheme w is not adapted to local conditions,42 and border

stores may not be representative of all stores; so there is no theoretical presumption that

a minimum wage hike should reduce pro�ts in a border store.43 However, pro�ts are42This institutional feature is discussed on page 17.43Footnote 7 provides a counterexample where pro�ts increase with the minimum wage because w is

not well-adapted to local conditions.

36

expected to decrease in the representative store. So we check whether pro�ts decrease in

the nationwide sample. (By contrast, the border sample is suitable for testing theoretical

predictions about worker behavior and store-level turnover, because both are optimized

store-by-store and so the theoretical predictions are supposed to hold for every worker and

even in non-representative stores).

What controls should be included in the nationwide speci�cation is an open question.

We run the three most-common state-level speci�cations in the literature (store and month

�xed e�ects; or with added linear state trends; or with added census-division×month �xed

e�ects). In all state-level speci�cations, the point estimates are negatives, as predicted by

the theory (see Table 8, Col. 2-4). However, pre-trends are an issue. The only speci�cation

that eliminates pre-trend in pro�ts and employment and individual sales per hour is the

census-division × month �xed e�ects (Tables A.5 and D.1). In this speci�cation, the

negative estimates are statistically signi�cant.44

Pro�ts per capita are predicted to cause a change in employment at the store level.

Lemma 7 predicts that store-level employment should co-move with per-worker pro�ts.

In Figure A.2 we show that this prediction holds in the data. This is a sanity check for

the theory, but it does not directly speak to the e�ect of the minimum wage because the

co-movement analysis does not isolate the e�ect of minimum-wage changes.

We conclude this section with a theoretical observation. In an e�ciency wage setting,

an intriguing general equilibrium e�ect might even cause pro�ts to increase. Indeed, if s,

the probability for an unemployed agent to be hired, is a decreasing function of M , the

worker's loss from termination grows with the minimum wage, whence incentives to exert

e�ort for given pay increase, and thus pro�ts may increase.45 This e�ect, if operative, is44For sake of comparison, we also present the results in the border sample. We estimate Eq. (14) with

pro�ts as the dependent variable and document a zero pro�ts e�ect in the border sample (Table 8, Col.1). At the risk of overinterpreting di�erences in estimates across non-nested regression speci�cations,one may conclude that border stores are somewhat di�erent from average stores. In any case, individualproductivity estimates by type are quite similar in the border and nationwide samples: compare Tables 4and D.5.

45The theory accommodates the case where s is a decreasing function of M : see page 7. Intriguingly,the hiring rate s in the local labor market has been shown to decrease with the minimum wage. See, e.g.,Brochu and Green (2013), Gittings and Schmutte (2016), Dube et al. (2016). Flinn's (2006, 2011) seminalanalyses consider endogenous contact rates between job seekers and �rms in a general equilibrium searchsetting: this endogeneity turns out to make a big di�erence for evaluating the policy implications of the

37

already accounted for in our estimates.

7 Alternative Explanations for Our Core Results

Our core results concern the e�ect of the minimum wage on individual productivity, by

type. In this section, we examine two alternative channels that could explain some of our

core �ndings.

7.1 Demand Channel

A demand increase that systematically coincides with a minimum wage hike might account

for the average increase in individual productivity.46 However, a demand increase alone

does not easily account for why high types fail to experience a productivity boost (Section

4). In addition, a demand increase is at odds with the productivity reduction observed

among low-monitored workers (Section 5.2). Therefore, variation in demand alone cannot

explain all our �ndings.

Still, demand shifts might confound our estimates. To check directly for demand shifts,

we now introduce parking lot occupancy as a proxy for demand (see Figure 8 for an example

of the satellite pictures from which the data are coded). These data have been used by

�nancial traders to forecast revenues for nationwide retailers,47 and they are suitable for

our purposes because they capture customer volume, which is exogenous to worker e�ort,

as opposed to quantity purchased which is not.48 We discuss this measure in Appendix E,

and show that: (1) at the worker-level, variation in occupancy a�ects the sales of high, not

minimum wage. We thank an anonymous referee for this observation.46The literature is split on whether there is pass-through from the minimum wage to the demand for

retail goods. Aaronson et al. (2012) show some pass-through for miscellaneous household items, whichare sold by retail stores. On the other hand, Leung (2017) shows that real sales of �General Merchandise�in mass merchandise stores decrease after a minimum wage hike.

47page 49, J.page Morgan's Guide to Big Data and AI Strategies. Published onMay 29, 2017 https://www.cfasociety.org/cleveland/Lists/Events%20Calendar/Attachments/1045/BIG-Data_AI-JPMmay2017.pdf

48However, a limitation is that we have no speci�c visibility on spending per shopper. This might beproblematic if there are distributional e�ects of the minimum wage such that the number of shoppers doesnot change but spending per shopper increases.

38

low types (Figure 9); (2) in our stores, variations in minimum wage do not cause variations

in occupancy (Table E.1), and, therefore: (3) controlling for occupancy does not a�ect our

worker-level results (Table E.2).

Figure 8: Satellite Image of One Store with Parking Lot Area and Car Counts Highlighted

Notes: Data c© 2018 RS Metrics; Imagery c© (CNES) 2018; Distribution Airbus DS Imagery c© 2018 DigitalGlobe

In Appendix E we also document that the minimum wage a�ects our workers' individ-

ual productivity independently of the share of the population in the county or state who

earns the minimum wage (Table E.4).49 If demand was an important channel, we would

expect this share to correlate with a demand-driven productivity boost.

A conceptually related channel is a change in demand per worker. Fix employee i.

Any decrease in the number of co-workers −i might change i's residual demand, and thus

increase i's individual productivity mechanically, quite apart from any incentive e�ect on

i. Such spillovers across workers do not exist in our model, but they could exist in reality.

We can rule out that our results on individual productivity are confounded by variation

in store-level employment because in Section 6.2 the number of salespeople employed by49 We compute two measures of �exposure to the minimum wage:� one at the county level and the

other at the state level. The former uses the QWI data to calculate the quarterly, county-level di�erencebetween the average hourly wage and the prevailing minimum wage (as in Renkin et al. 2018). Thelatter uses the individual-level CPS data to calculate the quarterly, state-level fraction of workers whoseearnings per hour is equal to the prevailing minimum wage (as in Cengiz et al. 2019). We thank twoanonymous referees for suggesting this �di�erential incidence� analysis. In the appendix, we also showthat low types are not disproportionately more located in high-share counties, and that our core resultsare robust to controlling for store parking lot occupancy interacted with the share.

39

Figure 9: A Positive Demand Shock Increases the Productivity of High Types but not ofLow Types

Notes: E�ects of being in the top quartile of demand on the percent change in productivity (Y:Sales/Hrs) for low, medium, and high types. Top quartile of demand is de�ned as being in thetop quartile of the parking-lot occupancy rates in a given month t. Vertical bars represent 95%con�dence intervals.

a store does not correlate signi�cantly with the minimum wage. Furthermore, controlling

for store-level employment does not a�ect our core estimates, either on average or by

type (Table E.5). A similar form of negative spillover would exist if increased e�ort

by co-workers at the intensive margin (choice of e−i, in our model) reduces worker i's

individual productivity through, e.g., �demand stealing.�50 This e�ect is di�cult to control

for directly, but if such a spillover existed it would depress every worker's productivity

given e�ort, and so our estimated coe�cients (which are based on productivity) would

under-represent the true e�ect of the minimum wage on e�ort.50We presume that spillovers are negative because, assuming that the intensive margin of −i's e�ort

has the same spillover e�ect on i as change in the extensive margin, Table E.5 shows this e�ect to benegative, if small.

40

7.2 Organizational Adjustments Channel

The second alternative channel is that stores could adjust to a higher minimum wage

in various organizational ways that might disproportionately increase the low types' pro-

ductivity. We list the following adjustments (see Appendix F for an in-depth analysis of

each):

1. Reallocate low types to �better-selling� departments, which could increase their sales

per hour. We �nd no signi�cant e�ect both in the aggregate and across types (Figure

10, Panel A and Table F.1).

2. Move low types from part-time to full-time status, which could also imply a better

shift and higher sales per hour for low types.51 Ditto (shown in Panel B).

3. Reduce the number of hours low types are scheduled to work, which may translate

into higher productivity per hour if this attenuates the fatigue of working long hours.

Ditto (shown in Panel C).

4. Adjust bene�ts of low types. Ditto (shown in Panel D).

5. Change the consumer price. First, in line with the �ndings of Della Vigna and

Gentzkow (2019), our company has a national pricing strategy and has uniform

prices across all US stores. We con�rm this by backing out a store-level aggregate

retail price index from each store's monthly �nancials, and showing that the index

does not vary with the local minimum wage (Table F.2). Second, an increase in prices

does not explain our core result because price changes a�ect sales for all types, not

speci�cally for the low types.

Overall, the above results indicate that the individual productivity gains that we mea-

sure across types do not re�ect organizational adjustments associated with minimum wage

increases, as far as we can measure.51The high-demand hours in our �rm are the 6-9pm ones, and are typically assigned to full-time workers.

41

Figure 10: Minimum Wage Has No Di�erential E�ect on Allocation to Top Departments,Part-Time Status, Hours Worked and Bene�ts by Type

Notes: E�ects of a $1 increase in minimum wage on the percent change in Y; where Y is an indicatorfor working in the top department (Panel A), an indicator for being a part-time worker (Panel B), thenumber of hours worked per month (Panel C), or bene�ts (in $) earned (Panel D). Vertical bars represent

95% con�dence intervals computed using the estimated coe�cients (β̂1, β̂1 + β̂4 and β̂1 + β̂5) from Eq.(12) and the associated standard errors.

8 External Validity and Connection With the Litera-

ture

To our knowledge, absolute changes in individual productivity (i.e., not relative to other

types) have not previously been documented in the minimum wage literature.52 Therefore,

documenting these changes and modeling the channels that produce them has value at

the �micro� level. With this being said, all our employees are from a single �rm, and so

the external validity of our �ndings must be assessed carefully. We do this next.52Ku (2018) and Hill (2018) provide relative estimates, as discussed in Section 1.

42

Individual Worker Productivity by Type Our �low types� only exert e�ort for fear

of losing their job (e�ciency wage motive). Their calculus is not a�ected by the shape

of w because their pay seldom exceeds the minimum wage. Since this calculus applies

verbatim to all US workers who earn minimum wage, we conjecture that those workers

would experience a productivity boost similar to our low types'. This group of workers is

policy-relevant because this is the most vulnerable sub-population and, also, the target of

minimum wage policy.

Our �medium types� also experience a productivity boost, albeit a smaller one. This

makes sense if e�ort is continuous, and not discrete as in our main model. To show this,

we present an analogue to Eq. (4) for the case when e�ort e is a continuous variable:

w (x, e;M)︷ ︸︸ ︷e�ciency wage

(increasing in M)

+

[q (e) + r

d (1− q (e))

]we (x, e;M)︷ ︸︸ ︷

pay for performance

(decreasing in M)

= ω + c′ (e)

[q (e) + r

d (1− q (e))

].

(4′)

This equation represents type x's �rst-order conditions for optimal e�ort. In this equation

c (e) is the cost of e�ort, q (e) represent the worker's probability of termination (decreasing

in e), and d captures the elasticity of the function q. As the minimum wage M increases,

the LHS increases if the positive e�ect due to w dominates over the negative e�ect due

to we. In this case, the e�ort of medium types increases with the minimum wage. See

Appendix B.2 for a formal treatment.

Eq. (4′) a�ords a counterfactual experiment that broadens the external validity of our

analysis. Take one of our medium types x, and contemplate the counterfactual scenario

where type x is employed under a �xed salaryW rather than under our factual compensa-

tion scheme w, and W is such that she exerts the same amount of e�ort in either scenario.

Suppose a minimum wage hike ∆M causes type x's pay level (the e�ciency-wage term

in Eq. 4′) to increase by some amount ∆w: then the LHS increases by less than ∆w,

owing to the pay-for-performance term which is decreasing in M . Compare to the �xed

salary scenario where type x's salary W is increased by the same amount ∆w: then the

LHS increases by the full ∆w because the pay-for-performance term is not present. This

indicates that a given pay increase translates into stronger incentives to exert e�ort under

43

�xed salary, than under w. The argument is presented formally in Appendix B.2. This

observation is of broad interest because most US workers are paid a �xed salary,53 and

because it has been documented that even �xed salaries above minimum wage increase

with the minimum wage � the so-called �ripple e�ect.�54 The above analysis suggests that

the �wage ripple e�ect� should cause a hitherto unexamined �productivity ripple e�ect�

among workers paid �xed wages and, furthermore, that the productivity estimates from

Section 4.1 represent lower bounds for the size of the �productivity ripple e�ect.�

Finally, our �highly paid� workers exhibit a vanishing productivity response. This

e�ect is trivially general: workers whose pay is barely a�ected by the minimum wage

would, logically, barely respond to it.

Another way to argue for external validity is to match empirical results with those in

the labor literature. While the literature does not speak to absolute changes in individual

productivity, there is a rich literature on terminations showing a decrease in the aggregate

termination of workers �most a�ected� by the minimum wage, after a minimum wage

increase.55 We, too, �nd that after a minimum wage increase our low and medium types

are terminated less often, consistent with the literature.

Firm-Level Outcomes Economic logic points to two factors that may limit the gen-

eralizability of our store-level �ndings. First, prices in our stores do not respond to the

minimum wage. This feature is not unusual,56 but some pass-through has been recorded53More than 60% of US workers are paid �xed salary: see Lemieux et al. (2009), Gittleman and Pierce

(2013).54See Neumark and Wascher (2008) for a review of the earlier literature and Dube et al. (2019), Cengiz

et al. (2019), and Phelan (2019) for more recent evidence, however, see Autor et al. (2016) for a skepticalview.

55Earlier papers use county- or state-level data to show that the minimum wage reduces worker turnover:e.g., Portugal and Cardoso (2006), Brochu and Green (2013), Dube et al. (2016), Gittings and Schmutte(2016), and Jardim et al. (2018). Note that this evidence goes against the �labor-labor substitution�argument that �rms optimally respond to the minimum wage by substituting away from low types to hiremore high types (e.g., DiNardo et al. 1996, Neumark et al. 2004).

56Della Vigna and Gentzkow (2019) show that US retail chains charge nearly uniform prices acrossstores, despite wide variation in consumer demographics and competition. In non-labor intensive settings,Harasztosi and Lindner (2019) and Ganapati and Weaver (2017) document minimal price pass-through.Gagnon and Lopez-Salido (2020) show that supermarket prices are unresponsive to large local shocks thata�ect the labor supply.

44

in some sectors;57 we will discuss pass-through when we discuss pro�ts. Second, the com-

position of worker types determines how the �rm as a whole responds to a minimum wage

increase.58 Our stores' wage distribution resembles the lower half of the US wage distribu-

tion, and this must be considered when making general statements based on our store-level

estimates.

Having acknowledged these theoretical caveats, our empirical �ndings on labor �ows,

employment, and pro�ts at the store level generally align with aggregate estimates from

the empirical labor literature. We discuss each in turn.

