Protection and unemployment

Journal of International Economics 69 (2006) 257–271

www.elsevier.com/locate/econbase

Protection and unemployment

Scott Bradford *

Economics Department, Brigham Young University, Provo, UT 84602, United States

Received 24 October 2003; received in revised form 10 September 2004; accepted 28 June 2005

Abstract

Job loss concerns strongly influence the politics of trade, yet the formal political economy of

trade literature has largely ignored unemployment. This paper seeks to extend the literature by

merging an unemployment model with a trade policy model. The theory implies that labor

turnover rates and unionization rates may significantly affect protection for individual industries. I

use US data to test the model and find that protection for an industry declines with its turnover

rate and increases with its unionization rate. The results also imply that protection does not

increase with output and increases with the number of unemployed workers.

D 2005 Elsevier B.V. All rights reserved.

Keywords: International trade; Unemployment; Political economy

JEL classification: D72; F13; J64

1. Introduction

Unemployment and the scarring it causes strongly influence the politics of trade

protection.1 Yet, the formal political economy of trade literature has largely ignored

0022-1996/$ -

doi:10.1016/j.

* Tel.: +1 80

E-mail add1 For instan

top reasons N

being cited ov

wages.)

see front matter D 2005 Elsevier B.V. All rights reserved.

jinteco.2005.06.013

1 422 8358; fax: +1 801 422 0159.

ress: [email protected].

ce, see Baldwin and Magee (2000). They analyzed the Congressional Record and tabulated the

AFTA opponents in Congress gave for their opposition. Jobs and wages dominated all others,

er five times more than any other reason. (It was not possible to get separate data on jobs and

S. Bradford / Journal of International Economics 69 (2006) 257–271258

unemployment.2 This paper seeks to extend the literature by incorporating an

unemployment model with search and recruiting frictions into a political economy of

trade model. The unemployment model is based on Mortensen and Pissarides (1999) and

resembles the model in Davidson et al. (1999).3 The political economy model is adapted

from Bradford (2003b).

The analysis implies that an industry’s labor turnover rate, a variable neglected by the

political economy of trade literature, may significantly influence how much protection that

industry gets. (While no other paper known to the author explores the connection between

labor turnover and protection levels, Magee et al., 2001 does provide an interesting

analysis of labor turnover and campaign contributions.) The modeling also implies that an

industry’s unionization rate plays a key role in protection, since unions can influence how

quasi-rents arising from search are divided between capitalists and workers. Other papers

have examined empirically the relation between unionization and protection but not within

the context of a rigorous model.4

This paper uses US data to test the implications of the theory for the structure of

protection across industries. The empirical results imply that protection for an industry

declines with its turnover rate and increases with its unionization rate. I also find that the

amount of protection an industry receives does not increase with output and does increase

with the number of unemployed workers in that industry.

2. The model

2.1. The economy

I assume that there are n +1 goods and that all consumers have identical preferences

given by u¼ x0 þPn

i¼1 ui xið Þ. Each ui is differentiable and strictly concave, and x0 is a

background numeraire good whose price is fixed at one. The population is normalized to

one, so that total consumer surplus for each good is s( pi)= ui[di( pi)]�pidi( pi), where piis the price and di( pi) is demand.

For production, I use a model similar to the continuous time search model of

Mortensen and Pissarides (1999) (MP). The model in this paper also resembles that of

Davidson et al. (1999) (DMM).5 Each sector has two types of agents: workers and

entrepreneurs, each of whom owns at any given time one unit of labor and capital,

respectively. In each sector, define units of capital so that production requires one unit of

3 See also Davidson et al. (1988, 1991).4 Gaston and Trefler (1995) present a model with endogenous tariffs and union bargaining and conduct an

interesting empirical analysis of the relation between tariffs and wages. They do not consider, however, the

connection between protection levels and unionization rates across industries.5 Except as noted in the discussion, the rest of this section replicates MP and DMM. Section 2.2 contains the

major theoretical innovation of this paper, wherein I merge this search framework with a political economy of

trade model.

2 Two exceptions are Magee et al. (2001) (mentioned in the next paragraph) and Wallerstein (1987), which

incorporates union-induced unemployment into an analysis of the demand for protection but ignores the

government supply of protection and thus does not model the equilibrium choice of protection.

