DecomposingWagePolarization - TAU · 2016-10-30 · WagePolarization 1980 1985 1990 1995 2000 2005...

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Decomposing Wage Polarization Oren Danieli TAU, 2016 Oren Danieli Decomposing Wage Polarization TAU, 2016 1 / 51

Transcript of DecomposingWagePolarization - TAU · 2016-10-30 · WagePolarization 1980 1985 1990 1995 2000 2005...

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Decomposing Wage Polarization

Oren Danieli

TAU, 2016

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Wage Polarization

1980 1985 1990 1995 2000 2005 2010

0.55

0.65

0.75

0.85

Log

hour

ly w

age

ratio 90/50 50/10

Figure : Wage Ratios - All Population

The vertical lines are changes in occupational coding.Data resource: CPS - ORG

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Preview of Results

This project has two parts1. Methodological

Introduce skewness decompositionMethod to decompose wage polarizationSimpler and more robustDiscuss other potential applications

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Preview of Results

2. EmpiricalFirst direct evidence that wage polarization is related to routineoccupationsDriven by a decrease in inequality within low-paying, routineoccupationsWages drop mostly for higher-paid routine workersNot due to a decrease of wages in middle-skill occupations as wethoughtNot a result of solely compositional changesStops around 2000

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Outline

1 Background

2 Methodology

3 Empirical Results

4 Theory and Current Working Directions

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Background Polarization - Empirics

Table of Contents

1 BackgroundPolarization - EmpiricsPolarization - Theory

2 Methodology

3 Empirical Results

4 Theory and Current Working Directions

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Background Polarization - Empirics

Polarization

Wage polarization

Late 80’s - Early 00’sRelative decline in middle wages in the U.S. (Autor et al., 2006, 2008)

Show More

Job polarization

Simultaneously there is a decline at employment levels for middle-skilljobs (Goos and Manning, 2007; Autor et al., 2006, 2008)Occurs in almost all developed countries (Goos et al., 2009)Accelerates in last decade Autor (2014)

Inequality increased in high paying occupations and decreased in lowpaying occupations (Firpo et al., 2013)

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Background Polarization - Theory

Table of Contents

1 BackgroundPolarization - EmpiricsPolarization - Theory

2 Methodology

3 Empirical Results

4 Theory and Current Working Directions

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Background Polarization - Theory

Potential Explanations

Routine Biased Technological Change (Autor et al., 2008)

Computers are substitutional to workers in routine tasks.Routine tasks are usually done by middle-skill workers.Decrease in demand for workers in middle-skill occupations.Works very well with employment trends (“job polarization”)Drop in routine task prices creates wage polarization (Acemoglu andAutor, 2011)

Changes in returns to skill (Firpo et al., 2013)Minimum wageEconomic boom

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Methodology Motivation

Table of Contents

1 Background

2 MethodologyMotivationSkewness Decomposition

3 Empirical Results

4 Theory and Current Working Directions

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Methodology Motivation

Motivation

A basic tool for inequality research is Variance DecompositionWe can write log wages (Y ) as the sum of group averages and residual

Y = E [Y |X ] + ε

for ε = Y − E [Y |X ]

Groups (X ) can be occupations, industry, skill group etc.Taking the variance we get

Var [Y ] = Var (E [Y |X ]) + E[ε2]

= Var (E [Y |X ])︸ ︷︷ ︸Between

+ E [Var (Y |X )]︸ ︷︷ ︸Within

Enables to decompose to between-group inequality and within-groupinequality.

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Methodology Motivation

Motivation

Need a single index for wage polarization

We used a set of wage quantiles ratios.

Also, quantile measures of inequality do not have a straightforwarddecomposition.Therefore people usually use decomposition methods that build anentire counterfactual distribution (Juhn et al., 1993; DiNardo et al.,1996; Autor et al., 2005)

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Methodology Motivation

Limitations of Counterfactual Distribution Methods

Decompose by composition, between group prices, within group prices.

No component for interaction of between and within group.

Decompose into marginal components (not independent)

Order mattersNot only technical

Depend on base yearCannot accommodate changes in categories coding.Skewness decomposition addresses all these issues.

