trade liberalization, unemployment, and inequality with endogenous job destruction

Trade liberalization, unemployment, and inequality with endogenousjob destruction

Priya Ranjan⁎University of California, Irvine, 3151 SSPA, Irvine, CA 92697, United States

a r t i c l e i n f o a b s t r a c t

Available online 8 October 2011 In a two sector extension of the Mortensen–Pissarides model of endogenous job destruction, itis shown that trade liberalization increases both job creation and job destruction in the importcompeting sector and reduces them in the export sector. Since trade liberalization increasesunemployment in the import competing sector and reduces it in the export sector, the impacton economy wide unemployment is ambiguous. While job destruction increases upon impactin the import competing sector, there is no immediate decrease in job destruction in the exportsector leading to short term spikes in the net job destruction and unemployment rates in re-sponse to trade liberalization. Trade liberalization increases intersectoral wage inequality,however, intra-sectoral wage inequality increases in the export sector but decreases in the im-port competing sector. Finally, a more generous unemployment benefit increases the respon-siveness of job destruction to trade liberalization.

© 2011 Elsevier Inc. All rights reserved.

JEL classification:F16

Keywords:Trade liberalizationJob destructionUnemploymentWage inequality

1. Introduction

The main worry of people concerned with the adverse effect of trade liberalization on jobs is that it leads to job destruction.However, much theoretical work in the literature on trade and unemployment uses models where job destruction is exogenous.In these models trade liberalization changes the incentives for job creation leaving the incentive for job destruction unaffected.Therefore, the rate of job destruction is unchanged. This is contrary to not only popular perception, but empirical work on jobflows as well. This paper aims to fill this gap in the literature by analyzing the impact of trade liberalization on unemploymentand job flows in a model where job destruction is endogenous a la Mortensen and Pissarides (1994).

It constructs a two sector general equilibrium model with search generated unemployment and endogenous job destruction.All new jobs are created at maximum productivity but the job specific productivity is subject to an idiosyncratic shock which canlower job productivity. If the productivity falls below a cutoff then the job is destroyed. Trade liberalization reduces the relativeprice of the import competing good and increases the relative price of the export good. This leads to a decrease in the value of ajob in the import competing sector and an increase in the value of a job in the export sector. This in turn increases the cutoff levelof productivity below which jobs are destroyed in the import competing sector and decreases the cutoff in the export sector. Theresult is an increase in the rate of job destruction in the import competing sector and a decrease in the rate of job destruction inthe export sector. Since the rates of job creation and destruction are equalized in steady state, the rate of job creation increases inthe import competing sector and decreases in the export sector. Even though the steady state results are symmetrically oppositein the two sectors, the impact effects are asymmetric. A lot of jobs in the import competing sector become unviable and aredestroyed immediately. The opposite happens in the export sector. That is, a lot of lower productivity jobs which were not viableto begin with survive now. However, since these lower productivity jobs were not viable earlier, they do not exist at the time of

International Review of Economics and Finance 23 (2012) 16–29

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trade liberalization. These jobs appear and survive in the export sector only in the medium run. This asymmetry can lead to shortterm spikes in job destruction and unemployment in response to trade liberalization.

Next, the paper looks at the impact of trade liberalization on wage inequality. Since wages are determined through Nash bar-gaining and there is renegotiation of wages following changes in job productivity, the model exhibits intra and intersectoral wageinequality. It is shown that the intersectoral wage inequality increases upon trade liberalization. As far as intra-sectoral wage in-equality is concerned, it increases in the export sector and decreases in the import competing sector.1 The paper also studies howgenerous unemployment benefits affect job flows and unemployment in the open economy. It finds that generous unemploymentbenefits increase the responsiveness of the rate of job destruction and unemployment to trade liberalization. The results of themodel are consistent with the empirical work described below.

In a recent paper studying the relationship between job flows and trade costs, Groizard, Ranjan, and Rodríguez-López (2011)find that a reduction in the industry trade cost significantly reduces job creation and significantly increases job destruction. More-over, the effect on job destruction is larger than the effect on job creation. Dutt, Mitra, and Ranjan (2009), using cross-countrydata on trade policy and unemployment, find that unemployment and trade openness are negatively related. Using panel data,they find an unemployment-increasing short-run impact of trade liberalization, followed by an unemployment-reducing effectleading to the new steady state. Even though this paper does not look at job creation and job destruction separately, the resulton the differential responses of trade liberalization in the short and long runs can be explained using our endogenous job destruc-tion framework. Our results are also consistent with the results in Hasan et al. (2012), which, using state level variation in theexposure to trade liberalization across Indian states, finds some weak evidence that the immediate short-run effect of a tariff re-duction is to increase unemployment prior to reduction to a lower steady-state unemployment rate.

While ourmodel studies the effect of trade liberalization on job flows, one could use the two sector set up to study the impact of realexchange rate changes on job flows in the traded and non-traded sectors. Since exchange rate appreciations increase the relative price ofnon-traded goods, the impact on the traded sector would be similar to the impact on the import competing sector in our framework.Sincemanufacturing produces traded goods, onewould expect the impact of exchange rate appreciation onmanufacturing to be similarto that on the import competing sector in our theoretical framework. Klein, Schuh, and Triest (2003) study the impact of real exchangerate changes on job flows in the U.S. manufacturing industries from 1974 to 1993. Their key finding is that movements in trend real ex-change rates significantly affect both job creation and destruction in the same direction and by similar magnitudes, thus they have largeallocation effects but no effect on net employment growth. In contrast, an appreciation of the cyclical component of real exchange ratesincreases job destruction but has little effect on job creation, thus it reduces net employment growth but has no other allocation effects.Also related is a recent paper byMoser, Urban, and diMauro (2010)which studies the impact of real exchange rate changes on job flowsusing a sample of establishment-level data from Germany. They find evidence of net job losses in response to a real exchange rate ap-preciation. Their most interesting finding is that the bulk of adjustment in response to a real exchange rate appreciation occurs throughless job creation than increased job destruction. They attribute this to rigid labor regulations that make job destruction costly for firms.

