Textbook models of international trade always posit well-functioning, frictionless factor markets. Policy-induced changes in relative output prices lead to the instantaneous reallocation of resources. While trade may result in some winners and losers (ala Stolper-Samuelson), factors are never unemployed and (ignoring terms-of-trade effects) the efficiency gains from trade liberalization always result in aggregate net benefits.

Rather than focussing on the well-understood benefits of liberalization, some policy makers and editorialists tend to focus on the potentially costly aspects of resource reallocation. Most workers who lose their jobs due to liberalization will find new employment opportunities, but there is typically a period of active search before such opportunities are found. Indeed, some workers may find that they have to re-tool before qualifying for employment in growing sectors. At the other end of the spectrum, some workers with little training and little innate ability may find themselves facing employment prospects so bleak that they choose to exit the labor force. Depending on the magnitude of the various effects, it is conceptually possible for the losses that occur during transition to outweigh the steady-state benefits of trade reform.

Our purpose in this paper is to construct and analyze a general equilibrium trade model that explicitly accounts for the dynamic aspects of labor market adjustment. Unlike earlier work in this area, we show how empirically observable parameters of the labor market determine the rate at which labor is released from the contracting sector and is absorbed into the expanding sector and therefore influence the magnitude and extent of the losses associated with trade reform. As a byproduct of the analysis, we are also able to show how the same parameters exert their own independent influence on the pattern and volume of trade.

After developing the model in the next section, we parameterize it in section 3 and use it to trace out the movement of the unemployment rate subsequent to the removal of a five percent import tariff. We find that the unemployment rate overshoots its new steady-state level as expected. We turn to the welfare analysis in section 4 where we show that subsequent to liberalization, the value of net output (measured at world prices) falls below what it would have been had the tariff not been removed and remains below that benchmark level for an extended length of time. However, the value of output ultimately rises above the level that would have been obtained had the tariff not been removed. In our numeric exercise, the present discounted value of output under free trade is higher than it is with the tariff in place. In section 5, we show how our model can be used to shed some light on the Bhagwati-Dehejia thesis that increased globalization has led to increased job turnover, and therefore has affected the distribution of income. Finally, we provide some suggestions for future research in section 6.

1. Labor Market Dynamics

To keep the model simple and to focus on labor market dynamics, we assume that labor is the only input in the production process. To allow us to examine the issues of interest, we introduce training costs and search frictions into the labor market. In particular, we assume that a worker must first undertake a period of training in order to obtain a job in either sector. Once training is complete, the worker must conduct a time-consuming search for employment.

We formulate the model in a continuous-time framework and assume that transitions from one employment or training status to another follow a Poisson process. Eight parameters completely specify all transitions in this economy (four parameters for each of two sectors). Unemployed workers searching for employment in sector i find jobs at rate . Employed workers in sector lose their jobs at rate . Finally, workers training for employment in sector exit the training process at rate . The Poisson process allows the nice interpretation that, for example, the expected duration of a spell of unemployment in sector is .

We want the model to be able to capture the notion that some skills are general while others are job-specific. General skills are those that transfer across jobs while job-specific skills do not. We therefore assume that in each sector there is a probability that a sector-i worker who loses his job can forego retraining and can immediately begin searching for a new job in the same sector.

The dynamics that occur within a given sector are illustrated in Figure 1 and are made explicit in (1) - (3). Define , , as the measure of workers employed, searching for employment, or training for employment in the i^th sector. Let a dot above a variable indicate the derivative of that variable with respect to time. Then the measure of workers in each category evolve as follows:

.

The change in employment over time equals the measure of workers who successfully complete the search process () less the measure of separations (). The pool of searchers expands when workers lose their jobs but retain their skills () and when workers complete training (). On the other hand, the pool contracts when searchers successfully find employment (). Finally, the measure of workers in training expands when workers lose their jobs and require retraining prior to search () and shrinks when workers complete training ().

Let represent the total measure of workers attached to sector i. By definition, . In writing (1) - (3), we have implicitly assumed that is held constant. For example, all workers who are training in sector i were once employed in that sector. There are no inflows from the other sector. In fact, intersectoral flows play a critical role in the adjustment process and we explicitly consider such flows below when we discuss the impact of trade liberalization. Until then, we have two adding-up constraints, expressed as (4) and (5):

where L is the total measure of labor available in the economy. The inequality in (5) allows for the possibility that some workers may choose to opt out of the labor force.