S. Bradford / Journal of International Economics 69 (2006) 257–271 259

each factor. Unemployed workers search for entrepreneurs with available capital. When

such searching agents meet, a match is created if, for each agent, the value of the match

exceeds the value of continuing to search. After agreeing to a match, they negotiate a wage

and produce an amount xi. Production continues until a shock destroys the match,

whereupon each agent begins searching again. I follow MP, DMM, and others and assume

that such shocks arrive according to a Poisson process, at the exogenous rate of bi per unit

time for sector i.

Let ui be the fraction of workers who are searching (unemployed) and vi, the fraction of

entrepreneurs who are searching. Define bmarket tightnessQ, tiu (vi/ui). The lower the

unemployment rate, relative to the searching capital rate, the tighter is the market. Let k(ti)and j(ti) be the arrival rates of matches for searching labor and capital, respectively, where

kVN0 and jVb0. (As MP discuss, ti ¼ k tið Þj tið Þ :)

Since this paper focuses on the politics of protection, a short-run framework is used.

Thus, I follow Diamond (1982) and Blanchard and Diamond (1989) and assume that each

sector has a fixed number of workers and entrepreneurs. (MP also fixes the number of

workers in each sector.) While such a framework does not allow us to address resource

allocation across sectors, it does make it possible to address cleanly the issues at hand. In

particular, having factors attached to particular sectors provides a clear rationale for

industry-based lobbying, which is ubiquitous in reality and plays a key role in the political

model below. Also, unlike many general equilibrium models, there is no need to limit the

analysis to one import-competing sector in order to preserve tractability.6

In each sector, the path of unemployment is given by Ni=(bi(1�ui)�k(ti)ui)LiS, where

Ni is the change in the number of unemployed workers and LiS is the total fixed supply of

labor in the sector. In this expression, bi(1�ui)LiS is the number of workers who lose their

jobs per time period, while k(ti)uiLiS is the number of unemployed workers who get hired

per time period. In equilibrium, Ni =0, which implies that

ui ¼bi

bi þ k tið Þ: ð1Þ

This is the so-called Beveridge relation.

So, for a given break-up rate, market tightness in a sector determines its unemployment

rate. It turns out that market tightness is jointly determined with the wage. I follow MP and

others and assume that the wage results from a generalized Nash bargain between labor

and capital, in which the two sides bargain over how to split the quasi-rents, which arise

from search frictions associated with a match. The value of output from a match is pixi.

Denote the wage with wi.

An asset pricing equation determines the value of a match for each factor. Letting Ji and

Vi be the expected lifetime utility7 of employed and searching capital, respectively, we

have

rJi ¼ pixi � wi � bi Ji � Við Þ; ð2Þ

6 Thus, going to the data will not create the awkward situation of having a model restricted to one import-

competing sector and data from many such sectors.7 As with MP, DMM, and many others, I assume risk neutrality.


where r is the fixed interest rate. In this equation, pixi�wi is the instantaneous utility of a

match to entrepreneurs, while �bi( Ji�Vi) captures the expected capital loss associated

with job destruction. Similarly,

rVi ¼ � hi þ j tið Þ Ji � Við Þ; ð3Þ

where hi is the cost of recruiting and hiring that searching capital must incur. For workers,

let Wi be the value of having a job and Ui be the value of searching. The analogous

expected lifetime utilities are

rWi ¼ wi � bi Wi � Uið Þ ð4Þ

and

rUi ¼ k tið Þ Wi � Uið Þ: ð5Þ

In (5), the value of leisure for workers is normalized to zero.

Surpluses from a match for workers and entrepreneurs, therefore, are Wi�Ui and

Ji�Vi, respectively, with total surplus given by Wi�Ui +Ji�Vi. A generalized Nash

bargain implies that the wage is wi=argmax(Wi�Ui)gi ( Ji�Vi)

1�gi, where gi reflects the

relative bargaining strength of workers and is the fraction of the total surplus that workers

capture:

Wi � Ui ¼ gi Wi þ Ji � Ui � Við Þ: ð6Þ

Substituting for W and J and solving for the wage, we get

wi ¼ rUi þ gi pixi � r Ui þ Við Þð Þ: ð7Þ

While entrepreneurs do not move between sectors, I assume that capital enters and

exits. Thus, as with Blanchard and Diamond (1989), I distinguish between idle capital and

capital that is unmatched but searching. Also, like MP, I assume that entry (idle capital

starts searching) or exit (searching capital quits searching and becomes idle) occur until all

rents associated with vacancies are exhausted, implying Vi =0. Using this condition in (2)

gives

Ji ¼pixi � wi

r þ bi: ð8Þ

Using this and Vi =0 in (3) and solving for the wage gives what MP call the bjob creation

conditionQ, which is analogous to a labor demand curve:

wi ¼ pixi �hi r þ bið Þ

j tið Þ: ð9Þ

The ratio on the right side captures the impact of hiring frictions, which drive down the

wage relative to what it would be with a perfectly competitive labor market. If hiring

costs for entrepreneurs were zero, or if their match arrival rate were infinite, then the

wage would simply equal the revenue product, as with perfectly competitive labor

markets.


