WPS6194 Policy Research Working Paper 6194 Trade Policy and Wage Inequality A Structural Analysis with Occupational and Sectoral Mobility Erhan Artuc John McLaren The World Bank Development Research Group Trade and Integration Team September 2012 Policy Research Working Paper 6194 Abstract A number of authors have argued that a worker’s cost to do so in a rational-expectations optimizing occupation of employment is at least as important as the environment. The authors find that the costs of switching worker's industry of employment in determining whether industry and occupation are both high, and of similar the worker will be hurt or helped by international trade. magnitude, but in simulations they find that a worker’s This paper investigates the role of occupational mobility industry of employment is much more important on the effects of trade shocks on wage inequality in than either the worker's occupation or skill class in a dynamic, structural econometric model of worker determining whether he or she is harmed by a trade adjustment. Each worker in the model can switch either shock. industry, occupation, or both, paying a time-varying This paper is a product of the Trade and Integration Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at eartuc@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Trade Policy and Wage Inequality: A Structural Analysis with Occupational and Sectoral Mobility∗ c (World Bank) and John McLaren (University of Virginia). Erhan Artu¸ September 6, 2012 Abstract A number of authors have argued that a worker’s occupation of employment is at least as important as the worker’s industry of employment in determining whether the worker will be hurt or helped by international trade. This paper investigates the role of occupational mobility on the effects of trade shocks on wage inequality in a dynamic, structural econometric model of worker adjustment. Each worker in the model can switch either industry, occupation, or both, paying a time-varying cost to do so in a rational-expectations optimizing environment. The authors �nd that the costs of switching industry and occupation are both high, and of similar magnitude, but in simulations they �nd that a worker’s industry of employment is much more important than either the worker’s occupation or skill class in determining whether he or she is harmed by a trade shock. Keywords: Sectoral Mobility, Occupational Mobility, Trade Policy JEL Classi�cation: F13, F16, E24 ∗ The views in this paper are the authors’ and not those of the World Bank Group or any other insti- tution. McLaren: Department of Economics, University of Virginia, P.O. Box 400182, Charlottesville, VA 22904-4182; jmclaren@virginia.edu. Artu¸ c: World Bank, Development Economics Research Group (Eco- nomic Policy), 1818 H Street, NW Washington DC, 20433 USA; eartuc@worldbank.org. We are grateful for the �nancial support of the Scienti�c and Technological Research Council of Turkey (TUBITAK), Turkish Academy of Sciences (TUBA), and the Bankard Fund for Political Economy at the University of Virginia. We thank seminar participants at the University of Cambridge, Johns Hopkins University (SAIS), Sabanci University, the London School of Economics, University of Oxford, GWU-WAITS, the University of Not- tingham, the University of Dundee, the University of Bayreuth, and the University of Erlangen-Nuremberg for helpful comments. 1 Matthew Crawford got a PhD in Political Philosophy from the University of Chicago. Then he abandoned academia after a year, abandoned a Washington DC think-tank job after �ve months, and opened a one-man motorcycle repair shop. He thinks more now than when he worked at think-tank. He’s part of a vi- brant, intuitive, well-educated community. He’s proud of his work, which matters deeply to his customers. His decisions aren’t arbitrarily changed by a superior. His job won’t suddenly be shipped to India. Of course, most people assume �xing motorcycles was the only job he could get. Business Insider, May 24, 2009. Among the key questions trade economists need to be able to answer is: When a trade shock strikes such as liberalization, trade agreement, or expansion of a foreign export power, who bene�ts and who is hurt, and by how much? There are as many ways of approaching these questions as there are ways of dividing people into economically meaningful subgroups. The oldest literature divided people by what can be called ‘class’ lines, making a distinc- tion between workers and the owners of physical or human capital – the Stolper-Samuelson approach. More recent approaches have divided up workers based on their industry of c, Chaudhuri employment (Revenga (1992), Pavcnik, Attanasio and Goldberg (2004), Artu¸ and McLaren (2010)); region of residence (Topalova (2007), Kovak (2010), Hakobyan and c (2012a)), in each case attempting to quantify how trade McLaren (2010)); and age (Artu¸ shocks affect people in the different groups differently. More recently, several studies have focussed on a division of workers by occupations, often making use of a data set explored by Autor, Levy, and Murnane (2003) that breaks down the ‘task’ composition of a wide range of occupations in US labor data. Authors who exploit these distinctions to look at the differential effects of trade shocks on workers with different types of occupations include Peri and Sparber (2009), Ebenstein, Harrison, McMillan, and Phillips (2009), and Liu and Trefler (2011). Some of the results in Ebenstein et. al. (2009), in particular, suggest that occupational distinctions may be more important than industry in identifying who loses from globalization, that it is workers in vulnerable occupations (namely, those that are the most offshorable) in affected industries who lose. 2 If this is right, it is important information for policymakers to have to be able to target compensation programs effectively. c, We take the focus on occupations in a new direction. Building on earlier work (Artu¸ Chaudhuri and McLaren (2010)) (henceforth ACM) in which we estimated the costs to work- ers of switching industries in a dynamic model in order to measure the welfare effects of trade shocks on workers in different industries, we expand our framework to allow workers to change both their industry and their occupations, estimating the costs of doing so in an integrated dynamic structural econometric model. Our strategy is to specify a rational-expectations model in which industry and occupational switching is a forward-looking investment decision by long-lived workers; estimate the key structural parameters (particularly means and vari- ances of moving costs) on worker data; and then simulate the effects of trade shocks using these estimates to analyze welfare and the time-path of the labor market’s adjustment. This approach has a number of advantages. First, it allows us to incorporate a real dynamic analysis into the effect on different occupations. Workers can and do change oc- cupation, but it is costly to do so, and the degree of cost will affect the wage effects of a trade shock as well as how those wage changes translate into welfare changes. Importantly, a dynamic analysis allows us to identify the role of option value, which has been shown to c, Chaudhuri and McLaren have a large effect on the welfare analysis of trade shocks (Artu¸ (2010)). If one’s wage in one’s own industry and occupation is reduced by a policy change, but wages in other occupations and industries to which one might consider switching are increased, then the positive option-value effect brought about by the latter may dominate the negative direct effect of the former. One needs a dynamic model with option value built in in order to �nd out what the net effect is. Second, we will argue that a full account of occupational choice can have a signi�cant effect on the whole pattern of gains and losses from trade shocks. Take a simple thought experiment as an example. Consider an economy with two goods and two types of worker, skilled and unskilled. Each good is produced by workers doing either of two tasks; output is a function of how many hours of each task are done, and the two goods differ in their task intensity. A worker’s ‘occupation’ is de�ned by which task he or she performs. Consider three cases. Case 1. If skilled workers can all do task 1 but unskilled workers can do only task 2 and 3 it is easy for a worker of either occupation to switch between industries, then this model is merely a thinly disguised Heckscher-Ohlin model, and standard Stolper-Samuleson results will obtain. If the country involved is skilled-labor abundant