We document a decrease in store-level terminations, hiring, and turnover, as the min-

imum wage increases. Earlier papers have documented a similar pattern by analyzing

aggregate �ows of low-paid workers.59 Our micro-level analysis adds the nuance that even

within a single establishment the e�ect comes from the low types � as predicted by the

model. To our knowledge, the literature on employment �ows has not connected their �nd-

ings to an endogenous increase in worker productivity, as we do in this paper. Also, our

null e�ect on store-level employment is typical within the border-discontinuity literature.60

Visibility on establishment-level pro�ts, albeit for a single �rm, is novel in the US con-

text, to our knowledge. The empirical literature on the pro�t e�ect of the minimum wage

is relatively sparse and tends to �nd non-positive e�ects, as we do also.61 A caveat is that57The minimum wage has been shown to increase prices in labor-intensive sectors: the local service

sector, see Lemos (2008) and MaCurdy (2015); labor intensive �rms in Harasztosi and Lindner (2019).58For example, in a �rm where most workers are at the minimum wage, �rm output is predicted to

respond like our theory's low types.59The literature is summarized in Footnote 55.60The large literature on the minimum wage and employment has recently been summarized by Wolfson

and Belman (2016), Card and Krueger (2017), and Neumark (2019). Geographically-proximate designstypically �nd that the minimum wage has no disemployment e�ects (e.g., Dube et al. 2010. Addisonet al. 2013, Allegretto et al. 2011, Gittings and Schmutte 2016), with some exceptions being Liu et al.2016 and Slichter 2016. State-panel designs yield elasticities of employment with respect to the minimumwage in the range of -0.1 to -0.2 for low-skilled workers. Our panel estimates fall within this range. Theliterature has also occasionally documented larger negative elasticities (e.g., Clemens and Wither 2019),or large positive elasticities (most notably, Card and Krueger 1994). Close to our paper, Giuliano (2013)uses similarly-detailed HR data from a large US retailer in the apparel industry and �nds that a higherminimum wage has a statistically insigni�cant e�ect on overall employment.

61We are aware of only three papers that directly assess the e�ect of minimum wage on �rm pro�ts,and the evidence is mixed. Draca et al. (2011) show that pro�ts go down in high-market power industriesin the UK while they do not change signi�cantly in low-market power industries. Harasztosi and Lindner(2019) show that �rm pro�t decrease in Hungary but only slightly. Mayneris et al. (2018) �nd no reductionin �rm pro�ts in China. There are also a number of papers on the e�ect of minimum wage on �rm-level

45

prices in our stores do not adjust to the minimum wage. If they did, one might conjecture

that store-level pro�ts would be less-negatively impacted, relative to our estimates and

then, according to our model, store-level employment would consequently decrease less.

Summary In sum, we have argued that our results on the individual productivity re-

sponse to a minimum wage increase generalize across the wage distribution (low, medium,

and high types), sometimes as lower bounds. We do not stress our store-level estimates

as much because they necessarily depend on the fraction of low types that are present in

a particular establishment. Also, in our setting prices and wages are �xed by national

HQ policy in response to a local minimum wage change, and this may not be the case in

other establishments. With this being said, our store-level estimates generally align with

aggregate estimates from the empirical labor literature.

9 Conclusions

We have studied individual worker productivity among more than 40,000 salespeople em-

ployed by a large US retailer that operates more than 2,000 stores. This setting is not

atypical: 23% of the US workforce is employed by �rms with more than 20,000 employees,

and the average such �rm has about 1,200 establishments.62

We have documented the e�ect of the minimum wage on individual productivity. A

border-discontinuity research design a�ords estimates in levels, beyond mere relative esti-

mates by worker type (types are de�ned according to how close their pay is to the minimum

wage). This is novel, to our knowledge.

Empirically, we have shown that types with pay �at the minimum wage� exhibit a

sizable productivity boost after a minimum wage increase. They are also terminated

less often. These �ndings point to an e�ciency wage channel, and bring into focus the

TFP and revenues (Riley and Bondibene 2017, Hau et al. 2020). These papers typically document anincrease in TFP conditional on survival. Finally, there are papers on �rm stock-market value (Card andKrueger 2015, Bell and Machin 2018). Bell and Machin (2018) exploit the unexpected announcement ofa change in the UK minimum wage and show a fall in the stock market value of low-wage �rms.

62Source: 2017 Statistics of U.S. Businesses (SUSB) Annual Data Tables by Establishment Industry.

46

individual worker's endogenous e�ort response to the minimum wage.

Workers whose average pay exceeds minimum wage were shown to exhibit the same

behavior, only less pronounced. At one level this is not too surprising: all our workers

are compensated based on performance, and since even decent performers sometimes earn

minimum wage, they react to its increase. At another level, however, it is instructive

that types �above minimum wage� work harder after a minimum wage increase. Indeed,

economic logic suggests that if workers are paid for performance, the minimum wage should

have a disincentive e�ect because it reduces the steepness of the incentive schedule. (Types

�at minimum wage� hardly experience this disincentive because the performance portion

of their pay is small).

To keep track of the con�icting incentive e�ects of the minimum wage, we have in-

troduced a new model that features both e�ects. Depending on parameter values, and

speci�cally on the quality of monitoring, the model specializes to a �pure pay for perfor-

mance� model or to a �pure e�ciency wage� model. By means of comparative statics, we

proved that our empirical setting is best captured by a �hybrid� parameterization where

both e�ects operate but the e�ciency wage e�ect dominates.

Economic logic suggests that the productivity boost experienced by our workers �at�

or �above minimum wage� after a pay increase should obtain, also, among workers who

are paid a �xed wage. Indeed, the boost should be even bigger because no �pay-for-

performance� disincentive would exist to attenuate the e�ciency wage boost. Based on

this logic, we have speculated that the �wage ripple e�ect� which has been documented

among US workers might cause a hitherto unexamined �productivity ripple e�ect.� While

speculative, this observation is intriguing because there are many more workers �at or

above� than just �at� the minimum wage.

By documenting the endogenous e�ort response of low-paid workers, this paper has

emphasized another channel through which their welfare is a�ected by the minimum wage,

above and beyond the traditional concern that they might lose their job. Even employees

who get to keep their job will experience greater disutility of e�ort after a minimum wage

increase, if they work harder. Therefore, their net welfare gain is less than the face value

of the pay increase. We leave this issue for future research.

47

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52

Table 1: Descriptive Statistics

Variables Mean S.D. p10 p50 p90 N(1) (2) (3) (4) (5) (6)

Panel A. Worker-level Variables

ProductivitySales/Hrs (Shrouded Units) 2.085 1.468 0.781 1.872 3.522 217,822

Tenure and HoursTenure (in months) 48.92 65.01 4 24 126 217,822Part-Time (in %) 60.25 48.94 0 100 100 217,822Number of Hours (Hrs) 106.5 44.12 46.47 107.6 162.3 217,822

CompensationBase Rate: Regular Pay/Hrs (in $) 6.120 1.181 4.500 6 7 217,822Comm. Rate: Variable Pay/Sales (in %) 3.462 3.188 1.057 2.343 7.531 213,726Variable Pay/Hrs (in $) 5.947 4.936 1.740 4.610 11.78 217,822MinW Adj/Hrs (in $) 0.225 1.736 0 0 0.771 217,822Total Pay (in $) 1,361 831.2 494.6 1,218 2,343 217,822Total Pay/Hrs (in $) 12.51 4.620 8.734 11.15 17.94 217,822

Panel B. Store-level Variables

Termination, Hiring, and TurnoverTerminated (in %) 4.755 7.692 0 0 12.50 12,359Hired (in %) 2.060 4.285 0 0 7.692 12,359Turnover (in %) 3.408 4.404 0 2.500 8.333 12,359

Employment and Pro�tsNumber of Workers 16.64 6.855 8 16 26 12,359Ratio Supervisors-Workers (in %) 6.990 4.886 3.448 5.882 11.11 12,359Ebitda/Hrs (Shrouded Units) 5.946 11.97 -8.010 5.630 19.97 12,359

Notes: This table presents summary statistics of worker-level variables in Panel A and of store-levelvariables in Panel B. Sales/Hrs are the sales per hour rescaled by a factor between 1/50 and 1/150relative to its $ value. Tenure is the number of months of tenure. Part-Time (in %) is the percentprobability that an employee is part-time in a given month (0 means full-time and 100 means part-time).Number of Hours is the total number of hours for which employee receives a compensation in a givenmonth. Base Rate: Regular Pay/Hrs are monthly regular earnings per hour worked (in $ per hour).Comm.Rate: Variable Pay/Sales are earnings from commissions and incentives divided by sales (in %).Variable Pay/Hrs are earnings from commissions and incentives per hour worked (in $ per hour). MinWAdj/Hrs are the monthly earnings from minimum wage adjustments per hour worked (in $ per hour).Total Pay (in $) is the monthly total pay from total take home pay. Total Pay/Hrs is the monthly totalpay from total take home pay per hour worked (in $ per hour). Terminated (in %) is the percent ofsales associates in the store who are terminated in a given month. Hired (in %) is the percent of salesassociates who are hired in a store in a given month. Turnover (in %) is de�ned as the percent of salesassociates in the store who are terminated or hired in a given month divided by two. Number of Workersis the number of sales associates employed by a store in a given month. Ratio Supervisors-Workers ismeasured as the number of supervisors per 100 sales associates. Ebitda/Hrs are equal to earnings beforeinterest, tax, depreciation and amortization, per hour worked in the store. We do not disclose the unitsfor con�dentiality reasons.

Table 2: E�ect of MinimumWage on Compensation Scheme w, and on Overall Pay Inclusive of MinimumWage Adjustment

Compensation scheme (w) Overall pay inclusive of minimum wage adjustmentDep.Var. Base Rate: Comm. Rate:

Reg.Pay/Hrs Var.Pay/Sales MinW.Adj./Hrs Var.Pay/Hrs Tot.Pay/Hrs Tot.Pay(in $) (in %) (in $) (in $) (in $) (in 100$)(1) (2) (3) (4) (5) (6)

MinW -0.059 0.126 0.250*** 0.439* 0.645*** 0.856**(0.042) (0.077) (0.044) (0.235) (0.172) (0.336)

Observations 217,822 213,697 217,822 217,822 217,822 217,822Units Workers Workers Workers Workers Workers WorkersMean Dep.Var. 6.120 3.462 0.225 5.947 12.51 13.61E�ect MinW (%) -0.957 3.628 111.3 7.390 5.154 6.289

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ects and control for worker tenure, worker department andcounty-level unemployment. Reg.Pay/Hrs is the base rate: monthly regular earnings per hour worked (in $ per hour). Var.Pay/Sales is thecommission rate: earnings from commissions and incentives divided by sales (in %). MinW.Adj./Hrs are monthly earnings from minimumwage adjustments per hour worked (in $ per hour). Var.Pay/Hrs are earnings from commissions and incentives per hour worked (in $ perhour). Tot.Pay/Hrs is the monthly total pay from total take-home pay per hour worked (in $ per hour). Tot.Pay is the monthly total payfrom total take-home pay (in 100$). MinW is the predominant monthly minimum wage (in $). E�ect MinW (%) is the percent e�ect ofa $1 increase in MinW on the outcomes. Standard errors are two-way clustered at the state level and at the border-segment level. ***p<0.01, ** p<0.05, * p<0.1.

54

Table 3: Descriptive Statistics for Low, Medium and High Types

Worker Types: Low Types Medium Types High Types(1) (2) (3)

% Workers 3.9% 72.4% 23.7%

Sales/Hrs 1.08 1.94 2.73

% Weeks with MinW Adjustment 48.9% 18.5% 12.2%

% Terminated 6.8% 5.2% 3.0%Notes: This table presents summary statistics for low, medium, and high types. LowTypes are workers paid at the minimum wage. Medium Types are workers paid betweenthe minimum wage and 180% of the minimum wage. High Types are workers paid morethan 180% of the minimum wage. The number of observations is 210k as in our mainspeci�cations. Sales/Hrs are the sales per hour rescaled by a factor between 1/50 and1/150 relative to its $ value. % Weeks with MinW Adjustment is the fraction of weeksper month in which worker's pay is topped up by the �rm. % Terminated is the fractionof workers terminated.

55

Table 4: E�ect of Minimum Wage on Individual Worker Productivity

Dep.Var. Sales/Hrs Sales/Hrs(1) (2)

MinW 0.094** 0.244***(0.039) (0.042)

Medium Type 0.354***(0.032)

High Type 1.169***(0.072)

MinW · Medium Type -0.085***(0.025)

MinW · High Type -0.182***(0.032)

Observations 217,822 209,513Units Workers WorkersMean Dep.Var. 2.085 2.085E�ect MinW (%) 4.485E�ect MinW for Low Type (%) 22.56p-value 0.001

E�ect MinW for Med. Type (%) 8.186p-value 0.001

E�ect MinW for High Type (%) 2.273p-value 0.179

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ectsand control for worker tenure, worker department, and county-level unemploy-ment. Sales/Hrs are the sales per hour rescaled by a factor between 1/50 and1/150 relative to its $ value. MinW is the predominant monthly minimumwage (in $). Medium Type is an indicator for whether the worker's total payin month t-1 is between the minimum wage and 180% of minimum wage. HighType is an indicator for whether the worker's total pay in month t-1 is above180% of minimum wage. The omitted group (Low Types) are workers forwhom total pay in t-1 is �at minimum wage�. E�ect MinW (%) is the percente�ect of a $1 increase in MinW on the outcomes. Standard errors are two-wayclustered at the state level and at the border-segment level. *** p<0.01, **p<0.05, * p<0.1.

56

Table 5: E�ect of Minimum Wage on Worker Productivity for High vs. Low MonitoringCoverage

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs Sales/Hrs Sales/HrsSample All High Coverage Low Coverage

(1) (2) (3) (4) (5)

Coverage 0.010***(0.003)

MinW 0.140*** 0.281*** -0.192** 0.020(0.040) (0.044) (0.081) (0.067)

Medium Type 0.368*** 0.336***(0.033) (0.044)

High Type 1.185*** 1.121***(0.071) (0.080)

MinW · Medium Type -0.083*** -0.111*(0.027) (0.054)

MinW · High Type -0.188*** -0.168**(0.031) (0.075)

Observations1 217,822 132,384 126,852 84,549 81,800Units Workers Workers Workers Workers WorkersMean Dep.Var. 2.085 2.118 2.085 2.030 2.085E�ect (%) 1.461 6.588 -9.444E�ect MinW for Low Type (%) 25.87 1.824p-value 0.001 0.773

E�ect MinW for Med. Type (%) 10.11 -4.953p-value 0.001 0.176

E�ect MinW for High Type (%) 3.298 -5.714p-value 0.077 0.114

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ects and control for workertenure, worker department, and county-level unemployment. Sales/Hrs are the sales per hour rescaledby a factor between 1/50 and 1/150 relative to its $ value. Coverage is measured as the ratiosupervisors-workers (number of supervisors per 100 sales associates). Low (High) coverage is anindicator for whether the store is in the bottom quartile (not in the bottom quartile) of coverage.MinW is the predominant monthly minimum wage (in $). Medium Type is an indicator for whetherthe worker's total pay in month t-1 is between the minimum wage and 180% of minimum wage. HighType is an indicator for whether the worker's total pay in month t-1 is above 180% of minimum wage.The omitted group (Low Types) are workers for whom total pay in t-1 is �at minimum wage�. E�ectMinW (%) is the percent e�ect of a $1 increase in MinW on the outcomes. Standard errors are two-wayclustered at the state level and at the border-segment level. *** p<0.01, ** p<0.05, * p<0.1.

57

Table 6: E�ect of Minimum Wage on Store-Level Outcomes, by Fraction of Low Types (Store-level)

Dep.Var. % Terminated % Hired % Turnover Tenure N.Workers(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

MinW -0.272 -0.282 0.213 0.084 -0.029 -0.099 7.205** 7.537** -0.217 -0.451(0.503) (0.538) (0.308) (0.310) (0.368) (0.393) (3.513) (3.479) (0.423) (0.405)

% Low Types 0.222 0.276** 0.249* -0.740* 0.146(0.207) (0.118) (0.124) (0.375) (0.117)

MinW · % Low Types -0.025 -0.029** -0.027* 0.077* -0.012(0.025) (0.013) (0.014) (0.044) (0.014)

Observations 12,359 12,025 12,359 12,025 12,359 12,025 12,359 12,025 12,359 12,025Units Stores Stores Stores Stores Stores Stores Stores Stores Stores StoresMean Dep.Var. 4.755 4.877 2.060 2.073 3.408 3.475 49.65 49.62 16.64 16.63

Notes: All the regressions include pair-month �xed e�ects, store �xed e�ects and control for county-level unemployment. % Terminatedis the percent of sales associates in the store who are terminated in a given month. % Hired is the percent of sales associates who arehired in a store in a given month. % Turnover is the percent of sales associates in the store who are terminated or hired in a given monthdivided by two. Tenure is the average number of months of tenure in the workforce. N.Workers is the number of sales associates in thestore. MinW is the predominant monthly minimum wage in the store (in $). % Low Types is the percent of workers who are low typesin the store (pay at minimum wage in t-1). Standard errors are two-way clustered at the state level and at the border-segment level. ***p<0.01, ** p<0.05, * p<0.1.