The paper is also related to the burgeoning theoretical literature on search generated unemployment in open economies. In aseries of papers spanning over two decades Carl Davidson and Steven Matusz have studied the implications of introducing unem-ployment arising from labor market frictions in trade models. The main focus of their work, as discussed in Davidson and Matusz(2004), has been the role of efficiency in job search, the rate of job destruction and the rate of job turnover in the determination ofcomparative advantage. Among more recent works, Moore and Ranjan (2005) show how trade liberalization in a skill-abundantcountry can reduce the unemployment of skilled workers and increase the unemployment of unskilled workers. Skill-biased tech-nological change on the other hand, can reduce the unemployment of unskilled workers. Helpman and Itskhoki (2010) use an im-perfectly competitive set upwith heterogeneous firms to look at how gains from trade and comparative advantage depend on labormarket rigidities, and how labor-market policies in a country affect its trading partner. Felbermayr, Prat, and Schmerer (2011) in-corporate search unemployment in a one sector model with firm heterogeneity to study the implications of a bilateral reduction intrade cost on unemployment. Mitra and Ranjan (2010) study the impact of offshoring in a two sector model where some jobs inone of the two sectors can be offshored while all the jobs in the other sector must remain onshore. In all these papers the rate ofjob destruction is exogenous, however. Therefore, trade liberalization affects unemployment through changes in job creation only.

The plan of the rest of the paper is as follows. The next section describes the two sector search model with endogenous jobdestruction. Section 3 studies the implications of trade liberalization and also studies how unemployment benefits affect theresponsiveness of job flows and unemployment to trade liberalization. Section 4 concludes.

2. The model

2.1. Product market

There is a single non-tradable final good Z which is produced using two potentially tradable inputs X and Y. The productionfunction for Z is given below.

Z ¼ AX1−αYα

αα 1−αð Þ1−α ð1Þ

1 See Ethier (2005) which constructs a rich 2 country model to study the impact of offshoring on wage inequality in both the source and the host country.

17P. Ranjan / International Review of Economics and Finance 23 (2012) 16–29

Given the prices px, and py, of inputs, the unit cost for producing Z is given as follows.

c px;py� �

¼ 1A

pxð Þ1−α py� �α ð2Þ

The market for good Z as well as the inputs X and Y is perfectly competitive. Since Z is chosen as the numeraire, pz=1, andtherefore, c(px, py)=1, or

1A

pxð Þ1−α py� �α ¼ 1 ð3Þ

The relative demand for the two inputs can be written as a function of the relative price as follows.

Xd

Yd¼ 1−αð Þpy

αpxð4Þ

2.2. Labor market

Our description of labor market adapts the endogenous job destruction model of Mortensen and Pissarides (1994) to a twosector setting. To produce either X or Y, a firm needs to open job vacancies and hire workers. Let Li be the total number of workerswho look for a job in sector i. We are implicitly assuming that workers are not mobile across sectors. This may be a good descrip-tion of the labor market in the presence of high mobility cost.2 Allowing the workers to move costlessly across sectors will convertit into a Ricardian model because then effectively there will be a single factor of production. In this case, trade liberalization willwipe out the sector with comparative disadvantage. Since we want to capture the impact of trade liberalization on job creationand job destruction in the import competing sector, we make the assumption of no worker mobility. Also, we think that in theshort to medium run, workers face high mobility costs which is the appropriate time frame for this kind of model and therefore,there is no loss of generality in assuming no worker mobility across sectors. In the long run, workers are likely to be mobile acrosssectors, therefore, the model and the results in the paper should be considered to be valid in a “medium run” scenario. Alterna-tively, the workers in the two sectors can be thought of as different types of labor such as skilled labor and unskilled labor.

Define θi ¼viui

as the measure of market tightness in sector i, where viLi is the total number of vacancies in sector i and uiLi is the

number of unemployedworkers searching for jobs in sector i. The probability of a vacancy filled isq θið Þ ¼ m vi;uið Þvi

wherem(vi, ui) is

a constant returns to scale matching function. Since m(vi, ui) is constant returns to scale, q′(θi)b0. The probability of an unem-

ployed worker finding a job ism vi;uið Þ

ui¼ θiq θið Þ which is increasing in θi.The productivity of a job is denoted by t with support

[0, 1] and a distribution function denoted by G(t).All jobs are created at the full productivity of 1.That is, a new job in either sectorproduces one unit of output. A job in sector-i is hit with an idiosyncratic shock that leads to a change in the job productivity. λi is thePoisson arrival rate of the shock. If the job productivity falls below a reservation productivity Ri (to be determined endogenously)the job is destroyed immediately.

Denote the asset values of an occupied job in sector-i with productivity t for a firm and for a worker by Ji(t) and Wi(t), respec-tively. Denote the wage for a job in sector i with productivity t by wi(t). Denoting the rate of discount by r, the expression for Ji(t)is given by

rJi tð Þ ¼ pit−wi tð Þ þ λi∫1RiJi sð ÞdG sð Þ−λiJi tð Þ ð5Þ

Denoting the asset value of an unemployed worker in sector-i by Ui, the expression for Wi(t) is given by

rWi tð Þ ¼ wi tð Þ þ λi∫1RiWi sð ÞdG sð Þ þ λiG Rið ÞUi−λiWi tð Þ ð6Þ

Denoting the unemployment benefit including the value of leisure by b, the asset value of an unemployed worker in sector-iis

rUi ¼ bþ θiq θið Þ Wi 1ð Þ−Ui½ � ð7Þ

Note that since all jobs are created at the full productivity of 1, Wi(1) is the value of a new job for a worker.

2 See Mitra and Ranjan (2010) for a search and offshoring model with varying degrees of mobility costs.

18 P. Ranjan / International Review of Economics and Finance 23 (2012) 16–29

Thewage rate,wi(t), is such that the surplus from the job is divided according to the bargaining shares. Assume that the bargainingweight ofworkers isβ. Denote the asset value of a vacant job in sector-i by Vi. Now, the total surplus froma job is Ji(t)−Vi+Wi(t)−Ui.Generalized Nash bargaining implies that the worker gets a fraction β of the surplus.

