metadata: authors: 0: author: Artuc, Erhan
1: author: McLaren, John
count: World
docna: 0: docna: Trade policy and wage inequality : a
            structural analysis with occupational and sectoral mobility
docty: Policy Research Working Paper
theme: Other trade and integration
majtheme: Trade and integration
subtopic: Construction Industry,Common Carriers Industry,Food & Beverage Industry,General Manufacturing,Pulp & Paper Industry,Plastics & Rubber Industry,Labor Markets,International Trade and Trade Rules,Food Security,Business Cycles and Stabilization Policies,Trade and Multilateral Issues
teratopic: Macroeconomics and Economic Growth,Social Protections and Labor,Communities and Human Settlements
abstracts: cdata!: 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 find that the costs of switching
            industry and occupation are both high, and of similar
            magnitude, but in simulations they find 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.
repnme: repnme: Trade policy and wage inequality : a
            structural analysis with occupational and sectoral mobility
display_title: Trade policy and wage inequality : a
            structural analysis with occupational and sectoral mobility
listing_relative_url: /research/2012/09/16711727/trade-policy-wage-inequality-structural-analysis-occupational-sectoral-mobility
topicv3: Agriculture and Food Security m1326205 435,Manufacturing Sectors m1326521 1281,Economic Shocks and Trade m1326672 1141,Trade m1326924 698,Jobs m1503931 2670
publishtoextweb_dt: 2000-01-07T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Social Protections and Labor,Communities and Human Settlements
no_of_pages: 46
model_extractions: 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 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 find that the costs of switching industry and occupation are both high, and of similar magnitude, but in simulations they find 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.

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<sup>_∗_</sup> Erhan Artu ̧c (World Bank) and John McLaren (University of Virginia). 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 find that the costs of switching industry and occupation are both high, and of similar magnitude, but in simulations they find 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 Classification: F13, F16, E24

> _∗_ The views in this paper are the authors’ and not those of the World Bank Group or any other institution. 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 (Economic Policy), 1818 H Street, NW Washington DC, 20433 USA; eartuc@worldbank.org. We are grateful for the financial support of the Scientific 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 Nottingham, 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 five 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 vibrant, 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 fixing 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 benefits 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 employment (Revenga (1992), Pavcnik, Attanasio and Goldberg (2004), Artu ̧c, Chaudhuri and McLaren (2010)); region of residence (Topalova (2007), Kovak (2010), Hakobyan and McLaren (2010)); and age (Artu ̧c (2012a)), in each case attempting to quantify how trade 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.

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If this is right, it is important information for policymakers to have to be able to target compensation programs effectively.

We take the focus on occupations in a new direction. Building on earlier work (Artu ̧c, Chaudhuri and McLaren (2010)) (henceforth ACM) in which we estimated the costs to workers 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 variances 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 occupation, 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 have a large effect on the welfare analysis of trade shocks (Artu ̧c, Chaudhuri and McLaren (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 out what the net is.

Second, we will argue that a full account of occupational choice can have a significant 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 defined 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 benefit. 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 To anticipate results, we find 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 find 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 benefits 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 workers 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-specific 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-specific human capital, again using Brazilian data. Each of these studies pursues similar themes but emphasizes 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 simplifies 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 _wt_<sup>_iks_</sup> 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 is _wt_<sup>_iks_</sup> + _ηt_<sup>_iks_</sup> + _ε_<sup>_nik_</sup> _t_ , where _ε_<sup>_nik_</sup> _t_ is a cell-specific iid utility shock with extreme value distribution with variance parameter _ν_ which are drawn separately by each worker in every period,<sup>1</sup> and _ηt_<sup>_iks_</sup> 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 that a worker in sector-occupation cell ( _i, k_ ) at the beginning of period _t_ enjoys wage _wt_<sup>_iks_</sup> and non-pecuniary benefit _ηt_<sup>_iks_</sup> for sure, but will receive the idiosyncratic benefit _ε_<sup>_nik_</sup> _t_ only if she remains in that cell. If she switches to cell ( _j, l_ ) during period _t_ , then at the end of the period she will receive idiosyncratic benefit _ε_<sup>_njl_</sup> _t_ instead.

