Patterns of Labor Market Adjustment to Trade Shocks with Imperfect Capital Mobility


 We explore how different investment frictions affect the patterns of responses of labour markets to tariff cuts. To investigate these patterns, we formulate a multi-sector dynamic model featuring capital and labour adjustment costs that we fit to Argentine data. Using counterfactual simulations of a tariff decline in the textile sector, we show that capital adjustment can create long-run responses of real wages that are larger than the short-run responses. This happens as textile firms disinvest during the transition. We also show that the reduction of tariffs on capital inputs boosts investment and real wages across sectors.


Introduction
Trade policy causes some sectors to expand and others to shrink, creating winners and losers along the way. The magnitudes of these impacts depend on factor adjustments to shocks. If labor and capital react slowly and can only be imperfectly reallocated from shrinking to expanding sectors, then the negative eects of a trade policy shock can be amplied. To account for imperfect factor adjustments, early international trade research mostly focused on the capital adjustment process (Mussa, 1978). More recent research focused instead only on labor market adjustments (Davidson and Matusz, 2004;Davidson and Matusz, 2006;Artuc, Chaudhuri and McLaren, 2010). This paper oers a new analysis that incorporates both labor mobility costs and capital adjustment costs and assesses their signicance simultaneously. This allows for an accurate quantication of the impact of trade policy because we not only measure both mechanisms in a consistent framework, but we also account for interactions that occur when the labor adjustment process aects the capital adjustment process and vice versa.
We claim that capital adjustment can re-shape the short-to long-run transition of wages. After a tari cut, the wages in the aected sector typically decline in the short-run.
1 When rms can disinvest in response to the loss of protection, the capital stock sluggishly decreases, thus further reducing labor productivity and wages through time. The impacts on wages can consequently be magnied. If instead capital adjustment is ignored, as it is often the case in the trade literature on labor markets, the wage impact of the tari cuts will be eroded in the long-run as labor moves out of the de-protected sectors and the marginal product of labor thus increases. 2 To investigate these issues and the attendant patterns of labor market adjustment, we formulate a dynamic structural model of trade with worker's intersectoral choice and rm's capital accumulation decisions. Our framework combines the labor supply model with workers' mobility costs of Artuc, Chaudhuri and McLaren (2010), extended to include non-employment as in Caliendo, Dvorkin and Parro (2019), with the labor demand model with capital adjustment costs of Bloom (2009) and 1 See Goldberg and Pavcnik (2005), Kovak (2013), Autor, Dorn and Hanson (2013), Autor, Dorn, Hanson, and Song (2014) and Hakobyan and McLaren (2016). 2 The labor adjustment cost literature is abundant, including models with workers' moving costs across sectors (Artuc, Chaudhuri and McLaren, 2010;Artuc and McLaren, 2015;and Dix-Carneiro, 2014) and workers' sectorspecic experience (Cosar, 2013;Dix-Carneiro, 2014;Davidson and Matusz, 2004;Davidson and Matusz, 2006;Ritter, 2014). Another branch focuses on rm behavior and studies ring and hiring costs (Kambourov, 2009;Dix-Carneiro, 2014) and market search frictions (Cosar, 2013;and Cosar, Guner and Tybout, 2016). The treatment of capital adjustment costs is succinct in the related trade literature. Dix-Carneiro (2014) works out examples of ad-hoc capital adjustment costs and labor markets; Rho and Rodrigue (2016) analyze the interaction between investment and export costs.
2 Cooper and Haltiwanger (2006). The labor supply side is characterized by a rational expectations optimization problem of workers facing mobility costs and time-varying idiosyncratic shocks. The labor demand side is characterized by the rational expectations intertemporal prot maximization problem of rms facing costs for adjusting their capital stock and time-varying technology shocks.
To deal with trade shocks, our model features multiple sectors. To deal with general equilibrium eects and labor market responses, we endogenize equilibrium wages across sectors. 3 We t our model to plant-level panel data and household survey data from Argentina for the [1994][1995][1996][1997][1998][1999][2000][2001]. We use the rm-level data to identify the technology and capital adjustment cost parameters that dene labor demand. We use the panel component of the household survey data to identify the labor mobility costs parameters. We recover the structural parameters that characterize the frictions faced by both workers and rms. A major feature of our estimation strategy is the joint estimation of these parameters: rms internalize workers decisions when choosing investment and workers internalize rm decisions when choosing sector of employment. Finally, we use the estimated parameters to compute counterfactual stationary adjustments of investment, capital, labor allocations and wage distributions across sectors following a cut in taris. We use these counterfactual adjustments to carefully assess the implication of imperfect capital adjustment when the economy responds to trade shocks.