58

Table 7: E�ect of Minimum Wage on Individual Worker Termination

Dep.Var. Terminated Terminated(1) (2)

MinW -0.159 -1.297*(0.517) (0.756)

Medium Type -2.240***(0.755)

High Type -3.753***(0.817)

MinW · Medium Type 0.912(0.620)

MinW · High Type 1.424**(0.573)

Observations 217,822 209,734Units Workers WorkersMean Dep.Var. 4.562 4.562E�ect MinW (%) -3.482E�ect MinW for Low Type (%) -19.16p-value 0.096

E�ect MinW for Med. Type (%) -7.434p-value 0.480

E�ect MinW for High Type (%) 4.247p-value 0.836

Notes: All the regressions include pair-month �xed e�ects, store �xed e�ects(not worker �xed e�ects) and control for worker tenure, worker departmentand county-level unemployment. Terminated is a dummy for whether a workeris terminated in a given month. MinW is the predominant monthly minimumwage (in $). Medium Type is an indicator for whether the worker's total payin month t-1 is between the minimum wage and 180% of minimum wage. HighType is an indicator for whether the worker's total pay in month t-1 is above180% of minimum wage. The omitted group (Low Types) are workers forwhom total pay in t-1 is �at minimum wage�. E�ect MinW (%) is the percente�ect of a $1 increase in MinW on the outcomes. Standard errors are two-wayclustered at the state level and at the border-segment level. *** p<0.01, **p<0.05, * p<0.1.

59

Table 8: E�ect of Minimum Wage on Pro�ts with Border-Discontinuity and State-Level Speci�cations

Dep.Var. Ebitda/Hrs Ebitda/Hrs Ebitda/Hrs Ebitda/HrsSample Border Stores All Stores All Stores All StoresModel Pair · Month FE Month FE Month FE + State-Trend Division · Month FE

(1) (2) (3) (4)

MinW 0.383 -1.683 -0.234 -0.781*(1.317) (1.088) (1.277) (0.436)

Observations 12,359 30,969 30,969 30,969Units Stores Stores Stores StoresMean Dep.Var. 5.946 4.824 4.824 4.824E�ect MinW (%) 6.441 -34.89 -4.861 -16.18

Notes: Col. 1: Sample restricted to bordering stores. The regression includes pair-month �xed e�ects, store �xed e�ects andcontrols for county-level unemployment. Standard errors are two-way clustered at the state level and at the border-segment level.Col. 2-4: Sample comprises of all stores (bordering + non-bordering). The regressions include month �xed e�ects, store �xede�ects and control for county-level unemployment. Col. 3 also controls for state-speci�c linear trends and Col. 4 controls for censusdivision-month �xed e�ects. Standard errors are clustered at the state-level. Ebitda/Hrs is equal to earnings before interest, tax,depreciation and amortization, per hour worked in the store. We do not disclose the units for con�dentiality reasons. MinW is thepredominant monthly minimum wage (in $). E�ect MinW (%) is the percent e�ect of a $1 increase in MinW on the outcomes. ***p<0.01, ** p<0.05, * p<0.1.

60

Appendices

A Appendix Tables and Figures

Figure A.1: Dynamic E�ect of Minimum Wage on Store-level Outcomes

Notes: Panels A-C present the dynamic e�ects of a $1 increase in minimum wage on the store-level percentage point change in Y; where Y is the percent of sales associates who are terminated(Panel A), the percent of sales associates who are hired (Panel B), or the turnover rate of a storein a given month (Panel C). Panel D-E present the dynamic e�ect of a $1 increase in minimumwage on the percent change in average worker tenure (Panel D) and on the number of salesassociates in a store (Panel E). Vertical bars represent 95% con�dence intervals.

61

Figure A.2: Comovement of Employment and Pro�ts Per Worker

Notes: In Panel A, the coordinates of each dot are a store's N.Workers in a given month, andthat store's Ebitda/Hrs averaged over the previous six months. The slope of the regression line,which is 0.32, is the �pooled� estimate of the linear relationship between these two variables. Apositive slope is consistent with the theoretical prediction that an increase in pro�ts per workercauses a store to hire more workers, though we do not interpret the present evidence causally.The same regression, but with store �xed e�ects, yields a coe�cient of 0.12, still positive. PanelB digs deeper into the within-store variation by reporting the c.d.f. of the coe�cients of manyregressions, one for each store, where N.Workers in a given month is regressed on the averageEbitda/Hrs in the previous six months. The c.d.f. in Panel B shows that 68% of the coe�cientsare positive, which we interpret as further supporting evidence for a comovement within storebetween employment, and store-level pro�ts per worker in previous periods. N.Workers is thenumber of sales associates in the store. Ebitda/Hrs is equal to earnings before interest, tax,depreciation and amortization, per hour worked in the store. We do not disclose the units forcon�dentiality reasons.

62

Table A.1: E�ect of Minimum Wage on Worker Total Pay per Hour

Dep.Var. Tot.Pay/Hrs Tot.Pay/Hrs(1) (2)

MinW 0.645*** 0.807***(0.172) (0.225)

Medium Type 0.469***(0.087)

High Type 1.037***(0.115)

MinW · Medium Type -0.097(0.105)

MinW · High Type -0.141*(0.083)

Observations 217,822 209,513Units Workers WorkersMean Dep.Var. 12.51 12.51E�ect MinW (%) 5.154E�ect MinW for Low Type (%) 8.146p-value 0.001

E�ect MinW for Med. Type (%) 6.281p-value 0.000

E�ect MinW for High Type (%) 3.978p-value 0.002

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ects,and control for worker tenure, worker department and county-level unemploy-ment. Tot.Pay/Hrs is the monthly total pay from total take-home pay perhour worked (in $100 per hour). MinW is the predominant monthly mini-mum wage (in $). Medium Type is an indicator for whether the worker's totalpay in month t-1 is between the minimum wage and 180% of minimum wage.High Type is an indicator for whether the worker's total pay in month t-1 isabove 180% of minimum wage. The omitted group (Low Types) are workersfor whom total pay in t-1 is �at minimum wage�. E�ect MinW (%) is thepercent e�ect of a $1 increase in MinW on the outcomes. Standard errorsare two-way clustered at the state level and at the border-segment level. ***p<0.01, ** p<0.05, * p<0.1.

63

Table A.2: Dynamic E�ect of Minimum Wage on Worker Productivity

Dep.Var Sales/Hrs(1)

t = −6 -0.019(0.102)

t = −3 -0.081(0.091)

t = 0 0.159(0.128)

t = +3 0.113(0.069)

t = +6 0.190**(0.079)

t = −6 · Medium Type 0.146(0.096)

t = −3 · Medium Type 0.117(0.074)

t = 0 · Medium Type -0.042(0.079)

t = 3 · Medium Type 0.073**(0.036)

t = 6 · Medium Type -0.038(0.023)

t = −6 · High Type -0.029(0.069)

t = −3 · High Type 0.008(0.062)

t = 0 · High Type -0.166(0.132)

t = 3 · High Type 0.050(0.061)

t = 6 · High Type -0.208***(0.043)

Observations 102,252Mean Dep.Var. Low Type .936Mean Dep.Var. Medium Type 1.853Mean Dep.Var. High Type 2.596

Notes: t = -6, -3 are leading coe�cients (pre-change). t = 3, 6 arecumulated lag coe�cients (post-change). All the regressions includepair-month �xed e�ects, worker �xed e�ects and control for workertenure, worker department, county-level unemployment. Sample re-stricted to workers who stayed on the job at least 12 consecutivemonths (six before the minimum wage change and six after). t =0 is the period of the minimum wage change. Medium Type is anindicator for whether the worker's total pay in month t-1 is betweenthe minimum wage and 180% of minimum wage. High Type is anindicator for whether the worker's total pay in month t-1 is above180% of minimum wage. The omitted group (Low Types) are work-ers for whom total pay in t-1 is �at minimum wage�. Standard errorsare two-way clustered at the state level and at the border-segmentlevel. *** p<0.01, ** p<0.05, * p<0.1.

Table A.3: E�ect of Minimum Wage on Worker Productivity by Hiring Rate

Dep.Var. Sales/Hrs Sales/Hrs(1) (2)

MinW 0.159*** 0.339***(0.049) (0.067)

MinW · Hiring Rate.Q2 -0.028 -0.067(0.036) (0.059)

MinW · Hiring Rate.Q3 -0.061* -0.126**(0.032) (0.051)

MinW · Hiring Rate.Q4 -0.200** -0.237***(0.098) (0.077)

MinW · Medium Type -0.113*(0.055)

MinW · Med. Type · Hiring Rate.Q2 0.047(0.063)

MinW · Med. Type · Hiring Rate.Q3 0.056(0.047)

MinW · Med. Type · Hiring Rate.Q4 0.038(0.054)

MinW · High Type -0.254***(0.046)

MinW · High Type · Hiring Rate.Q2 0.049(0.106)

MinW · High Type · Hiring Rate.Q3 0.140**(0.054)

MinW · High Type · Hiring Rate.Q4 0.070(0.064)

Observations 217,822 209,513Units Workers Workers

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ectsand control for worker tenure, worker department, county-level unemploymentand three dummies: Hiring Rate.Q2, Hiring Rate.Q3 and Hiring Rate.Q4. Theregression in Col. 2 also controls for the interaction of each of the latter threedummies withMediumType andHighType (6 extra x-variables), which we donot report due to space constraints. HiringRate.Q2 is a dummy for whetherstores are located in counties that have hiring rate in quartile 2 of the within-county distribution. Similar de�nitions for quartiles 3 and 4. MinW is thepredominant monthly minimum wage (in $). Medium Type is an indicator forwhether the worker's total pay in month t-1 is between the minimum wage and180% of minimum wage. High Type is an indicator for whether the worker'stotal pay in month t-1 is above 180% of minimum wage. The omitted group(Low Types) are workers for whom total pay in t-1 is �at minimum wage�.Standard errors are two-way clustered at the state level and at the border-segment level. *** p<0.01, ** p<0.05, * p<0.1.

65

Table A.4: Test of Endogenous Monitoring Coverage and Steady State

Dep.Var. Coverage N.Workers(1) (2)

MinW 0.202(0.490)

Time Trend -0.026(0.017)

Observations 12,359 12,359Units Stores StoresMean Dep.Var. 6.990 16.64E�ect (%) 2.883 -0.159

Notes: All the regressions include pair �xed e�ects, store�xed e�ects and control for county-level unemployment.The regression in Col. 1 also controls for pair-month �xede�ects. Coverage is the ratio supervisors-workers (numberof supervisors per 100 sales associates). N.Workers is thenumber of sales associates employed by a store in a givenmonth. MinW is the predominant monthly minimum wage(in $). Linear Trend is a montly linear time trend. Stan-dard errors are two-way clustered at the state level and atthe border-segment level. *** p<0.01, ** p<0.05, * p<0.1.

66

Table A.5: Test of Pre-Trends in Stores-Level Outcomes with Border-Discontinuity and State-Level Speci�cations

Dep.Var. Turnover Ebitda/Hrs N.Workers Turnover Ebitda/Hrs N.Workers % Turnover Ebitda/Hrs N.Workers % Turnover Ebitda/Hrs N.WorkersSample Store-Border All Stores All Stores All StoresModel County-Pair· Month FE Month FE Month FE + State-Trend Division · Month FE

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

Panel A: 6-Months Pre-Trend

Pre-Trend (6 Months) 0.333 -2.252 -0.355 0.064 -0.853* -0.034 0.097 -0.696 -0.209 -0.004 -0.343 -0.129(0.970) (1.364) (0.333) (0.155) (0.486) (0.133) (0.157) (0.466) (0.168) (0.236) (0.562) (0.181)

Observations 12,073 12,073 12,073 30,156 30,156 30,156 30,156 30,156 30,156 30,156 30,156 30,156

Panel B: 12-Months Pre-Trend

Pre-Trend (12 Months) -0.127 1.811 0.002 0.179 0.171 -0.099 0.182 0.337 -0.363* 0.161 0.268 -0.164(0.410) (1.372) (0.398) (0.157) (0.835) (0.0962) (0.166) (0.895) (0.214) (0.169) (0.879) (0.176)

Observations 11,753 11,753 11,753 29,176 29,176 29,176 29,176 29,176 29,176 29,176 29,176 29,176Units Stores Stores Stores Stores Stores Stores Stores Stores Stores Stores Stores Stores

Notes: In Panel A, Pre-Trend = η3−0− η6−3 estimated from: Yjt = α+ η6−3(MinWj,t+6−MinWj,t+3)+ η3−0(MinWj,t+3−MinWj,t)+ ρMinWj,t+ ηZjt+δj + εjt, where MinWj,t+m is the minimum wage m months after month t, η6−3 (η3−0) is a leading coe�cient that captures variations in the Y-variable6 to 3 (3 to 0) months before each change in the minimum wage (see Dube at al. 2010). In Panel B, we report the estimates from a longer-trend model:Pre-Trend = η12−6 − η6−0 estimated from: Yjt = α+ η12−6(MinWj,t+12 −MinWj,t+6) + η6−0(MinWj,t+6 −MinWj,t) + ρMinWj,t + ηZjt + δj + εjt. In Col.1-3 (4-12) pre-trends are tested in the sample of bordering stores (bordering+non-bordering stores). All regressions include store �xed e�ects and control forcounty unemployment rate. The regressions vary in the time controls: we include pair-month �xed e�ects in Col. 1-3, month �xed e�ects in Col. 4-6, month�xed e�ects and state-speci�c linear trends in Col. 7-9, census division·month �xed e�ects in Col. 9-12. % Turnover is the percent of sales associates in thestore who are terminated or hired in a given month divided by two. Ebitda/Hrs is equal to earnings before interest, tax, depreciation and amortization, perhour worked in the store. We do not disclose the units for con�dentiality reasons. N.Workers is the number of sales associates employed by a store in a givenmonth. Standard errors are two-way clustered at the state level and at the border-segment level in Col. 1-3 and at the state-level in col. 4-12. *** p<0.01,** p<0.05, * p<0.1.

67

B Model Appendix

B.1 Proofs for Section 2

Deriving condition (4)

V N (x) = w (x, 1)− c (x) +(1− q)(1 + r)

V N (x) +q

(1 + r)V A (15)

V S (x) = w (x, 0) +(1− q)(1 + r)

(1−D)V S (x) +[1− (1− q) (1−D)]

(1 + r)V A (16)

V A =sV + (1− s)V A

(1 + r)(17)

Isolate V N (x) from (15):

V N (x)

[1− (1− q)

(1 + r)

]= w (x, 1)− c (x) +

q

(1 + r)V A

V N (x) =(1 + r)

(r + q)

[w (x, 1)− c (x) +

q

(1 + r)V A

].

Isolate V S (x) from (16):

V S (x)

[1− (1− q)

(1 + r)(1−D)

]= w (x, 0) +

[1− (1− q) (1−D)]

(1 + r)V A

V S (x)

[r +D + q (1−D)

(1 + r)

]= w (x, 0) +

[D + q (1−D)]

(1 + r)V A

V S (x) =(1 + r)

r +D + q (1−D)

[w (x, 0) +

[D + q (1−D)]

(1 + r)V A

].