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Methodology Skewness Decomposition

Table of Contents

1 Background

2 MethodologyMotivationSkewness Decomposition

3 Empirical Results

4 Theory and Current Working Directions

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Methodology Skewness Decomposition

Wage Polarization Is Wage Skewness

So far we described polarization with a set of quantile ratios.The skewness of log hourly wages captures what we want in a singlenumber.Third standardized moment, and calculated with the following formula:

S (Y ) = E

[(Y − E [Y ]

σ

)3]

It increases when upper tail inequality rises and lower tail inequalitydrops.

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Methodology Skewness Decomposition

Skewness of Log-Wages

1985 1990 1995 2000 2005 2010

0.00

0.10

0.20

Figure : Skewness of Log-Hourly Wage

The vertical lines are changes in occupational coding.Wages at the top and bottom 5% weredropped.Data resource: CPS - ORG

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Methodology Skewness Decomposition

Skewness Decomposition

If Y is standardized log wage, skewness is E[Y 3]

So skewness decomposition is simply E[Y 3] = E

[(E [Y |X ] + ε)3

]=

E[ε3]

+ E[E [Y |X ]3

]+ 3E

[E [Y |X ] ε2

]Which can also be written as

E [µ3 (Y |X )]︸ ︷︷ ︸Within

+ µ3 (E [Y |X ])︸ ︷︷ ︸Between

+ 3COV (E [Y |X ] ,V [Y |X ])︸ ︷︷ ︸Covariance

µ3 is the third centralized moment

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Methodology Skewness Decomposition

Advantages of Skewness Decomposition

Decompose into independent (and not marginal) components.Does not depend on base year.The covariance component is first introduced (and turns out to beimportant).Does not assume any modelCan accommodate changes in X encoding

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Methodology Skewness Decomposition

Other Potential Applications

Skewness decomposition can be applied to other cases where we areinterested in the skewness of the distribution.Here are few examples:

Top end inequality (the 1%)Firm productivity (TFP)Capital distributionWage distribution without logsLife expectancy

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Empirical Results Decomposing by Occupations

Table of Contents

1 Background

2 Methodology

3 Empirical ResultsDecomposing by OccupationsSkewness Decomposition by Other CategoriesTrends in VarianceRoutine OccupationsCloser Look at Timing

4 Theory and Current Working Directions

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Empirical Results Decomposing by Occupations

Skewness Decomposition by Occupation

0.000

0.025

0.050

0.075

0.100

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Cha

nge

Component

Within

Between

3Cov

Total Skew

Figure : Skewness Decomposition Changes 1992-2002

Data resource: CPS-ORGOren Danieli Decomposing Wage Polarization TAU, 2016 21 / 51

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Empirical Results Decomposing by Occupations

Skewness Decomposition by Occupation

The within component is “residual” and it is small.

Suggests that the trend is related to occupations.This will not be the case when decomposing by other groups. Show

The between component is negligible.

Opposite of what we would predict from a model of decreasing demandfor middle-wage occupations.

Most of the increase is due to increase in correlation betweenExpectation and Variance

High paying occupations have larger inequality.Low paying occupations have smaller inequality.Documented before by Firpo et al. (2013)

Very similar results for Israeli data.

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Empirical Results Skewness Decomposition by Other Categories

Table of Contents

1 Background

2 Methodology

3 Empirical ResultsDecomposing by OccupationsSkewness Decomposition by Other CategoriesTrends in VarianceRoutine OccupationsCloser Look at Timing

4 Theory and Current Working Directions

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Empirical Results Skewness Decomposition by Other Categories

The Importance of Occupations

Other categories yield much larger residual (within) componentThe trend in the covariance is unique for occupationsWhen compared directly, occupations clearly seem to explain most ofthe increase in skewnessFor industries - using the linear model Skew Dec in Linear Models

lnwi = occi + indi + εi

All the increase is inCOV

(occi , ε

2i)

and nothing inCOV

(indi , ε

2i)

The only other important component is µ3 (occ) (betweenoccupations)

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Empirical Results Skewness Decomposition by Other Categories

Occupations and Industries

0.000

0.025

0.050

0.075

0.100

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Cha

nge

from

199

2

variable

all other terms

COV(IND,e^2)

COV(OCC,e^2)

Figure : Skewness Decomposition by Occupation and Industry

Data resource: CPS-ORGOren Danieli Decomposing Wage Polarization TAU, 2016 25 / 51

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Empirical Results Trends in Variance

Table of Contents

1 Background

2 Methodology

3 Empirical ResultsDecomposing by OccupationsSkewness Decomposition by Other CategoriesTrends in VarianceRoutine OccupationsCloser Look at Timing

4 Theory and Current Working Directions

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Empirical Results Trends in Variance

Changes in Variance 1992-2002

2.2 2.4 2.6 2.8 3.0 3.2

−0.