We focus on taris on textiles, a major import sector in Argentina that enjoyed signicant tari protection during the 1994-2001 period. In the benchmark simulation, we work with the full elimination of an initial tari on Textiles of 19.4 percent. This reduces textile prices and decreases protability in the sector. Capital gradually declines, as textile rms disinvest, and employment gradually declines, as workers are displaced. The capital stock decreases by 9.41 percent initially and by 25.47 percent in the new steady state. Employment decreases by 2.91 percent initially and by 4.64 percent in the new steady state. These are sizeable impacts.
At the time of the tari cut, the nominal wage in the textile sector goes down in proportion to the initial price decline. Lower textile prices imply a decline in the price index that reduces the cost of living. However, the real wage in textiles decreases on impact by 15.04 percent. Because of the dynamic adjustment of capital and labor during the transition, real wages continue declining gradually. In the new steady state, real wages are 20.32 percent lower than in the initial equilibrium.
There is no overshooting of wages as in xed capital models. This is because the negative eects of the reduction in capital caused by rm disinvestment on the marginal product of labor outweigh the positive eects caused by displaced workers. The possibility that capital mobility may impede the wage overshooting was advanced by Dix-Carneiro (2014). Using ad-hoc capital adjustment rules, Dix-Carneiro shows how the responses of the capital stock can indeed undo the overshooting of wages in Brazil. Our results conrm these predictions in a more complex model of capital adjustment costs.
We also provide quantitative evidence of when the overshooting of wages may or may not take place.
We show that even with capital mobility, though costly and imperfect, the overshooting of wages may occur if labor mobility costs are lower. In this case, workers can move out of the shocked sector faster than rms disinvest.
We model capital frictions to include xed costs, convex costs and irreversibility costs. This complex structure has implications for labor markets adjustment. We uncover an asymmetric response of the economy to negative shocks and positive shocks (of equal size). Concretely, the positive shock triggers a proportionately larger response of the capital stock, the real wage and employment than the negative shock, especially in the rst years of the transition. The reason is that a positive shock induces investment in the most productive rms. Instead, when the shock is negative, rms let capital depreciate and disinvest proportionately less in order to save on the capital adjustment costs.
We also explore the role of input taris on capital goods, which face a tari of 12.3 percent in the initial equilibrium. Because of lower prices of capital goods, textile rms still disinvest but much less. The total capital stock declines only by about 10 percent, compared to 25.47 percent in the benchmark experiment. The reduced disinvestment implies a higher capital stock that attenuates the continuous decline of the real wage. There is no overshooting, however: real wages are 16 percent lower in the new steady state, 1 percentage point lower than the initial decline. In the non-textile sectors, the reduction of taris on capital goods boosts investment, employment and real wages.
The liberalization of taris on capital goods also has sizeable impacts across industries and can cushion some of the direct negative eects on output of de-protected sectors (textiles).
The tari cuts on textiles have general equilibrium eects. As prices are initially lower, real wages increase on impact in all other sectors of the economy. This attracts workers from textiles, employment expands more than capital, and real wages decline slightly during the transition (in all non-textile sectors). Finally, as the textile sector shrinks because of the loss of tari protection, some 4 of the displaced workers end up non-employed, so that aggregate employment decreases steadily but only slightly during the transition. With tari cuts on capital goods as well, however, aggregate employment actually increases.
For robustness, we explore simulations where we allow for rm entry and exit. While our qualitative results do not change, the entry-exit mechanism amplies the impacts of the shock on investment, especially in the short-run. On impact, the capital stock in the textile sector declines by 40 percent more than in the baseline model without exit. In the steady state, the capital stock is only 2 percent smaller. There is also a more pronounced decline in employment and in real wages.