compared to the rest of the world, then trade opening will increase wage inequality. Further, to know whether a given worker gains or loses, all one needs to know is that worker’s skill class. The occupation and industry of employment are superfluous. Case 2. Now, suppose that a worker of either skill class can choose either occupation, and the choice is partly determined by idiosyncratic preferences; but once that choice has been made, it is very costly to switch to another occupation. At the same time, it is easy for a worker of either occupation to switch industries. In that case, there will be both skilled and unskilled workers in both occupations. Stolper-Samuelson logic will ensure that the occupation that is intensive in the import-competing industry will be made worse off due to trade opening, while the other occupation will bene�t. In this case, to know whether a given worker gains or loses, all one needs to know is that worker’s occupation. The worker’s skill class and industry of employment are superfluous. Case 3. However, if either kind of worker can do either task with equal ease, and can switch between them readily, then skilled and unskilled workers will have the same wage, with or without trade, and so a trade shock will raise (or lower) all boats equally. Clearly, even if all we are interested in is the effect of trade on income inequality as between skilled and unskilled workers, the degree of occupational mobility has an enormous effect. To anticipate results, we �nd that both inter-sectoral and inter-occupational switching costs are large, and that they are similar in magnitude. Nonetheless, idiosyncratic shocks to the switching decision are also large, so that a non-negligible fraction of US workers switch along both dimensions every year. We also �nd that these costs are sub-additive, in the sense that the cost of switching both sector and occupation is much less than the cost of switching only industry plus the cost of switching only occupation. In addition, these costs are quite different in character for college-educated and non-college-educated workers. Finally, despite the extremely high costs of switching occupation, the main determinant of whether a worker bene�ts from trade liberalization or not is that worker’s industry. In our simulations, one’s occupation of employment makes almost no difference to the direction of welfare effect once 4 industry has been taken into account. Aside from our previous efforts in ACM, this equilibrium approach is related to some other work on the relationship between occupational choice and income distribution. Liu and Trefler (2011) use an equilibrium Roy-type model with endogenous matching of work- ers to occupations to interpret patterns of occupational adjustment in tradeable services occupations in response to international offshoring. They show that increased competition with foreign workers tends to lead to increased switching to lower-wage occupations for some workers and to higher-wage occupations for others. Crucially, if one allows for unobserved heterogeneity in worker productivity the welfare losses to a worker from a trade-induced downward occupational switch are greatly diminished. Kambourov and Manovskii (2009) use a general-equilibrium model with optimal dynamic occupational choice to show that rises in the volatility of occupation-speci�c productivity can help explain increases in income inequality in the data. In addition, we are adding to the developing literature on dynamic general-equilibrium adjustment to trade shocks. Cosar (2010) studies a model with costly adjustment due to search frictions, calibrated to Brazilian data. Dix-Carneiro (2011) estimates a structural model of dynamic labor-market response with costly adjustment and sector-speci�c human capital, again using Brazilian data. Each of these studies pursues similar themes but em- phasizes different aspects of adjustment. In particular, our focus on occupational choice is complementary to the approaches of the other studies. The next section lays out our model and estimation method. The following section shows the data and estimations, and the last section details the simulation results. 1 Model We extend the model presented in ACM and Cameron Chaudhuri McLaren (2009) to include occupations along with sectors. Each worker chooses her sector i and occupation k jointly in each period in order to maximize her expected present discounted utility. Assume that there are I industries (sectors) and K occupations. There are two skill groups, indexed by s: College-educated workers, indicated by s = c, and non-college educated workers, indicated by s = n. Assume that workers cannot change their skill status. 5 For the moment, we take wages as exogenously given, because it simpli�es the discussion of the empirics. However, in Section 3 we will endogenize wages in each sector by specifying a spot market for labor in each sector that clears in each period (and of course the endogenous effect of trade shocks on wages is a major focus of this inquiry). Each period t, the wage iks wt for each sector i, occupation k and skill class s is realized and observed by all. Each worker understands the distribution of future wages and optimizes accordingly. In order to accommodate the fact that workers who appear identical to the econometrician often do different things, we introduce idiosyncratic shocks to workers’ preferences. If worker n in skill class s spends period t working in occupation k in sector i, her instantaneous utility iks iks nik nik is wt + ηt + t , where t is a cell-speci�c iid utility shock with extreme value distribution with variance parameter ν which are drawn separately by each worker in every period,1 and iks ηt is an iid shock to the attractiveness of working in industry-occupation cell (i, k ) that is common to all workers of skill class s. We will henceforth refer to these two shocks as the ‘idiosyncratic shock’ and the ‘common shock,’ respectively. We adopt the timing assumption iks that a worker in sector-occupation cell (i, k ) at the beginning of period t enjoys wage wt iks nik and non-pecuniary bene�t ηt for sure, but will receive the idiosyncratic bene�t t only if she remains in that cell. If she switches to cell (j, l) during period t, then at the end of the njl period she will receive idiosyncratic bene�t t instead. n We assume that a worker learns t = n11 n12 [ t , t , ..., nIK t ] , and then decides to move or stay, with moving cost C (i, k, j, l, s), where i and k are the worker’s initial sector and occupation, and j and l are her �nal sector and occupation. If a worker does not change her sector or occupation then the moving cost is equal to zero, so C (i, k, i, k, s) = 0. In principle, we could assume a different value for the moving cost for each value of (i, j, k, l, s) and estimate each one, but this would make the model impossible to estimate. We will therefore need to parameterize the moving cost function somehow, and we will show later on how we do this. 1 More precisely, we set the parameters for this two-parameter family of distributions equal to (−γν, ν ), 2 2 which ensures a mean of zero and a variance equal to π 6ν . See Patel, Kapadia, and Owen (1976). 6 1.1 Equilibrium Relationships The optimization problem for worker z can be summarized by the following Bellman equa- tion, in which Utiks ( z iks t , ηt ) is the ex post payoff to the worker in period t conditional on the realization of that period’s shocks, and Vtiks is the ex ante expected payoff to a worker, where the expectation is taken with respect to that period’s shocks: the vector of idiosyn- z iks cratic shocks, t, and the common preference shock ηt . zjl jls Utiks (εz iks iks iks t , ηt ) = wt + ηt + max{εt − Ct (i, k, j, l, s) + βEt [Vt+1 ]} j,l i iks zjl jls = wt + ηt + βEt [Vtiks iks +1 ] + max{εt − Ct (i, k, j, l, s) + βVt+1 − βVt+1 }. j,l Taking expectations with respect to all shocks, this yields: zjl jls iks Vtiks = E wt iks + ηt + βEt [Vtiks iks +1 ] + E max{εt − Ct (i, k, j, l, s) + β Vt+1 − Vt+1 } j,l iks iks ≡ E wt + ηt + βEt [Vtiks iks +1 ] + Ωt , (1) where Ωiks t is interpreted as an option-value term. In other words, the expected payoff to a worker in a given cell at a given date is equal to the current wage plus common non-pecuniary bene�t, plus the continuation value if the worker stays in that cell next period, plus the value of the option of moving to another sector and/or occupation. Due to the extreme value distribution of the t, it can be shown that workers’ optimal choice of sector-occupation cell in each period will satisfy: exp 1 ν