050.

000.

05

Expected Log Wage

Cha

nge

in V

aria

nce

Figure : Change in V [lnw |occ] by E [lnw |occ] 1992-2002

Data resource: CPS-ORGOren Danieli Decomposing Wage Polarization TAU, 2016 27 / 51

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Empirical Results Trends in Variance

Variance Trends in Other Decades

−0.6 −0.4 −0.2 0.0 0.2 0.4

−0.

040.

000.

04

Demeaned Log Wage

Cha

nge

in V

ar

1980s 1990s 2000s

Figure : Change in V [lnw |occ] by E [lnw |occ] - Binned Scatter Plot

Data resource: CPS-ORGOren Danieli Decomposing Wage Polarization TAU, 2016 28 / 51

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Empirical Results Trends in Variance

Trends Summary

Asymmetric trends in occupational inequality in the 1990s:

High-paying occupations experienced an increase in inequalityLow-paying experienced a decreaseThe drop in variance is more significant in absolute terms

Variance trend alone can explain the increase in covariance Show

And so is responsible for most of “wage polarization”

The increase in variance for high-paying occupations is steady across 3decadesThe 90s are unique for the drop in inequality within occupations at thebottom

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Empirical Results Routine Occupations

Table of Contents

1 Background

2 Methodology

3 Empirical ResultsDecomposing by OccupationsSkewness Decomposition by Other CategoriesTrends in VarianceRoutine OccupationsCloser Look at Timing

4 Theory and Current Working Directions

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Empirical Results Routine Occupations

Characterizing Occupations with Drop in Inequality

Showed inequality dropped in low paying occupations in the 1990sNow I’ll show that this happens mostly in routine occupationsWages relatively drop for higher paid workers in routine jobsI’ll show this in two ways

Using O*NET data that measure level of routine tasksRunning analysis separately on routine and non routine jobs

Routine defined as administrative workers, operators and producers

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Empirical Results Routine Occupations

O*NET Data

In addition to CPS, I’ll also use O*NET data:

Description of occupation characteristicsVery wide data (more variables than occupations)

Use standard indices from the literature:

Analytic, Routine Cognitive, Routine Manual, Non-routine Manual,Offshorability (from Acemoglu and Autor, 2011)Social (from Deming, 2015)

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Empirical Results Routine Occupations

O*NET Results

Dep Variable ∆V ∆P × 103

log-wage .055*** 5.71***(.011) (2.17)

NR Analytic .001 .012*** 1.92** 3.10***(.004) (.003) (.79) (.66)

Routine -.000 .001 -1.70*** -1.51***Cognitive (.002) (.002) (.46) (.45)Routine -.009*** -.009*** -.10 -.12Manual (.003) (.003) (.68) (.69)

NR Manual -.001 -.001 .20 .60(.003) (.003) (.66) (.65)

Offshorability -.002 -.000 .14 .32(.002) (.002) (.51) (.51)

Social -.003 .002 -.02 .57(.003) (.003) (.70) (.67)

Table : Correlation of Occupational Characteristics with Trends in Variance andEmployment

Data resource: CPS-ORG.

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Empirical Results Routine Occupations

Variance Trend in Routine/Non-routine Occupations

2.2 2.4 2.6 2.8 3.0 3.2

−0.

040.

00

Log Wage

Cha

nge

in V

ar

RoutineNon−Routine RoutineNon−Routine

Figure : Change in V [lnw |occ] by E [lnw |occ] 1992-2002

Data resource: CPS-ORG. Routine occupations are administrators, producers and operators. Categories are dividedsame as in Acemoglu and Autor (2011)Oren Danieli Decomposing Wage Polarization TAU, 2016 34 / 51

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Empirical Results Routine Occupations

Variance Trend in Routine/Non-routine Occupations

2.0 2.5 3.0 3.5

−0.

050.