For modeling tractability, we abstract from two additional channels that are sometimes present in the literature. Our model features intermediate inputs that are sourced only from own-sector output, and thus we do not incorporate comprehensive input-output linkages as in Caliendo and Parro (2015) or Caliendo, Dvorkin and Parro (2019). Also, because of data limitations, we do not study geographical patterns of adjustment, as in Dix-Caneiro and Kovak (2017) The paper is organized as follows. In section 2, we discuss the theoretical model of rm and worker behavior in the presence of capital adjustment costs and labor mobility costs. In section 3, we discuss the data, the estimation strategy and the main results. In section 4, we compute a stationary rational expectations equilibrium and we estimate the eects of tari cuts on investment and labor markets by performing counterfactual simulations. Finally, section 5 concludes.

Discussion
Here, we briey discuss some of the distinguishing features of our model vis-à-vis the related trade and macro literature. In this paper, we are interested in trade shocks and, for this purpose, we need to develop a multi-sector model. Some sectors compete with imports, others are net exporters, and yet others are non-traded. These sectors in principle respond dierently to trade shocks. In addition to the multi-sector feature, we endogenize equilibrium wages across sectors. This is done, as explained, by modeling labor demand on the rm side and labor supply of the workers side.
This implies that sectoral wages respond to the trade shock, which allows us to study labor market adjustment and distributional issues. This is a major dierence with the seminal papers on capital adjustment costs such as Bloom (2009) and Cooper and Haltiwanger (2006).
There is another important dierence with the literature. Bloom (2009) models a one-sector economy where rms face both capital and labor adjustment costs but workers move freely (and wages are not determined endogenously). We develop a model where workers face mobility costs and rms face capital adjustment costs, but not labor adjustment costs (such as ring and hiring costs). Our setting does not lend itself to adding labor adjustment costs on the rm side. The estimated labor mobility costs, as in Artuc, Chaudhuri, and McLaren (2010), are a reduced form measure of mobility costs imposed by labor market frictions, including the costs faced by both rms and workers. Thus, including labor adjustment costs to the rm optimization problem implies a double counting of some of the labor mobility costs. We prefer this setting because it allows for dierences in wages across sectors and for general equilibrium eects, in particular on wages.

Model
In this section we develop a multi-sector dynamic model. Our objective is to provide a framework that will allow us to describe how labor markets adjust to a trade shock to a specic sector in the presence of capital adjustment costs and labor mobility costs. We characterize the dynamic optimizing behavior of rms and workers and equilibrium results for employment, wages and investment.
In our model there are J sectors of production: J − 1 tradable manufacturing sectors and a large non-manufacturing non-tradable sector. They are indexed by j. There is also unemployment, or more generally non-employment, which we refer to as sector 0, or outside sector. 4 Within sectors, products are homogeneous and markets are competitive. The country is small and faces exogenously given international prices p * jt at time t. We allow for taris τ jt so that domestic prices are p jt = p * jt (1+τ jt ). In the non-tradable sector, prices are endogenously determined in a competitive domestic market. Wages are determined endogenously in each sector as well.

Firms
Each production sector j is composed of a continuum of rms. Firms produce output by combining labor, capital and materials. In each time period they face productivity shocks and price shocks that follow rst order Markov processes. Labor and materials are exible inputs that can be adjusted instantaneously through a static prot maximization problem. Capital is subject to adjustment 4 In the empirical implementation of the model we work with 5 manufacturing sectors: food and beverages, textiles and apparel, minerals, metals, other manufactures; and 1 non-tradable sector: services; for a total of J = 6 production sectors plus non-employment.
6 costs, as in Bloom (2009) and Cooper and Haltiwanger (2006), which makes the investment decision dynamic. At time t capital is predetermined; investment made at t transforms into working capital in t + 1.
We make two simplifying assumptions regarding participation. In our baseline specication, we do not model the decision to enter or exit the domestic market. That is, the number of rms is xed and there are no xed costs of production so that even the least productive rms nd it protable to produce. In the simulations (section 4), however, we explore an extension of our baseline model that allows for entry and exit of rm. We also do not model the decision to export. Since rms face a perfectly elastic demand, the decision to export does not play any role in this model.