βEt Vtjls iks +1 − Vt+1 − Ct (i, k, j, l, s) mikjls t = , (2) Σj =1...I,l =1...K exp 1 ν βEt Vtj ls iks +1 − Vt+1 − Ct (i, k, j , l , s) where mikjls t denotes the fraction of workers of s type in sector-occupation cell (i, k ) who choose to move to cell (j, l) in period t, which we will call the gross flow from that origin cell to that destination cell. This is the same as the functional form familiar from multinomial c, Chaudhuri logit problems (a full algebraic derivation can be found in the appendix of Artu¸ 7 and McLaren (2007)). Essentially, (2) says that the more attractive (j, l) is expected to be in the future relative to other cells, and the lower is the cost of switching to it from (i, k ), then the larger is the fraction of workers who will choose that location. Crucially, however, this response of the gross flow to the future relative attractiveness or current switching cost is determined by the parameter ν , which we may recall is proportional to the variance of the n idiosyncratic shocks t. A large value of ν implies that idiosyncratic preference shocks tend to be large; in the limit, those shocks are all workers care about, and so workers will disregard relative future pro�tability in choosing their sectors and occupations. More generally, the mikjls t will respond more to future expected wage differentials the smaller is ν . This point will be useful in identifying ν econometrically. 1.2 Econometric Method c (2012b). We need The estimation method is described in detail with full derivations in Artu¸ to estimate the parameters of the moving costs, Ctikjls , as well as the idiosyncratic variance iks ¯iks of the common preference shocks ηt ν . In addition, we need to estimate the means η . We do this in two stages, using the two equations discussed above, the gross-flows equation (2) and the Bellman equation (1). The �rst stage uses (2) with data on actual gross flows to estimate value differences and the moving cost function normalized with ν . Equation (2) can be estimated using the following Poisson Pseudo Maximum Likelihood regression equation ikjls yt = exp(λjls iks ikjls t + αt − Ct (i, k.j, l, s)/ν ) + ξt , (3) with destination �xed effect λjls iks t , origin �xed effect αt and bilateral resistance parameter Ct (i, k.j, l, s)/ν , where y ikjst is the number of type s workers switching from cell (ik ) to ikjls ikjls cell (jl) and ξt is an error term that arises from sampling error, since we compute yt ikjls ikjls from a �nite sample. Asymptotically yt = Liks t mt , where Liks t is the number of type s workers in cell (ik ) at time t. The econometric approach in the �rst stage is similar to Santos Silva and Tenreyro’s (2006) method of “gravity� estimation where the moving cost parameter corresponds to bilateral resistance term and the value differences correspond to the destination �xed effects. The destination �xed effects are equal to 8 1 λiks t ≡ βEt Vtiks 11s +1 − Vt+1 . (4) ν This estimation can be done for each year of the data as a separate cross section. These parameters for the �rst-stage regression can be identi�ed from gross flows alone. Consider, for example, a model with many cells, and suppose that at time t a large fraction of type-s workers in every other cell moves to cell (i, k ) and a large fraction also move to cell i , k (so that mjliks t and mjli t ks are both fairly big for (j, l) = (i, k ), (i , k )). However, only a low fraction of workers in (i, k ) switch to other cells in period t, while a large fraction of workers in (i , k ) switch cells (in other words, mikiks t is large while mi t kiks is small). Equation (2) then implies that λiks t is large relative to λjls t for (j, l) = (i, k ) (so that the numerator of mjliks t is large and the denominator of mikiks t is small), while Ct (j, l, i , k , s)/ν jli k s is small relative to switching costs for other destinations (so that the numerator of mt can be large at the same time as the denominator of mi t kiks is large). 1 iks Further, once these have been estimated, the option value terms ν Ωt can be calculated jks from them as Ωiks iks iks c (2012b)).2 t /ν = −αt − λt + log (Lt ) (the algebraic derivation is in Artu¸ The second stage uses the difference between (1) as written out for cell (i, k ) and the same equation as written out for cell (j, l), multiplied by β ν : jls β jls ik,s jl,s jls β jls λiks t − λt = iks Et wt − wt + ηt − ηt + β (λiks t+1 − λt+1 ) + Ωiks t − Ωt . (5) ν ν In (5), all of the variables are either in the data (namely, the wages) or estimated from iks iks Stage 1, except for the ηt ’s and the parameters β and ν . Recalling that ηt ¯iks is equal to η 1 ¯iks and plus an iid disturbance, we can treat (5) as a linear regression to estimate η ν with iks the data from all years pooled. The disturbance term to the ηt acts as the error term for the regression. Roughly, the idea is as follows. Stage 1 uses the observed gross flows of workers to infer the (i) ‘pull’ λiks t of each sector/occupation cell at each date, which is a combination of β the future relative pro�tability of each cell with the responsiveness ν of workers to that 2 A key to the derivation is the fact that with the extreme-value distribution for the εt matrix, Ωiks t = −ν log(mikik ). 9 future pro�tability; and (ii) the cost of switching. But that does not allow us to separate out the future relative pro�tability from the responsiveness. Having, then, a panel of such ‘pull’ estimates and the costs, we can put them together in Stage 2 with wages to see how much the ‘pull’ is affected by changes in wage differentials. This allows us to separate out β the ‘responsiveness’ factor ν and complete the estimation. Essentially, if gross flows do not β respond very much to future wage differentials, a low value of ν will be indicated, otherwise a high value. A quali�cation that should be noted is that in principle equation (5) can be used to estimate β as well as ν , but in practice it turns out to be difficult to do so. The reason is that signi�cant changes in β induce only small changes in equilibrium aggregates. As a result, we impose a value of β that seems reasonable based on the literature, and examine how robust results are to changes in its value. 2 Data and Regression Analysis 2.1 Sector and Occupation Categories. We use the March Current Population Surveys (CPS) from 1975 to 2000 of the US Census to estimate the model. Dimensionality issues force us to aggregate sectors and occupations, with the result that we consider 4 sectors and 5 occupations. The sectors are: 1. Agriculture and Construction; 2. Manufacturing; 3. Non-traded Service; and 4. Traded Service.3 Similarly, we need to aggregate occupations. We follow the Census categories to do this, with one small exception. The occupations we use are: 1. White collar (the Census category of “Managerial and Professional Specialty Occupa- tions,� occupation codes 3-199). Managers and accountants are examples. 3 “Agriculture and Construction� is composed of Census industries 1-3, respectively “Agriculture,� “Min- ing� and “Construction.� “Manufacturing� is composed of Census industries 4-5, respectively durables and non-durables manufacturing. “Non-tradable services� is composed of Census industries 8, 10, 14, and 16, respectively “Utilities,� “Retail Trade,� “Entertainment and Recreational Services,� and “Public Admin- istration.� “Tradable services� is composed of Census industries 6, 7, 9, 11, 12, 13, and 15, respectively “Transportation, Communication, and Other Public Utilities,� “Communications,� “Wholesale Trade,� “Fi- nance, Insurance, and Real Estate,� “Business and Repair Services,� and “Personal and Related Services,� and “Professional Services.� 10 2. Tech/Sales (the Census category of “Technical, Sales and Administrative Support Oc- cupations,� occupation codes 203-389). Dental hygienists (204) and computer pro- grammers (229) are examples. 3. Service (combination of the two smallest Census categories: “Service occupations,� occupation codes 403-469, and “Farming, Forestry and Fishing Occupations,� occupa- tion codes 473-499). Childcare workers (406), �re�ghters (417), and waiters (435) are examples. 4. Craft (the Census category of “Precision Production, Craft and Repair,� occupation codes 503-699). Automobile mechanics (505) and Drywall installers (573) are examples. 5. Laborer (Census category “Operators, Fabricators, and Laborers,� occupation codes 703-889.). Printing-press operators (734) and truck drivers (804) are examples. The only departure we make from the Census categories is to combine the last two categories into the ‘laborer’ occupation, since these two are quite small. In addition to sector and occupation, we group workers into two education groups, workers with no college education, workers with some college education. 