Given , it is straightforward to solve (1) - (3) for the steady-state values of , , and . Doing so, we obtain (6) - (8).

.

In the previous section, we took the allocation of labor (and ) across sectors as given. We show in this section how these values are determined endogenously by the behavior of income-maximizing workers. In our model, workers cannot choose to become employed. Rather, they choose a sector in which to train. Each worker makes this decision based on the discounted lifetime income that he could expect to earn if he were to train in a particular sector. Once this decision is made, the worker undertakes training until its (exogenously determined) completion, at which time he becomes a searcher, and then ultimately an employee. The purpose of this section is to formalize this decision process.

As stated in the introduction, we would like our model to account for worker heterogeneity in terms of innate abilities. To this end, we define the ability level of a type-j worker as and assume that this parameter is uniformly distributed over the interval [0,1]. We then assume that higher-ability workers are more productive than lower-ability workers are. In particular, we assume that a worker with ability can produce units of output when employed in sector i. In what follows, we assume that labor is the only input, so that

where is the price of the i^th good and is the wage earned by a type-j worker employed in sector i.

We now have all of the assumptions necessary to determine the discounted expected lifetime income of a type-j worker contingent upon his current labor market status. Let represent the discounted expected lifetime income of a type-j worker who is currently employed in sector , let represent the discounted expected lifetime income of a worker who is searching for a job in sector i, and let represent the discounted expected lifetime income of a type-j worker who is currently training for a job in sector i. Given the discount rate r and the wage rate , the asset-value equation for a worker who is employed in the i^th sector can be written as

To interpret (10), think of the discounted expected income generated by employment as an asset. Then is the flow income that is generated by the asset. This is equal to the instantaneous wage adjusted by the capital loss that would be realized if employment were terminated. The capital loss is represented by the expression in brackets. In the event of job loss, there is a probability that the worker will not have to retrain before searching for a new job. In that event, the worker has an asset with a value of . Otherwise, the worker does have to retrain and therefore has an asset worth . The capital loss is multiplied by , the rate at which losses are realized.

For simplicity, we assume that workers who are currently searching for employment earn no income and incur no explicit costs. As such, the asset value equation for a searching worker can be expressed as in (11):

Since searchers earn no income, the flow value of the asset just equals the capital gain (the expression in square brackets) multiplied by the rate at which the gain is realized.

Finally, we assume that those engaged in training earn no income, but must pay an instantaneous cost equal to , where is measured in units of sector-i output. Workers exit training and begin searching at a flow rate of . Given these assumptions, the asset value equation for a worker who is currently training becomes:

Given a worker’s level of ability, equations (10) - (12) can be solved for the six endogenous variables in terms of the exogenous parameters of the model. Defining to lighten the notation, we then have:

Equations (13) - (15) have fairly clean interpretations. First, suppose that the discount rate is zero and that all skills are job-specific, so that . Then the lifetime income for a worker is independent of the worker’s current status. This follows from the fact that the Poisson process implies that the expected durations of employment, search, and training are equal to , respectively. Therefore the ratio of time spent on the job relative to total time (employed, searching, or training) is . Likewise, the ratio of time spent training relative to total time is .

Putting the pieces together implies that the flow rate of income is a weighted average of the income earned when employed and the costs incurred while training, where the weights equal the share of time spent in each activity. The existence of a strictly positive discount rate implies that more weight is placed on the current activity at the expense of the weight placed on the future activity. For example, an employed person places more weight on the current wage than on the future costs of training, while a person who is training places more weight on training costs than on the wage. Finally, greater transferability of skills (higher values for ) implies a smaller share of a worker’s lifetime spent in training.

From (12) - (15), it is clear that, regardless of current status, discounted expected lifetime income is increasing in the wage rate, the share of skills that are transferable, the rate at which training is completed, and the rate at which searching workers become employed. Regardless of current status, discounted expected lifetime income is decreasing in the job separation rate and in the cost of training. An increase in the discount rate places more weight on the current activity. Therefore, an increase in the discount rate increases the discounted expected lifetime income of a worker who is currently employed, but reduces the discounted expected lifetime income of a worker who is currently training or searching.