We start by describing the production technology and the static prot maximization. The production function is a Leontief combination of materials and a Cobb-Douglas index of labor and capital given by where Y ijt is output, L ijt is labor, K ijt is the capital stock, and M ijt is materials. The variables b 0 jt and A ijt are sector-level and rm-level productivity shocks, respectively. Both are Hicks-neutral in the three inputs. The parameters α K and α L are the Cobb-Douglas output elasticities and v M is the unit input requirement for materials. The intuition behind the functional form is that there is substitution between labor and capital, with the capital-labor intensity being chosen by rms, whereas materials transform into output in xed proportions and cannot be substituted for with labor or capital.
We furthermore assume that rms source materials from their own sector only. Under these assumptions we can write instantaneous prots as a function of labor and capital as (2) where w jt is the sector wage and p jt the sector domestic price including taris. Notice that the price and productivity shocks enter instantaneous prots multiplicatively. We combine the two sectorlevel shocks into one prot shock, denoted by b jt = p jt b 0 jt . This prot shock includes price shocks and technology shocks that are common to all rms in a sector. It can also include uncertainty shocks to taris or trade policy (Handley and Limao, 2015). Firm-level shocks are only productivity 7 shocks (A ijt ), since this is a perfect competition model and all rms face the same price. We treat the sector-level prot shock b jt as a single random variable, and we assume that A ijt and b jt follow two independent time-invariant rst-order Markov processes. As in Cooper and Haltiwanger (2006), we assume that the prot shock b jt has two states, high and low.
The two assumptions on materialsthat materials transform into output in xed proportions and that rms source materials from their own sector onlyare key to keep the estimation tractable.
Sourcing only from own-sector implies that rms consider only own-sector state variables in the dynamic optimization problem; whereas the combination of the two assumptions on materials results on sector-level shocks entering multiplicatively into prots and therefore being treated as a single state variable. This is not the case in a Cobb-Douglas or CES production function case. We further assume that technology parameters are the same across sectors, so that all sectors can be treated symmetrically in the estimation. For suciently aggregate sectors such as ours, evidence from input-output tables shows that most input-output sourcing does occur within each sector. Given the rm-level predetermined capital and the idiosyncratic productivity shock (K, A), as well as the sector-level prot shock and wage (b, w), rms choose labor to maximize instantaneous prots. From the static prot maximization problem we obtain rm-level labor demand, output supply, and indirect instantaneous prots. We denote the indirect instantaneous prot function with π(K ijt , A ijt , b jt , w jt ). Let µ jt denote the cross-section joint distribution of capital and productivity shocks (K, A) in sector j at time t, and let the mass of rms be normalized to one. Integrating rm-level labor demand over the distribution of rms we obtain aggregate sector-level labor demand given by We now turn to the dynamic problem. Firms choose gross investment I ijt to maximize intertemporal 8 prots net of capital adjustment costs. Investment becomes productive with a one period lag. We adopt the specication of Bloom (2009) and Cooper and Haltiwanger (2006), with tree types of costs of adjustment of the capital stock: xed adjustment costs, quadratic adjustment costs, and partial investment irreversibilities. The investment cost function is  (Dixit and Pindyck, 1994). Finally, the last two terms in (4) capture partial irreversibilities related to transactions costs, reselling costs, capital specicity and asymmetric information (as in the market for lemons). These costs are incorporated into the model by assuming a gap between the buying price p b (1 + τ K ), which includes the tari on imported capital goods τ K , and selling price p s of capital so that p b > p s .
The presence of xed costs and irreversibilities generates a region of inaction for the rm, as well as regions of investment and disinvestment bursts. Following a negative shock rms may hold on to capital in order to avoid xed costs and reselling losses; conversely, in periods of high protability, rms may choose not to increase the capital stock as much, in anticipation of eventual future costs of selling that capital, or not at all, to avoid xed costs. Quadratic adjustment costs, on the other hand, create incentives to smooth out investment over time. The patterns of capital adjustment in turn aect next period's labor demand.
5 We assume that these costs are proportional to the pre-existing stock of capital Kijt at the rm level. Proportionality with respect to K captures the fact that as a rm grows larger xed costs of investment do not become irrelevant, and, on the contrary, the importance of indivisibilities, plant restructuring, worker retraining and production interruption, increase with rm size. Fixed costs can be modeled as proportional to the level of sales or prots at the plant-level; see for example Bloom (2009), Cooper andHaltiwanger (2006), Caballero and Engel (1999).