05

Log Wage 1992

Cha

nge

in D

emea

ned

Log

Wag

e 92

−02

Routine NR

Figure : Change in Relative Wages 1992-2002, Routine and Non-RoutineOccupations

Data resource: CPS-ORGOren Danieli Decomposing Wage Polarization TAU, 2016 35 / 51

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Empirical Results Routine Occupations

Routine Results Summary

Inequality is dropping mostly in low income routine occupationsDrop is much less significant in non-routine low income occupations(such as services)

In non routine occupations there is no wage polarizationBut relative wages do not drop for all routine workers

Only the higher paid onesHigher paid routine workers are concentrated at the middle of thedistribution

Relative drop in their wage leads to drop in middle wages in total

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Empirical Results Routine Occupations

Compositional Changes?

We know that there are huge compositional changes that also takeplace (“job polarization”)It is possible that drop in inequality is driven by compositional changes

Example: more high paid routine workers are leaving to non-routinejobs

I use PSID data, to exam the change in the distribution of “stayers”These are workers who stayed in routine occupations between1992-2001Inequality is also dropping in this sample.

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Empirical Results Routine Occupations

Convergence Among Stayers

1.5 2.0 2.5 3.0

0.40

0.43

0.46

Log Wage 1992

Log

Wag

e 20

01

Figure : Binned Scatter of Change in logw - Stayers

Data: PSIDOren Danieli Decomposing Wage Polarization TAU, 2016 38 / 51

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Empirical Results Closer Look at Timing

Table of Contents

1 Background

2 Methodology

3 Empirical ResultsDecomposing by OccupationsSkewness Decomposition by Other CategoriesTrends in VarianceRoutine OccupationsCloser Look at Timing

4 Theory and Current Working Directions

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Empirical Results Closer Look at Timing

Job Polarization by Year

1985 1990 1995 2000 2005 2010

0.40

0.45

0.50

Job Polarization

Rou

tine

Em

ploy

men

t

Figure : Share of Working Hours in Routine Occupations

Data resource: CPS-ORGOren Danieli Decomposing Wage Polarization TAU, 2016 40 / 51

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Empirical Results Closer Look at Timing

Demand Drop?

Seem to have a steady drop in demand for routine tasksA bit slower in early 2000s but accelerates rapidly during the recession

Simple hypothesis: the market adjusts to the drop in demand throughboth employment and wage levels.Look at total share of labor income that goes to routine workers sRThis equals relative wages in routine workers × Share of workers inroutine occupationsIn logs

log sR = logwR

wT+ log

LR

LT

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Empirical Results Closer Look at Timing

Share of Labor Income from Routine Workers

1985 1990 1995 2000 2005 2010

−0.

4−

0.2

0.0

Cum

ulat

ive

Cha

nge

Total Income Share Share of Workers Wage Ratio

Figure : Decomposition of Income Share by Routine Workers

Data resource: CPS-ORGOren Danieli Decomposing Wage Polarization TAU, 2016 42 / 51

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Empirical Results Closer Look at Timing

Inequality in Routine Occupations by Year

1985 1990 1995 2000 2005 2010

0.15

00.

160

0.17

0Variance of Log Wage in Routine

Var

ianc

e of

Log

W

Figure : V [logw ] for Workers in Routine Jobs

Data resource: CPS-ORGOren Danieli Decomposing Wage Polarization TAU, 2016 43 / 51

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Empirical Results Closer Look at Timing

Summary of Results

Job Polarization trend is almost linearWage Polarization stops around 2000

Wage ratio stabilizesInequality stops decreasing and starts even increasing back

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Theory and Current Working Directions

Main Puzzles

I showed some supporting evidence for why wage polarization seems tobe also related to the drop in demand for routine workers.There are two main questions that are left unanswered:

1 Why do wages drop mostly for the higher paid routine workers?2 Why did wage trends stopped around 2000, while employment trends

continue?

I will now review potential explanations and work in progress on them

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Theory and Current Working Directions Growth

Table of Contents

1 Background

2 Methodology

3 Empirical Results

4 Theory and Current Working DirectionsGrowthAdjustment Costs

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Theory and Current Working Directions Growth

Real Wage Growth in 1990s

Rapid real wage growth in the 1990sStops around year 2000When wages grow in other occupations, relative wages in routine jobsbecome lowerSince 2000, wages in non routine jobs has stagnated as well, so ratiodoesn’t change

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Theory and Current Working Directions Growth

Wage Growth and Inequality

But why should wage drop mostly for higher paid routine workers?Minimum wage?