Wi tð Þ−Ui ¼ β Ji tð Þ þWi tð Þ−Vi−Ui½ � ð8Þ

Denote the cost of posting a vacancy in sector-i in terms of good-i by ci. In a two sector model it is not obvious whether the costof posting a vacancy should be in terms of the sectoral output or the numeraire good. In fact, one can make an argument thatmodeling the recruitment cost in terms of the numeraire is more realistic. For example, if you want to post job vacancies tohire workers for a textile mill, you are more likely to pay the vacancy costs (recruitment or hiring cost) such as cost of job adver-tisement, paying a recruiter/head-hunter in terms of the final good rather than in terms of the textiles that your mill will produce.In the present model it turns out that modeling the recruitment cost in terms of the sectoral output makes the model slightlymore tractable. Therefore, we decide to make this assumption in the paper. In an optional appendix available upon request it isshown that the qualitative results are unchanged when the recruitment cost is in terms of the numeraire.

Since all jobs are created at the maximum productivity ti=1, the expected profit from a vacancy in sector-i is

rVi ¼ −pici þ q θið Þ Ji 1ð Þ−Vi½ � ð9Þ

Assuming no entry barrier in the posting of vacancy implies all rent from vacancies is dissipated: Vi=0. Therefore, the aboveimplies that the value of a new job satisfies

Ji 1ð Þ ¼ piciq θið Þ ð10Þ

The expression for wage can be derived as follows. Use Eqs. (8) and (10) to re-write Eq. (7) above as

rUi ¼ bþ β1−β

piciθi ð11Þ

To derive an expression for wage, multiply Eq. (6) by (1−β) and Eq. (5) by β and subtract the latter from the former and useEqs. (8) and (11) to get

wi tð Þ ¼ 1−βð Þbþ βpi t þ ciθið Þ ð12Þ

That is, the wage is increasing in the productivity of a job in addition to being increasing in the market tightness parameter, θi,and the unemployment benefit, b. The latter two improve the bargaining position of the worker and hence his wage. A change inthe productivity, on the other hand, affects the rent available from the job and hence the wage. Therefore, the model exhibits het-erogeneity in wages among identical workers. It is worth contrasting this result with those obtained in models with heteroge-neous firms (e.g. Felbermayr et al. (2011)) where identical wage is paid by heterogeneous firms. In those models, firms hiremany workers and the value of the marginal worker for the firm is equal to the expected recruitment cost for the worker.Since the recruitment cost is identical for all firms, the value of a marginal worker is equalized among heterogeneous firms. Animplication of Nash bargaining over wages is that the surplus of worker is a scalar multiple of the surplus of firms from the mar-ginal worker. Therefore, the equality of the surplus from the marginal worker across firms implies the equality of wages as well. Inour set up with single worker firms, all firms within a sector pay identical wages to a worker when the worker is hired. This isbecause the value of a new job is equated to the expected recruitment cost as can be seen clearly from Eq. (10). However, forexisting workers Eq. (10) does not apply and the wages are renegotiated to reflect the current productivity which determinesthe rent to be shared between the worker and the firm.

Next, we derive job creation and job destruction equations so that we can solve for Ri and θi as functions of pi. Note that inorder for a job to be destroyed, the firm's surplus from the job must be zero. Since the firm's share of the surplus is a fraction(1−β), the overall surplus must be zero as well. That is, Ji(Ri)=(1−β)(Ji(R)+Wi(Ri)−Ui)=0. Therefore, Wi(Ri)−Ui=0 aswell or Wi(Ri)=Ui. For t>Ri, Wi(t)>Ui, and hence the worker is better off staying employed, while for tbRi, Wi(t)bUi, andhence the worker would want to quit as well.

To derive the job creation curve, substitute the expression for wage given in (12) into (5) to get

r þ λð ÞJi tð Þ ¼ 1−βð Þ pit−bð Þ−βpiciθi þ λi∫1RiJi sð ÞdG sð Þ ð13Þ

Since Ji(Ri)=0, the above implies

λi∫1RiJi sð ÞdG sð Þ ¼ βpiciθi− 1−βð Þ piRi−bð Þ ð14Þ


Therefore, Eq. (13) can be written as

r þ λið ÞJi tð Þ ¼ 1−βð Þpi t−Rið Þ ð15Þ

Next, note that the job creation condition Eq. (10) can be written using Eq. (15) as

1−βð Þ 1−Rið Þr þ λið Þ ¼ ci

q θið Þ ð16Þ

The left hand side of the above expression is the gain from a new job, while the right hand side is the expected recruitmentcost. An increase in θi implies higher recruitment cost and hence requires a lower Ri for the job creation to be viable. That is,the jobs should last longer. Alternatively, a higher Ri implies a greater probability of job destruction λiG(Ri), and therefore, recruit-ment costs should be low as well which requires a lower θi.Therefore, in (θ, R) space, the curve representing Eq. (16) is downwardsloping.

To get a simple expression for the job destruction condition, substitute Eq. (15) into (13) to get

r þ λið ÞJi tð Þ ¼ 1−βð Þ pit−bð Þ−βpiciθi þλi 1−βð Þpi

r þ λi∫1Ri

s−Rið ÞdG sð Þ ð17Þ

Now, the job destruction condition Ji(Ri)=0 can be written as

Ri−bpi− β

1−βciθi þ

λi

r þ λi∫1Ri

s−Rið ÞdG sð Þ ¼ 0 ð18Þ

It can be verified that the l.h.s of Eq. (18) is increasing in Ri and decreasing in θi. Intuitively, a higher θi implies stronger bar-gaining position of workers, and therefore, reservation productivity must be higher for firms to break even or marginal jobs aredestroyed. Therefore, the curve above is upward sloping in (θ, R) space.

The two Eqs. (16) and (18) determine the two key endogenous variables of interest: θi and Ri.The unemployment rate in sector-i evolves according to

ui ¼ λiG Rið Þ 1−uið Þ−θiq θið Þui ð19Þ

The above implies that in steady-state (ui ¼ 0Þ ui is given by

ui ¼λiG Rið Þ

λiG Rið Þ þ θiq θið Þ ð20Þ

2.3. Measures of inequality

We define our measure of intra-sectoral inequality as the ratio of the top wage to the bottomwage:wi 1ð Þwi Rið Þ. If the workers in the

two sectors are different, then this can be viewed as a measure of within group inequality. Using the wage Eq. (12) this measurecan be written as

ωi≡wi 1ð Þwi Rið Þ ¼

1−βð Þbþ βpi 1þ ciθið Þ1−βð Þbþ βpi Ri þ ciθið Þ ð21Þ

We can also construct a measure of intersectoral wage inequality by computing the ratio of the average wages in the two sec-tors as follows. Define �wi to be the average wage in sector-i where �wi is the total wage bill in sector-i, denoted by WBi, divided bythe number of employed: (1−ui)Li. The equation for the evolution of the total wage bill is as follows.