Using (3), (5), (6), and Vi=0 to solve for Ui and then substituting into (7), we get a

second equation relating wi and ti, the bwage equationQ, which is analogous to a labor

supply curve:

wi ¼ gi pixi þ hitið Þ: ð10Þ

(The fact that ti ¼ k tið Þj tið Þ was used in this derivation.) As worker bargaining power, hiring

costs, and market tightness all increase, so does the wage.

The wage, wi, is a positive function of ti in (10) and, since jV(ti)b0, a negative functionof ti in (9). Thus, these two conditions jointly determine unique values of wi and ti, as long

as the wage from the job creation condition (9) exceeds the wage from the wage equation

(10) for some range of ti. Fig. 1 illustrates. Plugging the value of ti determined by these

two conditions into (1) gives the unemployment rate in sector i. Note that (1) implies that

market tightness and unemployment are inversely related.Let us examine the relation

between the output price and unemployment, since this will play a key role in the political

model below. Fig. 1 helps us to see that an exogenous increase in the price of the good will

decrease the unemployment rate. Such a price increase will cause both the job creation

condition andwage equation to shift up, but the former will shift up bymore, as long as gib1

(which we assume), since (Bwi/Bpi)=xi in the job creation condition and (Bwi/Bpi)=gixi in

the wage equation. Thus, an increase in the price, as would occur if protection were

increased, will cause market tightness to increase and unemployment to decrease.

More formally, setting the wage equation equal to the job creation condition gives us a

condition that implicitly defines equilibrium market tightness: pixi � hi rþbið Þj tið Þ ¼ gi pixiþð

hitiÞ. Totally differentiating this, we find that:

Bti

Bpi¼ 1� gið Þxi j tið Þ½ �2

gihi j tið Þ½ �2 � hi ri þ bið ÞjV tið Þ: ð11Þ

Since jV(ti)b0 and 0bgi b1, this expression is positive, confirming the graphical intuition.

iw

Wage Equation

)0()( ii

iibrh

xp+ )( iiiiii thxpgw +=

*iw

Job Creation Condition

)()(

i

iiiii t

brhxpw

+=

*it it

iii xpg

COMPARATIVE STATICS:

)(,

)(,

)(,

iiii

iiii

iiii

utwg

utwb

utwp

⇒⇒⇒

κ

κ

Fig. 1. Wage and market tightness equilibrium.


2.2. The polity

For each industry, the government chooses a protection level.8 I do not model which

trade policies are chosen, so choosing protection for each import-competing sector is

equivalent to choosing a domestic price, pi, greater than the fixed world price, denoted by

piFT. I assume that revenues from trade taxes and the rents from other barriers are rebated

lump-sum to consumers.9

As is usual, I assume that consumers do not form lobbies. Factor owners in import-

competing sectors combine to form a single lobby to represent the entire industry. (In this

partial equilibrium framework, there is no cross-industry lobbying.) Since lobbying only

changes the price of one of many goods, I assume that lobbying has a negligibly small

impact on any lobby’s consumer surplus. Thus, welfare for each producer lobby is given

by total revenues arising from production in that sector. With a single, unified lobby for

each industry, wage changes do not play a role in the politics, since wage changes affect

the division of the industry pie without changing its size. Since wages increase with

protection (see Fig. 1), if we were to include them in the politics, this would reinforce this

model’s implication that protection generates political support from workers.