2.2 The Switching-Cost Function We can now show how we implement the switching-cost function Ct (i, k, j, l, s) empirically. In principle, we could assume a different value for the moving cost for each value of (i, j, k, l, s) and estimate each one, but this would create a vast number of parameters and make iden- ti�cation of those parameters impossible. Therefore, we need to parameterize the moving cost function somehow. We have attempted to build a speci�cation that is rich but at the same time parsimonious, and have allowed for four types of effect on switching cost that might or might not turn out to be important in the data. First, we allow for the possibility that some industries or occupations are harder to get into than others. This leads us to estimate an ‘entry cost’ for each sector and for each occupation. Second, we allow for the possibility that the cost of switching both sector and occupation is different from the sum of the cost of switching sector and the cost of switching occupations – that there may be some non-linearity in the cost of joint switching. Finally, we allow for the possibility of a 11 pecking order in occupations such that it may be more costly to switch to occupation j from a lower-ranked occupation than from a higher-ranked occupation. To do this as simply as possible, we note that occupational categories 1 and 2 above are mainly office-type work while 3-5 are mainly not, and that the industries are ranked in inverse order of share of college-educated workers. We will call a switch from occupation 2 to 1 a movement upward within the office occupations; a movement from 5 to 3 or 4 or form 4 to 3 a movement upward within non-office occupations; and a movement from 3, 4, or 5 to 1 or 2 a movement into the office category. We will allow each of these three moves to generate an additional cost. More precisely, we specify the function as follows: Ct (i, k, j, l, s) = 0 if i = j , k = l; (6) = Ct1,j,s if i = j , k = l; (7) = Ct2,l,s + Ct3,k,l,s if i = j , k = l; (8) = Ct1,j,s + Ct2,l,s + Ct3,k,l,s + Ct4,s if i = j , k = l, (9) where Ct1,j,s , Ct2,l,s , Ct3,k,l,s , and Ct4,s are parameters common to all workers. The interpre- tation is as follows. First, the value Ct1,j,s is the ‘entry cost’ mentioned above for switching sectors, and the cost indicated in line (7) applies when the worker switches sectors (i = j ) but not occupations (k = l). The value Ct2,l,s is the corresponding ‘entry cost’ for switching occupations, and the cost indicated in line (8) applies when the worker switches occupation (k = l) but not sector (i = j ). Second, for each educational class s, the function Ct3,k,l,s captures the possible ‘pecking- order’ effects discussed above, and can take one of three values: (i) The value Ctwithin office,s , if 2 ≥ k > l, so that the transition takes place from one office occupation to another higher on the pecking order; (ii) The value Ctnon-office,s , if k > l ≤ 3, so that the transition takes place from one non-office occupation to another that is higher on the pecking order; or (iii) The value Ctto office,s , if k ≥ 3 > l, so the transition takes place from a non-office occupation to an office occupation.4 4 4,s In earlier drafts, the Ct term was absent. We are grateful to many seminar participants who have suggested richer cost structures than the simple one we started with; this speci�cation is a fairly parsimonious way of incorporating some of those ideas. It does not, in the end, change the results dramatically; results 4,s with the Ct term omitted are available on request. 12 Third, we allow for the possibility that the cost of switching in one dimension is affected by whether or not the worker is switching in the other dimension. For example, if a worker is switching sectors, that may raise the cost of also switching occupations, since there is a rising marginal cost of additional complexity in decision making; or it may lower the cost of switching occupations, since switching sectors already creates as much disruption in the worker’s life as it is possible to create. In other words, we allow for the possibility that these switching costs are not simply additive. The parameter Ct4,s captures this in line (9) where both sector and occupation are changing (i = j , k = l), and could be positive (as in the �rst case just mentioned) or negative (as in the second). All of these parameters may differ by skill class s. 2.3 Descriptive Statistics We normalize annual real wages so that the average annual real wage across all workers in the sample is unity. Table 1 shows the distribution of normalized wages across occupations and sectors along with the number of observations for each type. The highest average wages are found in White-collar occupations, followed by the Tech/Sales category. 2.4 Rates of Mobility: Transition Matrices Tables 2 and 3 summarize occupational and sectoral mobility of the workers in our sample respectively, showing transition from row to column. The main diagonal of Table 2 shows the fraction of workers in each occupation who stay in that occupation each year, on average. This varies from 95% for service occupations to 96.7% for craft occupations. Clearly, most workers do not switch industry in a given year, which is hardly surprising, but the fraction who do varies from 3.3% to 5% which is signi�cant. In addition, note that the off-diagonal elements are all positive, ranging from the 0.5% of laborers who move to white-collar jobs each year (or white-collar to service) to the 2.1% of service workers who move to laborer occupations. The distinction made above between office occupations and non-office occupations ap- pears to be meaningful. All of the rates of flow between office categories (White collar and Tech/Sales) and between non-office categories (Service, Craft and Laborer) are, with one 13 Table 1: Normalized Wages and Number of Observations Wages Number of observations Mean SE Mean Min Max White Aggr/Cons 1.19 0.05 252 172 410 Manuf 1.22 0.06 587 309 1002 Non-traded 0.99 0.05 603 322 1214 Traded 1.08 0.05 934 612 1439 Tech/Sales Aggr/Cons 0.97 0.08 63 36 95 Manuf 0.95 0.03 424 240 631 Non-traded 0.85 0.04 840 619 1076 Traded 0.95 0.04 1052 703 1390 Service Aggr/Cons 0.51 0.03 341 226 412 Manuf 0.71 0.06 101 41 151 Non-traded 0.74 0.04 670 558 744 Traded 0.56 0.03 627 480 758 Craft Aggr/Cons 0.89 0.07 1096 844 1496 Manuf 0.95 0.04 1331 661 2051 Non-traded 0.88 0.03 652 362 937 Traded 0.86 0.06 863 586 1209 Laborer Aggr/Cons 0.78 0.06 461 288 702 Manuf 0.78 0.05 1844 984 2616 Non-traded 0.69 0.05 433 280 644 Traded 0.79 0.05 1026 721 1219 14 exception, 1% or above. All of the rates of flow between office and non-office categories (for example, between Tech/Sales and Craft) are 1% or below. Table 2: Occupational Mobility Martix White Tech/Sales Service Craft Laborer White 0.965 0.014 0.005 0.008 0.007 Tech/Sales 0.014 0.962 0.006 0.007 0.010 Service 0.008 0.008 0.950 0.012 0.021 Craft 0.007 0.006 0.006 0.967 0.015 Laborer 0.005 0.007 0.010 0.015 0.964 The matrix for sectoral mobility is similar. The rate of switching varies from 2.8% for manufacturing to 5.3% for agriculture and construction. The off-diagonal elements range from the 0.7% of manufacturing workers who switch to agriculture and construction each year to the 2.5% of non-traded services workers who switch to traded services each year. The biggest inflows from any initial sector are into traded services. Table 3: Sectoral Mobility Matrix Aggr/Cons Manuf Non-traded Traded Aggr/Cons 0.947 0.015 0.014 0.024 Manuf 0.007 0.972 0.007 0.013 Non-traded 0.008 0.009 0.958 0.025 Traded 0.010 0.011 0.015 0.965 We are, of course, interested in joint mobility decisions, and so we need to think about the possibility that a worker will move along both dimensions at once. Table 4 shows how frequently this occurs compared to switching along only one dimension. For each of the twenty sector-occupation cells, the third column of the table shows the average fraction of workers who change sector but not occupation each year, the fourth column shows the fraction who change occupation but not sector, and the �fth column shows the fraction who change both. The fraction who change along both dimensions is consistently similar in magnitude to the number who change in either dimension alone. Indeed, for some cells 15 sectoral switches alone are more frequent than occupational switches alone; for other cells the