WBi ¼ θiq θið ÞuiLiwi 1ð Þ þ λi 1−uið ÞLi∫1Riw sð ÞdG sð Þ−λiWBi ð22Þ

The first term above is the wage bill from the new jobs created at full productivity. The second term is the wage bill from theexisting jobs which are hit by a shock and survive and the last term is the loss in wage bill due to the change in the productivity ofjobs resulting from the idiosyncratic shock. Therefore, the wage bill in steady state (WBi ¼ 0Þ is given by

WBi ¼θiq θið ÞuiLiwi 1ð Þ

λiþ 1−uið ÞLi∫1

Riw sð ÞdG sð Þ ð23Þ


And, the average wage is given by

�wi ¼θiq θið Þuiwi 1ð Þ

1−uið Þλiþ ∫1

Riw sð ÞdG sð Þ ð24Þ

Upon using the expression for ui from Eq. (20) the above becomes

�wi ¼ G Rið Þwi 1ð Þ þ ∫1Riw sð ÞdG sð Þ ð25Þ

Our measure of intersectoral wage inequality is going to be �wx�wy:

2.4. Impact of a sectoral price change on unemployment and inequality

Let us first work out the implications of an increase in pi on Ri and θi.It is easy to verify from Eqs. (16) and (18) that while thejob creation curve remains unchanged, the job destruction curve shifts to the right because marginal jobs become viable now asfirms have to pay less to workers due to a decrease in the outside opportunity of workers (bpi decreases). Therefore, an increase inpi leads to an increase in θi and a decrease in Ri.

Since an increase in pi leads to an increase in θi and a decrease in Ri, it can be verified from Eq. (20) that it must lead to a de-crease in ui as well.

An increase in the sectoral price pi affects wage inequality through three channels. First, there is a direct effect working to in-crease inequality because the value of a job at full productivity increases more than the value at the cutoff productivity Ri, whilethe unemployment benefit is the same for all workers and does not depend on job productivity. Second, a decrease in the cutoffproductivity Ri increases inequality. Finally, an increase in θi tends to reduce inequality because the bargaining positions of allworkers increases by the same magnitude. Therefore, the impact of an increase in pi on ωi is theoretically ambiguous.

To resolve the ambiguity, we assume a Cobb-Douglas matching function of the form below.

Assumption1 : M viLi;uiLið Þ ¼ mi viLið Þγ uiLið Þ1−γ

It is shown in Appendix A that under Assumption 1 a sufficient condition fordωi

dpi> 0 isβpi

γciθi1−γ

−1� �

b 1−βð Þb. This conditionis easily satisfied for reasonable parameter values used in the search literature. As mentioned in the numerical example later, areasonable value of γ in the literature is 0.5. For this value of γ the inequality in the sufficiency condition is satisfied irrespectiveof the values of b, β, and pi as long as ciθib1 which is very reasonable given the estimates of ci and θi in the literature. Therefore, itis reasonable to expect ωi to be increasing in pi.

2.5. General equilibrium

The model can be solved as follows. Start with a relative price pxpy. Obtain px and py in terms of the numeraire final good from

Eq. (3). Now, obtain the corresponding Ri and θi from Eqs. (16) and (18). Then, obtain the unemployment rate ui from Eq. (20).Next, the total output of good-i can be computed as follows. Denote the total amount of labor available for employment ingood-i by Li. The amount of labor employed in sector-i is (1−ui)Li. Denote the output per unit of labor force in the two sectorsby x and y, respectively. That is: x=X/Lx ;y=Y/Ly. The equation for the evolution of the sectoral output per unit of labor forceis given below.

i ¼ θiq θið Þui þ λi 1−uið Þ∫1RisdG sð Þ−λii; i ¼ x; y ð26Þ

The first term above is the output resulting from new matches which are created at full efficiency. The second term is the out-put of the existing jobs that are hit by a shock and survive. The last term is the output that is lost due to the arrival of the idio-syncratic shock. In steady state i=0, therefore,

i ¼ θiq θið Þλi

ui þ 1−uið Þ∫1RisdG sð Þ; i ¼ x; y ð27Þ

Next, note from Eq. (19) that in steady-state θiq(θi)ui must equal λiG(Ri)(1−ui). Therefore, Eq. (27) can be written as

i ¼ 1−uið Þ G Rið Þ þ ∫1RisdG sð Þ

h i; i ¼ x; y ð28Þ


Thus, we can write the relative output of good-X at relative pricepxpy

as

XY

� �s

¼1−uxð Þ G Rxð Þ þ ∫1

RxsdG sð Þ

� �h iLx

1−uy

� �G Ry

� �þ ∫1

RysdG sð Þ

� �h iLy

ð29Þ

Next, we establish that the relative supply above is increasing in the relative pricepxpy. An increase in

pxpy

implies an increase in px

and a decrease in py.This in turn implies that ux and Rx decrease while uy and Ry increase. While changes in ui raise the relativesupply of X, the impact of changes in Ri is ambiguous. To get intuition for the ambiguity, note from Eq. (28) that decreases in uiand Ri increase the output from existing jobs ((1−ui) ∫Ri

1 sdG(s)), but they have an ambiguous effect on the output from newjobs ((1−ui)G(Ri)).

To resolve the ambiguity in the response of relative supply to the relative price, we make the following functional form as-sumption which is also useful in deriving some later results.

Assumption2 : ti∼Uniform 0;1½ �

Under the above functional form assumption

i ¼ 1−uið Þ Ri 1−Ri

2

� �þ 12

� �ð30Þ

Therefore,

didpi

¼ − Ri 1−Ri

2

� �þ 12

� �dui

dpiþ 1−uið Þ 1−Rið Þ dRi

dpið31Þ

As well, using Assumption 1 for the matching function, the expressions for job creation Eq. (16) and job destruction Eq. (18)can be written as

1−βð Þ 1−Rið Þr þ λið Þ ¼ ci

miθ1−γi ð32Þ

rr þ λi

Ri þλi

r þ λi

R2i

2− β

1−βciθi þ

λi

2 r þ λið Þ ¼bpi

ð33Þ

Using the above two it is shown in Appendix A that

didpi

> bð Þ0 iff ui > bð Þ 2Ri 1−Rið Þ2 1−γð Þ1−Rið Þ 1−γð Þ þ γRið Þ Ri 2−Rið Þ þ 1ð Þ≡Ψ Rið Þ ð34Þ

Numerical simulations using the standard values of parameters taken from the search literature3 suggest thatdidpi

> 0.