Let total sector output be given by yi =lixi, where li is the number of matches in sector

i. Total revenues, therefore, are given by ri( pi)=piyi. Lobbying consists of making

contributions. Each lobby engages in a bilateral Nash cooperative game with the

government, so that total surplus is maximized, with the division of the surplus

indeterminate.10 Contributions received by the government from the producer lobbies

are Ci( pi)= ri( pi)�Ai, where Ai is the amount of revenues that lobbies retain in the

bargain. In this Nash set-up, the price chosen does not affect the Ai term.11

I follow Baldwin (1987), Peltzman (1976), and a long tradition in the political economy

of trade literature and assume that the government maximizes votes.12 The government’s

objective function is:

V pð Þ ¼Xn

i¼1uFTi � ui pi;dð Þ� �

LSi þ cCi pið Þ þ a pi � pFTi� �

mi pið Þ þ si pið Þ � sFTi� ��

;�

ð12Þ

8 This paper does not analyze why protection is chosen over more efficient tools, taking as given that protection

is ubiquitous. Rodrik (1986) and Mitra (2000) model the choice of protection over subsidies. Also, while

governments can choose from a variety of possible protection policies, to keep things clean, I, as with much of the

political economy of trade literature, only analyze the overall effect of the entire package of policies on a single

unidimensional measure: the output price.9 Bradford (2003b) tests a lump-sum rebating model against one that allows for political competition for import

rents and revenues and does not reject the former, simpler model.10 Each lobby takes prices in other sectors as given. See Helpman (1995) for a discussion of why such a series of

bilateral bargains might be a more reasonable approach than a multilateral menu auction game.11 For clarity, I assume no transactions costs associated with lobbying. Bradford (2003b) explores this and finds

evidence that such costs could be important. They would not, however, change any of the conclusions of this

paper.12 The model could be reformulated to have the government maximize bpowerQ or bwealthQ. See Becker’s

comments on Peltzman (1976).


where V(p) is total votes and p is the vector of prices in all sectors; uiFT is the free

trade unemployment rate; mi( pi) is the quantity of imports; siFT is the free trade level

of consumer surplus; c is the weight that the government places on each contribution

dollar; and a is the corresponding weight on consumer surplus. This is a political

support function:13 the government grants benefits to special interests, but the loss of

support from those who must pay constrains the size of the benefits.

The first term, [uiFT�ui( pi,d )]Li

S, gives the number of votes that protection

generates from workers in that industry: uFTLiS is the number of unemployed

workers that the industry would have with free trade, while ui( pi,d )LiS is the

(smaller) number of unemployed workers with some higher protected price, pi. As

discussed above, the unemployment rate falls with the price. So, raising the price

through protection reduces the number of unemployed workers14 and produces votes. I

assume that all workers hired as a result of protection switch from opposing the

government, because they were unemployed, to supporting the government. (All the

results go through if we assume that some exogenous fraction switch votes. One could

extend this model, though, by explicitly analyzing who switches.) I also assume that

changes in employment status override price changes in determining how workers vote.15

The second term captures contributions induced by protection: the government uses these

funds to bbuyQ votes at a rate of c votes per dollar.16 The last terms in square brackets

capture lost support from consumers who face higher prices, with the number of votes lost

directly proportional to the loss of consumer surplus and tariff revenue which is rebated

lump-sum.

Maximizing V with respect to a representative price, pi, gives:

PPi ¼pi4� pFTi

pi4¼ eu;iuiL

Si þ c� að Þyi

eu;iuiLSi þ aem;imi

; ð13Þ

where eu,i is the absolute value (and thus the negative) of the price elasticity of

unemployment, yi =yipFT

is the value of output at free trade prices, em,i is the absolute

value of the price elasticity of import demand, and mi =mipFT

is the value of imports

at free trade prices.17 An appendix showing the derivation is available upon request.

13 See Hillman (1982) for a pioneering analysis of political support functions within the context of trade policy.14 Note that this is a partial equilibrium result. For the economy as a whole, protection could easily reduce total

employment because of inefficiencies caused by trade barriers.15 Price changes in other industries could affect one’s employment status. I assume, though, that such influences

are either negligibly small or unnoticed by workers.16 See Potters et al. (1997) for a model of how campaign spending buys votes.17 Unemployment, output, imports, and the elasticities all depend on the price, but this is not shown for

notational simplicity. Also, Pi, takes on values in the [0,1) interval. This formulation follows Grossman and

Helpman (1994) and Goldberg and Maggi (1999). It is assumed that there are no import subsidies, so that Pi is

bounded below by zero, because they go against the assumptions that producers do not lobby against each other

and consumers do not lobby at all. Ruling out negative protection appears justified since all the industries in the

sample get positive protection.


3. Discussion of the model

Two elements distinguish this model from most of the literature: treating workers as a

separate source of support, instead of lumping them with consumers as a whole, and

modeling unemployment. To do this while preserving tractability, I have assumed that all

potential lobbies organize and that lobbying has a negligible impact on that lobby’s

consumer surplus.