Now begin by considering an untrained worker of ability who is trying to determine whether to train for a job in sector i or whether to opt out of the labor force. A worker will choose to train for a job in sector i if and only if the following two conditions are satisfied:

.

At this point, it is useful to provide an interpretation of our two sectors so that we may sensibly place more structure on the model.

We can think of sector 1 as the "low-tech" sector where jobs are plentiful. In the limiting case, studied below, tends to infinity and jobs are instantaneously found. Furthermore, we can envision the skills necessary to perform any particular task in this sector as being very much specific to the job. For example, a store clerk may need to learn the layout of the store in which he is employed, the procedures involved in opening the store in the morning, the functioning of a particular type of cash register, and so on. These sorts of skills do not transfer across jobs. We capture this notion by setting . By contrast, we can think of sector 2 as the "high-tech" sector where more training is necessary for employment and where jobs are not instantaneously available upon completion of the training. Formally, this means is strictly finite. In addition, the sector-2 jobs that are available require relatively more general, and therefore transferable, knowledge. For example, the most important part of a lawyer’s training is learning the law. Therefore we assume that .

Given our interpretation of the two sectors, it seems reasonable to set up the model so that higher-ability workers sort into the high-tech sector and lower-ability workers sort into the low-tech sector. This will be the case only if expected lifetime training costs are higher in sector 2 than in sector 1 and if expected lifetime income increases more rapidly with ability in sector 2 than it does in sector 1. These restrictions are implicit in the way we have drawn Figure 2.

We have drawn in Figure 2 a representative worker’s discounted expected lifetime income if he obtains training in sector i. It is easily seen from inspection of (14) that is linear and increasing .

Using (9) to substitute for the wage, letting tend to infinity and setting , we can solve (15) for the level of ability at which the discounted expected lifetime income of training in sector 1 equals zero. Denoting this level of ability by , we have

.

A worker with ability would earn negative lifetime income if he were to enter the labor force. That is, the income he could expect to earn while actually employed cannot compensate for the costs incurred while training. There exist no appealing job opportunities in this economy for these low-ability workers.

The ability level denoted by in Figure 2 is the solution to . This is the critical level of ability below which workers choose to train in sector 1 (or opt out of the labor force for sufficiently low ability) and train in sector 2 otherwise.

Recall that we have assumed a uniform distribution of ability. Therefore, the proportion of the labor force sorting into the low-tech sector is and the proportion sorting into the high-tech sector is . Defining to be the measure of workers who opt out of the labor force, we then have

.

Substituting (9) into (15), it is easy to see that is proportional to . This implies that the ability level at which is independent of price. In the context of Figure 2, a higher value of merely rotates the curve counterclockwise about its intercept with respect to the ability axis.

Consider the steady-state supply side of the economy. Take good 1 to be the numeraire and define . For a sufficiently low value of p, the discounted expected lifetime income of training in sector 2 just equals that for training in sector 1 for the person with the highest ability level (i.e., for the person for whom ). In terms of Figure 2, this means that . Given the assumed parameters of the model, this means that in the steady state no one would choose to train in sector 2 and therefore there would ultimately be no employment or production in that sector. As p increases, falls and the proportion of the labor force training in sector 2 expands while the proportion training in sector 1 falls. This leads to more output of good 2 and less of good 1 in the steady state. As p tends to infinity, the curve becomes vertical. There are some workers who just do not have sufficiently high ability to profitably train in sector 2. To an extent, this is an artifact of our assumption that training costs in sector i are paid in units of that sector’s output. Increases in raise both the wage and the cost of training simultaneously.

Combining the logic in the previous paragraph with an assumption that all workers have identical homothetic preferences, we can sketch the relative demand (RD) and steady-state relative supply curves (RS) for this economy (see Figure 3). The intersection of the two curves determines the steady-state value of autarkic prices.

Observe that demand shifts change both outputs and prices despite the fact that we have assumed a Ricardian production technology. This follows from the fact that workers have heterogeneous abilities, of which some are better suited to the low-tech sector and some of which are better suited to the high-tech sector.

Note also that there is a role for absolute advantage (in terms of the production technology) in determining the pattern of trade. To see this, imagine two countries identical in every respect except that one country is proportionately more productive in both sectors compared with the other country. At any given price, will be the same in both countries (holding worker ability constant). However, in the high productivity country is relatively large compared with training costs in both sectors. As such, some workers who would opt out of the labor force in the low-productivity country choose to train in sector 1 in the high productivity country. Furthermore, some workers with moderate ability who would train in sector 1 in the low-productivity country will choose to train in sector 2 in the high productivity country. Output in both sectors expands, but the expansion is not necessarily proportional. Which sector experiences the greater expansion depends on the complex interaction of all of the remaining parameters in the model.