Numerical example1 : r ¼ :0033; λ ¼ :035; m ¼ :64;γ ¼ :5;β ¼ :5; b ¼ :7; c ¼ :4

With these parameter values, the initial wage turns out to be 0.98 when the price is set at 1.Therefore, the unemployment ben-efit and home production is roughly 75% of the initial wage and the recruitment cost is roughly 40% of the initial wage, which isbroadly consistent with the literature (example, Delacroix (2006)). Also, these parameters lead to reasonable values of the markettightness variable, θ, of 0.65, and the unemployment rate of 6%. For these parameters, u is always greater than Ψ(R) defined in

Eq. (34) for any value of p and therefore,didpi

> 0:

Small perturbations of the parameters above leave the result intact. Therefore, we acknowledge the theoretical possibility ofdidpi

b0, but assumedidpi

> 0 in rest of the paper. Effectively, we are assuming that the output effect from existing jobs dominates the

output effect from the new jobs in response to an increase in pi. In this case we get an upward sloping relative supply curve. Giventhe downward sloping relative demand in Eq. (4), we get a unique equilibrium in autarky.

What are the determinants of the pattern of comparative advantage in the model? One obvious determinant of comparative

advantage is the relative endowment of the two types of workers:LxLy. The greater the

LxLy

the greater the relative supply of X and

3 In the numerical example below r=.0033, (monthly rate of discount) corresponds to 4% annual rate of interest; η=.5; β=.5; λ=.035 (monthly job destruc-tion rate); m=.64 (scale parameter in the matching function). These parameters are taken from Felbermayr et al. (2011).


hence the lower the relative price of X. Therefore, a country with a greaterLxLy

will have a comparative advantage in X. In addition, it

is possible for parameters like b, ci, mi, λi, β etc. to differ across sectors and countries and give rise to comparative advantage. Werefer the reader to Davidson, Martin, and Matusz (1999) for a rich discussion of the determinants of pattern of comparative ad-vantage in a search model of this type.

3. Trade liberalization

Suppose the economy has a comparative advantage in producing input X. That is, the autarky relative price pxpyis less than the

world price. In this case, trade liberalization will lead to an increase in the relative price of good X. This implies from Eq. (3) that pxincreases and py decreases. Below we study the impact of these changes in the input prices on the job creation, job destructionand unemployment in the two sectors.

It can be verified from Eqs. (16) and (18) that an increase in px leads to an increase in θx and a decrease in Rx. A decrease in pyleads to a decrease in θy and an increase in Ry. It is clear from Eq. (20) that ux decreases and uy increases. Therefore, the impact oftrade liberalization on aggregate unemployment is ambiguous.

While the result on steady state unemployment is similar to those obtained in a model with exogenous job destruction, weobtain interesting results on job flows below which are absent in models with exogenous job destruction.

3.1. Impact of trade liberalization on job creation and job destruction

Define job destruction rate as the ratio of total job destruction to employment:λiG Rið Þ 1−uið ÞLi

1−uið ÞLi¼ λiG Rið Þ. Similarly, the rate of

job creation is equal to the number of matches over employment:θiq θið Þui

1−ui.

The discussion earlier implies that there is an increase in the rate of job destruction in the Y sector due to import competition.Now, in steady-state this also implies an increase in the rate of job creation since the two are equal. Therefore, trade liberalizationleads to increases in the rates of job creation and job destruction in the Y sector and decreases in the rates of job creation and jobdestruction in the X sector. The result is summarized in the proposition below.

Proposition 1. Trade liberalization increases job flows in the import competing sector and reduces job flows in the export sector.The result above is consistent with the findings of Groizard et al. (2011) where a reduction in the trade cost in an industry

leads to greater job destruction for the industry. If one interpreted the two sectors as tradable and non-tradable sectors, thenthe model would imply an increase in job destruction in the traded sector in response to an appreciation of the real exchangerate. This is consistent with the evidence in Klein et al. (2003) that exchange rate appreciation is associated with increased jobdestruction in the manufacturing industries in the U.S.

Since much of the literature on trade and unemployment uses models with exogenous job destruction we can contrast our re-sult with that in the exogenous job destruction model as follows. The exogenous job destruction model is a special case of ourmodel where Ri=1. Note that, by definition this also implies G(Ri)=1. Therefore, the rate of job destruction is identicallyequal to λi. Thus, trade liberalization has no effect on job destruction in either sector.

3.1.1. Transition dynamicsSince the equations determining R and θ, Eqs. (16) and (18), do not depend on the unemployment rate, R and θ jump to their

new steady-state values instantaneously in response to trade liberalization. However, the unemployment rate adjusts gradually.Denote the pre-liberalization values of the endogenous variables with a superscript 0 and the post-liberalization values with asuperscript 1.We assume that firms can destroy jobs costlessly and therefore, the job destruction condition Ji(Ri)=0 alwaysholds (even outside steady-state). We prove the following result below.

Proposition 2. During transition from the pre-liberalization steady-state to the post-liberalization steady-state, the rate of job de-struction exceeds the rate of job creation in the import competing sector while the rate of job creation exceeds the rate of job destructionin the export sector.