pattern is the reverse; but for most cells the frequency of switching along both dimensions is either between the frequency of switching only sector and the frequency of switching only occupation or – more often – higher than either. Put differently, the probability that a worker switches sector is quite similar to the probability that a worker switches occupation, and a worker who switches in one dimension is at least as likely also to switch in the other dimension as not. This all suggests that the costs of switching along either dimension are likely quite similar, and the cost of switching both is likely not signi�cantly greater than the cost of switching only one, which would imply a negative value of C 4,s . This is all borne out in the estimates, as will be seen shortly. Table 4: Sector and Occupation Change (Percent) No-College College Sec Occ Both Stay Sec Occ Both Stay White Aggr/Cons 1.1 1.8 2.0 95.2 2.9 0.5 1.2 95.3 Manuf 1.2 1.1 1.2 96.5 1.9 0.4 0.7 96.9 Non-traded 1.1 1.7 2.6 94.5 3.1 0.8 1.1 94.9 Traded 0.9 2.0 1.7 95.5 1.1 0.9 0.6 97.3 Tech/Sales Aggr/Cons 2.5 2.0 3.0 92.4 3.7 1.3 4.1 90.9 Manuf 1.4 1.5 2.1 95.0 3.0 1.8 2.4 92.8 Non-traded 1.6 1.3 2.8 94.3 2.8 1.4 3.5 92.4 Traded 1.2 1.9 1.7 95.2 1.5 3.3 1.6 93.7 Service Aggr/Cons 1.3 2.2 6.0 90.4 0.9 1.3 9.7 88.1 Manuf 1.5 1.6 1.7 95.2 2.5 1.7 4.2 91.5 Non-traded 1.2 1.3 2.7 94.8 0.9 1.4 4.1 93.6 Traded 1.3 1.9 2.7 94.2 1.5 8.9 4.6 85.0 Craft Aggr/Cons 1.8 1.8 2.9 93.4 1.4 2.2 7.6 88.8 Manuf 0.9 1.2 1.4 96.5 0.8 2.6 2.6 94.1 Non-traded 2.3 1.1 1.7 94.9 2.0 2.3 2.6 93.0 Traded 2.0 1.4 1.6 95.0 1.8 3.5 2.7 92.0 Laborer Aggr/Cons 3.2 3.2 2.9 90.7 3.4 4.3 12.0 80.4 Manuf 1.1 0.7 1.9 96.2 0.6 2.2 6.0 91.2 Non-traded 2.6 1.6 2.8 93.0 2.1 4.2 7.5 86.2 Traded 2.3 1.6 2.2 93.9 1.5 5.2 3.8 89.4 In Table 5, we present the ratio of industry-occupation cells for each industry and occu- 16 pation and the ratio of college graduates in each cell. The �rst column shows the share of each occupation in the corresponding sector’s labor force. For example, 35% of manufactur- ing employees are classed as Laborers, higher than any other sector. By contrast, 44% of Traded Services workers are White-collar, making it the most white-collar intensive sector. The second column shows the share of each occupation working in each sector. For example, only 7 percent of “white collar� workers are in the “agriculture and construction� sector. About half of office workers are in the traded services sector, and about half of laborers are in manufacturing. The last column shows the ratio of college graduates in each industry- occupation cell. For example, 72 percent of traded services sector white collar workers are college graduates, while only 3% of manufacturing-sector laborers are. Table 5: Ratio of Industry-Occupation Cells Share in Sector Share in Occupation Ratio of College White Aggr/Cons 0.17 0.07 0.43 Manuf 0.26 0.21 0.58 Non-traded 0.29 0.19 0.52 Traded 0.44 0.52 0.72 Tech/Sales Aggr/Cons 0.03 0.02 0.25 Manuf 0.11 0.17 0.27 Non-traded 0.26 0.32 0.23 Traded 0.22 0.49 0.37 Service Aggr/Cons 0.15 0.19 0.10 Manuf 0.02 0.05 0.04 Non-traded 0.18 0.40 0.14 Traded 0.09 0.35 0.08 Craft Aggr/Cons 0.46 0.28 0.05 Manuf 0.26 0.34 0.06 Non-traded 0.16 0.16 0.05 Traded 0.12 0.22 0.06 Laborer Aggr/Cons 0.19 0.12 0.03 Manuf 0.35 0.49 0.03 Non-traded 0.11 0.12 0.04 Traded 0.14 0.28 0.05 17 3 Results The estimation results from the �rst stage are presented in Table 6, and the results from the second stage are presented in Table 7. Recalling that estimation in Stage 2 depends on β , and that we are not estimating β , the results in Table 7 are presented for an assumed value of β = 0.97 and also for β = 0.9. These two values bracket the great majority of discount factors used in the literature. For our purposes, the results are virtually identical (which underscores the difficulty of estimating β ). For simplicity, we will unless otherwise stated refer to the β = 0.97 estimates. The estimated moving costs are all quite large. For example, the ratio C 2js /ν corre- sponding to the cost of entering a white-collar occupation for a non-college educated worker 1 is 5.24, which, given our estimate of ν as 3.89 (from Table 7) and hence ν = 0.257 im- 2js plies C = 1.35. In other words, given our normalization of wages, the cost of entering a white-collar occupation for a non-college educated worker is something more than an aver- age worker’s annual income (ignoring for the moment the additional cost of ‘pecking-order effects’ captured by Ct3,k,l,s in (8) above. These will be discussed below.). This should not be taken literally, but rather indicates that there are large frictions in the reallocation of labor that are picked up by the estimation – gross flows of workers do respond to future wage differentials, but only weakly. At the same time, as indicated by the mobility matrix tables, a small but positive fraction of workers do switch both sector and occupation each year. This is possible within the model because of a large value of ν . The implied value of nik ν = 0.257, given the extreme-value distribution, amounts to a standard deviation for t of 0.33. In other words, the standard deviation of the idiosyncratic preference shock for non- pecuniary enjoyment of a given sector-occupation cell is one third of average annual income, indicating that occasionally, even with no differences in wages across cells at all, a worker will be willing to incur a large cost in order to switch from the low-idiosyncratic-bene�t cell to the high-bene�t cell. In interpreting results, it should be pointed out that the moving cost for any worker is actually Ctikjls + iks jls t − t , the common moving cost plus the idiosyncratic part. As a result, for workers who actually move, the cost incurred will generally be less than C ikjls , since it is workers with low idiosyncratic costs who will chose to move. At the same time, note that the cost of entering white-collar occupations for a college- 18 educated worker is less than for a non-college educated worker, at (4.55)(0.257) = 1.17. As one might have expected, it is easier for a college-educated worker to get a white-collar job than for a non-college-educated worker. For non-college educated workers, there are two groups of occupations: The easy occupations to enter are Tech/Sales and Laborer, with entry-cost parameters around 4.8, while the difficult ones are all the others including White collar, with parameters between 5.24 and 5.4. For college-educated workers, the costs range from a low of 4.55 for White collar to a high of 5.57 for Crafts. The comparative advantage of the two educational classes is clear: The cost of entering White collar jobs for a non-college educated worker is substantially higher than the cost of entering a Laborer job, but the reverse is true for college-educated workers. The costs of switching sectors are similar in magnitude to the costs of switching oc- cupation, but unlike for occupations, the patterns of costs are quite similar for the two educational groups. For both, it is much easier to move into the traded services sector than the manufacturing sector, for example. Clearly, these estimates do not imply any tendency for wages to be equated across sectors or occupations, either in the short run or in the long run. A worker chasing high wages would need to see a very substantial wage difference, expected to persist quite a long time, in order to justify incurring switching costs of the magnitude observed here. In addition, the high variance of the idiosyncratic shocks, as measured by ν , suggests that workers behave as if they take factors other than wages into account in their career decisions. This is true despite the fact that workers are quite mobile in the sense that there are always workers switching sector and occupation, as shown in Tables 2 to 4. This feature of this sort of model is c, Chaudhuri and McLaren (2008). discussed at some length in Artu¸ Importantly, note that the last row of Table 6 shows a value for C 4 that is always negative, with a value around 4. This means that the cost of switching both sector and occupation is roughly the same as switching either sector or occupation, which is consistent with the patterns noted in Table 4. ‘Pecking-order effects’ are captured by the last three rows of each panel of Table 6. Clearly the costs up moving up the occupation ladder within the office-job category and within the non-office category are both essentially zero and statistically insigni�cant. There is weak evidence for a cost of switching from the non-office category to the office category, but the 19 magnitude of the coefficient is small and it is not statistically signi�cant. Note that although the entry costs we have estimated are sizable, they are an order of magnitude smaller than estimates obtained with a similar model in ACM. The main reason iks is that here we have allowed for the sector-occupation aggregate preference shocks ηt , which were absent in ACM. They are not of independent interest, but their estimated values are presented in Table 7. 