We assume that a worker learns _ε_<sup>_n_</sup> _t_<sup>=[</sup><sup>_εn_</sup> _t_<sup>11</sup> _, ε_<sup>_n_</sup> _t_<sup>12</sup> _, ..., ε_<sup>_nIK_</sup> _t_ ]<sup>_′_</sup> , 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 final 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.

> 1More precisely, we set the parameters for this two-parameter family of distributions equal to ( _−γν, ν_ ), which ensures a mean of zero and a variance equal to<sup>_<u>π</u>_2</sup> 6<sup>_<u>ν</u>_2.SeePatel,Kapadia,andOwen(1976).</sup>

6
# **1.1 Equilibrium Relationships**

The optimization problem for worker _z_ can be summarized by the following Bellman equation, in which _Ut_<sup>_iks_</sup> ( _ε_<sup>_z_</sup> _t_<sup>_, η_</sup> _t_<sup>_iks_)isthe</sup><sup>_expost_payofftotheworkerinperiod</sup><sup>_t_conditionalon</sup> the realization of that period’s shocks, and _Vt_<sup>_iks_</sup> is the _ex ante_ expected payoff to a worker, where the expectation is taken with respect to that period’s shocks: the vector of idiosyncratic shocks, _ε_<sup>_z_</sup> _t_<sup>,andthecommonpreferenceshock</sup><sup>_η_</sup> _t_<sup>_iks_.</sup> Taking expectations with respect to all shocks, this yields: where Ω<sup>_iks_</sup> _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 benefit, 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 _εt_ , it can be shown that workers’ optimal choice of sector-occupation cell in each period will satisfy: where _m_<sup>_ikjls_</sup> _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 logit problems (a full algebraic derivation can be found in the appendix of Artu ̧c, Chaudhuri 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 idiosyncratic shocks _ε_<sup>_n_</sup> _t_<sup>.Alargevalueof</sup><sup>_ν_impliesthatidiosyncraticpreferenceshockstend</sup> to be large; in the limit, those shocks are all workers care about, and so workers will disregard relative future profitability in choosing their sectors and occupations. More generally, the _m_<sup>_ikjls_</sup> _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**

The estimation method is described in detail with full derivations in Artu ̧c (2012b). We need to estimate the parameters of the moving costs, _Ct_<sup>_ikjls_</sup> , as well as the idiosyncratic variance _ν_ . In addition, we need to estimate the means _η_ ̄<sup>_iks_</sup> of the common preference shocks _ηt_<sup>_iks_.</sup> We do this in two stages, using the two equations discussed above, the gross-flows equation (2) and the Bellman equation (1).

The first 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 with destination fixed effect _λ_<sup>_jls_</sup> _t_<sup>,originfixedeffect</sup><sup>_α_</sup> _t_<sup>_iks_</sup> and bilateral resistance parameter _Ct_ ( _i, k.j, l, s_ ) _/ν_ , where _y_<sup>_ikjst_</sup> is the number of type _s_ workers switching from cell ( _ik_ ) to cell ( _jl_ ) and _ξt_<sup>_ikjls_</sup> is an error term that arises from sampling error, since we compute _yt_<sup>_ikjls_</sup> from a finite sample. Asymptotically _yt_<sup>_ikjls_</sup> = _L_<sup>_iks_</sup> _t_<sup>_m_</sup> _t_<sup>_ikjls_</sup> , where _L_<sup>_iks_</sup> _t_ is the number of type _s_ workers in cell ( _ik_ ) at time _t_ . The econometric approach in the first 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 fixed effects. The destination fixed effects are equal to 8
This estimation can be done for each year of the data as a separate cross section.