Proof: As shown earlier, uy0buy1. As well, λyG R1y

� �¼

θ1yq θ1y� �

u1y

1−u1y

, since in steady-state the rate of job destruction must equal the

rate of job creation. Therefore, λyG R1y

� �>

θ1yq θ1y� �

u′y

1−u′y

for u′ybuy1. By a similar argument it follows that λxG R1

x

� >

θ1xq θ1x�

u′x

1−u′x

for

u′xbu′x. QED.What is even more interesting is the impact effect of trade liberalization. Since the rate of job destruction jumps up to λyG(Ry1),

on impact a fraction λy[G(Ry1)−G(Ry0)] of extra jobs are destroyed in the Y sector immediately. That is, all the jobs with produc-tivity t∈(Ry0, Ry1) were viable before liberalization, however, now they must be destroyed. In the X sector the rate of job destruc-tion goes down from λxG(Rx0) to λxG(Rx1). However, this has no immediate effect because there are no jobs with productivityt∈(Rx1, Rx0) in the X sector at the time of trade liberalization that can survive now. Thus, on impact the rate of job destruction


does not decrease in the X sector. Therefore, there is an asymmetry in the impact effect of trade liberalization on the two sectors.While a fraction λy[G(Ry1)−G(Ry0)] of jobs are destroyed in the Y sector immediately leading to a large increase in unemploymentupon impact, there is no commensurate decrease in job destruction in the X sector immediately upon trade liberalization. Thelower rate of job destruction in the X sector will show up in the medium run when jobs with t∈(Rx1, Rx0) will survive.

The impact effect on the rate of unemployment is as follows.

u′y ¼ u0

y þ uy ¼ u0y þ λyG R1

y

� �1−u0

y

� �−θ1yq θ1y

� �u0y > u0

y ð35Þ

Note from the expression for u′y that if u′y>uy1, then there is overshooting of unemployment. That is, the unemployment rate

jumps up and then decreases gradually to its new steady state. Therefore, it is possible for the unemployment rate to shoot up inthe import competing sector in response to trade liberalization and then come down gradually.

The results on the impact effect of trade liberalization are consistent with some stylized facts which are hard to reconcile withthe model of exogenous job destruction. For example, Dutt et al. (2009) find that trade liberalization leads to short term spikes inunemployment followed by long-run declines. The short term spike in unemployment can be explained using the asymmetric re-sponses of the two sectors above with regard to job destruction.

In the model with exogenous job destruction, all the adjustment in the jobs takes place through job creation. Therefore, duringtransition from pre-liberalization steady-state to post-liberalization steady-state, the rate of job destruction will remainunchanged, but the rate of job creation will slow down to a rate below the rate of job destruction in the import competing sector.In steady-state the rate of job creation will go back to the autarky level. The opposite will happen in the export sector. Since all theaction takes place through job creation, one cannot get an asymmetric response across the two sectors either.

Before ending this section, it is worth pointing out another interesting implication of trade liberalization in a model with en-dogenous job destruction. Since the productivity cutoff increases in the import competing sector, trade liberalization increases theproductivity of the import competing sector. This is similar to the selection effect of globalization operating in the Melitz type het-erogeneous firm models due to a fixed cost of trading. It arises in the current framework due to labor market frictions.

3.2. Trade liberalization and wage inequality

Given the discussion of the impact of sectoral price, pi, on the intra-sectoral wage inequality, ωi, in the previous section, it isstraightforward to study the impact of trade liberalization onωi. Since trade liberalization leads to an increase in px and a decreasein py, it also leads to an increase inωx and a decrease inωy. In other words, in the short to medium run, trade liberalization leads toan increase in the within group inequality among workers employed in the export sector and a decrease in the within group in-equality among workers employed in the import competing sector.

Given our functional form Assumption 2, the measure of intersectoral wage inequality defined earlier can be written as

�wx�wy

¼ Rxwx 1ð Þ þ ∫1Rxwx sð Þds

Rywy 1ð Þ þ ∫1Rywy sð Þds

ð36Þ

Since wi(s) is increasing in pi as is easily verified from Eq. (12), wx(s) increases and wy(s) decreases upon trade liberalization.This would tend to increase the intersectoral wage inequality. However, Rx decreases and Ry increases. The decrease in Rx de-creases the first term in the numerator but increases the second term. Similarly, an increase in Ry increases the first term, but de-creases the second term. Therefore, the only force that works against an increase in intersectoral wage inequality is the impact ofa change in Ri on the first terms in both the numerator and the denominator. Intuitively, a decrease in Rx implies less job destruc-tion and consequently less job creation as well in the X sector. A lower job creation in steady state implies smaller number of jobsat full productivity which serves to lower the average wage. The opposite happens in the Y sector. However, this effect by itselfcannot outweigh the other effects tending to raise intersectoral wage inequality. It is shown in Appendix A that a sufficient con-dition for intersectoral wage inequality to increase is

βciθi þ β Ri þ1−R2

i

2

!þ βpici

dθidpi

þ βpi 1−Rið ÞdRi

dpi> 0 ð37Þ

Note that sincedθidpi

> 0, the only negative term on the l.h.s of the inequality above is the last term becausedRi

dpib0. This captures

the effect on average wage arising from lower job creation. However, the last term by itself is unlikely to outweigh the first threeterms. In fact, if ciθi>(1−γ)(1−Ri)2, then, as shown in Appendix A, the sum of last two terms is positive which is sufficient forthe above inequality to be true. The condition ciθi>(1−γ)(1−Ri)2 is easily satisfied in the numerical simulations with reason-able parameter values.

Therefore, we conclude that the intersectoral wage inequality is likely to increase upon trade liberalization.


3.3. Impact of unemployment benefits on job flows and unemployment in the open economy

In this section we study how generous unemployment benefits interact with trade liberalization. In particular, whether a gen-erous unemployment benefit amplifies or moderates the impact of trade liberalization on unemployment.

Taking the total derivative of Eqs. (32) and (33) with respect to b obtain

− 1−βð Þr þ λið Þ

dRi

db¼ ci

mi1−γð Þθ−γ

idθidb

ð38Þ

1r þ λi

r þ Riλið ÞdRi

db− βci

1−βdθidb

¼ 1pi

ð39Þ

To reduce notational clutter, use the following definition

Definition : Φ Ri; θið Þ≡ rþ Riλi þβmiθ

γi

1−γ

Now, Eqs. (38) and (39) imply

Φ Ri; θið Þr þ λi

dRi

db¼ 1

pið40Þ

Therefore,

dRi

db¼ r þ λi

piΦ Ri; θið Þ > 0;dθidb

¼ − 1−βð Þmiθγi

r þ λið Þci 1−γð ÞdRi

dbb0 ð41Þ

Taking the total derivative of the expression for unemployment in Eq. (20) with respect to b we obtain

dui

db¼ ui 1−uið Þ 1

Ri

dRi

db− γ

θi

dθidb

� �> 0 ð42Þ

That is, a higher unemployment benefit implies greater rate of job destruction, lower market tightness and a higher unemploy-ment rate. Again, it is worth pointing out that in a model with exogenous job destruction, the impact of unemployment benefit onjob flows works only through job creation. An increase in unemployment benefit will reduce job creation resulting in a lowermarket tightness and higher unemployment. The steady state rates of job creation and job destruction are left unaffected.