4 Simulations We can now turn to simulation of a trade liberalization. For this, we need to complete the general-equilibrium model and calibrate it. We specify production functions for each sector below, and assume a spot market for labor in each sector that clears each period given the number of workers in each cell as of the beginning of the period. We will also specify trade policy that determines the prices of all tradeable goods for each date, and assume that all iks workers know that sequence. In addition, for this exercise, we suppress the shocks (ηt ) to preferences (see (1)), since they are a distraction from our interest in the effects of a trade shock. We also take the mean value of the parameters (Ct1is )’s, (Ct2ls )’s, Ct3,k,l,s ’s, and (Ct4s )’s and hold them constant for the simulation. Given this structure, an equilibrium can be described as follows. (i) Consider a sequence V of matrices of cell payoffs Vt ≡ {Vtiks }i=1,...I,k=1,...K from t = 0 to ∞ and an initial allocation of workers across the cells given by the matrix L0 ≡ {Liks 0 }i=1,...I,k=1,...K for s = c, n. (ii) Given L0 and product prices at t = 0, marginal value products of labor for each type of labor in each cell and hence period-0 wages can be computed, and given expected next-period values V1 , the gross-flows matrix can be computed from (2). Therefore, the next-period allocation of labor L1 and next-period wages can also be computed. Proceeding in this way, the whole in�nite sequence of labor allocations and wages can be computed, and from (1), the implied sequence of cell payoffs can be computed, and can be denoted V ˜ . (iv) The value sequence ˜ . Existence and V is, then, an equilibrium with initial allocation L0 if and only if V = V uniqueness of equilibrium are proven for a very similar model in Cameron, Chaudhuri and McLaren (2007), and a slight modi�cation of the proof would ensure the same result here. c, Chaudhuri and McLaren (2008). Computational details are discussed in Artu¸ 20 Table 6: Regression Results - Stage 1 C/ν - Non-college Mean Change Min Max Min SE Max SE White 5.24 0.69 4.56 6.05 (0.23) (0.36) Tech/Sales 4.80 -0.13 4.03 5.40 (0.24) (0.38) Service 5.40 0.11 5.02 5.89 (0.19) (0.31) Craft 5.35 -0.03 4.81 5.84 (0.18) (0.27) Laborer 4.84 0.12 4.26 5.54 (0.17) (0.26) Aggr/Cons 5.29 0.76 4.90 5.80 (0.14) (0.23) Manuf 5.78 -0.35 5.47 6.33 (0.14) (0.22) Non-Traded 5.19 0.21 4.91 5.55 (0.14) (0.21) Traded 4.53 -0.10 4.16 4.82 (0.13) (0.20) Ch Both -4.42 0.05 -4.84 -4.16 (0.10) (0.16) Within office 0.02 -0.61 -0.81 0.55 (0.33) (0.49) Within non-office -0.06 -0.14 -0.62 0.33 (0.21) (0.32) To office 1.37 -0.60 0.85 1.80 (0.25) (0.41) C/ν - College Mean Change Min Max Min SE Max SE White 4.55 1.74 2.76 5.62 (0.34) (0.80) Tech/Sales 4.64 -0.77 3.46 5.32 (0.34) (0.55) Service 5.30 0.13 3.71 7.81 (0.45) (1.15) Craft 5.57 -1.00 4.45 7.26 (0.45) (1.08) Laborer 5.44 0.26 3.67 7.89 (0.46) (1.08) Aggr/Cons 6.00 -0.66 4.93 7.25 (0.27) (0.50) Manuf 5.77 -1.23 5.03 6.57 (0.24) (0.41) Non-Traded 5.15 1.30 4.44 5.87 (0.22) (0.37) Traded 3.86 -0.12 2.94 4.48 (0.21) (0.35) Ch Both -4.00 -0.11 -4.28 -3.56 (0.16) (0.24) Within office -0.04 -0.80 -1.08 1.62 (0.50) (0.94) Within non-office -0.09 1.49 -2.80 1.40 (0.55) (1.23) To office 1.01 -0.78 -1.06 2.41 (0.55) (1.13) 21 Table 7: Regression Results - Stage 2 β = 0.97 β = 0.90 1/ν SE 1/ν SE 3.89 1.05 4.72 1.27 β = 0.97 β = 0.90 Fixed Effects Time Trend Eff. Fixed Effects Time Trend Eff. Param SE Param SE Param SE Param SE η 2,1 0.05 0.09 -0.02 0.01 0.12 0.10 -0.03 0.02 η 3,1 0.96 0.13 -0.02 0.01 1.18 0.15 -0.02 0.01 η 4,1 0.78 0.11 -0.02 0.01 0.96 0.13 -0.02 0.01 η 1,2 0.83 0.18 0.01 0.02 0.96 0.21 0.01 0.02 η 2,2 1.02 0.17 -0.01 0.02 1.26 0.20 -0.02 0.02 η 3,2 1.64 0.24 -0.01 0.02 1.99 0.28 -0.01 0.02 η 4,2 1.11 0.17 -0.01 0.02 1.33 0.20 -0.02 0.02 η 1,3 2.74 0.43 -0.01 0.03 3.29 0.51 -0.01 0.03 η 2,3 1.20 0.31 0.03 0.04 1.42 0.36 0.03 0.04 η 3,3 1.85 0.30 0.00 0.02 2.21 0.35 -0.01 0.02 η 4,3 2.63 0.38 0.00 0.02 3.13 0.45 0.00 0.02 η 1,4 1.16 0.24 0.03 0.03 1.38 0.27 0.04 0.03 η 2,4 0.78 0.20 0.03 0.02 0.97 0.22 0.03 0.02 η 3,4 1.43 0.26 0.00 0.03 1.69 0.30 0.00 0.03 η 4,4 1.44 0.26 0.01 0.02 1.68 0.30 0.01 0.02 η 1,5 1.34 0.28 0.04 0.03 1.55 0.32 0.05 0.04 η 2,5 1.68 0.30 0.03 0.03 2.04 0.35 0.03 0.03 η 3,5 1.98 0.37 0.03 0.03 2.35 0.43 0.03 0.04 η 4,5 1.61 0.31 0.03 0.03 1.89 0.35 0.03 0.03 22 We assume Cobb-Douglas production functions for each sector i: ik i qt = Ai (Li,k t ) α , (10) k i where qt is the value of output, Li,k t is the effective human capital in sector i and occupation k , which is the human-capital-adjusted sum of number of college graduates and non-college graduates: Li,k t = ψ ik Li,k,c t + Li,k,n t .5 We do not require the αik weights in (10) to sum to unity for any sector, in order to allow for sector-speci�c capital, which is absorbed by the Ai factor, together with the price of sector-i output. The consumers have identical Cobb-Douglas preferences with shares θi . This matters because all wages are real wages, meaning the marginal value product of the particular kind of labor in the particular sector-occupation cell, divided by the consumer price index (CPI) derived from the common utility function. For example, real wages in a non-import- competing sector will tend to rise with liberalization because it tends to lower the prices of other sectors’ output and therefore the CPI. We set the values Ai and αik to minimize a loss function; speci�cally, for any set of parameter values, we can compute the predicted wage for each sector and that sector’s predicted share of GDP using (10) and its derivatives together with empirical employment levels for each sector. The loss function is then the sum across sectors and across years of the square of each sector’s predicted wage minus mean wage in the data, plus the square of the sector’s predicted minus its actual share of GDP. (The sector GDP �gures are from the BEA, but the wages are from our sample.) In addition, we assume that all workers have identical Cobb-Douglas preferences, using consumption shares from the BLS consumer price index calculations for the consumption weights. The values of ψ ik are given by the average skill premium within each cell. The calibration results are presented in Table 8. Note that, 5 We examined a more flexible CES within-occupation aggregation of the two types of labor, but our estimates of the elasticity of substitution between the two types of labor within occupations produced very high values, 60 and above. Perfect substitutability within each industry-occupation cell seems like a good approximation. Please note that this is different from the elasticity of substitution between high- and low- skilled workers examined by other authors in models without occupations, such as Ottaviano and Peri (2012, Table 5), for example. Their estimates of the elasticity of substitution between high- and low-skilled labor take a value around 2, but since generally high- and low-skilled workers have different mixes of occupations, this should be thought of as picking up substitutability across occupations as well as across educational classes. 23 consistent with the patterns observed in Table 5, the Traded and Non-traded Services sectors are the most White-collar intensive (as indicated by their high values of α1 in Table 8), and Manufacturing is the most Laborer intensive (as indicated by its high value of α5 ). Table 8: Parameters for Simulation Aggr/Const Manuf Non-Traded Traded θ 0.37 0.30 0.10 0.23 A 1.60 2.13 2.10 2.40 α1 0.17 0.20 0.24 0.24 α2 0.02 0.06 0.16 0.10 α3 0.06 0.01 0.10 0.02 α4 0.30 0.13 0.10 0.04 α5 0.10 0.15 0.05 0.05 ψ Aggr/Const Manuf Non-Traded Traded White Coll. 1.24 1.29 1.33 1.25 Tech/Sales 1.19 1.36 1.23 1.34 Service 1.49 1.38 1.34 1.28 Craft 1.13 1.21 1.15 1.15 Laborer 1.14 1.09 1.05 1.05 We treat manufacturing and traded services as goods whose prices are determined on world markets, while the other two sectors produce non-traded output whose prices adjust to clear the domestic market. Our simulation is not intended to reproduce the historical data in detail, but to provide an example of a liberalization that produces changes in trade volumes roughly of the same order of magnitude as what has been experienced in the period of the data. With that in mind, the liberalization experiment is set up as follows. The world prices of manufactures and traded services are 0.85 and 1 respectively. Initially, there is a 30% tariff on manufactures, so the domestic price is 1.15, and this is expected by all to continue permanently. From that initial steady state, suddenly at t = 0 the tariff is eliminated, and is expected to stay at zero permanently.6 Our simulation, then, begins at date t = 0, with 6 Since the Ai factor includes the price, we operationalize this by reducing Ai , holding all other param- eters constant. The non-traded sectors’ prices, thus Ai ’s, are re-calculated for each time period during the transition. 