These parameters for the first-stage regression can be identified 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_<sup>_′_</sup> _, k_<sup>_′_</sup> (so that _m_<sup>_jliks_</sup> _t_ and _m_<sup>_jli_</sup> _t_<sup>_′k′s_</sup> are both fairly big for ( _j, l_ ) = ( _i, k_ ) _,_ ( _i_<sup>_′_</sup> _, k_<sup>_′_</sup> )). 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_<sup>_′_</sup> _, k_<sup>_′_</sup> ) switch cells (in other words, _m_<sup>_ikiks_</sup> _t_ is large while _mt_<sup>_i′k′i′k′s_</sup> is small). Equation (2) then implies that _λ_<sup>_iks_</sup> _t_ is large relative to _λ_<sup>_jls_</sup> _t_ for ( _j, l_ ) = ( _i, k_ ) (so that the numerator of _m_<sup>_jliks_</sup> _t_ is large and the denominator of _m_<sup>_ikiks_</sup> _t_ is small), while _Ct_ ( _j, l, i_<sup>_′_</sup> _, k_<sup>_′_</sup> _, s_ ) _/ν_ is small relative to switching costs for other destinations (so that the numerator of _m_<sup>_jli_</sup> _t_<sup>_′k′s_</sup> can be large at the same time as the denominator of _mt_<sup>_i′k′i′k′s_</sup> is large).

Further, once these have been estimated, the option value terms _ν_<sup><u>1</u>Ω</sup> _t_<sup>_iks_</sup> can be calculated from them as Ω<sup>_iks_</sup> _t_<sup>_/ν_=</sup><sup>_−α_</sup> _t_<sup>_iks_</sup> _−λ_<sup>_iks_</sup> _t_<sup>+</sup><sup>_log_(</sup><sup>_L_</sup> _t_<sup>_jks_</sup> ) (the algebraic derivation is in Artu ̧c (2012b)).<sup>2</sup> 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<sup>_<u>β</u>_</sup> _ν_<sup>:</sup> In (5), all of the variables are either in the data (namely, the wages) or estimated from Stage 1, except for the _ηt_<sup>_iks_’s and the parameters</sup><sup>_β_and</sup><sup>_ν_.Recalling that</sup><sup>_η_</sup> _t_<sup>_iks_</sup> is equal to _η_ ̄<sup>_iks_</sup> ̄ plus an iid disturbance, we can treat (5) as a linear regression to estimate _η_<sup>_iks_</sup> and _ν_<sup><u>1</u>with</sup> the data from all years pooled. The disturbance term to the _ηt_<sup>_iks_</sup> 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’ _λ_<sup>_iks_</sup> _t_ of each sector/occupation cell at each date, which is a combination of the future relative profitability of each cell with the responsiveness _<u>βν</u>_<sup>ofworkerstothat</sup>

> 2A key to the derivation is the fact that with the extreme-value distribution for the _εt_ matrix, Ω _ikst_ =

> _−ν_ log( _m_<sup>_ikik_</sup> ).

9
future profitability; and (ii) the cost of switching. But that does not allow us to separate out the future relative profitability 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 the ‘responsiveness’ factor<sup>_<u>β</u>_</sup> _ν_<sup>andcompletetheestimation.Essentially,ifgrossflowsdonot</sup> respond very much to future wage differentials, a low value of<sup>_<u>β</u>_</sup> _ν_<sup>willbeindicated,otherwise</sup> a high value.

A qualification 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 significant 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.<sup>3</sup> 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 Occupations,” occupation codes 3-199). Managers and accountants are examples.

> 3“Agriculture and Construction” is composed of Census industries 1-3, respectively “Agriculture,” “Mining” 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 Administration.” “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,” “Finance, 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 Occupations,” occupation codes 203-389). Dental hygienists (204) and computer programmers (229) are examples.