To help in interpreting Eq. (13), consider how unemployment affects it. The uiLiS

terms capture the independent influence of unemployment and workers on protection.

Without unemployment in the model, these terms would disappear, and the equilibrium

would be PPi ¼ c�að Þyiaem;imi

. This resembles more closely Grossman–Helpman (GH) type

models, in which protection depends on the output–import ratio, the weight that

contributions get relative to consumer surplus (c vs. a), and the elasticity of import

demand. GH normalizes by setting c =1+a, which further reduces equilibrium to

PPi ¼ yiaem;imi

. This is the expression for protection that comes out of their framework with

separate bilateral bargains when all industries lobby and each lobby’s consumer surplus is

ignored.18

In the GH setup, if the government does not give extra weight to campaign contributions,

thus putting full weight on consumer welfare, this implies that a goes to infinity, which

means protection goes to zero. In our model, if the government does not give extra weight to

campaign contributions, then c =a. Referring to Eq. (13), this does not necessarily imply

free trade (Pi=0) if a is finite (as long as free trade imports, m, are positive and the

elasticity of import demand is finite). In this case, if there are some unemployed workers

(uiLiSN0), and the price elasticity of unemployment is positive, the government will

protect because of its abiding concern with unemployed workers. If a does become

infinite, however, implying that national welfare is all that matters, then free trade results,

as with GH.

The model in this paper implies two key ceteris paribus results for import-competing

industries. First, protection increases with the number of unemployed workers searching in

an industry. More of such workers means more potential votes for the government when it

imposes protection. By incorporating unemployment, this model provides theoretical

backing for the widely accepted claim that jobs play an important role in the protection game.

Second, protection increases with the absolute value of the elasticity of unemployment. The

more that unemployment in an industry shrinks with a given price increase, the more votes

that industry will deliver.

While not made explicit in Eq. (13), key parameters of the search model influence

protection levels through the unemployment term, eu,iui. From the search model,

unemployment, and thus its elasticity, are functions of the price and various parameters:

b, g, x, r, and h. In addition to the price, this paper focuses on the breakup rate, bi, and

worker bargaining power, gi. To see more clearly how these variables influence the

18 Referring to Helpman (1995), all industries being organized means that the equation on page 22 of

that article applies to all industries, and abstracting from changes in lobbies’ consumer surplus means that

a j =0.


choice of protection, we can use a bnon-elasticityQ expression for the equilibrium

choice of protection:

pi4 ¼

Bui pi; bi; gi;: : :ð ÞBpi

LSi � c� að Þyi

amiV pið Þþ pFT:

(SinceBui pi;bi;gi;

: : :ð ÞBpi

b0; LSi N0; cNaN0; yiN0 and mV pið Þb0, the ratio on the right-hand side is

positive.) Thus, whether protection increases with the breakup rate or worker bargaining

power depends on whether the derivative of unemployment, not its level, increases with

these two parameters. So, the cross-partials,B2ui pi;bi;gi;

: : :ð ÞBpiBbi

andB2ui pi;bi;gi;

: : :ð ÞBpiBgi

, are key. It

turns out that their signs are ambiguous. An appendix demonstrating this is available upon

request.

What is the economic intuition for these ambiguities? In the case of worker turnover, bi,

higher break-up rates in an industry have two opposing effects. On the one hand, higher

break-up rates mean that jobs are less valuable, reducing workers’ inclination to accept an

offer. On the other hand, higher break-up rates raise the unemployment rate, which

increases workers’ inclination to accept matches. In the case of worker bargaining power,

gi, increases in it raise the value of a match for workers but reduce the value for

entrepreneurs. In the end, for break-up rates and for worker bargaining power, we cannot

tell whether changes in these variables will cause hiring to be more or less responsive to a

given price increase, making the impact on equilibrium protection ambiguous.

4. Empirics

Let us now turn to estimating the model. First, I develop an empirical specification

based on the theoretical model. Then, I briefly describe the data. Finally, I present and

analyze the regression results.