24 initial allocation of labor given by the old steady state. We run the simulation under the assumptions β = 0.9 and β = 0.97. The results from the simulation with β = 0.97 are shown in the �gures. (The �gures for β = 0.9 are almost identical.) Figure 1 shows the evolution of the allocation of labor across the four sectors in the data from 1975 to 2000, while Figure 2 shows the same evolution in our simulation, starting 5 years before the liberalization. Although our simulation has not been calibrated to match this time-path for labor allocations, the broad patterns in the data are echoed in the simulation. The driving force in the simulation is a simple elimination of the manufacturing tariff, while in the historical data the same effect – a dwindling manufacturing labor force and relocation of workers especially to traded services – has been driven by progressive reduction in trade barriers together with the rise of manufactured exports from low-wage economies. Note that despite the liberalization as a sudden shock with immediate elimination of the tariff, the simulation mimics the data with a gradual movement of labor out of manufacturing. This is because of the idiosyncratic shocks in the model, and is reflected in the structure of the gross flows equation (2) which shows the fraction of workers who move in any given direction in each period. Immediately after the liberalization, wages in manufacturing are much lower than wages in other sectors, but only a portion of workers leave. Those who leave nik are the ones whose current idiosyncratic moving costs (the difference in the t values across sectors) are particularly low. Workers with higher idiosyncratic moving costs bide their time, and wait for a better moment to move to another sector. As a result, no matter how large the wage differential is between sectors, only a fraction of workers leave the disadvantaged sector in any one year. Figure 3 shows the allocation of labor in the data from the point of view of occupations. Despite the large-scale sectoral reallocation shown in Figure 1, there has not been much change along the occupational dimension. White-collar occupations still are by far the largest category, with Service occupations by far the smallest. That pattern and its overall stability are reproduced in the simulation, as shown in Figure 4, with the exception that the simulation shows a partial exodus from the Laborer occupations. Figures 5 through 7 show the effect of the trade liberalization on real wages in the simulation. Figure 5 shows the average wage for each skill group, as well as the skill premium 25 (which here means the percentage gap between the average college-educated wage and the average non-college-educated wage). The real wage jumps up slightly for both groups due to the liberalization, with barely any change in the skill premium, which remains between 60% and 70%. (Of course, by construction, the skill premium within a sector-occupation cell does not change, but wages across cells can change and the allocation of each type of worker across cells can change, so in principle the aggregate skill premium could change.) Figure 6 shows the average wage for workers in each occupation class. The liberalization causes a modest increase in average real wages for both office occupations and for service occupations. Other non-office occupations see a slight drop in wages. In each case, gradual adjustment following the initial jump in wages moves in the opposite direction of the initial jump. All of these subtle movements in wages stand in contrast to the dramatic effects of Fig- ure 7, which plots average wages by sector. At the date of the liberalization, manufacturing wages drop abruptly. This drop is well-understood with the help of Figure 8, which plots the changes in prices. The price of manufactured output falls from 1.15 to 0.85 when the tariff is eliminated. This causes a direct drop in the consumer price index (CPI) because manufac- tures are consumed, but it also causes an indirect drop in the CPI because consumer demand shifts toward manufactures and away from the two non-traded sectors, forcing reductions in those two sectors’ prices as well. Consequently, CPI falls by about 11%. The net effect on the 0.85 1 price of manufactures relative to CPI is therefore a drop of about 1 − 1.15 (1−0.11) 0.17. Since at date t = 0 no labor reallocation has yet had a chance to occur, the marginal products of labor are unchanged and so the percentage change in real wages is exactly the percentage change in each sector’s relative price. Manufacturing wages fall by 17%, while 1 real wages in tradeable service rise due to the drop in CPI, by 1−0.11 −1 12.3%. Since the prices of output in agriculture and construction and in non-traded services have been forced down, the wage increases in those sectors are much smaller. Figure 8 makes it clear that, unlike wage changes by educational class or by occupation, wage changes by sector due to the liberalization are not subtle. Once again, however, the large initial jumps in wage are attenuated by subsequent gradual adjustment. As workers leave the manufacturing sector, for example, the marginal product of labor in the various occupations rises, gradually raising manufacturing wages. 26 Figure 9 shows the effect of the liberalization on the manufacturing sector’s share of GDP, both in the simulation and in the data. The loss of tariff protection results in a progressive reallocation of labor out of manufacturing and a consequent reduction of manufacture’s GDP share by approximately 4 percentage points over �fteen years, a shift that is closely parallel to the actual trend observed in the data. We present some key statistics from the simulation in Table 9 and Table 11 for the case β = 0.97 and in Table 10 and Table 12 for the case β = 0.9. Tables 9 and 10 show the impact effect of the liberalization on wages and welfare for each group at date 0, while Tables 11 and 12 show the long-run effect, meaning the comparison of the new steady state with the old one. The three boxes of Table 9 and 10 show, respectively, the date-0 percentage change in wage, percentage change in welfare for non-college-educated workers, and percentage change in welfare for college-educated workers for each sector-occupation cell, for the two values of β . Tables 11 and 12 follow the same format but for steady-state changes. The welfare changes in Tables 9 and 10 are the most relevant for our purposes because they measure the change in expected discounted lifetime utility starting from the moment of the policy change into the in�nite future, and thus take full account of the transition to the new steady state. Note that, for both values of β , wages for all occupations in manufacturing drop at date 0 (by exactly the drop in the relative price of manufacturing output, 17%), while real wages for all occupations not in manufacturing rise at date 0 (bene�tting from the reduction in the consumer price of manufactured output). However, over time workers of all occupations leave manufacturing and wages there rise, so that in the long run manufacturing wages for all occupations are slightly higher than their original values (�rst box of Tables 11 and 12). At the same time, workers enter the other sectors, especially traded services, pushing down the marginal products of labor there, and also pushing down the prices of non-traded sector output. Therefore, wages in sectors other than manufacturing fall gradually after date 0, coming to rest just slightly above their old steady-state value (for both values of β , the smallest steady-state wage increase found in manufacturing (0.89% for white-collar workers with β = 0.97 and 0.75% for service workers with β = 0.9 respectively), and the largest is for service