The final point to make is that labor market characteristics exert their own independent influence on autarky prices and therefore the pattern of comparative advantage. Suppose, for example, that there is an increase in the rate at which workers in sector 1 complete training. This change leads to an upward shift of the curve, drawing low-ability workers into sector 1 who had originally opted out of the labor force and drawing moderate-ability workers into sector 1 who had originally chosen to train in sector 2. In the new steady state, the output of good 1 will have increased, while the output of good 2 will have fallen.

As an alternative, suppose that increases. That is, the job separation rate for workers in sector 2 increases. This reduces the discounted income from working in sector 2, making such employment less attractive. The marginal moderate-ability workers who had been training in this sector immediately switch to train in sector 1. Over time, as workers become separated from their sector 2 jobs, they too switch. In the end, the output of good 2 falls because fewer workers choose sector 2, and because (for any worker who stays in sector 2) a smaller fraction of time is actually spent employed. On the other hand, the output of good 1 increases. Both effects work to increase the price of good 2 relative to good 1.

An increase in would have exactly the opposite effect. By increasing discounted expected lifetime income, more workers are drawn to sector 2 at the expense of sector 1. Furthermore, each worker attached to sector 2 spends a larger fraction of his life employed. Similar results hold for an increase in .

In summary, we have constructed a model that allows us to study the impact of trade on the distribution of labor between high-tech and low-tech jobs and, by implication, the steady state levels of output, unemployment, and training. The model also allows us to show how labor market parameters can exert an independent influence on the pattern of comparative advantage. Furthermore, the parameters of our model are generally observable. However, changes in the economic environment that lead to a new steady state take time to play themselves out. For proper policy analysis, it is important to know the behavior of the economy along the adjustment path. For example, removal of an import tariff might very well yield long-run benefits, but the short-term adjustment costs could potentially dominate. This is the issue that we address in the next section.

Suppose that the country under consideration is a small importer of the low-tech good (i.e., an importer of ). Further suppose that the country begins from a steady-state equilibrium and is considering the removal of an import tariff (). With the tariff in place,. After removal of the tariff,. As shown in Figure 4, the curve rotates clockwise while the curve remains unchanged. The net result is that falls, meaning that more workers will choose to train in sector 2 and fewer will choose to train in sector 1. But the shift between sectors occurs gradually.

Recall that for simplicity we have assumed that the rate at which workers become employed in sector 1 is infinite so that there is no period of search. At the instant of trade liberalization, all workers with ability who were training in sector 1 will switch to training in sector 2. However, assuming that the tariff was initially small enough, workers in that ability range who are employed in sector 1 at the moment of liberalization will choose to remain so until they are exogenously separated. That is, as long as , no one will voluntarily quit his or her job. However, once separated, these workers will begin training in sector 2. Therefore, the measure of trainers in sector 2 will jump up at the instant of liberalization, then gradually continue to expand until the new steady state equilibrium is attained.

The path taken by the measure of sector 2 searchers is less clear and depends on the relative magnitudes of the parameters in that sector. Suppose, for instance, that training is relatively quick, but searchers take a long time to find employment. Then the initial bulge in trainers will transmit itself to the pool of searchers, which will climb rapidly, overshoot its steady-state level, then return to the steady-state level. On the other hand, if training is lengthy compared with the time required by searchers to find a job, the bulge of trainers will be released only gradually into the search pool and the measure of searchers will increase monotonically toward the new steady-state level. In any event, the steady-state level of unemployment is bound to expand, since the measure of unemployed workers is a fraction of the measure of people tied to sector 2, which is larger in the new steady state (there is no unemployment in sector 1).

We want to stress that we are able to provide an analytic closed-form solution for the entire adjustment path. This is a unique feature of our model. A more typical approach might require linearization of the adjustment path near the new steady state. We do not need to make such an approximation. The closed-form solution to the complete system of differential equations is contained in Appendix A. Unfortunately, the solution is rather opaque and does not provide much insight on its own. We therefore close this section by providing results from a numerical exercise in order to gain some sense regarding the likely speed of adjustment.