The no-shirking condition V N (x) ≥ V S (x) can be written as:

68

r +D + q (1−D)

(r + q)

[w (x, 1)− c (x) + q

V A

(1 + r)

]≥ w (x, 0) + [D + q (1−D)]

V A

(1 + r)

r +D + q (1−D)

(r + q)w (x, 1)− w (x, 0) ≥

[D + q (1−D)−

q

(r + q)[r +D + q (1−D)]

]V A

(1 + r)+r +D + q (1−D)

(r + q)c (x)

r +D + q (1−D)

(r + q)w (x, 1)− w (x, 0) ≥

[rD − rqD(r + q)

]V A

(1 + r)+r +D + q (1−D)

(r + q)c (x)

r + q +D − qD(r + q)

w (x, 1)− w (x, 0) ≥D (1− q)(r + q)

r

(1 + r)V A +

r +D + q (1−D)

(r + q)c (x)

[r + q +D (1− q)]w (x, 1)− (r + q)w (x, 0) ≥ [D (1− q)]r

(1 + r)V A + [r +D + q (1−D)] c (x)

D (1− q)w (x, 1) + (r + q) [w (x, 1)− w (x, 0)] ≥ [D (1− q)]r

(1 + r)V A + [r +D + q (1−D)] c (x)

w (x, 1) +(r + q)

D (1− q)[w (x, 1)− w (x, 0)] ≥

r

(1 + r)V A +

[r +D + q (1−D)

D (1− q)

]c (x)

w (x, 1) +(r + q)

D (1− q)[w (x, 1)− w (x, 0)] ≥

r

(1 + r)V A +

[1 +

r + q

D (1− q)

]c (x) (18)

Isolate V A (x) from (17) to get:

V A =s

(r + s)V . (19)

Plug into (18) to get expression (4).

Lemma 8. The di�erence w (x, 1;M)− w (x, 0;M) is decreasing in M.

Proof. Denote by FW (x,e) the c.d.f. of w (Y (x, e)) . Denote by FW (x,e;M) the c.d.f. ofmax [M,w (Y (x, e))], so that:

FW (x,e;M) (t) =

{0 for t < M

FW (x,e) for t ≥M.

69

We have, for M < M ′:

w (x, 1;M)− w (x, 0;M)

= E (max [M,w (Y (x, 1))])− E (max [M,w (Y (x, 0))])

=

∞∫0

(1− FW (x,1;M) (t)

)dt−

∞∫0

(1− FW (x,0;M) (t)

)dt

=

∞∫0

(FW (x,0;M) (t)− FW (x,1;M) (t)

)dt

=

∞∫M

(FW (x,0) (t)− FW (x,1) (t)

)dt

≥∞∫

M ′

(FW (x,0) (t)− FW (x,1) (t)

)dt

=

∞∫0

(FW (x,0;M ′) (t)− FW (x,1;M ′) (t)

)dt

= w (x, 1;M ′)− w (x, 0;M ′) ,

where the inequality re�ects stochastic dominance: since Y (x, 1) % Y (x, 0) , then w (Y (x, 1)) %w (Y (x, 0)) . �

Proof of Lemma 3

Proof. Part 1. First, note that all types x′ > xM exert e�ort. Indeed, the LHS of (4)evaluated at x′ is no smaller than its value at x because w (·, 1;M) is non-decreasing andw (x′, 1;M) − w (x′, 0;M) ≥ 0 (because w (x′, ·;M) is nondecreasing); and the RHS isdecreasing in x. Next, note that for any type z < xM also w (z, 1;M) = w (z, 0;M) = M

(because w (·, e;M) is nondecreasing and bounded below byM). Therefore, if type z exertse�ort, by the above logic all types above it also exert e�ort. This shows that the set oftypes is partitioned into two adjacent intervals, with types above some xM exerting e�ortand types below xM shirking. Condition (4) holds with equality for xM , and since thepiece rate channel vanishes at xM , condition (4) reduces to (7).

Part 3. Since w (xM , 1;M) = M , it must be w (Y (xM , 1)) ≤ M < M ′. Therefore,w (xM , 1;M ′) = w (xM , 0;M ′) = M ′. Hence, plugging the scheme w (x, e;M ′) into condi-

70

tion (4) we get the required condition for type xM to exert e�ort under M ′:

M ′ ≥ ω (M ′) + c (xM)

[1 +

q + r

D (1− q)

]. (20)

Now, M ′ − ω (M ′) > M − ω (M) since the function x − ω (x) is strictly increasing in x.Therefore, (7) implies that (20) holds with strict inequality. Therefore, the threshold typexM ′ that achieves equality in (20) must be strictly smaller than xM . �

Proof of Lemma 4

Proof. Part 1. Eq. (6) does not depend on s.

Part 2.

ω (M) =rs

(1 + r) (r + s)V (M) .

In light of Assumption 1 a marginal increase in M cause types just below xM to startexerting e�ort, and no other type changes their behavior. The per-period productivity ofthe marginal worker increases by:

E [Y (xM , 1)− Y (xM , 0)] . (21)

Because ω (M) is an increasing function of s, if s decreases to s̃, the new threshold typeis x̃M ≤ xM (refer to equation 7) and the per-period productivity of the marginal workerincreases by:

E [Y (x̃M , 1)− Y (x̃M , 0)] .

This e�ect is larger than expression (21) by Assumption 2. �

Proof of Lemma 5

Proof. Part 1: E (0,M ′) ⊆ E (0,M) .

When D ≈ 0 a type x exerts e�ort if and only if

w (x, 1;M)− w (x, 0;M) ≥ c (x) .

The LHS is nonincreasing in M (see Lemma 8). Therefore, the set of types who exerte�ort is nonincreasing in M .

71

Part 2: E (0,M) ⊂ E(D,M

).

Denote by xM the solution to Eq. (7) with D = D. By construction, this type iswilling to exert e�ort if D = D. As D ≈ 0 the no-shirking condition (4) for type xMapproaches:

w (xM , 1;M)− w (xM , 0;M) ≥ c (xM) .

This condition is violated because xM is a MMW-type, and so the left-hand side equalszero. Thus type xM , and indeed every type below it, do not exert e�ort for D ≈ 0.Therefore, the set of shirking types expands when D goes from D to ≈ 0.

Part 3: E(D,M

)⊆ E

(D,M ′) .

When D = D the set of types that exert e�ort is an interval of the form [xM ,∞). SincexM is decreasing in M, the set of types that exert e�ort is larger for M ′. �

Proofs for the Steady-State Type Distribution In this section only, denote byq′ = q +D (1− q) the probability that a monitored worker with type below xM separatesfrom the �rm.

A steady-state distribution f is the distribution of �rm-speci�c productivity typesamong the �rm employees, that is self-perpetuating. Self-perpetuating means that, giventhe termination policy baked into equations (1, 2), replacement workers are hired fromthe unemployment pool so as to exactly replace the lost workers, and in the next periodthe distribution f is reproduced identically.

Suppose �rst that µ = 1. Denote by

λ = q′F (xM) + q (1− F (xM)) (22)

the (per capita) out�ow of workers given the termination policy baked into equations(1, 2). To replace the lost workers, λ must also be the mass of workers hired from theunemployment pool. Then

f (x) =

{(1− q′) f (x) + λ (h (x)) for x < xM

(1− q) f (x) + λ (h (x)) for x ≥ xM .

Isolating f yields:

f (x) =

{λq′h (x) for x < xM

λqh (x) for x ≥ xM .

Intuitively, this expression shows that in steady state there are fewer workers below xM .

72

This is because the �rm selects against those types in its termination policy.

Let us compute the value of λ based on primitives. We have:

F (xM) =

∫ xM

0

f (z) dz =

∫ xM

0

λ

q′h (z) dz =

λ

q′H (xM) .

Then from (22):

λ = q′F (xM) + q (1− F (xM))

= λH (xM) + q

(1− λ

q′H (xM)

)= q + λH (xM)

(1− q

q′

).

So λ solves:

λ

[1−H (xM)

(q′ − qq′

)]= q.

The term q′−qq′∈ (0, 1) , so the term in bracket ∈ (0, 1) and is decreasing in xM . Therefore,

λ is increasing in xM .

Now suppose µ = 0. Then the out�ow λ̂ = q and f̂ (x) = h (x) .

In a �rm with µ ∈ (0, 1) out�ows are:

µλ+ (1− µ) q,

and the steady-state distribution equals:

µf (x) + (1− µ)h (x) .

73

B.2 Continuous E�ort

The main model assumes that e�ort is discrete. In this section, we derive an equivalent toEq. (4) when e�ort is a continuous variable e.We also provide conditions such that optimalcontinuous e�ort is increasing in the minimum wage. Finally, we provide conditions suchthat a given amount of pay increase increases e�ort by more in the pure e�ciency wagecase than in the pay for performance case.

Type x's bene�t from increasing e�ort continuously from e (shirking) to e+ε (exertinge�ort) is given by an analog of Eq. (4). First, replace c (x) by c (e+ ε) − c (e).63 Then,replace the probability of termination q by a decreasing function q (e) of e�ort. By analogywith equations (1, 2) the function q (·) solves:

1− q (e)︸ ︷︷ ︸prob of retention

when shirking

=

[1− q (e+ ε)︸ ︷︷ ︸

]prob of retention

when exerting e�ort

· (1−D (ε)) .

Letting for simplicity D (ε) = dε, the above equation rewrites as:

q (e+ ε)− q (e) = −dε · (1− q (e+ ε)) ,

and taking limits as ε→ 0 yields:

d =∂

∂elog (1− q (e)) > 0,

which implies that d is interpreted as an elasticity of the probability of termination. Sub-stitute for c (x) , q, and D into (4) to get:

w (x, e+ ε)+

[q (e) + r

d (1− q (e))

][w (x, e+ ε)− w (x, e)]

ε≥ ω+

[c (e+ ε)− c (e)]

ε

[ε+

q + r

d (1− q (e))

]Take limits as ε→ 0 and replace w (x, e) with w (x, e;M) . We get:

w (x, e;M) +

[q (e) + r

d (1− q (e))

]we (x, e;M) ≥ ω + c′ (e)

[q (e) + r

d (1− q (e))

]. (23)

63This replacement introduces the simplifying restriction that the cost of exerting e�ort is now inde-pendent of x. Note that type-independence is a limiting case in our discrete-e�ort setting anyway.

74

At the optimal choice of e�ort, the above equation holds with equality.

This equation is the counterpart to Eq. (4) in the continuous e�ort case. When istype x's optimal e�ort increasing? Fix x, and consider any e for which this inequalityholds. If as M increases the LHS grows and the RHs does not change, then optimale�ort is increasing in M . We know that, as M grows, w (x, e;M) increases (weakly) whilewe (x, e;M) decreases (weakly). Thus for MMW types e�ort always increases becausewe (x, e;M) = 0. For all other types, the �rst e�ect is more likely to dominate if q and rare small, and d is large. These observations are collected in the following result.

Lemma 9. (optimal continuous e�ort as a function of the minimum wage)

Optimal continuous e�ort is increasing in M for MMW types. For other types in the

hybrid case, optimal e�ort is more likely to increase in M if the worker is more patient,

if the equilibrium probability of termination is lower, and if the probability of termination

is very sensitive to e�ort. Optimal continuous e�ort is decreasing in M if d ≈ 0, i.e., in

the pure pay-for-performance case.

These conditions are intuitive: when they hold, the worker is more motivated by thefuture bene�ts of a higher minimum wage (e�ciency wage motive) relative to the presentdisincentive e�ect (pay for performance). In some theoretical examples, optimal e�ort fornon-MMW types may even be increasing inM for any value of q, r, and d. We derive onenext. Ultimately, however, it is an empirical question whether optimal e�ort is increasingor decreasing for types �above the minimum wage.�

Example 1. (optimal continuous e�ort is nondecreasing in M for any type x)

Suppose the compensation scheme is base plus commission, e ≥ 0 is a continuous vari-

able, and type x's productivity equals xe with probability α and 0 with probability (1− α) .

Formally:

w (Y ) = b+ ρY

Y (x, e) =

{0 w.p. 1− αxe w.p. α.

Then:

w (Y (x, e)) =

{b w.p. 1− α

b+ ρxe w.p. α.

75

Assuming b < M, for any type x above MMW we have:

max [M,w (Y (x, e))] =

{M w.p. 1− α

b+ ρxe w.p. α

and so:

w (x, e;M) = (1− α)M + α (b+ ρxe) .

Note that w (x, e;M) is increasing in M and we (x, e;M) is independent of M. Therefore

optimal continuous e�ort is increasing in M for any type x above MMW. Since e�ort is

nondecreasing in M for MMW types, it follows that optimal continuous e�ort is nonde-

creasing in M for any type x.

We close this section by comparing of the e�ects of the same increase in pay betweentwo regimes: a pure e�ciency wages, and a hybrid regime. The comparison is designed toillustrate the principle that a pay increase increases e�ort in a pure e�ciency wage regime,by more than in a hybrid one.

Denote by e∗ and e∗∗ type x's equilibrium e�ort in the hybrid and pure e�ciency wageregimes, respectively. Denote:

g (e) =

[q (e) + r

d (1− q (e))

].

We assume that the �rst order conditions characterize the optimal e�ort level. The �rstorder conditions in the hybrid case read:

w (x, e∗;M)− ω = [c′ (e∗)− we (x, e∗;M)] g (e∗) . (24)

In the pure e�ciency wage case where W > M represents the �xed wage we have w = W

and we ≡ 0, so the above equation specializes to:

W − ω = c′ (e∗∗) g (e∗∗) , (25)

For future reference, we assume that the RHS of (25) is increasing in e∗∗, which impliesthat e∗∗ grows with W, i.e., that increasing the wage level increases equilibrium e�ort inthe pure e�ciency wage setting. This is a reasonable assumption.

To meaningfully compare regimes, we must start from �the same� status quo andincrease pay by the same amount, in the two regimes. We start from a status quo whereequilibrium e�ort is the same in the two regimes, so we set e∗ = e∗∗. We increment the

76

minimum wage M by a small amount ε > 0 and we increment W by a �xed amount δsuch that

δ = ε · d

dMw (x, e∗;M) , (26)

where the total di�erential indicates that the variation of e∗ is taken into account also.Condition (26) means that pay increases by the same amount in the two regimes. We seekto show that e�ort increases more in the pure e�ciency wage regime, i.e., that:

ε∂e∗

∂M< δ

∂e∗∗

∂W. (27)

Totally di�erentiate (24) w.r.t. M and multiply by ε; totally di�erentiate (25) w.r.t.W and multiply by δ. After these operations the LHSs of (24) and (25) become the sameby (26), and so we get the identity:

εd

dM{[c′ (e∗)− we (x, e∗;M)] g (e∗)} = δ

d

dW{c′ (e∗∗) g (e∗∗)}

ε∂e∗

∂M· ∂∂e{[c′ (e)− we (x, e;M)] g (e)}e=e∗ − εweM (x, e∗;M) g (e∗) = δ

∂e∗∗

∂W· ∂∂e

[c′ (e) g (e)]e=e∗∗ .(28)

Since the RHS of (25) is increasing in e∗∗, all three terms on the RHS of (28) are positive,and then (27) is the same as:

ε∂e∗

∂M· ∂∂e{[c′ (e)− we (x, e;M)] g (e)}e=e∗−εweM (x, e∗;M) g (e∗) > ε

∂e∗

∂M· ∂∂e

[c′ (e) g (e)]e=e∗∗ .