Alternatively xed costs can also be modeled as independent of rm size, as in Rho and Rodrigue (2016).

9
The dynamic rm problem is represented by the following Bellman equation: where π are maximized instantaneous prots, G is the cost of adjusting the capital stock, Λ jt is a set of aggregate state variables, β ∈ (0, 1) is a discount factor, and E t is the expectation operator conditional on the set of state variables at time t. The vector of aggregate state variables Λ includes sector prot shocks, b jt , and sector wages, w jt . Since the sector wage is an endogenous variable determined in equilibrium, we assume that economic agents form expectations about wages following a linear prediction rule as in Krusell and Smith (1998) and Lee and Wolpin (2006). Details are discussed in Section 2.3 after introducing the worker problem and the equilibrium in labor markets.
The solution to the Bellman equation leads to an investment policy function that we denote with I(K ijt , A ijt , Λ jt ), and an optimal capital stock for next period given by K(K ijt , A ijt , Λ jt ).
Aggregating over next period's capital stock K ijt+1 and the rst order Markov distribution of idiosyncratic shocks A ijt+1 , we obtain next period's rm distribution µ jt+1 .

Workers
To characterize the behavior of workers, we follow the labor mobility cost model of Artuc, Chaudhuri, and McLaren (2010). Workers choose next period's sector of employment based on sector wages, sector job quality, and idiosyncratic shocks to preferences for being employed in each sector. We extend the model to allow for the choice of non-employment, as in Caliendo, Dvorkin and Parro (2019) and Dvorkin (2014). We treat non-employment as an outside option. Switching from the current sector of employment (or non-employment) to a dierent sector has a xed mobility cost.
The model predicts equilibrium worker mobility, equilibrium wage dierentials across sectors, and dynamic responses in aggregate sector employment.
The economy is populated by a continuum of risk-neutral workers with measureN and indexed by . A worker that is employed in sector j receives a wage w jt , and derives utility from a Cobb-Douglas composite of consumption of goods and from the time-invariant average job quality in his sector, denoted by η j , which is the same for all workers. Workers can also be in the outside sector, or non-employment, which we denote with j = 0. The wage of non-employed workers is set to zero and the average job quality is u 0t = η 0 (Dvorkin, 2014).
At the end of period t, workers choose their sector of employment for the next period. The utility cost of moving from sector j to sector k is denoted by C jk . The mobility cost is assumed to be C u when moving in or out of non-employment, C e when moving across production sectors, and zero when workers remain in their current sector. Formally where 1[.] are indicator functions. Workers are further assumed to have idiosyncratic preference shocks over the next sector of employment, denoted by ε kt .
Utility is assumed to be additive in its components. Consumption of goods is optimized by spending a constant fraction φ j of the labor income in good j. Utility of worker , consuming an optimal bundle of goods, employed in sector j and switching to sector k is thus given by where P t is a Cobb-Douglas price index. 6 The worker's problem is to choose the optimal sector of employment for next period taking into consideration the mobility cost, the idiosyncratic shock and the expected discounted value. We assume that ε kt is iid over workers, sectors and time, and that it follows a type 1 extreme value distribution with location parameter −νγ and scale parameter ν. 7 This assumption is standard in the discrete choice literature because of its analytical convenience. The idiosyncratic preferences can be integrated out to achieve closed form solutions for aggregate choices (conditional probabilities of each sector of employment given the current sector). When estimating parameters and simulating scenarios it is thus only necessary to simulate aggregate choices and not individuals.
Given these assumptions it is convenient to dene a Bellman equation as an ex-ante value function, by integrating the expected discounted value of sector j over the distribution of idiosyncratic 6 Utility prior to optimization with respect to consumption is u jkt = Optimizing with respect to x we obtain the indirect utility function (7) with a price index given by log P = J h=1 φ h log p h . 7 The cdf is F (ε jt ) = exp (− exp (−ε jt /ν − γ)), with E (ε jt ) = 0, and V ar (ε jt ) = π 2 ν 2 /6. The parameter γ is the Euler's constant.

11
shocks. For an individual employed in sector j the ex-ante value function is where E ε is the expectation taken over the (J + 1) × 1 vector of idiosyncratic shocks of worker .