We do not claim that this particular parameterization mimics an actual economy. In particular, it would be too much to ask of this simple two-sector model to accurately reflect all characteristics of a particular economy (e.g., the unemployment rate, the average duration of employment, the average duration of unemployment, the share of workers in the high-tech sector, and so on), but the numbers we have chosen strike us as lying in the range one might expect to see in many industrial countries.

In this exercise, we assume that we are dealing with a small country that begins with a 5% tariff on imports of . At time zero, the tariff is fully removed. We assume that tariff revenues had been redistributed in a lump-sum fashion, so their loss does not affect anyone’s decision regarding sector in which to train. Without loss of generality, we assume that units are normalized so that the world price of good 2 equals the world price of good 1. We summarize the values chosen for the remaining parameters that are used in this exercise in Table 1.

In our numeric example, we interpret one period as one year. Therefore, setting implies that the expected tenure for a low-skill job is one year. By contrast, the expected tenure for a high skill job is 10 years. This latter figure is roughly in line with the average job destruction rate in U.S. manufacturing as reported by Davis, Haltiwanger, and Schuh (1996). A value of 2 for means that the average duration of a spell of unemployment is 6 months. This is probably too long for the U.S., with actual unemployment spells being closer to 3 months. However, doubling (and therefore halving the expected duration of unemployment) would lead to excessively low values of unemployment in this simple version of the model.

The values for and imply training periods of 1 week and 3 months for low-skill and high-skill jobs, respectively. Combining this with the values of implies training costs of approximately one week of wages for a worker of average productivity in sector 1, (for low-skill jobs) and approximately 10 months worth of wages for a worker of average productivity in sector 2. To calculate these figures, just note that the total amount of training cost for a worker training in sector i equals . A worker of average ability in sector 1 produces during the course of a year. A worker of average ability in sector 1 produces in one year. Given the parameterization provided in Table 1, and . Therefore, a worker of average ability in sector 2 produces approximately .8344 units of output in a year, whereas a worker of average ability in sector 1 produces approximately .096 units of output. That is, the average high-skilled worker produces between 8 and 9 times more output per year as the average low-skilled worker.

The outcome of this exercise is illustrated in Figures 5 - 7. Figure 5 shows that the measure of unemployed workers shoots up immediately following liberalization. Given this parameterization, overshooting does occur, with the measure of the unemployment pool declining after just one period and nearing the new steady state within about 5 periods.

Figure 6 shows that the labor force dips immediately following liberalization, returning fairly quickly to the steady-state level. The dip is caused by workers exiting sector 1 employment to begin training in sector 2 and by workers who had been training in sector 1 (where the duration of training was short) starting to train in sector 2 (where training takes longer). Compared with the time required to return the measure of searchers to the steady state, a slightly shorter period is required for the labor force to return to the steady state. This follows because, in our parameterization, training is a less time-intensive process than searching.

Figure 7 combines the information contained in Figures 5 and 6 to illustrate the movement of the unemployment rate over time. Again, the unemployment rate overshoots the steady-state level, but begins coming down after 1 period and closely approximates the new steady-state level after roughly 4 periods.

In examining Figures 5 - 7, two features stand out. First, the length of the adjustment period is neither trivial, nor does it appear to be excessive. Second, the magnitude of the short-run effect is noticeable. The unemployment rate climbs nearly three-quarters of a percentage point during the first year after liberalization before returning to a level less than two tenths of a percentage point higher than in the initial steady state.

Even though labor is the only input in our model, workers are heterogeneous and therefore trade reform will benefit some workers while harming others.

First consider those workers with ability levels below . In our model, such workers receive no income and therefore they are unaffected by reform. In a more elaborate version of the model, we might assume that such workers receive public assistance. We would then have to ask how that assistance is funded and how the funding changes with the removal of the tariff. These individuals benefit if the nominal amount of the assistance remains unchanged since the real value would increase in terms of while remaining the same in terms of .

Clearly all workers who remain in sector 1 are harmed by the reform. When employed, their wage is unchanged in terms of but falls in terms of . Similarly, those workers who are initially in sector 2 clearly benefit, with their wage increasing in terms of while remaining constant in terms of .