Minimum wages increased during 1990sMaybe this prevented low wages in routine jobs to drop furtherSimilar timing in Israel

Outside option?High paid workers in routine jobs may have skills that are hard totransfer to other jobsLess skilled workers may have higher elasticity of substitution betweenjobsShould predict that job polarization would be more significant forlow-wage workersNo evidence for that

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Theory and Current Working Directions Adjustment Costs

Table of Contents

1 Background

2 Methodology

3 Empirical Results

4 Theory and Current Working DirectionsGrowthAdjustment Costs

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Theory and Current Working Directions Adjustment Costs

Technological Change Starts from Top?

There are adjustment costs for automation that replaces workersIf this cost is orthogonal to wagesExpect firms to first replace the more expensive workersOnce again, this predicts that job polarization should be moresignificant among low-wage workersNo empirical evidence for that

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Theory and Current Working Directions Adjustment Costs

Summary

New method to quantify the contribution of independent factors tothe decline in middle wages

Skewness decomposition

Direct evidence that the decline in middle wages is related tooccupationsDriven by a decrease in inequality within low-paying routineoccupations

Wages relatively fall for higher paid workers in routine occupationsNot due to a decrease of wages in middle-skill occupationsOccurs only during 1990s

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Minimum Wage Positive Evidence

Table of Contents

5 Minimum WagePositive EvidenceNegative Evidence

6 Compositional Changes

7 More Slides

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Minimum Wage Positive Evidence

Support for Minimum Wage Hypothesis

Timing: during the 90’s there is an increase of the minimum wage(Autor et al., 2015)Should reduce inequality in low paying occupationsWhy is it mostly seen in occupations?

Occupations might be a good predictor of being close to the minimumwage (more than education or industry)

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Minimum Wage Negative Evidence

Table of Contents

5 Minimum WagePositive EvidenceNegative Evidence

6 Compositional Changes

7 More Slides

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Minimum Wage Negative Evidence

Other Predictors of Closeness to Minimum Wage

Within low paying occupations, race and gender should also be goodpredictors of being close to minimum wage.Minimum wage mostly affect female workers (Autor et al., 2015)However, trends in variance are similar for both genders (even strongerfor males)Decomposing by occupations, gender and race

lnwi = occi + occi × genderi + occi × racei + εi

shows all the increase is in

COV(E [lnw |occi ] , ε

2i)

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Minimum Wage Negative Evidence

Decomposition by Occupation Gender and Race

0.00

0.03

0.06

0.09

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Cha

nge

from

199

2

variable

all other terms

COV(DEMO,e^2)

Between − OCC

COV(OCC,e^2)

COV(OCC,DEMO^2)

Figure : Skewness Decomposition by Occupation Gender and Race

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Minimum Wage Negative Evidence

Changes in Variance 1992-2002

2.2 2.4 2.6 2.8 3.0 3.2

−0.

100.

00

Expected Log Wage

Cha

nge

in V

aria

nce female

male

Figure : Change in Variance of Log wages by Expected Log Wage - By Gender

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Minimum Wage Negative Evidence

Correlation With Share Affected by Minimum Wage

Minimum wage should affect workers at the very bottom much moreAt max, less than 9% are being paid the minimum wage or below(Autor et al., 2015)Less than 6% in the 90sI look at the correlation of ∆V (lnw |occi ) between 1992-2002, withshare of workers with wages below the 10th percentile in 1992

(1) (2)

P(w92 < F−1 (0.1) |occi

)-0.104 0.054

(0.014)*** (0.025)**

E [logw |occi ] 0.088

(0.011)***

Table : Correlation With Change in Occupational Variance 1992-2002

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Compositional Changes Motivation

Table of Contents

5 Minimum Wage

6 Compositional ChangesMotivationPSID Data

7 More Slides

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Compositional Changes Motivation

Compositional Changes

If the distribution of s at a certain occupation changes, the variance oflogw will change

lnwi = ln pj + ln fj (s) + εi

Changes in pj are expected to influence V (ln fj (s))

Increase in demand (pj) should attract more workers, and increase thespan of ln fj (s), hence

∂V (ln fj (s))

∂pj> 0

But demand for low-wage occupation only seem to increase at the 90s.

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Compositional Changes Motivation

Compositional Changes

Could also cancel out some other trends

If pj and E [ln fj (s)] move in opposite directionEffect of pj on between occupations skewness would be attenuated

I try to use PSID data to address thisResults seem to suggest that compositional changes have only minoreffect

But sample size is too small to determine

Show More

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Compositional Changes PSID Data

Table of Contents

5 Minimum Wage

6 Compositional ChangesMotivationPSID Data

7 More Slides

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Compositional Changes PSID Data

Decomposition by Occupation - All Data

1992 1994 1996 1998 2000 2002

−0.