The ex-ante value function is interpreted as the value of being in sector j prior to the realization of the idiosyncratic shocks. It depends on current sector wage and mean job quality, and on optimally choosing a sector for next period. The choice for next period depends on the mobility costs, the idiosyncratic shocks and the expected discounted values.
The conditional probability is the share of agents who switch from sector j to sector k. The total number of workers moving from j to k, or gross ow, is equal to m jk (Λ jt )N jt , where N jt is the number of workers employed in sector j at time t The transition equation governing the allocation of labor between sectors, or labor supply, is thus given by On aggregate, individual choices at t determine sector-level labor supply and non-employment at time t + 1. 8 8 A useful result for the empirical implementation is the closed for solution of the ex-ante value function (Rust, 1987), given by Notice that (8) is true for any iid distribution of the idiosyncratic shocks, while the latter holds in the extreme-value case. A closed form solution for the ex-ante value function in turn implies a closed form solution for the conditional probabilities m jk and for labor supply in equation (10).
Regarding aggregate consumption, with Cobb-Douglas preferences aggregate expenditure in each good is a xed share φ j of total income, given by the sum of total labor income and prots net of adjustment costs across all sectors.

Equilibrium
We start by discussing equilibrium in labor markets. At time t workers dene their sector of employment for time t + 1. This implies that at time t, sector labor supply is xed at the current labor allocations, given by N jt (equation 10). Sector labor demand is given by equation (3). The predetermined allocations together with labor demand determine equilibrium wages across sectors. Labor demand is shifted by sector-level prot shocks b jt and the distribution of rms µ jt . Consequently, we can write equilibrium wages as function of current state variables Regarding dynamic decisions, rms choose investment and future capital stock based on current protability shock and capital stock, and future prot shocks and wages. Supply of capital is assumed to be perfectly elastic with time-invariant prices (as in a small economy open to international capital ows). Workers choose their sector of employment for next period based on current sector of employment, idiosyncratic shocks, and future sector wages.
Future wages are endogenous variables determined by equation (11). To keep the computation of the Bellman equations (5) and (8) feasible, we follow Krusell and Smith (1998) and Lee and Wolpin (2006) and use a linear prediction rule for wages.
9 We adopt an augmented AR(1) process for the stochastic evolution of wages, given by is an indicator variables that is equal to one when the sector shocks b jt and b jt+1 are both high or both low; D 2jt+1 is equal one when the sector shocks b jt and b jt+1 switch from high to low; and D 3jt+1 is equal to one when the sector shocks b jt and b jt+1 switch 9 Using a linear prediction rule avoids having to deal with labor allocations Njt and, in particular, with rm distributions µjt as state variables.
13 from low to high. The intuition is that when there are no changes in aggregate shocks (D 1 = 1), wages follow an AR(1) with correlation coecient ρ w . When instead there are changes in aggregate conditions (D 2 = 1 or D 3 = 1); wages jump discretely downwards or upwards in the rst period (they overshoot) and adjust gradually afterwards. This rst-period response occurs in models with imperfect labor mobility such as Artuc, Chadhuri and McLaren (2010) and Dix-Carneiro (2014).
Product prices of tradable sectors are determined in international markets. Domestic prices are equal to international prices plus taris. Sectors in which supply is larger than demand are net exporters, whereas sectors in which supply is smaller than demand are net importers. Gross trade ows are not determined. In the non-tradable sector, prices are determined endogenously by the equilibrium of domestic supply and domestic demand.
The previous equilibrium conditions hold for all time periods and all vectors of aggregate state variables. We are also interested in dening a stationary equilibrium, which we will use in simulation exercises to study trade shocks. In a stationary equilibrium, there are rm-specic productivity shocks A ijt and worker-specic utility shocks ε t , but there are no aggregate prot shocks b jt . As a consequence, while we observe uctuations in rm-level labor demand, investment and output, and in worker-level mobility, there are no uctuations at the aggregate level. Labor allocations, aggregate capital, output, wages, prices of non-tradables, and the distribution of rms are time-invariant in a stationary equilibrium.

Estimation
In this section we discuss the estimation of the model structural paramters. We use two sources of data from Argentina.

Demand and technology parameters
Our main parameters of interest are the capital adjustment cost and labor mobility cost parameters.