3. _Service_ (combination of the two smallest Census categories: “Service occupations,” occupation codes 403-469, and “Farming, Forestry and Fishing Occupations,” occupation codes 473-499). Childcare workers (406), firefighters (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 identification of those parameters impossible. Therefore, we need to parameterize the moving cost function somehow. We have attempted to build a specification 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: where _Ct_<sup>1</sup><sup>_,j,s_</sup> , _Ct_<sup>2</sup><sup>_,l,s_</sup> , _Ct_<sup>3</sup><sup>_,k,l,s_</sup> , and _Ct_<sup>4</sup><sup>_,s_</sup> are parameters common to all workers. The interpretation is as follows. First, the value _Ct_<sup>1</sup><sup>_,j,s_</sup> 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 _Ct_<sup>2</sup><sup>_,l,s_</sup> 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 _Ct_<sup>3</sup><sup>_,k,l,s_</sup> captures the possible ‘peckingorder’ effects discussed above, and can take one of three values: (i) The value _Ct_<sup>_withinoffice,s_</sup> , if 2 _≥ k > l_ , so that the transition takes place from one office occupation to another higher on the pecking order; (ii) The value _Ct_<sup>_non-office,s_</sup> , 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 _Ct_<sup>_tooffice,s_</sup> , if _k ≥_ 3 _> l_ , so the transition takes place from a non-office occupation to an office occupation.<sup>4</sup>

> 4In earlier drafts, the _Ct_<sup>4</sup><sup>_,s_</sup> term was absent. We are grateful to many seminar participants who have suggested richer cost structures than the simple one we started with; this specification is a fairly parsimonious way of incorporating some of those ideas. It does not, in the end, change the results dramatically; results with the _Ct_<sup>4</sup><sup>_,s_</sup> 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 _Ct_<sup>4</sup><sup>_,s_</sup> captures this in line (9) where both sector and occupation are changing ( _i_ = _j_ , _k_ = _l_ ), and could be positive (as in the first 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 significant. 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 appears 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

|||Wag|es|Numbe|r of obs|ervations|
|---|---|---|---|---|---|---|
|||_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 fifth 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 significantly greater than the cost of switching only one, which would imply a negative value of _C_<sup>4</sup><sup>_,s_</sup> . This is all borne out in the estimates, as will be seen shortly.

Table 4: Sector and Occupation Change (Percent)

||||**No-C**<br>|**ollege**<br>|||**Co**<br>|**llege**<br>||
|---|---|---|---|---|---|---|---|---|---|
|||_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 occu16
pation and the ratio of college graduates in each cell. The first column shows the share of each occupation in the corresponding sector’s labor force. For example, 35% of manufacturing 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 industryoccupation 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 first 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_<sup>2</sup><sup>_js_</sup> _/ν_ corresponding to the cost of entering a white-collar occupation for a non-college educated worker is 5.24, which, given our estimate of _ν_ <u>1</u><sup>as3.89(fromTable7)andhence</sup><sup>_ν_=0</sup><sup>_._257im-</sup> plies _C_<sup>2</sup><sup>_js_</sup> = 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 average worker’s annual income (ignoring for the moment the additional cost of ‘pecking-order effects’ captured by _Ct_<sup>3</sup><sup>_,k,l,s_</sup> 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 _ν_ = 0 _._ 257, given the extreme-value distribution, amounts to a standard deviation for _ε_<sup>_nik_</sup> _t_ of 0.33. In other words, the standard deviation of the idiosyncratic preference shock for nonpecuniary 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-benefit cell to the high-benefit cell.

In interpreting results, it should be pointed out that the moving cost for any worker is actually _Ct_<sup>_ikjls_</sup> + _ε_<sup>_iks_</sup> _t − ε_<sup>_jls_</sup> _t_<sup>,the common moving cost plus the idiosyncratic part.As a result,</sup> for workers who actually move, the cost incurred will generally be less than _C_<sup>_ikjls_</sup> , 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 college18
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 occupation, 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 discussed at some length in Artu ̧c, Chaudhuri and McLaren (2008).

Importantly, note that the last row of Table 6 shows a value for _C_<sup>4</sup> 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 insignificant. 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 significant.