10.

10.

2

chan

ge

TotalWithinBetween 3*COV

Figure : Skewness Decomposition by Occupation - PSID Data

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Compositional Changes PSID Data

Variance Trends - PSID

Looking only at people who stayed at their occupation in the 90s

Dependent Variable: All StayersVariance Trend (1) (2)

E [ln (w) |occ] 0.022 0.018(0.005)*** (0.011)*

Table : Correlation of E [ln (w) |occ] on trend in Var [ln (w) |occ]

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Compositional Changes PSID Data

Using Skewness Decomposition

Originally we decomposed by the terms

lnwit = E [lnwit |occ] + ξit

Both terms could be influenced by compositional effects

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Compositional Changes PSID Data

Occupation Premium

E [lnwit |occ] could also be influenced by compositionI want to distinguish between compositional part and occupationpremiumUsing PSID, I estimate a fixed effect model

lnwit = occit + βtXit + ηi + εi

I then decompose into occupation premium, occupation mean skill andresidual

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Compositional Changes PSID Data

Occupation Premium

lnwit = occit︸︷︷︸premium

+ E [βtXit + ηi |occit ]︸ ︷︷ ︸mean skill

+βtXit + ηi + εi − E [βtXit + ηi |occit ]︸ ︷︷ ︸residual

Occupation premium + mean skill are exactly occupation mean logwageResidual is ξit = lnw − E [lnw |occit ]

The within component identical to decomposing just by occupations

The between and covariance component can be further decomposed

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Compositional Changes PSID Data

Between Component

1992 1994 1996 1998 2000 2002

−0.

100.

050.

15

chan

ge fr

om 1

992

Skew − TOTBetween − TOT Occ Premium Occ Mean Skill Prem−M.S. corr

Figure : Change in Variance of Log wages

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Compositional Changes PSID Data

Covariance Component

0.00

0.05

0.10

0.15

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Cha

nge

from

199

2

variable

Occ Premium

Mean Skill

Figure : Change in Variance of Log wages

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Compositional Changes PSID Data

Using Skewness Decomposition

The variance of ξ could change with the compositionI try to address that and distinguish between returns to observableskills (education and experience) and residual

ξit = βocc,tXit + εit

Most (but not all) of the increase in covariance is with ε

COV(E [lnwit |occ] , ε2

)

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Compositional Changes PSID Data

Decomposing Occupation Residual

0.000

0.025

0.050

0.075

0.100

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Cha

nge

from

199

2

variable

all other terms

COV(OCC,b*X)

COV(OCC,e^2)

Figure : Skewness Decomposition with Occupational Mincer Equation

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Relative Change at Different Percentiles

From: Acemoglu and Autor (2011) return

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In Linear Models

More generally - if we are willing to assume some linear model (i.e.Mincer equation)

Y =∑

i

Xi

We can use that to decompose the skewness of Y to a sum ofskewness, and covariances of the linear components

E(Y 3) =

∑i

E(X 3

i)

+ 3∑

i

∑j 6=i

COV(X 2

i ,Xj)

+6∑

i

∑j 6=i

∑k 6=i ,j

E [XiXjXk ]

This will be useful when we want to decompose by more than onecategory return

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Proof

µ3 (Y ) = E[(Y − E [Y ])3

]=

E[E[(Y − E [Y |X ] + E [Y |X ]− E [Y ])3 |X

]]=

= E[E[(Y − E [Y |X ])3 |X

]]+ E

[(E [Y |X ]− E [Y ])3

]+

+3E [E [(Y − E [Y |X ]) (E [Y |X ]− E [Y ]) (Y − E [Y ]) |X ]] =

= E [µ3 (Y |X )] + µ3 (E [Y |X ]) +

+3E [(E [Y |X ]− E [Y ]) E [(Y − E [Y |X ]) (Y − E [Y ]) |X ]] =

= E [µ3 (Y |X )] + µ3 (E [Y |X ]) + 3COV (E [Y |X ] ,V [Y |X ])

return

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[label=Full]Full Distribution