Referring to Eq. (13), output, imports, and unemployment are all endogenous with

respect to the level of protection.19 I follow Goldberg and Maggi (1999) and Trefler (1993)

and instrument for these variables using industry-level factor shares. The presumption is

that factor shares are correlated with imports, output, and unemployment but not with the

dependent variable, price.20

4.1. Econometric model

Since (Bui/Bpi) is a complicated function of the search model parameters, so is the

unemployment elasticity, eu,i. Rather than making an already somewhat complex

estimation unwieldy, I do not include a theoretically derived formula for eu,i in the

19 Both elasticities can be thought of as endogenous. We will assume that the elasticity of import demand is

constant around equilibrium. We discuss how we treat the unemployment elasticity below.20 The factor instruments are physical capital, inventories, cropland, pasture land, forest land, coal, minerals,

petroleum, engineers/scientists, white collar workers, skilled workers, and unskilled workers. The results are

robust to various subsets of these instruments. The data are from Trefler (1993).


empirics.21 Instead, for the purposes of estimation, it is assumed that eu,i is a linear

function of the two model variables for which we have reasonable industry-level data, the

job destruction rate (bi) and worker bargaining power (gi): eu,i =e0+e1bi +e2gi. The other

two industry variables that the theory says should determine eu,i are the value of each

match (xi) and hiring costs (hi).22 Industry-level data do not exist for these, so, to the

extent possible, the theory has determined the choice of variables. Direct measures of the

job destruction rate do exist. There are not such measures for worker bargaining power, but

industry level unionization rates make reasonable proxies. The data are described in the

next section.

Thus, the econometric model can be written as:

PPi ¼e0 þ e1DESi þ e2UNIOið ÞUNEMi þ v� að ÞOUTi

e0 þ e1DESi þ e2UNIOið ÞUNEMi þ a ELASið Þ IMPið Þ þ mi; ð14Þ

where DESi is the job destruction rate in industry i (bi); UNIOi is the unionization rate

( gi); UNEMi is the number of unemployed workers (uiLiS); OUTi is the value of output

(yi); ELASi is the elasticity of import demand (em,i); IMPi is the value of imports (mi); a,v, e0, e1, and e2 are parameters to be estimated or fixed, corresponding to a, c, e0, e1, and

e2, respectively; and mi is an error term with expected value 0.

4.2. The data

I use 1983 US data for 191 SIC 4-digit industries. This choice of country and time

period stems from the fact that the US endowments data needed for instruments are only

available in 1983 (Trefler, 1993). The protection data come from Bradford (2003a), which

provides details on the construction of these data and discusses why they are probably

more trustworthy than other commonly used measures, such as NTB indices and unit value

comparisons. Briefly, detailed price data from a sample of more than 3000 products in six

OECD countries were used to construct tariff equivalent price gaps. This approach is based

on the proposition that barriers to arbitrage across national borders are trade barriers. In

addition to standard trade policy instruments, such barriers could include inefficient

customs procedures, unneeded health and safety standards,23 onerous labeling laws,

burdensome testing and certification requirements, and threats. Only a price gap approach

can capture all such barriers. These measures do not include non-trade reasons for price

gaps because distribution margins and transport costs were carefully stripped out of the

data.24 These data are not available for 1983, so the closest available year was used: 1985.

22 The fifth and final variable that determines eu,i is the interest rate, r, which does not vary by industry and thus

would only affect the constant term in the regression.23 Such barriers plague the agro-food sectors. See Josling et al. (2004).24 Incomplete pass-through of exchange rate changes does not affect the results because it is a symptom of

barriers, not a cause. Also, export subsidies do not affect the results because the method only compares domestic

producer prices to import prices.

21 Doing so would require specifying a particular matching function, and all reasonable matching functions

known to the author lead to complex expressions for the elasticity of unemployment. An appendix showing one of

the simpler cases is available upon request.


The employment data also come from Trefler and are 1983 US data. These data were

adjusted to account for intra-industry trade. Since some output from almost all industries

gets exported, the number of workers was multiplied by the ratio of non-exported

production to total production, to arrive at an estimate of the number of import-competing

workers for that sector.

The imports and exports data are from the Feenstra data set, and the output data are

from the Bartelsman, Becker, and Gray data set, both of which are on the NBER web site.

All of these data are from 1983. As with employment, output was adjusted downward so

that it only reflects import-competing production. This was done by simply subtracting

exports from output. These NBER data sets give the value of imports and output at current

(protected) prices. These values were converted to values at world prices by dividing the

current value by the ad valorem protection rate.

The job destruction rates are from Davis et al. (1996). Industry level unionization rates

are also from Trefler. Both of these come from 1983, as well.

Like Goldberg and Maggi (1999) and Gawande and Bandyopadhyay (2000), I take the

import demand elasticity data from Shiells et al. (1986). These estimates are probably the

best available at the level of disaggregation used in this empirical analysis. For a few

industries, the elasticity estimates were positive and were dropped from the sample. Since

the elasticity data are estimated, I used the errors-in-variables correction presented in

Gawande (1997) to bpurgeQ the elasticities data. Summary statistics for all variables are

shown in Table 1.