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 is that here we have allowed for the sector-occupation aggregate preference shocks _ηt_<sup>_iks_, which</sup> 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 workers know that sequence. In addition, for this exercise, we suppress the shocks ( _ηt_<sup>_iks_)to</sup> 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 ( _Ct_<sup>1</sup><sup>_is_)’s, (</sup><sup>_C_</sup> _t_<sup>2</sup><sup>_ls_)’s,</sup><sup>_C_</sup> _t_<sup>3</sup><sup>_,k,l,s_</sup> ’s, and ( _Ct_<sup>4</sup><sup>_s_)’s</sup> 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 ≡{Vt_<sup>_iks_</sup> _}i_ =1 _,...I,k_ =1 _,...K_ from _t_ = 0 to _∞_ and an initial allocation of workers across the cells given by the matrix _L_ 0 _≡{L_<sup>_iks_</sup> 0<sup>_}i_=1</sup><sup>_,...I,k_=1</sup><sup>_,...K_for</sup><sup>_s_=</sup><sup>_c, n_.(ii) Given</sup> _L_ 0 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 _V_ 1, the gross-flows matrix can be computed from (2). Therefore, the next-period allocation of labor _L_ 1 and next-period wages can also be computed. Proceeding in this way, the whole infinite 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_<sup> ̃</sup> . (iv) The value sequence _V_ is, then, an equilibrium with initial allocation _L_ 0 if and only if _V_ = _V_<sup> ̃</sup> . Existence and uniqueness of equilibrium are proven for a very similar model in Cameron, Chaudhuri and McLaren (2007), and a slight modification of the proof would ensure the same result here. Computational details are discussed in Artu ̧c, Chaudhuri and McLaren (2008).

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 ofce_|0.02|-0.61|-0.81|0.55|_(0.33)_|_(0.49)_|
|_Within non-ofce_|-0.06|-0.14|-0.62|0.33|_(0.21)_|_(0.32)_|
|_To ofce_|1.37|-0.60|0.85|1.80|_(0.25)_|_(0.41)_|

|||_C/ν - C_|_ollege_||||
|---|---|---|---|---|---|---|
||_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 ofce_|-0.04|-0.80|-1.08|1.62|_(0.50)_|_(0.94)_|
|_Within non-ofce_|-0.09|1.49|-2.80|1.40|_(0.55)_|_(1.23)_|
|_To ofce_|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_||S|E|1/_ν_||S|E|
||3.8|9|1.|05|4.7|2|1.|27|
|||_β_|= 0_._97|||_β_|= 0_._90||
||Fixed E|fects|Time Tr|end Ef.|Fixed E|fects|Time Tr|end Ef.|
||Param|SE|Param|SE|Param|SE|Param|SE|
|_η_<sup>2</sup><sup>_,_1</sup>|0.05|0.09|-0.02|0.01|0.12|0.10|-0.03|0.02|
|_η_<sup>3</sup><sup>_,_1</sup>|0.96|0.13|-0.02|0.01|1.18|0.15|-0.02|0.01|
|_η_<sup>4</sup><sup>_,_1</sup>|0.78|0.11|-0.02|0.01|0.96|0.13|-0.02|0.01|
|_η_<sup>1</sup><sup>_,_2</sup>|0.83|0.18|0.01|0.02|0.96|0.21|0.01|0.02|
|_η_<sup>2</sup><sup>_,_2</sup>|1.02|0.17|-0.01|0.02|1.26|0.20|-0.02|0.02|
|_η_<sup>3</sup><sup>_,_2</sup>|1.64|0.24|-0.01|0.02|1.99|0.28|-0.01|0.02|
|_η_<sup>4</sup><sup>_,_2</sup>|1.11|0.17|-0.01|0.02|1.33|0.20|-0.02|0.02|
|_η_<sup>1</sup><sup>_,_3</sup>|2.74|0.43|-0.01|0.03|3.29|0.51|-0.01|0.03|
|_η_<sup>2</sup><sup>_,_3</sup>|1.20|0.31|0.03|0.04|1.42|0.36|0.03|0.04|
|_η_<sup>3</sup><sup>_,_3</sup>|1.85|0.30|0.00|0.02|2.21|0.35|-0.01|0.02|
|_η_<sup>4</sup><sup>_,_3</sup>|2.63|0.38|0.00|0.02|3.13|0.45|0.00|0.02|
|_η_<sup>1</sup><sup>_,_4</sup>|1.16|0.24|0.03|0.03|1.38|0.27|0.04|0.03|
|_η_<sup>2</sup><sup>_,_4</sup>|0.78|0.20|0.03|0.02|0.97|0.22|0.03|0.02|
|_η_<sup>3</sup><sup>_,_4</sup>|1.43|0.26|0.00|0.03|1.69|0.30|0.00|0.03|
|_η_<sup>4</sup><sup>_,_4</sup>|1.44|0.26|0.01|0.02|1.68|0.30|0.01|0.02|
|_η_<sup>1</sup><sup>_,_5</sup>|1.34|0.28|0.04|0.03|1.55|0.32|0.05|0.04|
|_η_<sup>2</sup><sup>_,_5</sup>|1.68|0.30|0.03|0.03|2.04|0.35|0.03|0.03|
|_η_<sup>3</sup><sup>_,_5</sup>|1.98|0.37|0.03|0.03|2.35|0.43|0.03|0.04|
|_η_<sup>4</sup><sup>_,_5</sup>|1.61|0.31|0.03|0.03|1.89|0.35|0.03|0.03|