Now consider workers who switch sectors. On the one hand, sector 2 is more attractive after trade reform, so some workers are drawn into that sector. On the other hand, sector 1 is less attractive after reform, so some workers are pushed out of sector 1 into sector 2. We can envision these effects in two stages. First, hold constant the function while shifting upward by the amount corresponding to trade reform. Any workers moving under these circumstances are better off. Now, shift down, commensurate with trade reform. The remaining movers are worse off than they would have been had the tariff not been removed, but the reduction in welfare is softened by the ability to switch sectors.

Perhaps a more interesting question regards the impact on overall welfare. A complete analysis of this question would require us to postulate some utility function so that we might talk about both the consumption and production aspects of reform. However, we can obtain some interesting results by focussing exclusively on the production side of the economy.

Define as the value of output (net of training costs) produced at time t and measured using world prices.

Even though the new steady state is plagued by higher unemployment, we show in Appendix B that the free trade steady-state equilibrium is efficient. As such, steady state "welfare" with free trade is higher than steady state "welfare" with the tariff. In this context, "welfare" is measured by the value of output net of training costs measured at world prices. However, welfare along the adjustment path is certainly lower than it is at the new steady state, and possibly lower than it was in the initial steady state. Could it be that the losses during the adjustment path outweigh the long-run gains from liberalization? The answer to this is no, since we have shown in Appendix B that the free trade equilibrium is dynamically efficient (which means that a small movement away from the free trade equilibrium lowers welfare, taking into account the adjustment path). But, it is conceivable that the short-run losses during the adjustment process might eat away almost all of the long-run gains. This is an empirical question, but the model provides clear guidance regarding the proper data necessary to evaluate the experiment.

Formally, define as the measure of workers who remain employed in sector i subsequent to liberalization. Define as the measure of workers who eventually switch from sector 1 to sector 2, but who are employed in sector 1 at time t. A similar expression, , represents the measure of workers who were employed in sector 1 prior to liberalization, but are employed in sector 2 at time t. We then have the following:

To derive (20), note that the average ability for workers who remain in sector 1 is , implying that average output per worker employed in that sector is . The other terms are obtained similarly.

We show as the solid line in Figure 8 for . The dashed horizontal line represents the value of steady-state output prior to liberalization. Conforming with the intuition discussed above, the value of output falls below its pre-liberalization level for the first several years after liberalization. In this example, based on the parameters of Table 1, output does not climb above the pre-liberalization level until sometime during the fourth year after the reform.

Reform is beneficial only if net losses during the early years of reform are compensated by the future gains. Formally, let represent the present discounted value of welfare under free trade, and let represent the present discounted value of welfare consistent with the tariff-distorted steady state. Then removal of the tariff is beneficial if and only if , where

Based on the parameters in Table 1, . That is, there is a welfare gain, but the gain is less than .02 percent of pre-liberalization income. The measured welfare gain would be larger if we simply compare steady states. In this example, steady-state income with free trade is approximately .14 percent higher than steady-state income in the distorted economy. While adjustment costs do not reverse the benefits of tariff reform, they are substantial. Thus, although Appendix B tells us that this economy will benefit from liberalization, our numerical exercise tells us that the gains will be almost trivial.

Our main concern in this paper has been to develop a tractable model suited to predicting adjustment costs based on observable parameters. We can also use our model, however, to shed some light on the raging debate regarding the impact of globalization on the distribution of income.

As is well documented, income distributions within OECD countries have worsened, with the rich getting richer and the poor getting poorer. At the same time, imports from developing countries have exploded. The natural inclination among many economists is to apply the Stolper-Samuelson theorem to argue that increased globalization caused deterioration of the income distribution. The problem is that (depending upon one’s interpretation) the data do not seem to support this hypothesis.

Jagdish Bhagwati and Vivek Dehejia have suggested the possibility that globalization might impact relative income even without Stolper-Samuelson effects. They hypothesize that increased globalization means increasing competition, with razor-thin profit margins. Firms that are competitive today might be out of business tomorrow. They refer to this phenomenon as "kaleidoscopic comparative advantage" and argue that one implication is that job turnover rates might have increased due to this effect. In turn, the higher rates of job turnover might reduce incentives for workers to acquire human capital, flattening out the growth profile of earnings. They argue that this could result in an increase in the income differential between skilled and unskilled workers if skilled workers have greater transferability of workplace skills than do unskilled workers (as we model). While our model is not tailored to address this thesis head on, we clearly have the machinery to explore some possibilities.