Taking the derivatives w.r.t. e yields:

ε∂e∗

∂M· {[c′′ (e∗)− wee (x, e∗;M)] g (e∗) + [c′ (e∗)− we (x, e∗;M)] g′ (e∗)} − εweM (x, e∗;M) g (e∗)

> ε∂e∗

∂M· [c′′ (e∗∗) g (e∗∗) + c′ (e∗∗) g′ (e∗∗)]

Since e∗ = e∗∗ by construction, the above condition simpli�es to:

ε∂e∗

∂M· {−wee (x, e;M) g (e)− we (x, e;M) g′ (e)} − εweM (x, e∗;M) g (e∗) > 0.

If ∂e∗/∂M ≤ 0 there is nothing to prove. Else, since we, g′ (e) , and weM are all nonpositive,the inequality holds provided that wee < 0. This condition means that expected wages areconcave in e�ort and is a reasonable condition

In sum, we have shown that, starting from the same e�ort level in the two regimes,

77

and giving both workers the same amount of pay increase in the two regimes, if expectedwages are concave in e�ort, then e�ort increases more in the pure e�ciency wage regime.

B.3 Alternative Speci�cation of Local Labor Market

The local labor market is exactly a RT world. It is composed of type-less workers who allreceive the minimum wage independent of performance, and have the same cost of exertinge�ort c. This means that, exactly as in RT, the value functions V N

loc and VSloc satisfy (1, 2)

except with w (x, 1) = w (x, 0) = M, and:

V A = ω +sV N

loc + (1− s)V A

(1 + r), (29)

where ω is a �xed nonnegative number (this is the same as RT Eq. 4).

Manipulating (29) yields:

V Nloc =

V A (r + s)− ω (1 + r)

s,

and substituting into (1) we get, after noting that in the local labor market w (x, 1) = M :[1− (1− q)

(1 + r)

]V Nloc = M − c+

q

(1 + r)V A.

Substitute for V Nloc into the above expression and isolate V A to get:

V A =(1 + r)

r

[s

(r + q + s)(M − c) + ω

r + q

(r + q + s)

].

Substitute this expression into condition (18) to get the no-shirking condition within the

78

�rm:

w (x, 1) +(r + q)

D (1− q)[w (x, 1)− w (x, 0)] ≥

[s

(r + s+ q)[M − c] + r + q

(r + s+ q)ω

]+ c (x) + c (x)

[r + q

D (1− q)

]w (x, 1)

(r + s+ q)

r + q+

(r + s+ q)

D (1− q)[w (x, 1)− w (x, 0)] ≥ s

r + q[M − c] + ω + c (x)

[1 +

r + q

D (1− q)

](r + s+ q)

r + q{w (x, 1)

(r + s+ q)

r + q− s

r + qM

}+

(r + s+ q)

D (1− q)[w (x, 1)− w (x, 0)] ≥ − s

r + qc+ ω + c (x)

[1 +

r + q

D (1− q)

](r + s+ q)

r + q{w (x, 1)

(r + s+ q)

r + q− s

r + qM

}+

(r + s+ q)

D (1− q)[w (x, 1)− w (x, 0)] ≥ − s

r + qc+ ω + c (x)

[(r + s+ q)

r + q+

(r + s+ q)

D (1− q)

]{w (x, 1) +

s

r + q[w (x, 1)−M ]

}+

(r + s+ q)

D (1− q)[w (x, 1)− w (x, 0)] ≥ ω + c (x)

[1 +

(r + s+ q)

D (1− q)

]+

s

r + q[c (x)− c]

We want to show that Lemma 3 holds here. The �rst property we need to show is thatif Eq. (30) holds for a MMW type, then it holds for all types higher than it. For a MMWtype w (x, 1) = w (x, 0) = M and the equation reads:

M = ω + c (xM)

[1 +

(r + s+ q)

D (1− q)

]+

s

r + q[c (xM)− c] . (30)

Note that the term in curly brackets in Eq. (30) grows with x, and the second addend isalways greater than zero which is its value at xM . Hence, the LHS is greater for x > xMthan it is at xM . In contrast, the RHS gets smaller as x grows. This shows that theinequality holds for every type greater than the MMW type xM . Furthermore, (30) is suchthat increasing M decreases xM . These two properties are su�cient to prove Lemma 3.

Now rewrite:

M = ω + c (xM )

[1 +

(r + s+ q)

D (1− q)

]+

s

r + q[c (xM )− c]

M = ω + c

[1 +

(r + s+ q)

D (1− q)

]+ [c (xM )− c]

[1 +

(r + s+ q)

D (1− q)

]+

s

r + q[c (xM )− c]

M − ω − c[1 +

(r + s+ q)

D (1− q)

]= [c (xM )− c]

[1 +

(r + s+ q)

D (1− q)+

s

r + q

].

We know that the LHS is nonnegative due to the local labor market no-shirking condition(Eq. (5) in RT, which is reproduced below):

M ≥ ω + c

[1 +

q + r + s

D (1− q)

].

Therefore [c (xM)− c] ≥ 0. Therefore Eq. (30) implies that xM is increasing in s. This issu�cient to prove Lemma 4.

79

B.4 Endogenous Monitoring

Let FM (x; E) denote the steady-state type distribution if the set of types that exert e�ortis E . The steady-state pro�t function is:

π (E ,M) =

∫ ∞0

[E [Y (x,1E (x))]− w (x,1E (x) ;M)] dFM (x; E) .

For a given M, the �rm solves:

maxµ

(1− µ) · π (E (0,M) ,M) + µ · π(E(D,M

),M)−K (µ) , (31)

where K (·) is a convex cost function with K ′ (0) = 0, that captures the cost to the �rmof increasing monitoring.

Next, we leverage Lemma 5 to rank-order steady-state pro�ts.

Assumption 3. (pro�ts increase with e�ort) FixM. For every x, Y (x, e)−w (x, e;M)

is increasing in e.

This is a mild assumption. It says that if type x exerts e�ort, pro�ts are greater thanwith no e�ort. If w (Y ) = b + cY (the �base plus commission� wage schedule), then theresulting schedule w satis�ed the assumption if c < 1.

If this assumption holds, then with no monitoring, pro�ts are decreasing in the mini-mum wage. This is because increasing M worsens the wage bill and, in addition, causesfewer workers to exert e�ort (Lemma 5). Thus the pro�t term π (E (0,M) ,M) in expres-sion (31) is decreasing in M .

The second pro�t term in expression (31) could, according to theory, be either increas-ing or decreasing in M . Empirically, however, expression (31) in its entirety is shown notto decrease with M . This means that the value of the �rm's maximization problem hasnot decreased. This is only possible if the term π

(E(D,M

),M)is increasing in M . If

that's the case, then the �rm's optimal µ must increase with M , as indeed it does in thedata. This discussion is summarized in the following lemma.

Lemma 10. (testable prediction of minimum wage on endogenous monitoring)

Suppose that Assumption 3 holds, and that total pro�ts in expression (31) do not decrease

as the minimum wage increases. Then optimal monitoring must increase with the mini-

mum wage.

80

C Data Appendix

Minimum Wage Data Our data contain information on the geographical location ofstores (latitude and longitude), which we match with the monthly statutory minimumwage level in that store, extracted from the public dataset maintained by the WashingtonCenter for Equitable Growth. Variations in minimum wage take place at state, countyand city levels; with city and county minimum wages always set to be higher than thestate minimum wage.

From February 2012 to June 2015, our sample of stores is a�ected by 70 variations inminimum wage: 49 variations are at the state level, and 21 are at the county or city level.The exact timing of each minimum wage change is reported in Table C.1 and presentedvisually in Figure C.1.

There is a notable event related to the minimum wage that is speci�c to California.In November 2014 our company chose to increase the base pay in its California stores tothe prevailing minimum wage levels, not in response to a minimum wage increase (therewas none in November 2014) but, rather, to avoid costly record-keeping requirementsregarding the hour-by-hour nature of each worker's task. We account for this variationby including an interaction term for California post November 2014 in all speci�cationsthroughout the paper. The results are qualitatively and quantitatively robust to removingthe post-November 2014 data from California.

Figure C.1: Variations in Minimum Wage from February 2012 to June 2015

Notes: Store locations are withheld for con�dentiality reasons.

Border Discontinuity Design We use a border discontinuity design, as implementedin Card and Krueger (2000), Dube et al. (2010, 2016), Allegretto et al. (2013, 2017). Thisapproach exploits minimum wage policy discontinuities at the state- or county-border bycomparing workers on one side of the border where the minimum wage increased (treatment

81

group) to workers on the other side where the minimum wage did not increase (controlgroup). As shown in Dube et al. (2010), this research design has desirable properties foridentifying minimum wage e�ects since workers on either side of the border are more likelyto face similar economic conditions and are likely to experience similar shocks at the sametime.

Following Card and Krueger (2000), Dube et al. (2010, 2016) and Allegretto et al.(2013, 2017), we restrict our sample to stores (and their respective workers) located inadjacent counties that share a border. For state-level minimum wage variations, we keepstores located in county pairs that: share a state border, and whose centroids are within75 km of each other (see Figure C.2). For county-level minimum wage variations, we�seed� the sample with stores located in those counties that increased their minimumwage, and then add as controls all adjacent counties whose centroids are within 75 km ofthe seed county. Minimum wage changes at the city level are attributed only to storeswithin the city limits, but not to stores in the county containing that city. Such storesare included as controls, as are stores in all neighboring counties. (In our sample thereare no municipalities that lie in more than one county). For instance, for the city of SanFrancisco (which increased its minimum wage) we include all the counties that share acounty-border with San Francisco County and whose centroids are within 75 km of itscentroid (i.e., the counties of Marin, Alameda and San Mateo).

Figure C.2: Variations in Minimum Wage in Bordering Counties

Notes: Store locations are withheld for con�dentiality reasons.

82

Table C.1: Changes in Minimum Wages from February 2012 and June 2015

State State Date C.1 Wt−1 Wt Date C.2 Wt−1 Wt Date C.3 Wt−1 Wt Date C.4 Wt−1 Wt

Alaska AK 2015m2 7.75 8.75Arkansas AR 2015m1 7.25 7.5Arizona AZ 2013m1 7.65 7.8 2014m1 7.8 7.9 2015m1 7.9 8.05California CA 2014m7 8 9Colorado CO 2013m1 7.64 7.78 2014m1 7.78 8 2015m1 8 8.23Connecticut CT 2014m1 8.25 8.7 2015m1 8.7 9.15DC DC 2014m7 8.25 9.5Delaware DE 2014m6 7.25 7.75 2015m6 7.75 8.25Florida FL 2013m1 7.67 7.79 2014m1 7.79 7.93 2015m1 7.93 8.05Hawaii HI 2015m1 7.25 7.75Massachusetts MA 2015m1 8 9Maryland MD 2015m1 7.25 8Michigan MI 2014m9 7.4 8.15Minnesota MN 2014m8 7.25 8Missouri MO 2013m1 7.25 7.35 2014m1 7.35 7.5 2015m1 7.5 7.65Montana MT 2013m1 7.65 7.8 2014m1 7.8 7.9 2015m1 7.9 8.05Nebraska NE 2015m1 7.25 8New Jersey NJ 2014m1 7.25 8.25 2015m1 8.25 8.38New York NY 2013m12 7.25 8 2014m12 8 8.75Ohio OH 2013m1 7.7 7.85 2014m1 7.85 7.95 2015m1 7.95 8.1Oregon OR 2013m1 8.8 8.95 2014m1 8.95 9.1 2015m1 9.1 9.25Rhode Island RI 2013m1 7.4 7.75 2014m1 7.75 8 2015m1 8 9South Dakota SD 2015m1 7.25 8.5Vermont VT 2014m1 8.6 8.73 2015m1 8.73 9.15Washington WA 2013m1 9.04 9.19 2014m1 9.19 9.32 2015m1 9.32 9.47West Virginia WV 2015m1 7.25 8

County State Date C.1 Wt−1 Wt Date C.2 Wt−1 Wt Date C.3 Wt−1 Wt

Bernalillo NM 2013m7 7.5 8 2014m1 8 8.5 2015m1 8.5 8.65Johnson IA 2015m11 7.25 8.2Montgomery MD 2014m10 7.25 8.4Prince George's MD 2014m10 7.25 8.4Santa Fe NM 2014m4 7.5 10.66 2015m3 10.66 10.84

City State Date C.1 Wt−1 Wt Date C.2 Wt−1 Wt Date C.3 Wt−1 Wt Date C.4 Wt−1 Wt

Alburquerque NM 2013m1 7.5 8.5 2014m1 8.5 8.6 2015m1 8.6 8.75Berkeley CA 2014m10 9 10Las Cruces NM 2015m1 7.5 8.4Oakland CA 2015m3 9 12.25 2016m1 12.25 12.55Richmond CA 2015m1 9 9.6 2016m1 9.6 11.52San Diego CA 2015m1 9 9.75San Francisco CA 2013m1 10.24 10.55 2014m1 10.55 10.74 2015m1 10.74 11.05 2015m5 11.05 12.25San Jose CA 2013m3 8 10 2014m1 10 10.15 2015m1 10.15 10.3Santa Fe NM 2012m3 9.5 10.29 2013m3 10.29 10.51 2014m3 10.51 10.66 2015m3 10.66 10.84SeaTac WA 2013m1 9.04 9.19 2014m1 9.19 15Seattle WA 2013m1 9.04 9.19 2014m1 9.19 9.32 2015m1 9.32 9.47 2015m4 9.47 11Sunnyvale CA 2015m1 9 10.3Tacoma WA 2013m1 9.04 9.19 2014m1 9.19 9.32 2015m1 9.32 9.47Washington DC 2014m7 8.25 9.5

Notes: This table reports all state/county/city variations in statutory minimum wage from 2/1/2012 to 6/30/2015, irrespective ofwhether there is a store located in that state/county/city. The data are extracted from the public dataset maintained by the WashingtonCenter for Equitable Growth. Our identi�cation strategy e�ectively leverages only a sub-sample of these changes (70 out of 89), i.e.,those that a�ect at least one store in our sample. We do not report which ones are the 70 variations we leveraged in the paper forcon�dentiality reasons. Wt (Wt−1) refers to the minimum wage level after (before) the change. The states with no change in minimumwage from February 2012 and June 2015 are: AL, GA, IA, ID, IL, IN, KS, KY, LA, ME, MS, NC, ND, NH, NM, NV, OK, PA, SC, TN,TX, UT, VA, WI, WY.

83

D Threats to Identi�cation and Robustness Appendix

Pre-Trends Our test of pre-trends follows Dube at al. (2010).

Table D.1, Panel A tests for pre-trends in the 6 months preceding the minimum wagechange by estimating η3−0 − η6−3 from the following speci�cation:

Yijpt = α + η6−3(MinWj,t+6 −MinWj,t+3) + η3−0(MinWj,t+3 −MinWj,t)

+ρMinWj,t +Xit · ζ + ηZjt + δi + φpt + εijpt, (32)

where MinWj,t+m is the minimum wage m months after month t and all other variablesare de�ned as in Eq. (11). η6−3 (η3−0) is a leading coe�cient that captures variations inthe Y-variable 6 to 3 (3 to 0) months before each change in the minimum wage. We testfor the presence of pre-trends by estimating whether η3−0 − η6−3 is statistically di�erentfrom zero.

Table D.1, Panel B tests for pre-trends in the 12 months preceding the minimum wagechange by estimating η12−6 − η6−0 from the following speci�cation:

Yijpt = α + η12−6(MinWj,t+12 −MinWj,t+6) + η6−0(MinWj,t+6 −MinWj,t)

+ρMinWj,t +Xit · ζ + ηZjt + δi + φpt + εijpt, (33)

(11). η12−6 (η6−0) is a leading coe�cient that captures variations in the Y-variable 12 to6 (6 to 0) months before each change in the minimum wage.

We also present the type-interacted version of Eq. (32) and (33) in the bottom ofPanels A and B.

Cross-border Worker Movements See Table D.2.

Worker Selection See Tables D.3 and D.4.

Alternative Research Designs See Table D.5.