−2 −1 0 1 2

0.0

0.2

0.4

Std Dev From Mean of Log−Wages

Den

sity

1988 2012

Figure : Standardized Log of Hourly Wages

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Skewness Decomposition by Industry

0.000

0.025

0.050

0.075

0.100

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Cha

nge

Component

Within

Between

3Cov

Total Skew

Figure : Skewness Decomposition Changes 1992-2002

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Skewness Decomposition by School × Experience

0.000

0.025

0.050

0.075

0.100

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Cha

nge

Component

Within

Between

3Cov

Total Skew

Figure : Skewness Decomposition Changes 1992-2002

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Occupations With Largest Increase in Variance

Occupation Pr E ∆V

Financial Managers 0.006 3.071 0.054

Computer system analysts 0.006 3.192 0.04

Sales reps 0.013 2.924 0.036

Electricians 0.007 2.952 0.031

Sales workers, other comm. 0.009 2.295 0.03

Managers and administrators n.e.c. 0.047 3.021 0.029

Table : Occupations With Largest Increase in Variance of Log Wages 1992-2002

Data resource: CPS-ORG. Only occupations with at least 0.5% of total working hours. return

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Occupations With Largest Decrease in Variance

Occupation Pr E ∆V

Grinding, buffing machine operators .001 2.58 -.113

Supervisors - food preparation .003 2.33 -.101

Butchers and meat cutters .003 2.48 -.093

Punching and stamp machine operators .001 2.56 -.093

Stock handlers and baggers .008 2.33 -.093

Bus drivers .004 2.60 -.091

Table : Occupations With Largest Decrease in Variance of Log Wages 1992-2002

Data resource: CPS-ORG. Only occupations with at least 0.1% of total working hours. Largest Increase

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Broad Categories

Occupation Pr E ∆V

Managers & Professional .28 2.97 .010

Technicians .30 2.62 -.005

Production .12 2.79 -.013

Service .12 2.38 -.022

Operators/Laborers .17 2.54 -.046

Table : Summary Statistics of Broad Occupational Categories

Data resource: CPS-ORG.

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Change in Inequality Within Occupation

By definition COV (E [Y |X ] ,V [Y |X ]) =∑x

Pr (X = x)︸ ︷︷ ︸Composition

(E [Y |X = x ]− E [Y ])︸ ︷︷ ︸Mean

V (Y |X = x)︸ ︷︷ ︸Inequality

Increase in correlation between occupational wage level and inequalitycan be the result of:

Composition effectChanges in wage levelsChanges in inequality

I will show that this is the result of changes in inequality∆V (Y |X = x)

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Counterfactual Covariance

Fix composition and wage levels to their average throughout the entireperiod.Let only the inequality (variance) change each year.In formula:

C̃OVt =∑x

Pr (X = x) · (E [Y |X = x ]− E [Y ]) · V (Yt |X = x)

We will get thatC̃OVt ≈ COVt

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Counterfactual Covariance

1992 1994 1996 1998 2000 20020.03

00.

045

0.06

0

CO

V

Real COVCounterfactual COV Real COVCounterfactual COV

Figure : Covariance of Expectation and Variance of Log-Wage

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References

Acemoglu, D., Autor, D., 2011. Chapter 12 - Skills, Tasks andTechnologies: Implications for Employment and Earnings. Vol. 4, Part Bof Handbook of Labor Economics. Elsevier, pp. 1043–1171.URL http://www.sciencedirect.com/science/article/pii/S0169721811024105

Autor, D., Manning, A., Smith, C. L., 2015. The Contribution of theMinimum Wage to U.S. Wage Inequality over Three Decades: AReassessment.

Autor, D. H., 2014. Polanyi’s Paradox and the Shape of EmploymentGrowth.

Autor, D. H., Katz, L. F., Kearney, M. S., Sep. 2005. Rising WageInequality: The Role of Composition and Prices. Working Paper 11628,National Bureau of Economic Research.URL http://www.nber.org/papers/w11628

Autor, D. H., Katz, L. F., Kearney, M. S., 2006. The Polarization of the USLabor Market. The American Economic Review 96 (2), 189–194.

Autor, D. H., Katz, L. F., Kearney, M. S., Apr. 2008. Trends in U.S. WageInequality: Revising the Revisionists. Review of Economics and Statistics

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References

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Juhn, C., Murphy, K. M., Pierce, B., 1993. Wage inequality and the rise inreturns to skill. Journal of political Economy, 410–442.

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