Suppose that globalization implies an increase in and , all else equal. Consider first what happens when increases. Sector 1 becomes less attractive. Some low-ability workers are pushed into economic inactivity. Some higher-ability workers are pushed into sector 2. Workers who remain in sector 1 spend a higher fraction of their lifetime in training and a smaller fraction actually employed. Whether the total amount of training goes up or down depends on the interaction of a smaller sector size with more time spent in training by those who continue to work in the sector.

Similar effects are seen in sector 2. An increase in will make sector 2 less attractive. Some lower-ability workers will be pushed into sector 1. Those workers who remain in sector 2 will spend a smaller fraction of their lifetime working, and a larger fraction searching and in training. Whether sector 2 shrinks or expands depends upon the magnitude by which increases compared with the increase in . Even here, there is no simple comparison because all of the other parameters have a role to play.

We can use our model to derive three results, all of which are consistent with the Bhagwati-Dehejia thesis. First, if both turnover rates increase proportionately, it is likely that workers will shift out of sector 2 and into sector 1. If such is the case, there will be a reduction in the aggregate amount of training. Second, higher turnover rates imply lower lifetime incomes for all agents, but the impact is proportionately less for agents with higher ability. Therefore we can infer that such an increase in turnover rates will improve the welfare of the highest ability workers with respect to the welfare of the lowest ability workers. Finally, the degree to which income falls as a result of higher turnover is inversely related to the ease with which skills transfer between jobs.

To illustrate these results, we differentiate (15) with respect to , holding all other variables constant. Doing so, we find

At the initial steady state, . By assumption, training costs are low in sector 1, so . The fractions and are not directly comparable. Given the parameters in Table 1, has the slightly larger value. However, in our example, . A proportionate increase in and reduces the expected lifetime income from training in sector 2 by more than the reduction in sector 1 for the person with ability . Workers therefore shift gradually from sector 2 to sector 1, illustrating our first result.

Inspection of (24.a) and (24.b) reveals that the proportionate impact on expected lifetime income of an increase in diminishes as ability increases, therefore confirming our second result. Higher turnover rates in both sectors hurt everyone, but mostly impact those with the lowest abilities (i.e., workers in the bottom tail of the income distribution).

Finally, differentiating the right hand side of (24.a) with respect to shows that the coefficient on becomes smaller in absolute value as skills become more transferable across jobs (i.e., as increases), therefore reducing the elasticity of with respect to . This confirms our third result.

The vast majority of public debate about trade policy centers on its impact on the jobless and the poor and the short run adjustment costs generated by changes in the pattern of trade. With only a few notable exceptions, the vast majority of the academic literature on trade policy ignores such issues. In this paper, we have offered a simple model of trade that incorporates some of the more important features that the public seems concerned about. In our opinion, the two most important features are unemployment and a class of workers who are shut out of the labor market because they do not have the ability to acquire the skills required for the jobs that are available. We have shown that not only is it possible to build a simple model with such features, but that it is also possible to solve analytically for the adjustment path that connects steady states. This allows us to weigh the short run costs of adjustment against any long run gains that may arise from changes in trade policy. Moreover, the key parameters of our model (labor market turnover rates) are all observable, making it a natural framework for future policy analysis.

Our main goal in this paper was to demonstrate the usefulness of the model in dealing with some basic issues. For example, we began by examining the impact of globalization on unemployment and economic welfare. We show that, in our model, the short-run costs of adjustment cannot outweigh the long-run gains from globalization. However, our numeric exercise suggests that adjustment costs are substantial in the short run (the value of output net of training costs falls by more than 1.5% one year after liberalization), and that they may be large enough to eat away almost all the long run efficiency gains.

We also examined the impact of globalization on the distribution of income. When we assume that protection is removed from the low-skill sector, we obtain Stolper-Samuelson type results, even though labor is the only input in our model. In this case, those workers who continue to be attached to the low-skill sector are worse off while those who were initially attached to the high-skill sector benefit. Liberalization causes some workers to switch from the low-skill to the high-skill sector. Of those who shift between sectors, those with higher abilities benefit from the liberalization, while those with lower abilities are harmed.