State vs. Local Variation in the Minimum Wage See Table D.6

Alternative De�nitions of �Bordering Stores� We show that our results are robustto changing the de�nition of �bordering� stores. In our main estimates, we follow theexisting literature by restricting the sample to all stores located in counties that: (a)share a border and (b) whose centroids are less than 75 km apart (Card and Krueger

84

1994, Dube et al. 2010, Allegretto et al. 2013). In Table D.7, we check the robustnessof our results to restricting our sample to a subset of stores: those stores whose distancefrom the border is less than 75 km, less than 37.5 km, and less than 18.75 km. Therationale behind this test is that by narrowing down the de�nition of �bordering� store inour main sample, we lose a few observations but we increase the comparability of treatedand control stores around the borders. Reassuringly, our results are broadly consistentacross these samples.

Robustness to �Unstacking� In Table D.8 we show that our results are robust toan experimental approach that considers each of the 44 unique border-segments as an�experimental event� with a treated and a control county each. The e�ect of minimumwage is estimated in a regression model similar to Eq. (12) but without stacking thedata,64 with experimental event × month (border-segment × month) �xed e�ects andstandard errors clustered at the experimental event (border-segment) level.

Alternative Classi�cations of Low, Medium and High Types In Section 4, wede�ned low, medium, or high types as those whose total pay in month t-1 is �at minimumwage,� between the minimum wage and 180% of the minimum wage, and above 180% ofthe minimum wage (about equal to the top quartile), respectively. We now assess therobustness of our results to alternative classi�cations. Table D.9 presents the results withalternative thresholds: 120%, 140%, or 160% (rather than 180%). Notice that as thethreshold increases (i.e., from 120% to 180%), the mass of low types remains unchangedbut the top category of high types becomes thinner and more outstanding. In this sense,the highest the threshold, the most �productive� is the top category and the least a�ectedthis category should be by the minimum wage hike. Consistent with this, we �nd thatthe productivity e�ect on the top category of workers vanishes as the threshold increases,achieving a precisely estimated zero at the highest (180%) threshold.65 In contrast, theproductivity of low types is found to increase by 19% - 23% regardless of the threshold;while the productivity of medium types increases by 7% - 9%.

Using the 180% threshold, Table D.10 Col. 1 divides workers into low, medium, orhigh types based on their average pay in the three months before a minimum wage change(t-1, t-2 and t-3 ) rather than on the past month only. Table D.10 Col. 2 follows a similarapproach but divides workers based on their maximum pay in the three months before aminimum wage change. This reduces the likelihood of mis-categorizing a high type as a lowone due to surprisingly low demand in t-1, but also shrinks the sample size.66 Similarly,

64As a result, the sample size drops.65Mean reversion is an unlikely explanation for this phenomenon because the estimated coe�cient for

�high type� is consistently positive, not negative.66We de�ne low types as those whose average (or maximum) pay per hour in the past three months

85

Table D.10 Col. 3 divides workers into low-medium-high types based on their pay in the�rst month on the job.

Finally, Table D.10 Col. 4 divides workers in low-medium-high types using their pro-ductivity (sales per hour) during the �rst quarter on the job. To do so, we estimateworkers' �xed e�ects based on their sales per hour in the �rst quarter and we use thatto then divide workers into terciles. This latter classi�cation has the advantage of betterisolating permanent unobserved heterogeneity from state dependence or mean-revertingshocks, but it has the disadvantage of being time-invariant and does not allow us to quan-tify level e�ects in our speci�cation with worker �xed e�ects. Reassuringly, the �ndingspaint the same picture regardless of the classi�cation method: the low types become sig-ni�cantly more productive, while the high types do not become more productive whenminimum wage increases.

Alternative Controls Table D.11 Col. 1-2 show that the results are robust to ex-tending our main Eq. (12) to also include department · store time-trends (i.e., uniquedepartment ID · time), in order to account for potential di�erential trends across depart-ments of a given store. We do so because one may be concerned that a higher minimumwage induces demand/price changes that are con�ned into departments that exclude themost productive salespeople, thus potentially confounding the heterogeneous productivitye�ects identi�ed in the paper. We attenuate this concern by showing that our �ndings areuna�ected by the inclusion of department-speci�c trends.

The results are also robust to running our main speci�cation department-by-department(Table D.12).

Finally, the results are also robust to removing worker tenure and unemployment.This is reassuring as one might worry that these are �bad controls� directly a�ected bythe minimum wage increase. Refer to Table D.11 Col. 3-4.

equal to the minimum wage, while medium (high) types are de�ned as those whose average (or maximum)pay per hour in the past three months is below (above) 180% of the minimum wage.

86

Table D.1: Test of Pre-Trends in Worker Productivity with Border-Discontinuity andState-Level Speci�cations

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs Sales/HrsSample Border Stores All Stores All Stores All StoresModel Pair·Month FE Month FE Month FE+State-Tr. Division·Month FE

(1) (2) (3) (4)

Panel A: 6-Months Pre-Trend

Uninteracted ModelPre-Trend (6 Months) -0.126 -0.089** -0.081** -0.021

(0.095) (0.037) (0.036) (0.040)

Observations 149,642 276,825 276,825 276,825

Interacted ModelPre-Trend (6 Months) -0.035 0.127 0.132 0.190

(0.108) (0.119) (0.119) (0.123)Pre-Trend · Medium Type -0.064 -0.228 -0.226 -0.230*

(0.087) (0.141) (0.141) (0.131)Pre-Trend · High Type -0.003 -0.151 -0.151 -0.150

(0.112) (0.174) (0.173) (0.162)

Observations 144,298 266,702 266,702 266,702

Panel B: 12-Months Pre-Trend

Uninteracted ModelPre-Trend (12 Months) 0.029 -0.038 -0.027 0.036

(0.069) (0.046) (0.041) (0.030)

Observations 111,057 201,106 201,106 201,106

Interacted ModelPre-Trend (12 Months) -0.013 0.132 0.139 0.164*

(0.126) (0.115) (0.105) (0.086)Pre-Trend · Medium Type 0.083 -0.120 -0.125 -0.101

(0.116) (0.090) (0.090) (0.085)Pre-Trend · High Type 0.028 -0.232*** -0.238*** -0.200***

(0.068) (0.065) (0.064) (0.061)

Observations 106,981 193,434 193,434 193,434Units Workers Workers Workers Workers

Notes: In Panel A, Pre-Trend = η3−0 − η6−3 estimated from Eq. (32). In Panel B, Pre-Trend = η6−0 − η12−6

estimated from Eq. (33). We also present the type-interacted version of Eq. (32) and (33) in the bottom ofPanels A and B. In Col. 1 (3-4) pre-trends are tested in the sample of bordering stores (bordering+non-borderingstores). All regressions include worker �xed e�ects and control for worker tenure, worker department and for countyunemployment rate. The regressions vary in the time controls: we include pair-month �xed e�ects in Col. 1, month�xed e�ects in Col. 2, month �xed e�ects and state-speci�c linear trends in Col. 3, census division · month �xede�ects in Col. 4. Standard errors are two-way clustered at the state level and at the border-segment level in Col. 1and at the state-level in Col. 3-4. *** p<0.01, ** p<0.05, * p<0.1.

Table D.2: E�ect of Minimum Wage on Work-to-Home Distance

Dep.Var. Distance Distance DistanceSample of Workers New hires All All

(1) (2) (3)

MinW -0.309 0.409 0.052(0.909) (0.573) (0.653)

Medium Type -0.012(0.416)

High Type 0.482(0.510)

MinW · Medium Type 0.442(0.441)

MinW · High Type 0.138(0.432)

Observations 10,783 212,509 204,761Units Workers Workers WorkersMean Dep.Var. 9.666 4.641 4.562E�ect MinW (%) -3.201 4.186E�ect MinW for Low Type (%) 0.753p-value 0.937

E�ect MinW for Med. Type (%) 5.126p-value 0.392

E�ect MinW for High Type (%) 1.837p-value 0.764

Notes: All the regressions include pair-month �xed e�ects, store �xed e�ectsand control for county-level unemployment. Col. 2 and 3 also include worker�xed e�ects, tenure and worker departments. Col. 1 restricts the sample tothe newly hired workers in the month in which they are hired in a given store.Distance is the distance between the worker's home and the store in whichhe/she works in a given month. MinW is the predominant monthly minimumwage (in $). Medium Type is an indicator for whether the worker's total payin month t-1 is between the minimum wage and 180% of minimum wage. HighType is an indicator for whether the worker's total pay in month t-1 is above180% of minimum wage. The omitted group (Low Types) are workers forwhom total pay in t-1 is �at minimum wage�. E�ect MinW (%) is the percente�ect of a $1 increase in MinW on the outcomes. Standard errors are two-wayclustered at the state level and at the border-segment level. *** p<0.01, **p<0.05, * p<0.1.

88

Table D.3: Test of Pre-Trends in Worker Productivity for Balanced vs. Not BalancedSample

Dep.Var. Sales/Hrs Sales/Hrs(1) (2)

Pre-Trend (6 Months) -0.128(0.091)

Pre-Trend (6 Months) · Balanced Sample -0.016(0.052)

Pre-Trend (12 Months) 0.043(0.077)

Pre-Trend (12 Months) · Balanced Sample -0.055(0.046)

Observations 149,615 111,035Units Workers Workers

Notes: See Eq. (32) and (33) for details on the underlying empirical speci�cation, which wefurther interact with �Balanced Sample.� All the regressions include pair-month �xed e�ects,worker �xed e�ects and control for worker tenure, worker department and county-level employ-ment. Balanced Sample is a time-invariant indicator for whether the worker is observed through-out the entire sample period. Sales/Hrs are the sales per hour rescaled by a factor between 1/50and 1/150 relative to its $ value. Standard errors are two-way clustered at the state level and atthe border-segment level. *** p<0.01, ** p<0.05, * p<0.1.

89

Table D.4: E�ect of Minimum Wage on Worker Productivity with Balanced Sample

Dep.Var. Sales/Hrs Sales/HrsSample Balanced Balanced

(1) (2)

MinW 0.137* 0.264*(0.0675) (0.135)

Medium Type 0.413***(0.086)

High Type 1.317***(0.114)

MinW · Medium Type -0.060(0.083)

MinW · High Type -0.168**(0.080)

Observations 32,224 31,439Units Workers WorkersMean Dep.Var. 2.093 2.100E�ect MinW (%) 6.524E�ect MinW for Low Type (%) 32.55p-value 0.063

E�ect MinW for Med. Type (%) 10.55p-value 0.002

E�ect MinW for High Type (%) 3.745p-value 0.305

Notes: The sample is restricted to workers who we observe throughout theentire sample period (i.e., balanced sample). All the regressions include pair-month �xed e�ects, worker �xed e�ects and control for worker tenure, workerdepartment and county-level employment. Sales/Hrs are the sales per hourrescaled by a factor between 1/50 and 1/150 relative to its $ value. MinW isthe predominant monthly minimum wage (in $). Medium Type is an indicatorfor whether the worker's total pay in month t-1 is between the minimumwage and 180% of minimum wage. High Type is an indicator for whether theworker's total pay in month t-1 is above 180% of minimum wage. The omittedgroup (Low Types) are workers for whom total pay in t-1 is �at minimumwage�. E�ect MinW (%) is the percent e�ect of a $1 increase in MinW on theoutcomes. Standard errors are two-way clustered at the state level and at theborder-segment level. *** p<0.01, ** p<0.05, * p<0.1.

90

Table D.5: E�ect of Minimum Wage on Worker Productivity with State-Level Speci�ca-tions

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs Sales/Hrs Sales/Hrs Sales/HrsSample All stores All stores All storesModel Month FE Month FE + State-Trend Division · Month FE

(1) (2) (3) (4) (5) (6)

MinW -0.008 0.140*** 0.033 0.161*** 0.038 0.175***(0.034) (0.026) (0.041) (0.029) (0.031) (0.030)

Medium Type 0.296*** 0.296*** 0.293***(0.033) (0.033) (0.032)

High Type 1.160*** 1.160*** 1.140***(0.055) (0.054) (0.055)

MinW · Medium Type -0.057*** -0.060*** -0.059***(0.021) (0.020) (0.021)

MinW · High Type -0.163*** -0.164*** -0.151***(0.029) (0.029) (0.029)

Observations 416,439 399,100 416,439 399,100 416,439 399,100Units Workers Workers Workers Workers Workers WorkersMean Dep.Var. 2.196 2.196 2.196 2.196 2.196 2.196E�ect MinW (%) -0.344 1.486 1.753E�ect for Low (%) 13.27 15.26 16.57p-value 0.001 0.001 0.001

E�ect for Med. (%) 4.065 4.979 5.703p-value 0.001 0.001 0.001

E�ect for High (%) -0.792 -0.098 0.804p-value 0.457 0.934 0.526

Notes: The sample comprises of all stores (bordering + non-bordering). All the regressions includeworker �xed e�ects, month �xed e�ects and control for worker tenure, worker department and county-level unemployment. Col. 3-4 also control for state-speci�c linear trends and Col. 5-6 control forcensus division · month �xed e�ects. Sales/Hrs are the sales per hour rescaled by a factor between1/50 and 1/150 relative to its $ value. MinW is the predominant monthly minimum wage (in $).Medium Type is an indicator for whether the worker's total pay in month t-1 is between the minimumwage and 180% of minimum wage. High Type is an indicator for whether the worker's total pay inmonth t-1 is above 180% of minimum wage. The omitted group (Low Types) are workers for whomtotal pay in t-1 is �at minimum wage�. E�ect MinW (%) is the percent e�ect of a $1 increase in MinWon the outcomes. Standard errors are clustered at the state level. *** p<0.01, ** p<0.05, * p<0.1.

91

Table D.6: E�ect of Minimum Wage on Worker Productivity with State and Local Vari-ations in the Minimum Wage

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs Sales/HrsMinW Variations State State Local Local

(1) (2) (3) (4)

MinW 0.100 0.271*** 0.102 0.195***(0.066) (0.076) (0.071) (0.052)

Medium Type 0.350*** 0.339***(0.024) (0.029)

High Type 1.163*** 1.192***(0.051) (0.047)

MinW · Medium Type -0.096*** -0.099***(0.028) (0.025)

MinW · High Type -0.212*** -0.168***(0.028) (0.050)

Observations 212,916 204,641 192,663 184,638Units Workers Workers Workers WorkersMean Dep.Var. 2.088 2.088 2.253 2.253E�ect MinW (%) 4.810 4.533E�ect MinW for Low Type (%) 25.39 19.85p-value 0.001 0.001

E�ect MinW for Med. Type (%) 9.003 4.657p-value 0.016 0.032

E�ect MinW for High Type (%) 2.150 0.905p-value 0.435 0.610

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ects andcontrol for worker tenure, worker department and county-level employment. Col. 1-2 leverage state-level minimum wage variations only. Col. 3-4 leverage within-state(county or city) minimum wage level variations. Refer to Table C.1 for the list ofminimum wage variations in our sample. Sales/Hrs are the sales per hour rescaled by afactor between 1/50 and 1/150 relative to its $ value. MinW is the monthly predominantminimum wage (in $). Medium Type is an indicator for whether the worker's total payin month t-1 is between the minimum wage and 180% of minimum wage. High Type isan indicator for whether the worker's total pay in month t-1 is above 180% of minimumwage. The omitted group (Low Types) are workers for whom total pay in t-1 is �atminimum wage�. E�ect MinW (%) is the percent e�ect of a $1 increase in MinW onthe outcomes. Standard errors are two-way clustered at the state level and at theborder-segment level. *** p<0.01, ** p<0.05, * p<0.1.