workers in the traded-services sector (2.85% and 3.00% respectively)). Across the board, the smallest long-run real wage increase is for workers in manufacturing, not surprising since that is the industry hit by the liberalization and the industry that suffers 27 large initial wage losses at the date of the policy change. The question that has animated this paper is the welfare question: Who bene�ts from the trade liberalization? For manufacturing workers, the liberalization sharply reduces their wages in the short run, very modestly increasing them in the long run. In addition, it raises the wages of workers in all other sectors in both the short and the long run. This is important for each manufacturing worker, because in each period there is a chance that she will choose to switch to those sectors. As a result, the current wage for a manufacturing- sector worker is reduced, but her option value is improved – recall the Ωiks t term in equation (1). Whether the manufacturing worker bene�ts from the liberalization or not depends on the balance between these two effects. The last two boxes of Table 10 show that if workers are relatively impatient (β = 0.9), the short-run manufacturing wage effect dominates, and welfare is lowered for manufacturing workers, in all occupations, by something between 0% and 2%. The last two boxes of Table 9 show that with more patient workers (β = 0.97) the two effects roughly cancel each other out; the net welfare effect on workers is positive more often than negative, but less than 1% in magnitude for each occupation and educational class. For workers in all other sectors, the welfare effect of the liberalization is positive and of signi�cant magnitude for all occupations, ranging from approximately one percent to approximately four percent. In other words, with a low discount factor, workers in the manufacturing sector suffer harm from the liberalization, regardless of occupation; while with a high discount factor, workers in the manufacturing sector enjoy a modest bene�t from the liberalization, regardless of occupation. For either discount factor, workers in all other sectors enjoy a signi�cant welfare improvement from the liberalization, regardless of occupation. This speaks to the question raised in the introduction: Is a worker’s occupation more or less important than the worker’s industry for determining whether or not she gains from a trade liberalization? Despite the high costs of switching occupations, these results suggest that for the most part it is still what industry the worker is in and not what occupation she works in that is key.7 It should also be underlined that these results underscore the importance of a dynamic approach. A reduced-form regression that identi�ed the short-run effect on wages, such as 7 This overall message survives if we relax the Cobb-Douglas assumption in (10). We have experimented with CES production functions with an elasticity of substitution of 0.5 and 2.0 and found that this point emerged essentially intact. Details are available on request. 28 is recorded in the �rst box of Tables 9 and 10, would be a very misleading indicator of welfare, as indicated in the bottom two boxes. The effects on welfare are much smaller, and – depending on the discount factor – can also be in the opposite direction than the short-run wage effect. Table 9: Simulation Results - Short Run Effects (Percent Change) Change in Wages, β = 0.97 Aggr/Cons Manuf NonTraded Traded White Collar 6.42 -17.00 6.42 12.29 Tech/Sales 6.42 -17.00 6.42 12.29 Service 6.42 -17.00 6.42 12.29 Craft 6.42 -17.00 6.42 12.29 Laborer 6.42 -17.00 6.42 12.29 Change in Welfare, No-College, β = 0.97 Aggr/Cons Manuf NonTraded Traded White Collar 1.57 0.31 1.53 1.93 Tech/Sales 1.43 0.41 1.50 1.71 Service 1.30 0.37 1.39 1.51 Craft 1.38 -0.22 1.35 1.58 Laborer 1.31 -0.12 1.28 1.55 Change in Welfare, College, β = 0.97 Aggr/Cons Manuf NonTraded Traded White Collar 1.60 -0.10 1.60 1.94 Tech/Sales 1.55 0.14 1.57 1.86 Service 1.46 0.27 1.50 1.59 Craft 1.53 0.37 1.53 1.67 Laborer 1.51 0.76 1.51 1.63 29 Table 10: Simulation Results - Short Run Effects (Percent Change) Change in Wages, β = 0.90 Aggr/Cons Manuf NonTraded Traded White Collar 6.42 -17.00 6.42 12.29 Tech/Sales 6.42 -17.00 6.42 12.29 Service 6.42 -17.00 6.42 12.29 Craft 6.42 -17.00 6.42 12.29 Laborer 6.42 -17.00 6.42 12.29 Change in Welfare, No-College, β = 0.90 Aggr/Cons Manuf NonTraded Traded White Collar 2.40 -1.70 2.28 3.39 Tech/Sales 2.03 -1.25 2.17 2.92 Service 1.65 -1.13 1.90 2.26 Craft 1.89 -2.64 1.82 2.52 Laborer 1.70 -2.30 1.61 2.42 Change in Welfare, College, β = 0.90 Aggr/Cons Manuf NonTraded Traded White Collar 2.46 -2.43 2.45 3.46 Tech/Sales 2.33 -1.76 2.34 3.23 Service 2.02 -1.39 2.16 2.48 Craft 2.24 -1.43 2.25 2.72 Laborer 2.21 -0.13 2.20 2.61 30 Table 11: Simulation Results - Long Run Effects (Percent Change) Change in Wage, β = 0.97 Aggr/Cons Manuf NonTraded Traded White Collar 1.18 0.89 1.34 1.37 Tech/Sales 1.56 1.03 1.71 1.47 Service 2.67 0.92 1.89 2.85 Craft 1.74 1.12 1.71 1.94 Laborer 2.02 1.51 2.36 2.18 Change in Welfare, No-College, β = 0.97 Aggr/Cons Manuf NonTraded Traded White Collar 1.16 1.10 1.15 1.18 Tech/Sales 1.16 1.08 1.15 1.15 Service 1.15 1.03 1.16 1.19 Craft 1.15 0.99 1.16 1.19 Laborer 1.16 0.99 1.16 1.19 Change in Welfare, College, β = 0.97 Aggr/Cons Manuf NonTraded Traded White Collar 1.15 1.01 1.15 1.18 Tech/Sales 1.16 1.01 1.16 1.18 Service 1.21 0.98 1.18 1.17 Craft 1.16 1.06 1.16 1.16 Laborer 1.16 1.08 1.16 1.16 31 Table 12: Simulation Results - Long Run Effects (Percent Change) Change in Wage, β = 0.90 Aggr/Cons Manuf NonTraded Traded White Collar 1.26 0.77 1.44 1.49 Tech/Sales 1.62 0.89 1.78 1.62 Service 2.76 0.75 1.96 3.00 Craft 1.81 0.86 1.77 2.05 Laborer 2.08 1.16 2.43 2.31 Change in Welfare, No-College, β = 0.90 Aggr/Cons Manuf NonTraded Traded White Collar 1.23 0.99 1.20 1.29 Tech/Sales 1.24 0.95 1.21 1.24 Service 1.21 0.85 1.21 1.30 Craft 1.21 0.76 1.22 1.31 Laborer 1.23 0.76 1.22 1.31 Change in Welfare, College, β = 0.90 Aggr/Cons Manuf NonTraded Traded White Collar 1.24 0.86 1.24 1.31 Tech/Sales 1.26 0.86 1.25 1.32 Service 1.37 0.79 1.30 1.31 Craft 1.26 0.93 1.26 1.28 Laborer 1.28 1.02 1.27 1.28 32 References c, Erhan. 2012a. “Workers’ Age and the Impact of Trade Shocks.� World Bank [1] Artu¸ Working Paper. c, Erhan. 2012b. “A Tractable Method for Estimating Dynamic Discrete Models [2] Artu¸ with Policy Shocks.� Mimeo: World Bank. c, Erhan, Shubham Chaudhuri, and John McLaren. 2007. “Trade Shocks [3] Artu¸ And Labor Adjustment: A Structural Empirical Approach.� NBER Working Paper #13465 (October). c, Erhan, Shubham Chaudhuri, and John McLaren. 2008. “Delay and [4] Artu¸ Dynamics in Labor Market Adjustment: Simulation Results.� Journal of International Economics, 75(1): 1-13. c, Erhan, Shubham Chaudhuri, and John McLaren. 2010. “Trade Shocks [5] Artu¸ and Labor Adjustment: A Structural Empirical Approach.� American Economic Re- view, 100(3). 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Chicago: University of Chicago Press, pp. 291-336. 35 Figure 1: Data − Labor Allocation − Sectors 0.5 0.45 0.4 Fraction of Labor Force 0.35 0.3 0.25 0.2 0.15 Agr/Cons Manuf Non−traded Serv Traded Serv 0.1 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 time Figure 2: Simulation − Labor Allocation − Sectors − β=0.97 0.5 0.45 0.4 Fraction of Labor Force 0.35 0.3 0.25 0.2 0.15 Agr/Cons Manuf Non−traded Serv Traded Serv 0.1 −5 0 5 10 15 20 25 time Figure 3: Data − Labor Allocation − Occupations 0.4 0.35 0.3 Fraction of Labor Force 0.25 0.2 0.15 0.1 White Collar Tech/Sales Service Craft Laborer 0.05 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 time Figure 4: Labor Allocation − Occupations − β=0.97 0.4 0.35 0.3 Fraction of Labor Force 0.25 0.2 0.15 0.1 White Collar Tech/Sales Service Craft Laborer 0.05 −5 0 5 10 15 20 25 time Figure 5: Average Real Wages − Education Level − β=0.97 1.8 1.7 1.6 1.5 1.4 Wage 1.3 1.2 1.1 1 0.9 No College Wage College Wage Skill Premium 0.8 −5 0 5 10 15 20 25 time Figure 6: Average Real Wages − Occupation − β=0.97 1.4 1.3 1.2 1.1 Wage 1 0.9 0.8 White Collar 0.7 Tech/Sales Service Craft Laborer −5 0 5 10 15 20 25 time Figure 7: Average Real Wages − Sector − β=0.97 1.25 Agr/Cons Manuf Non−traded Serv 1.2 Traded Serv 1.15 1.1 Wage 1.05 1 0.95 0.9 0.85 −5 0 5 10 15 20 25 time Figure 8: Manufacturing Price and CPI − β=0.97 1.25 Manuf CPI 1.2 1.15 1.1 1.05 Wage 1 0.95 0.9 0.85 0.8 −5 0 5 10 15 20 25 time Figure 9: Change in Manufacturing Sector Output − β=0.97 5 Data Simulation 0 −5 Change as % of GDP −10 −15 −20 −25 0 2 4 6 8 10 12 14 16 18 time