Next, we study how unemployment benefit affects the impact of trade on the rate of job destruction and unemployment. Usethe following definition:

Definition : εRipi¼ pi

Ri

dRi

dpi; εθib ¼ b

θi

dθidb

It is shown in Appendix A that

dεRipi

db¼ εRipi

b1þ Riλi þΦ Ri; θið Þ

Φ Ri; θið Þ − Riγβmiθγi

Φ Ri; θið Þ 1−Rið Þ 1−γð Þ2 !

εRipi

!ð43Þ

That is, the sign ofdεRipi

dbis theoretically ambiguous. However, numerical simulations with the parameter values in the neigh-

borhood of those in numerical example 1 confirm thatdεRipi

dbb0:

Numerical Example 2: r=.0033; λ=.035;m=.64; γ=.5; β=.5; b=.7; c=.4; for pi=1, thendεRipi

db¼ −:15 and it asymptotes

towards zero for higher values of pi. For lower values of pi it is a larger negative number. For example, for pi=.75,dεRipi

db¼ −1:5:

Since εRipi is negative,dεRipi

dbb0 implies that an increase in b increases the magnitude of εRipi. That is, an increase in b increases

the responsiveness of Ri to trade liberalization. Therefore, other things equal, a more generous unemployment benefit is likely toamplify the effect of trade liberalization on job destruction.


It is also shown in Appendix A that

dεθipidb

¼ − Ri

1−Ri

dεRipi

db− 1

1−Rið Þ2 1−γð Þ εRipi

dRi

dbð44Þ

Again, the sign of the derivative above is theoretically ambiguous. However, ifdεRipi

dbb0 as found in the numerical simulations,

thendεθipidb

> 0. That is, a more generous unemployment benefit increases the responsiveness of the market tightness to trade

liberalization.

Next, it is shown in Appendix A thatdεRipi

dbb0 also implies

d duidpi

� �db

b0. Sincedui

dpib0, it implies that a more generous unemployment

benefit increases the responsiveness of unemployment to trade liberalization as well. Note again that compared to the modelwith exogenous job destruction where changes in unemployment benefits affect unemployment only through job creation(see for example, Moore and Ranjan (2005)), here they have an impact on job destruction as well. Therefore, the responsivenessof job flows as well as the rate of unemployment to trade liberalization is larger when the unemployment benefit is moregenerous.

Even though a more generous unemployment benefit increases the responsiveness of unemployment as well as job flows totrade liberalization, this cannot be an argument against having a more generous unemployment benefit in an open economy.To arrive at a normative conclusion about unemployment benefits, one will have to introduce risk aversion in the household util-ity function because the key motivation behind unemployment benefits is to insure households against labor market risk arisingfrom unemployment. We leave this exercise for future research.

4. Conclusions

This paper has shown how studying trade liberalization in a model of endogenous job destruction can provide results on jobflows and unemployment consistent with the recent empirical work. It was shown that trade liberalization increases both jobcreation and job destruction in the import competing sector and reduces them in the export sector. Since trade liberalizationalso increases unemployment in the import competing sector and reduces it in the export sector, the impact on economywideunemployment is ambiguous. More interestingly, trade liberalization also has an asymmetric impact effect on the two sectors.While there is a lot of job destruction in the import competing sector upon impact, the reduction in job destruction in theexport sector takes effect only in the medium run. This can lead to short term spikes in the net job destruction and unemploy-ment rates in response to trade liberalization. The paper also shows how trade liberalization could lead to an increase inthe within group wage inequality in the export sector and a decrease in the within group wage inequality in the importcompeting sector. The intersectoral wage inequality is likely to increases as well as a consequence of trade liberalization.Finally, it was shown that a more generous unemployment benefit increases the responsiveness of job destruction to tradeliberalization.

Before ending the paper, it should be noted that the framework can also be used to study the implications of other labor mar-ket regulations such as more stringent firing restrictions on job flows and unemployment in the open economy. Since unemploy-ment benefits and firing restrictions are two alternative instruments used to protect workers against the volatility in the labormarket, it would be a useful exercise to study the implications of firing restrictions as well. To prevent the paper from becomingtoo cumbersome, this is left for future research.

Acknowledgement

I would like to thank an anonymous referee for very useful comments.

Appendix A

Impact of an increase in pi on wage inequality

From Eq. (21) in the text obtain the expression fordωi

dpi, which after canceling terms can be written as

dωi

dpi¼

β 1−βð Þb 1−Rð Þ−β2p2i ci 1−Rið Þ dθidpi

− 1−βð Þbþ βpi 1þ ciθið Þð Þβpi dRidpi

1−βð Þbþ βpi Ri þ ciθið Þð Þ2 ð45Þ


From Eqs. (16) and (18) in the text obtain


dRi

dpi¼ ci


idθidpi

1r þ λi

r þ λiG Rð Þð Þ dRi

dpi− βci

1−βdθidpi

¼ − bp2i

ð46Þ

The above two imply that

dθidpi



dpi¼ − θi

1−γð Þ 1−Rið ÞdRi

dpi;dRi

dpi¼ − b r þ λið Þ

p2i r þ λiG Rið Þ þ βmiθγi

1−γð Þ

! ð47Þ

where the last expression fordθidpi

is obtained upon using Eq. (16). Next, substitute the expression fordθidpi

indωi

dpiabove to get

dωi

dpi¼

β 1−βð Þb 1−Rð Þ þ βpi βpiγciθi1−γ

−1� �

− 1−βð Þb� �

dRi

dpi1−βð Þbþ βpi Ri þ ciθið Þð Þ2 ð48Þ

Therefore, a sufficient condition fordωi

dpi> 0 is βpi

γciθi1−γ

−1� �

− 1−βð Þb� �

b0.