92

Table D.7: E�ect of Minimum Wage on Worker Productivity with Alternative De�nitionsof �Bordering Stores�

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs Sales/Hrs Sales/Hrs Sales/HrsDistance Store-Border 75km 75km 37.5km 37.5km 18.75km 18.75km

(1) (2) (3) (4) (5) (6)

MinW 0.094** 0.244*** 0.098** 0.255*** 0.088** 0.261***(0.039) (0.042) (0.038) (0.042) (0.042) (0.049)

Medium Type 0.354*** 0.359*** 0.370***(0.032) (0.033) (0.041)

High Type 1.169*** 1.171*** 1.173***(0.072) (0.073) (0.082)

MinW · Medium Type -0.085*** -0.091*** -0.108***(0.025) (0.027) (0.039)

MinW · High Type -0.182*** -0.192*** -0.199***(0.032) (0.034) (0.042)

Observations 217,822 209,513 208,451 200,506 159,352 153,329Units Wrk Wrk Wrk Wrk Wrk WrkMean Dep.Var. 2.085 2.085 2.089 2.089 2.077 2.077E�ect MinW (%) 4.485 4.701 4.234E�ect for Low Type (%) 22.56 23.69 23.68p-value 0.001 0.001 0.001

E�ect for Med. Type (%) 8.186 8.476 7.981p-value 0.001 0.001 0.001

E�ect for High Type (%) 2.273 2.339 2.269p-value 0.179 0.158 0.171

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ects and control forworker tenure, worker department and county-level employment. Col. 1-2 (3-4) [5-6] restrict thesample to stores within 75 km (37.5 km) [18.75 km] from the border. Sales/Hrs are the sales perhour rescaled by a factor between 1/50 and 1/150 relative to its $ value. MinW is the predominantmonthly minimum wage (in $). Medium Type is an indicator for whether the worker's total pay inmonth t-1 is between the minimum wage and 180% of minimum wage. High Type is an indicatorfor whether the worker's total pay in month t-1 is above 180% of minimum wage. The omittedgroup (Low Types) are workers for whom total pay in t-1 is �at minimum wage�. E�ect MinW(%) is the percent e�ect of a $1 increase in MinW on the outcomes. Standard errors are two-wayclustered at the state level and at the border-segment level. *** p<0.01, ** p<0.05, * p<0.1.

Table D.8: E�ect of Minimum Wage on Worker Productivity without �Stacking� the Data(Experimental Event Approach)

Dep.Var. Sales/Hrs Sales/Hrs(1) (2)

MinW 0.112** 0.221***(0.051) (0.063)

Medium Type 0.314***(0.029)

High Type 1.159***(0.051)

MinW · Medium Type -0.049(0.031)

MinW · High Type -0.152***(0.032)

Observations 128,958 123,745Units Workers WorkersMean Dep.Var. 2.094 2.094E�ect MinW (%) 5.365E�ect MinW for Low Type (%) 19.83p-value 0.001

E�ect MinW for Med. Type (%) 8.773p-value 0.003

E�ect MinW for High Type (%) 2.485p-value 0.165

Notes: The sample comprises of bordering stores without stacking thedata. All the regressions include worker �xed e�ects, border-segment-month �xed e�ects and control for worker tenure, worker department andcounty-level unemployment. Sales/Hrs are the sales per hour rescaled bya factor between 1/50 and 1/150 relative to its $ value. MinW is thepredominant monthly minimum wage (in $). Medium Type is an indicatorfor whether the worker's total pay in month t-1 is between the minimumwage and 180% of minimum wage. High Type is an indicator for whetherthe worker's total pay in month t-1 is above 180% of minimum wage.The omitted group (Low Types) are workers for whom total pay in t-1is �at minimum wage�. E�ect MinW (%) is the percent e�ect of a $1increase in MinW on the outcomes. Standard errors are clustered at theborder-segment level. *** p<0.01, ** p<0.05, * p<0.1.

94

Table D.9: E�ect of Minimum Wage on Worker Productivity with Alternative Classi�ca-tions of Low, Medium and High Types

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs Sales/HrsThreshold 120% 140% 160% 180%

main spec.(1) (2) (3) (4)

MinW 0.209*** 0.228*** 0.234*** 0.244***(0.035) (0.035) (0.035) (0.042)

Medium Type 0.230*** 0.283*** 0.326*** 0.354***(0.028) (0.030) (0.032) (0.032)

High Type 0.625*** 0.870*** 1.051*** 1.169***(0.043) (0.055) (0.068) (0.072)

MinW · Medium Type -0.099*** -0.076*** -0.075*** -0.085***(0.026) (0.026) (0.025) (0.025)

MinW · High Type -0.056*** -0.079*** -0.130*** -0.182***(0.016) (0.021) (0.029) (0.032)

Observations 209,513 209,513 209,513 209,513Units Workers Workers Workers WorkersMean Dep.Var. 2.085 2.085 2.085 2.085E�ect MinW for Low Type (%) 19.33 21.13 21.67 22.56p-value 0.000 0.000 0.000 0.000

E�ect MinW for Med. Type (%) 7.424 9.021 8.673 8.186p-value 0.001 0.000 0.000 0.000

E�ect MinW for High Type (%) 6.622 5.963 3.944 2.273p-value 0.000 0.000 0.009 0.179

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ects and controlfor worker tenure, worker department and county-level employment. Medium Types is anindicator for whether the worker's total pay in month t−1 is between the minimum wage andX% of minimum wage, where X is 120 in Col. 1, 140 in Col. 2, 160 in Col. 3 and 180 in Col.4. (Col. 4 is equivalent to our main speci�cation). High Types is an indicator for whetherthe worker's total pay in month t − 1 is above X% of minimum wage. As the thresholdincreases (i.e., from 120% to 180%), the mass of low types remains unchanged but the topcategory of high types becomes thinner and more outstanding. High types represent 75% ofthe workforce with the 120% threshold, 52% with the 140% threshold, 35% with the 160%threshold and 25% with the 180% threshold. Sales/Hrs are the sales per hour rescaled bya factor between 1/50 and 1/150 relative to its $ value. MinW is the predominant monthlyminimum wage (in $). Standard errors are two-way clustered at the state level and at theborder-segment level. *** p<0.01, ** p<0.05, * p<0.1.

95

Table D.10: E�ect of Minimum Wage on Worker Productivity with Alternative Classi�-cations of Low, Medium and High Types (Continued)

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs Sales/Hrs�Type� De�nition Avg pay Max pay Pay in Sales/Hrs in

from t=-1,-3 from t=-1,-3 1st month 1st quarter (FE)(1) (2) (3) (4)

MinW 0.153*** 0.210*** 0.168*** 0.178***(0.041) (0.040) (0.033) (0.045)

Medium Type 0.334*** 0.372***(0.042) (0.026)

High Type 1.087*** 1.026***(0.044) (0.030)

MinW · Medium Type -0.061 -0.098*** -0.104*** -0.113**(0.047) (0.030) (0.023) (0.044)

MinW · High Type -0.158*** -0.206*** -0.028 -0.121***(0.052) (0.031) (0.070) (0.026)

Observations 187,137 187,137 209,513 216,444Units Workers Workers Workers WorkersMean Dep.Var. 2.085 2.085 2.092 2.085E�ect MinW for Low Type (%) 15.65 22.47 9.709 9.153p-value 0.001 0.001 0.001 0.001

E�ect MinW for Med. Type (%) 4.850 6.071 3.030 2.883p-value 0.011 0.001 0.057 0.152

E�ect MinW for High Type (%) -0.214 0.170 6.483 2.152p-value 0.916 0.930 0.043 0.220

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ects and control for workertenure, worker department and county-level employment. In Col. 1, Medium Type (High Type) is anindicator for whether the worker's average pay in the three months before the minimum wage changeis between the minimum wage and 180% of minimum wage (above 180% of minimum wage). In Col. 2,Medium Type (High Type) is an indicator for whether the worker's maximum pay in the three monthsbefore the minimum wage change is between the minimum wage and 180% of minimum wage (above180% of minimum wage). In Col. 3, Medium Type (High Type) is an indicator for whether the worker'stotal pay in the �rst month in which she appears in our dataset is between the minimum wage and180% of minimum wage (above 180% of minimum wage). In Col. 4, Medium Type (High Type) is anindicator for whether the worker's productivity in the �rst quarter in which he/she appears in thedataset is in the second (third) tercile of the productivity distribution based on the estimated worker�xed e�ects. Sales/Hrs are the sales per hour rescaled by a factor between 1/50 and 1/150 relativeto its $ value. MinW is the monthly predominant minimum wage (in $). MinW is the predominantmonthly minimum wage (in $). Standard errors are two-way clustered at the state level and at theborder-segment level. *** p<0.01, ** p<0.05, * p<0.1.

96

Table D.11: E�ect of Minimum Wage on Worker Productivity with Alternative Controls

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs Sales/HrsControls Dept.-Trends Dept.-Trends No Tenure&UR No Tenure&UR

(1) (2) (3) (4)

MinW 0.121* 0.271*** 0.094** 0.244***(0.063) (0.064) (0.038) (0.042)

Medium Type 0.349*** 0.353***(0.033) (0.032)

High Type 1.159*** 1.168***(0.071) (0.072)

MinW · Medium Type -0.085** -0.085***(0.032) (0.025)

MinW · High Type -0.187*** -0.182***(0.033) (0.033)

Observations 217,822 209,513 217,822 209,513Units Workers Workers Workers WorkersMean Dep.Var. 2.085 2.085 2.085 2.085E�ect MinW (%) 5.788 4.526E�ect for Low Type (%) 25.06 22.58p-value 0.001 0.001

E�ect for Med. Type (%) 9.566 8.196p-value 0.004 0.001

E�ect for High Type (%) 3.074 2.274p-value 0.236 0.173

Notes: All the regressions control for pair-month �xed e�ects, worker �xed e�ects, worker department.Col. 1 and 2 also controls for worker tenure, unemployment rate, and department-store speci�c time-trends(unique department ID · time-trend). Sales/Hrs are the sales per hour rescaled by a factor between 1/50and 1/150 relative to its $ value. MinW is the predominant monthly minimum wage (in $). Medium Typeis an indicator for whether the worker's total pay in month t-1 is between the minimum wage and 180% ofminimum wage. High Type is an indicator for whether the worker's total pay in month t-1 is above 180%of minimum wage. The omitted group (Low Types) are workers for whom total pay in t-1 is �at minimumwage�. E�ect MinW (%) is the percent e�ect of a $1 increase in MinW on the outcomes. Standard errorsare two-way clustered at the state level and at the border-segment level. *** p<0.01, ** p<0.05, * p<0.1.

97

Table D.12: E�ect of Minimum Wage on Worker Productivity by Department

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs Sales/HrsDepartment Dpt 1 Dpt 2 Dpt 3 Dpt 4

(1) (2) (3) (4)

MinW 0.395*** 0.259* 0.139 0.726(0.104) (0.139) (0.092) (0.586)

Medium Type 0.513*** 0.388*** 0.306*** 0.365***(0.109) (0.047) (0.062) (0.128)

High Types 1.354*** 1.015*** 0.743*** 1.321***(0.160) (0.062) (0.077) (0.197)

MinW · Medium Type -0.238*** -0.161*** -0.145* -0.073(0.080) (0.041) (0.084) (0.134)

MinW · High Type -0.208*** -0.259*** -0.087 0.298(0.063) (0.072) (0.110) (0.234)

Observations 72,616 48,062 36,107 19,793Units Workers Workers Workers WorkersMean Dep.Var. 2.587 2.123 1.595 2.639E�ect MinW for Low Type (%) 27.19 24.90 15.32 44.75p-value 0.001 0.0719 0.146 0.226

E�ect MinW for Med. Type (%) 6.462 5.559 -0.499 25.85p-value 0.001 0.474 0.924 0.248

E�ect MinW for High Type (%) 4.768 -0.007 2.748 22.78p-value 0.027 0.999 0.449 0.112

Notes: This speci�cation isolates the four largest departments, making up approximately 90%of the observations. The remaining observations are split among eight small departments, notreported here. All the regressions include pair-month �xed e�ects, worker �xed e�ects and controlfor worker tenure, and county-level unemployment. Sales/Hrs are the sales per hour rescaled bya factor between 1/50 and 1/150 relative to its $ value. MinW is the predominant monthlyminimum wage (in $). Medium Type is an indicator for whether the worker's total pay in montht-1 is between the minimum wage and 180% of minimum wage. High Type is an indicator forwhether the worker's total pay in month t-1 is above 180% of minimum wage. The omitted group(Low Types) are workers for whom total pay in t-1 is �at minimum wage�. E�ect MinW (%) is thepercent e�ect of a $1 increase in MinW on the outcomes. Standard errors are two-way clusteredat the state level and at the border-segment level. *** p<0.01, ** p<0.05, * p<0.1.

98

E Demand Channel Appendix

We proxy store-level demand with the monthly occupancy rate in the parking aroundeach store. More precisely, we extracted parking lot tra�c data from high-resolutionsatellite imagery by RS Metrics (see Figure 8 for an example of a satellite image).67

Each satellite image is digitized using a machine learning and computer vision algorithmwhich (1) identi�es parking lot areas around each store, (2) counts the number of parkingspaces in the parking lot, and (3) counts the number of cars parked. We aggregate thesehigh-frequency satellite data at the store-month level and create a store-speci�c monthlymeasure of parking occupancy, i.e., the average proportion of parking spaces that are �lledin a given store and in a given month.68 In our sample, the average parking lot holds 125cars and the average occupancy rate is 23%.69

As explained in Section 7.1, using occupancy rate as a proxy of demand is ideal be-cause, unlike other possible measures, it captures customer volume, which is exogenousto worker e�ort, without capturing quantity purchased, which is instead endogenous toworker e�ort. This means, however, that we can only detect the e�ect of minimum wageon the number of shoppers rather than on spending per shopper. This is problematic ifthere are distributional e�ects of the minimum wage such that the number of shoppersdoes not change but spending per shopper increases. To validate our proxy for store-leveldemand, we start by showing that it is highly co-moves with store output. Table E.1Col. 1 shows that a one unit increase in occupancy rate is associated with a statisticallysigni�cant 12% increase in store output. Figure E.1 moreover shows that the two variablesco-move over time with peaks around holiday seasons.

We use the data on parking occupancy to show that store-level demand. First, anincrease in minimum wage does not a�ect parking lot occupancy rate (Table E.1, Col. 2).Second, the e�ect of minimum wage on individual worker productivity does not shrinkwhen we control for parking lot occupancy rate, indicating that the observed productivitygains is not explained by a demand surge (Table E.2, Col. 2-3).70

67The same satellite parking data have been used by Nsoesie et al. (2015) as a proxy of �hospitalattendance� and by UBS Investment Research as a proxy of �Walmart store-level demand� (see McCarthyand Harris 2012). For a general overview of the use of satellite imagery in economics see Donaldson andStoreygard (2016).

68During our sample period, the data contain about 51,000 satellite images of the parking lots of thestores in our data. Images cover 93% of the stores in our dataset and, conditional on having at least onepicture in a given month, the average store has 2.6 images per month. Missing images are attributable toindoor parking lots that could not be caught by satellites, and to the lower frequency of satellite imagesin less populated areas.

69Because we control for store �xed e�ects, using the occupancy rate as a proxy of demand is equivalentto using the number of cars in the parking lot.

70The results hold if we further control for parking lot occupancy rate interacted with a county measure

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Figure E.1: Parking-lot Occupancy Rates Co-move With Store Output

Notes: This �gure plots the evolution over time of �store output� and �parking lot occupancy rates�,averaged at the store-month level. Output/Hrs is the (average) total monthly store sales generated byall sales associates in our sample divided by the total number of hours worked by these sales associates.We do not disclose the units for con�dentiality reasons. Parking lot occupancy rates is the (average)occupancy rate of the store's parking lot.