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We assume Cobb-Douglas production functions for each sector _i_ : where _qt_<sup>_i_is the value of output,</sup><sup>_Li,k_</sup> _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: _L_<sup>_i,k_</sup> _t_ = _ψ_<sup>_ik_</sup> _L_<sup>_i,k,c_</sup> _t_ + _L_<sup>_i,k,n_</sup> _t_ .<sup>5</sup> We do not require the _α_<sup>_ik_</sup> weights in (10) to sum to unity for any sector, in order to allow for sector-specific capital, which is absorbed by the _A_<sup>_i_</sup> factor, together with the price of sector- _i_ output.

The consumers have identical Cobb-Douglas preferences with shares _θ_<sup>_i_</sup> . 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-importcompeting 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 _A_<sup>_i_</sup> and _α_<sup>_ik_</sup> to minimize a loss function; specifically, 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 figures 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_<sup>_ik_</sup> are given by the average skill premium within each cell. The calibration results are presented in Table 8. Note that,

> 5We 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 lowskilled 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.

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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 _α_ 1 in Table 8), and Manufacturing is the most Laborer intensive (as indicated by its high value of _α_ 5).

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|
|_α_1|0.17|0.20|0.24|0.24|
|_α_2|0.02|0.06|0.16|0.10|
|_α_3|0.06|0.01|0.10|0.02|
|_α_4|0.30|0.13|0.10|0.04|
|_α_5|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.<sup>6</sup> Our simulation, then, begins at date _t_ = 0, with

> 6Since the _Ai_ factor includes the price, we operationalize this by reducing _Ai_ , holding all other parameters constant. The non-traded sectors’ prices, thus _Ai_ ’s, are re-calculated for each time period during the transition.

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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 figures. (The figures 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 are the ones whose current idiosyncratic moving costs (the difference in the _ε_<sup>_nik_</sup> _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 Figure 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 manufactures 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 price of manufactures relative to CPI is therefore a drop of about 1 _−_ � <u>01</u> _<u>..</u>_ <u>8515</u> � (1 _−_ 01 _._ 11)<sup>_≃_0</sup><sup>_._17.</sup> 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 real wages in tradeable service rise due to the drop in CPI, by � 1 _−_ 01 _._ 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 fifteen 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 infinite 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 (benefitting 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 (first 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 benefits 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 Ω<sup>_iks_</sup> _t_ term in equation (1). Whether the manufacturing worker benefits 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 significant 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 benefit from the liberalization, regardless of occupation. For either discount factor, workers in all other sectors enjoy a significant 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.<sup>7</sup> It should also be underlined that these results underscore the importance of a dynamic approach. A reduced-form regression that identified the short-run effect on wages, such as

> 7This 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 first 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, _<u>β</u>_ = 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, _<u>β</u>_ = 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|

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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, _<u>β</u>_ = 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, _<u>β</u>_ = 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|

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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, _<u>β</u>_ = 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, _<u>β</u>_ = 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|

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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, _<u>β</u>_ = 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, _<u>β</u>_ = 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