Impact of an increase in pi on sectoral output

Take the total derivatives of Eqs. (32) and (33) in the text with respect to pi to obtain


dRi

dpi¼ ci


idθidpi

ð49Þ

1r þ λi

r þ Riλið ÞdRi

dpi− βci

1−βdθidpi

¼ − bp2i

ð50Þ

Using the definition, Φ Ri; θið Þ≡ r þ Riλi þβmiθ

γi

1−γ, already defined in the text, write

Φ Ri; θið Þr þ λi

dRi

dpi¼ − b

p2ið51Þ

or

dRi

dpi¼ − b r þ λið Þ

p2i Φ Ri; θið Þb0;dθidpi



dpi> 0 ð52Þ

Given Assumption 1 regarding the functional forms, the expression for unemployment in Eq. (20) becomes

ui ¼λiRi

λiRi þmiθγi

ð53Þ

Next, take the derivative of the expression for unemployment in Eq. (20) to get

dui

dpi¼ ui 1−uið Þ 1

Ri

dRi

dpi− γ

θi

dθidpi

� �b0 ð54Þ

Next, using Eq. (54), re-write Eq. (31) in the text as

didpi

¼ − Ri 1−Ri

2

� �þ 12

� �ui 1−uið Þ 1

Ri

dRi

dpiþ γθi

1−βð Þmiθγi


dpi

!þ 1−uið Þ 1−Rið ÞdRi

dpið55Þ

Next, using Eq. (49) re-write Eq. (55) as

didpi

¼ − 1−uið ÞdRi

dpi

2Ri−R2i þ 1

2

!1−Rið Þ 1−γð Þ þ γRiÞ

1−Rið ÞRi 1−γð Þ� �

ui− 1−Rið Þ" #

ð56Þ


SincedRi

dpib0, the sign of

didpi

depends on the sign of the term in the square bracket in Eq. (56). In particular,

didpi

> bð Þ0 if ui > bð Þ 2Ri 1−Rið Þ2 1−γð Þ1−Rið Þ 1−γð Þ þ γRið Þ Ri 2−Rið Þ þ 1ð Þ≡Ψ Rið Þ ð57Þ

Impact of trade liberalization on intersectoral wage inequality

Upon using the expression for wi(t) from Eq. (12), the intersectoral wage ratio can be written as

�wx�wy

¼1−βð Þbþ βpxcxθx þ βpx Rx þ 1−R2

x2

� �1−βð Þbþ βpycyθy þ βpy Ry þ 1−R2

y

2

� � ð58Þ

Note from above that it is enough to show that βpiciθi þ βpi Ri þ1−R2

i

2

� �is increasing in pi. Taking the derivative of βpiciθi þ

βpi Ri þ1−R2

i

2

� �with respect to pi obtain


i

2

!þ βpici

dθidpi

þ βpi 1−Rið ÞdRi

dpið59Þ

Re-write the above as


i

2

!− ciθi

1−γð Þ 1−Rið Þ− 1−Rið Þ� �

βpidRi

dpið60Þ

Therefore, sincedRi

dpib0, a sufficient condition for

�wx

�wyto increase upon trade liberalization is ciθi>(1−γ)(1−Ri)2.

Impact of generous unemployment benefit in the open economy

From Eq. (51) above obtain

εRipi¼ −b r þ λið Þ

piRiΦ Ri; θið Þ ¼ −εRibð61Þ

where the last equality can be verified from the expression fordRi

dbgiven in the text in Eq. (42).

Therefore,

dεRipi

db¼ ∂εRipi

∂b þ ∂εRipi

∂Ri

dRi

dbþ ∂εRipi

∂θidθidb

ð62Þ

Using Eq. (49) the above can be re-written as

dεRipi

db¼ εRipi

bþ ∂εRipi

∂Ri− 1−βð Þmiθ

γi

r þ λið Þci 1−γð Þ∂εRipi

∂θi

!dRi

dbð63Þ

Next, note from Eq. (61) that

∂εRipi

∂Ri¼ −εRipi

Φ Ri; θið Þ þ Riλi

RiΦ Ri; θið Þ > 0;∂εRipi

∂θi¼ −εRipi

γβmiθγ−1i

Φ Ri; θið Þ 1−γð Þ > 0 ð64Þ

Using Eq. (64) in Eq. (63), and making use of the fact that εRipi=−εRib we get

dεRipi

db¼ εRipi

b1þ Φ Ri; θið Þ þ Riλi

Φ Ri; θið Þ −Riγβmiθγ−1i

Φ Ri; θið Þ1−βð Þmiθ

γi

1−γð Þ2 r þ λið Þci

!εRip

" #ð65Þ


Next, using Eq. (32) in the text, re-write the above as

dεRipi

db¼ εRipi

b1þ Φ Ri; θið Þ þ Riλi

Φ Ri; θið Þ − Riγβmiθγi

Φ Ri; θið Þ 1−Rið Þ 1−γð Þ2 !

εRipi

" #ð66Þ

Next, we find outdεθipidb

:

Using Eq. (52) above obtain

εRipi¼ − ci

mi

r þ λið Þ 1−γð Þθ1−γi

1−βð ÞRiεθipi ð67Þ

Upon using Eq. (32), the above can be written as

εθipi ¼ − Ri

1−Rið Þ 1−γð Þ εRipið68Þ

Therefore,

dεθipidb

¼ − Ri

1−Rið Þ 1−γð ÞdεRipi

db− 1

1−γð Þ 1−Rið Þ2 εRipi

dRi

dbð69Þ

Next, using the expression for unemployment in Eq. (53) obtain

dui

dpi¼ ui 1−uið Þ

pi1þ γRi

1−Rið Þ 1−γð Þ� �

εRipib0 ð70Þ

Therefore,

ddui

dpi

� �db

¼ 1−2uið Þ 1þ γRi

1−Rið Þ 1−γð Þ� �

εRipi

dui

dbþ 1−uið Þ γ

1−Rið Þ2 1−γð Þ εRipi

dRi

db

þ 1−uið Þ 1þ γRi

1−Rið Þ 1−γð Þ� � dεRipi

db

ð71Þ

The sign of the derivative above is ambiguous, however, whendεRipi

dbb0, the derivative above is negative under the reasonable

assumption that uib1/2 because all 3 terms are negative.

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trade liberalization, unemployment, and inequality with endogenous job destruction

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