4.3. Results

The estimating equation is homogeneous of degree zero in all of the parameters, which

necessitates pegging one of them. I follow Bradford (2003b) and peg a. That article shows

Table 1

Summary statistics (191 US Industries, 1983)

Mean Median Min Max S.D.

Regression variables

Protection: P .188 .138 .000999 .627 .150

Job destruction rates (% loss): DES 15.4 13.6 1.29 50.3 8.06

Unionization rate (%): UNIO 33.3 30.8 6.30 75.4 12.6

Unemployed workers (thousands): UNEM 6.33 2.79 0.00 145 12.9

Production ($ million, valued at world prices): OUT 4360 1920 42.1 165,000 12,800

Imports ($ million, valued at world prices): IMP 443 144 .0129 16,200 1410

Elasticity of import demand (corrected): em,p or ELAS 1.62 1.33 .221 3.78 .876

Underlying data

Tariff equivalent: ( p/p*) 1.28 1.16 1.001 2.68 .295

Raw employment (thousands) 57.4 26.0 2.20 999 106

Raw production ($ million, valued at domestic prices) 5640 2690 73.1 183,000 14,600

Raw imports ($ million, valued at domestic prices) 509 187 .0167 17,500 1510

Exports ($ million) 424 124 0 10,400 1150

Uncorrected elasticities 2.00 1.07 .0420 23.9 2.65

Table 2

Nonlinear two-stage least squares estimation of the model

Parameter Estimate (t-score)

e0 5.50a (2.40)

e1: Break-up rate �0.483a (�2.42)e2: Unionization 0.231a (2.42)

v: Industry output 0.000999 (�0.980)bPseudo sum of squared residuals 1.89

Variance of the residuals 0.0725

Dependent variable: P=(( p*�pw)/p*).

Number of observations: 191.a Significant at the 5% level.b t-score refers to whether v ba =0.001. If so, then protection is decreasing in output.


that a reasonable value for a is .001, which implies that every $1000 reduction in

consumer surplus results in the loss of one vote.25

Table 2 shows the results of estimating the model using nonlinear two-stage least

squares (see Amemiya, 1983). The standard errors are robust White. The coefficient on

e1 is negative at the 5% level, indicating that industries with higher break-up rates

receive less protection from the political process. It appears then that higher break-up

rates make the labor market less responsive to price increases, reducing the incentive of

the government to protect. Recalling the discussion above, this means that the reduced

value of a job to workers outweighs the effect of higher unemployment making workers

more willing to accept job offers. To the author’s knowledge, this result connecting

protection to worker turnover is novel. The results also imply that protection for an

industry increases with that industry’s unionization rate, since this coefficient is also

significant at the 5% level. Thus, stronger worker bargaining power as reflected in

unionization rates seems to increase the responsiveness of hiring to price increases. It

appears that the increased eagerness of workers to accept job offers caused by

strengthened worker bargaining power outweighs the reduced incentive for entrepreneurs

to accept matches.

Perhaps wages play a key role in the opposite signs on the coefficients for break-

up rates and unionization rates. Fig. 1 shows that the break-up rate is negatively

related to the wage, while the unionization rate is positively related to the wage.

Higher break-up rates increase unemployment by reducing the demand for labor;

higher unionization rates increase unemployment by increasing the share of quasi-rents

that workers collect, which drives up the wage. The political component of the model

assumes that employment status overrides wages in determining whether workers

support the government. This seems reasonable, but unionized workers might care

more about wages than employment status. More explicit modeling of unions’ role in

the structure of protection across industries would probably provide further insights.

25 None of the conclusions depends on the value at which a is pegged. The homogeneity of the parameters

means that changing a scales the point estimates and the standard errors by the same percentage and thus does not

affect the t-scores.


Are these connections economically significant? If one evaluates each variable at

its mean, increasing unionization by 10 percentage points would increase protection

by about two percentage points. Thus, the actual impact of unionization, while not

trivial, does not appear to be large. The results also imply that a 10 percentage

point increase in the break-up rate would decrease protection by about four

percentage points. Thus, the economic impact of break-up rates on protection levels

is not trivial.