Table E.3 (and the corresponding Figure 9) show that � even if there was a positivedemand shock as a result of a higher minimum wage � this shock would unlikely beconcentrated among low types only. We use a regression model similar to Eq. (12) withthe only di�erence that indicators for worker types are interacted with a dummy for highdemand (top quartile of occupancy rate) rather than with the minimum wage. Figure9 plots the estimated coe�cients β̂1, β̂1 + β̂4 and β̂1 + β̂5 and the associated con�denceintervals. We �nd that sales per hour are higher in high-occupancy than low-occupancyperiods only for medium and high types, while higher occupancy does not increase salesper hour of low types. The fact that minimum wage raises the productivity of low typesonly is thus inconsistent with a demand shock.

One may wonder whether the productivity boost we observe among low types is ex-plained by these workers being disproportionately located in high-exposure counties (wherethe demand response might be stronger) relative to high types. This is unlikely the case.First, all our estimates are based on comparisons across types within the same store. Sec-ond, Table E.1 show that low types are not disproportionately located in high-exposurecounties (Col. 4) and, moreover, that the e�ect of the minimum wage on parking occu-pancy rates is not stronger in high-exposure counties (Col. 3).

of how binding the minimum wage is (�county-level exposure�, see below for more information).

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Finally, we show that the minimum wage a�ects our workers' individual productivityindependently of the share of the population who earn minimum wage (Table E.4). Wecompute two measures of �exposure to the minimum wage:� one at the county level andthe other at the state level. The former uses the QWI data to calculate the quarterly,county-level di�erence between the average hourly wage and the prevailing minimum wage(as in Renkin et al. 2018).71 The latter uses the individual-level NBER Merged OutgoingRotation Group of the Current Population Survey for 2012-2015 (CPS) to calculate thequarterly, state-level fraction of workers whose earnings per hour is equal to the prevailingminimum wage (as in Cengiz et al. 2019).

Table E.1: Minimum Wage, Parking Occupancy and Store Output

Dep.Var. Output/Hrs Parking Parking % Low TypesOccupancy Occupancy

(1) (2) (3) (4)

MinW -0.005 0.001(0.017) (0.019)

Parking Occupancy 0.252**(9.610)

Exposure 0.020 -0.117(0.021) (0.250)

MinW * Exposure -0.002(0.002)

Observations 12,359 12,275 12,359 12,275Units Stores Stores Stores StoresMean Dep.Var. 2.135 0.230 0.230 5.964E�ect (%) 11.81 -2.028 0.343 -

Notes: All the regression includes pair-month �xed e�ects, store �xed e�ects and controls forcounty-level unemployment. Output/Hrs are computed by aggregating the sales produced by allsales associates in our sample in a given month divided by the total number of hours these salesassociates worked in that month (the units are hidden for con�dentiality reason). MinW is thepredominant monthly minimum wage (in $). Parking Occupancy is the average occupancy rateof the store's parking lot (0 means no-occupancy, 1 means full-occupancy). Standard errors aretwo-way clustered at the state level and at the border-segment level. *** p<0.01, ** p<0.05, *p<0.1.

71The assumption is that counties with a low average wage relative to the minimum wage are states inwhich the minimum wage is binding for a larger share of the population.

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Table E.2: E�ect of Minimum Wage on Worker Productivity Controlling for Demand

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs(1) (2) (3)

MinW 0.092** 0.230*** 0.085**(0.039) (0.042) (0.038)

Medium Type 0.383***(0.030)

High Type 1.174***(0.046)

MinW · Medium Type -0.041(0.025)

MinW · High Type -0.165***(0.031)

Controls included in the regression:

Parking Occupancy Yes Yes YesParking Occupancy · Med. Type No Yes NoParking Occupancy · High Type No Yes NoExposure No No YesParking Occupancy*Exposure No No Yes

Observations 217,822 209,513 217,822Units Workers WorkersMean Dep.Var. 2.085 2.085 2.085E�ect MinW (%) 4.424 4.055E�ect MinW for Low Type (%) 21.30p-value 0.000

E�ect MinW for Med. Type (%) 9.766p-value 0.000

E�ect MinW for High Type (%) 2.400p-value 0.153

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ects and control forworker tenure, worker department and county-level unemployment. Parking Occupancy is theaverage occupancy rate of the store's parking lot (0 means no-occupancy and 100 means fulloccupancy). Exposure corresponds to the di�erence (in $) between the average hourly wage inthe state and the predominant monthly minimum wage. Sales/Hrs are the sales per hour rescaledby a factor between 1/50 and 1/150 relative to its $ value. MinW is the predominant monthlyminimum wage (in $). Medium Type is an indicator for whether the worker's total pay in montht-1 is between the minimum wage and 180% of minimum wage. High Type is an indicator forwhether the worker's total pay in month t-1 is above 180% of minimum wage. The omitted group(Low Types) are workers for whom total pay in t-1 is �at minimum wage�. E�ect MinW (%) is thepercent e�ect of a $1 increase in MinW on the outcomes. Standard errors are two-way clusteredat the state level and at the border-segment level. *** p<0.01, ** p<0.05, * p<0.1.

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Table E.3: E�ect of Positive Demand Shock on Worker Productivity

Dep.Var. Sales/Hrs Sales/Hrs(1) (2)

High Parking Occupancy 0.045** -0.045(0.020) (0.029)

Medium Type 0.291***(0.039)

High Type 1.102***(0.093)

High Parking Occupancy · Medium Type 0.081***(0.021)

High Parking Occupancy · High Type 0.107***(0.030)

Observations 217,822 209,513Units Workers WorkersMean Dep.Var. 2.085 2.085E�ect High Occupancy (%) 2.156E�ect High Occupancy for Low Type (%) -4.155p-value 0.138

E�ect High Occupancy for Med. Type (%) 1.859p-value 0.028

E�ect High Occupancy for High Type (%) 2.287p-value 0.016

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ectsand control for worker tenure, worker department and county-level unemployment.High Parking Occupancy is an indicator for whether the average occupancy rate isin the top quartile of the store distribution. MinW is the predominant monthlyminimum wage (in $). Sales/Hrs are the sales per hour rescaled by a factor between1/50 and 1/150 relative to its $ value. MinW is the predominant monthly minimumwage (in $). MinW is the predominant monthly minimum wage (in $). MediumType is an indicator for whether the worker's total pay in month t-1 is between theminimum wage and 180% of minimum wage. High Type is an indicator for whetherthe worker's total pay in month t-1 is above 180% of minimum wage. The omittedgroup (Low Types) are workers for whom total pay in t-1 is �at minimum wage�.E�ect MinW (%) is the percent e�ect of a $1 increase in MinW on the outcomes.Standard errors are two-way clustered at the state level and at the border-segmentlevel. s*** p<0.01, ** p<0.05, * p<0.1.

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Table E.4: E�ect of Minimum Wage on Worker Productivity by Exposure

Dep.Var. Sales/Hrs Sales/Hrs Sales/Hrs Sales/Hrs(1) (2) (3) (4)

MinW 0.082* 0.231*** 0.115** 0.278***(0.042) (0.040) (0.045) (0.050)

Exposure -0.033 -0.038* -1.028 -0.768(0.022) (0.021) (0.816) (1.171)

MinW · Exposure 0.002 0.002 -0.685 -1.469(0.006) (0.009) (0.950) (0.977)

MinW · Medium Type -0.089*** -0.099***(0.020) (0.021)

MinW · High Type -0.201*** -0.180***(0.023) (0.065)

MinW · Exposure · Medium Type -0.002 0.316(0.007) (0.335)

MinW · Exposure · High Type 0.021** 2.831**(0.010) (1.306)

Other regressors:Medium Type No Yes No YesHigh Type No Yes No YesExposure · Medium Type No Yes No YesExposure · High Type No Yes No Yes

Observations 217,822 209,513 217,822 209,513Units Workers Workers Workers WorkersMean Dep.Var. 2.085 2.085 2.085 2.085

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ects and control forworker tenure, worker department and county-level unemployment. In Col. 1-2, Exposure corre-sponds to the di�erence (in $) between the average hourly wage in the county and the predominantmonthly minimum wage. In Col. 3-4, Exposure corresponds to the fraction of workers in the state(in %) whose earnings are at minimum wage. Sales/Hrs are the sales per hour rescaled by a factorbetween 1/50 and 1/150 relative to its $ value. MinW is the predominant monthly minimumwage (in $). Medium Type is an indicator for whether the worker's total pay in month t-1 isbetween the minimum wage and 180% of minimum wage. High Type is an indicator for whetherthe worker's total pay in month t-1 is above 180% of minimum wage. The omitted group (LowTypes) are workers for whom total pay in t-1 is �at minimum wage�. Standard errors are two-wayclustered at the state level and at the border-segment level. *** p<0.01, ** p<0.05, * p<0.1.

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Table E.5: E�ect of Minimum Wage on Worker Productivity Controlling for Employment

Dep.Var. Sales/Hrs Sales/Hrs(1) (2)

MinW 0.090** 0.237***(0.038) (0.043)

N.Workers -0.019** -0.048**(0.007) (0.018)

Parking Occupancy 0.212** 0.178**(0.104) (0.083)

Medium Type 0.220***(0.035)

High Type 0.901***(0.049)

MinW · Medium Type -0.081***(0.026)

MinW · High Type -0.173***(0.035)

N.Workers · Medium Type 0.025*(0.012)

N.Workers · High Type 0.048***(0.014)

Observations 217,822 209,513Mean Dep.Var. 2.085 2.092E�ect N.Workers (%) -0.932E�ect N.Workers for Low Type (%) -2.305p-value 0.0101

E�ect N.Workers for Med. Type (%) -1.126p-value 0.002

E�ect N.Workers for High Type (%) -0.028p-value 0.949

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ectsand control for worker tenure, worker department and county-level unemploy-ment. N.Workers is the number of sales associates in the store. ParkingOccupancy is the average occupancy rate of the store's parking lot (0 meansno-occupancy and 100 means full occupancy). Sales/Hrs are the sales perhour rescaled by a factor between 1/50 and 1/150 relative to its $ value.MinW is the predominant monthly minimum wage (in $). Medium Type isan indicator for whether the worker's total pay in month t-1 is between theminimum wage and 180% of minimum wage. High Type is an indicator forwhether the worker's total pay in month t-1 is above 180% of minimum wage.The omitted group (Low Types) are workers for whom total pay in t-1 is �atminimum wage�. E�ect (%) is the percent e�ect of a 1 unit increase in theindependent variable on the outcomes. Standard errors are two-way clusteredat the state level and at the border-segment level. *** p<0.01, ** p<0.05, *p<0.1.

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F Organizational Adjustments Channel Appendix

Another alternative channel is that a higher minimum wage leads to �rm organizationaladjustments targeting low types, namely, after a minimum wage increase the �rm mighthave improved the earning opportunities of low types relative to high ones, which inour �rm is done mainly by scheduling them to better shifts (typically assigned to full-time workers), or by moving them to the top (best-selling) department.72 Alternatively,the �rm might have reduced the number of hours that low-types are scheduled to workrelative to high types. This may translate into higher productivity per hour for low-typesif working fewer hours positively a�ects their productivity, even per hour.If that were thecase, the observed productivity boost among the low types might re�ect a re-organizationand not necessarily of higher e�ort by low types.

Table F.1 (and the corresponding Figure 10) show that the minimum wage has nostatistically signi�cant e�ect on the proportion of low vs. high types who are moved toa top department (Col. 1-2) or moved to part-time status (with worse shifts, Col. 3-4).The e�ect of minimum wage on hours worked also does not di�er for low vs. high types(Col. 5-6).73 Finally, Col. 7-8 show that �rm did not adjust other types of formal bene�ts(vacation and illness bene�ts) as a result of a higher minimum wage, neither for the lowtypes nor for the high types.

Another �rm adjustment that is consistent with sales associates selling a higher dollaramount after a minimum wage hike is an increase in consumer prices. Note, however, thatan increase in prices should be a tide that lifts all boats, and should thus increase salesfor all workers, not just for the low types. Moreover, as with many national nationwideretailers, our company has a national pricing strategy and has uniform prices across allUS stores (Della Vigna and Gentzkow 2019). In line with this, Table F.2 shows that theminimum wage does not a�ect our company cost-to-price index. We compute the cost-to-price index as the ratio between: (a) monthly store output minus gross margin (cost ×quantity), and (b) store output (price × quantity).

Overall, the �ndings indicate that the productivity gains of low types do not re�ectorganizational adjustments targeting them.

72One of the store departments is more popular than others and attracts more demand. Sales associatesworking in this �popular� department tend to sell more and hence earn higher commissions, holding e�ortconstant.

73The e�ect of minimum wage on hours (part-time status) is positive (negative) for all worker typesbut is never statistically signi�cant, even when we aggregate data across all worker types.

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Table F.1: E�ect of MinimumWage on Allocation to Top Departments, Part-Time Status,Hours Worked and Bene�ts

Dep.Var. Top Dept. Part-Time Hrs Bene�ts(1) (2) (3) (4) (5) (6) (7) (8)

MinW -0.454 0.044 -2.395 -2.291 1.942 2.720 8.006 7.402(0.655) (0.623) (1.434) (1.665) (1.265) (1.637) (7.281) (7.622)

Medium Type -0.092 -2.220 4.762*** 0.213(0.283) (1.392) (1.181) (2.144)

High Type -1.218*** -2.381 5.439*** 4.904*(0.265) (1.768) (1.549) (2.609)

MinW · Medium Type -0.160 -0.028 -0.856 1.406(0.218) (0.826) (0.851) (1.161)

MinW · High Type -0.878* 0.036 -0.240 2.424(0.466) (0.917) (1.236) (1.961)

Observations 217,822 209,514 217,822 209,513 217,822 209,513 217,822 209,513Units Workers Workers Workers Workers Workers Workers Workers WorkersMean Dep.Var. 44.29 44.29 60.25 60.25 106.5 106.5 48.23 48.23E�ect MinW (%) -1.024 -3.975 1.824 16.60E�ect MinW for Low (%) 0.128 -3.090 3.052 38.08p-value 0.944 0.178 0.106 0.339

E�ect MinW for Med. (%) -0.225 -3.790 1.754 22.680.849 0.100 0.161 0.255

E�ect MinW for High (%) -3.535 -4.268 2.179 11.56p-value 0.265 0.150 0.121 0.209

Notes: All the regressions include pair-month �xed e�ects, worker �xed e�ects and control for workertenure, worker department and county-level unemployment. Top-Dept. is an indicator for being in thetop (best-selling) departments (takes value 0 in a given month if a worker is not in top-departmentsand takes value 100 if the worker is in top-departments). Part-time is the percent probability that anemployee is a part-time employee in a given month (takes value 0 in a given month if a worker is full-timeand takes value 100 if the worker is part-time). Hrs is the total number of hours for which employeereceives a compensation in a given month. Bene�ts are the vacation and illness bene�ts (in $) receivedby an employee in a given month. MinW is the predominant monthly minimum wage (in $). MediumType is an indicator for whether the worker's total pay in month t-1 is between the minimum wage and180% of minimum wage. High Type is an indicator for whether the worker's total pay in month t-1 isabove 180% of minimum wage. The omitted group (Low Types) are workers for whom total pay in t-1 is�at minimum wage�. E�ect (%) is the percent e�ect of a 1 unit increase in the independent variable onthe outcomes. Standard errors are two-way clustered at the state level and at the border-segment level.*** p<0.01, ** p<0.05, * p<0.1.

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Table F.2: E�ect of Minimum Wage on Cost-to-Price Index

Dep.Var. Costs/Prices Ratio(1)

MinW -0.004(0.003)

Observations 12,359Units StoresMean Dep.Var. 0.693E�ect (%) -0.531

Notes: The regression includes pair-month �xede�ects, store �xed e�ects and controls for county-level unemployment. Costs/Prices Ratio is com-puted as the ratio between: (a) store output mi-nus gross margin, and (b) store output. MinWis the predominant monthly minimum wage (in$). Standard errors are two-way clustered at thestate level and at the border-segment level. ***p<0.01, ** p<0.05, * p<0.1.

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