Our model also provides support for the Bhagwati-Dehijia thesis that if globalization leads to higher job turnover it may lead to a more unequal distribution of income. In particular, we show that an increase in job turnover has a smaller (negative) impact on workers of higher ability compared with lower ability and greater transferability of skills across jobs reduces the sensitivity of lifetime income to changes in job turnover.

In the future, we intend to use our model to address some issues that have received very little attention is the trade literature. Since our model explicitly allows for unemployment and heterogeneity in skills across workers and jobs (which generates a non-trivial income distribution), we can carry out careful policy analysis of a wide variety of labor market policies aimed at helping the jobless and the poor who are adversely affected by changes in the pattern of trade. For example, we could incorporate training subsidies, unemployment compensation, trade adjustment assistance, government sponsored training or job search services and wage subsidies with virtually no change to the underlying structure of the model. We could then choose a target (say, a certain level of income for low-ability workers) and find the policy that achieves the target with the smallest social cost. Moreover, by varying the turnover rates to mimic the structure of the labor markets in different regions of the world, we can investigate how the optimal policy depends on the flexibility of the labor market. After all, there is little reason to believe that policies that may be affective in the United States, where the durations of employment and unemployment are low relative to Europe and Japan, will be equally effective in other parts of the world where turnover rates are vastly different.

We sketch the derivation of closed-form solutions for the adjustment path in this appendix. In addition to the notation introduced in the text, define as the measure of workers who switch from sector 1 to sector 2 and are training at time t. Similarly define as the measure of workers who switch from sector 1 to sector 2 and are searching at time t. The system of differential equations then can be written as in (A.1) - (A.4):

where, for notational convenience, we have suppressed the time argument.

Equation (A.4) is a simple differential equation, the solution of which is

.

In solving (A.1), we make use of the initial condition that .

To solve (A.2) - (A.4), first substitute (A.5) into (A.4) and then solve for in terms of and . Substitute the result into (A.3). Then (A.2) and (A.3) form a system of two differential equations which can be written in matrix form:

where . The method for solving a system of this form is provided by Boyce and DiPrima (1977), pp. 329-331. Using the initial conditions that , the solutions are

where and are the eigenvalues of the coefficient matrix in (A.6) and are equal to:

.

Our goal is to show that the equilibrium in our model is efficient. To do so, we must calculate the dynamic marginal product of labor in each sector and show that these values are equal in the market equilibrium.

The dynamic marginal product of labor in a sector measures the increase in net output that occurs if the steady state is disturbed by adding an additional worker to that sector taking into account the adjustment path to the new steady state. To calculate the dynamic marginal products we follow the method developed in Diamond (1980).

We begin by defining as the present discounted value of output net of training costs produced in sector i when a (small) measure q of new workers is added to that sector. These workers are assumed to have ability level a_H. Equilibrium is efficient if .

Start with sector 1. We have

where andis an indicator function that takes on the value of 1 when the worker is employed and equals zero at all other times. To find we start by using the fundamental equation of dynamic programming which states that

Substituting for from above allows us to write this as

Differentiating with respect to yields

but, at the initial moment, none of the new workers are employed. That is, , so that we have

To complete our derivation, we must now calculate . To do so, we solve (B.1) for . We obtain

In the initial steady state, the right-hand side of this equation equals 0/0. Applying L’Hopital’s Rule, we have (note that we are differentiating with respect to , which is the same as )

or

We can now substitute this value into (A.2) to obtain the dynamic marginal product of labor in sector 1:

Note that this dynamic marginal product equals.

Turn next to sector 2. We have

where, , I(t) is an indicator function that equals one when the worker is employed and zero otherwise and H(t) is an indicator function which equals one when the worker is searching and zero otherwise.

As above, we start by applying the fundamental equation of dynamic programming which implies that

If we now use the equations of motion to substitute for and and then differentiate with respect to we obtain

But, in the initial steady state (at ), we know that ; so that

The final step requires us to solve for and then substitute that value into (B.4). Again following Diamond (1980), we differentiate the fundamental equation of dynamic programming with respect to and . We obtain

Solving this system of equations for yields

Substituting (B.5) into (B.4) and collecting terms results in

Note that (B.6) is also equal to . Thus, since the dynamic marginal products both equal the expected lifetime income for a worker training in that sector, and, since workers are allocated so that the expected lifetime income from training is the same in both sectors, the dynamic marginal products are equal in equilibrium. As a result, equilibrium is efficient.