The regression results also confirm the model’s prediction that protection increases

with the number of unemployed workers in an industry. Recall that uiLiS gives the

number of unemployed. In the regression, this term is multiplied by e0+ e1DESi + e2UNIOi, so that uiLi

S is interacted with DESi and UNIOi. While the estimates of e0 and e2are significantly positive, the point estimate for e1 is significantly negative. Thus,

assessing the impact of number of unemployed workers on protection is not

straightforward, since it is possible for e0+ e1DESi + e2UNIOi to take on significantly

positive or negative values. Nevertheless, using all nine combinations of the three quartile

cut-off points for DESi and UNIOi, we find that e0+ e1DESi + e2UNIOi is significantly

positive at the 1% level.

The Grossman–Helpman framework and models that adhere closely to it imply that

protection increases with output, and Goldberg and Maggi (1999) and Gawande and

Bandyopadhyay (2000) provide empirical evidence in favor of this hypothesis. The results

in this paper, however, do not imply that protection increases with industry output.

Referring to the regression Eq. (14), output has a positive influence on protection if v is

significantly larger than a. Since a has been set at 0.001, an estimated value of v that

exceeds 0.001 indicates a positive relation between output and protection. The point

estimate is, in fact, less than 0.001 (though not significantly so). One possible reason for

the different result in this paper is that including unemployment in the model corrects an

omitted variables bias. It turns out that estimating our model without the unemployment

terms generates a positive but insignificant coefficient on the output variable. (The p-value

is about 0.25.) Thus, omitted variables bias provides only a partial explanation. The new

protection measures used in this paper do not drive the different result because using the

standard coverage ratios does not give a significantly positive coefficient on output either.

One strategy used in Goldberg and Maggi (1999) and Gawande and Bandyopadhyay

(2000) but not in this paper and which may be driving the significant positive coefficient

on output is their assumption that some industries do not lobby for protection even though

all industries in their sample get protection. Exploring whether that empirical finding

disappears if one assumes that all protected industries do in fact lobby may be interesting

but is beyond this paper’s scope.

I checked the robustness of the results in Table 2 in a few ways. As mentioned

above, I experimented with different subsets of instruments, and this had no effect.

Since the break-up data may have random errors from year to year, I also explored

whether the results were sensitive to using the break-up data from the single year,

1983. I used a 3-year average of the break-up rates (1982–1984) and a 5-year average

(1981–1985). The 3-year average produced equivalent results: the same sign and

significance for each coefficient. Using the 5-year average did not change the sign on

any of the coefficients, but the standard errors on the break-up rate and unionization


rate (and the constant term) were large enough to render the coefficients insignificant.

Since this is a short-run political model, using shorter run averages matches the theory

better than longer run averages, even though the latter may have less noise. Thus, the

strong confirmation from the 3-year results appears to outweigh the uncertainty created

by the 5-year results. I also ran the regression using uncorrected elasticities. Break-up

rates in this case were significantly negative at the 10% level, while the unionization

coefficient was positive but insignificant. The elasticity correction appears to sharpen

the results without driving them.

5. Conclusion

This paper has developed a protection model that explicitly accounts for search

friction unemployment. This has enabled us to analyze formally the key role that

concerns over unemployment play in the political economy of protection. The modeling

and empirics imply that the job break-up rate in an industry has a significant negative

effect on protection. I know of no other results in the literature that connect break-up

rates and protection. The analysis also tests, for the first time to the author’s

knowledge, the impact of industry-level unionization rates on protection within the

context of a rigorous model. The results imply that higher unionization rates lead to

more protection.

This paper takes an early step toward formally accounting for the role of unemployment

in the politics of protection. More work remains and should prove fruitful. For instance,

adopting a general equilibrium framework would allow one to account for factor flows

across industries. Also, taking account of wage concerns and more careful modeling of

unions and other labor groups would probably produce interesting results. In addition,

using more recent data would certainly be welcome. I hope that this paper helps with any

such efforts.

Acknowledgements

I thank Ben Ferrett, John Matusz, Doug Nelson, Scott Schuh, and other participants in

the June 2003 bTrade and Labour Perspectives on Worker TurnoverQ conference,

sponsored by the Leverhulme Centre for Research on Globalization and Economic

Policy, University of Nottingham. Special thanks go to Carl Davidson, Jonathan Eaton,

Chris Magee, and an anonymous referee. I also thank participants in the Brigham Young

University Raw Research (R2) Seminar and the 2003 International Economics and Finance

Society Workshop, held at Central Michigan University. I take responsibility for all errors.

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Protection and unemployment

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