We denote them with the vector Γ = (γ 1 , γ 2 , γ 3 ; C e , C u ). We estimate Γ by simulated method of moments (SMM, McFadden, 1989;Pakes and Pollard, 1989). Prior to the estimation of Γ we dene or estimate values for the other model parameters. Table 1 provides a list of the parameters that are predened or estimated prior to the SMM.
We set the discount factor β to 0.95. The depreciation rate δ is 0.0991. Due to lack of data for Argentina, we compute it as a weighted average of sectoral depreciation rates for the U.S. reported by the Bureau of Economic Analysis, using number of rms as weights. From National Accounts, we recover the consumption weights for each sector φ j in order to compute sector demand. Because demand is assumed to be Cobb-Douglas, a constant fraction given by the CPI weights is spent on each product. Argentine families spend on average 31.3 percent of the budget on food and beverages, 37.4 percent on non-tradables and 21.1 percent on other manufactures; textiles and apparel account of 5.2 percent, and minerals and metals for about 2.5 percent each.
The technology parameters, including coecients of the production function and the stochastic processes for the sector-level and rm-level shocks, are estimated with the rm panel and reported in Table 1 as well. We estimate the Cobb-Douglas output elasticities using the regression method of Ackerberg, Caves and Frazer (2015) with data on revenue, employment and capital stock. The estimates for α L and α K are 0.619 and 0.283, both statistically signicant. The input requirement for materials v m is computed as a weighted average of the share of expenditure in materials on total value of production. The estimate is 0.41.
We assume that the sector-level and rm-level shocks, b jt and A ijt follow independent AR (1) processes with correlation coecients ρ b , ρ a , variance of the innovation terms σ 2 b and σ 2 a , constant b for the aggregate shocks and, without loss of generality, a constant of zero for the idiosyncratic shocks. Since the shocks are not observable we rst infer rm-level prot shocks from data on prots and inputs, the functional form assumption of the prot function, and the estimates of the production function parameters, as in Cooper and Haltiwanger (2006). We split rm-level prot shocks into b and A by computing sector-year means and subtracting them from rm-level shocks.
We then run two separate AR(1) regressions to estimate the correlation coecients, variance and constant.
For the rm-level shocks we estimate a correlation coecient of ρ a = 0.902 and a variance for the innovation term of σ 2 a = 0.118. For the sector-level shocks we estimate a constant of b = 0.318, a correlation coecient of ρ b = 0.777, and variance of σ 2 b = 0.044. Once we have the AR(1) parameters we discretize the state space for A ijt and b jt and compute their Markov transition matrices following the approximation of Tauchen-Hussey. We dene an 8-point grid for A ijt and two values for b jt , high and low. The estimated probability of staying in the same state is 0.827 and the probability of switching is 0.172 (Table 1). More details about the estimation of the production function and stochastic process parameters are in on-line Appendix A.
Note that the rm survey covers only the manufacturing sector. For the non-manufacturing sector, which we want to include in the analysis given its importance in the overall economy, we use the production function and shock processes parameters estimated for the manufacturing sector.

Adjustment cost parameters
We now turn to the estimation of the vector of adjustment cost parameters Γ = (γ 1 , γ 2 , γ 3 ; C e , C u ).
Recall that γ 1 , γ 2 and γ 3 are the capital adjustment parameters: the xed cost, the convex cost and the irreversibility cost. On the worker side, C e and C u are the costs of moving between production sectors and in or out of non-employment.
The SMM is based on comparing a vector of empirical moments computed from rm and worker actual data, with moments computed from rm and worker simulated data. The simulated moments depend on the choice of Γ through optimal investment I ijt and equilibrium labor allocation N jt .
The estimator for the adjustment costs minimizes the weighted distance between the empirical and simulated moments. 10 Within the SMM algorithm we further estimate the worker utility function parameters η (sector quality shifters) and ν (worker shock variance) using a linear regression derived from the workers' Bellman equation. This step is done within the SMM because the Bellman equation is a function 10 We use six moments: the serial correlation of the investment rate, corr(Iijt, Iijt−1); the correlation between the investment rate and the protability shocks, corr(Iijt, Aijt); the negative spikes rates, dened as the percentage of rms with investment below negative 10 percent; the correlation between sector deviations in wages and employment with respect to the sector mean, corr((wjt − wj), (Njt − N j ); the serial correlation in non-employment, corr(N0t, N0t−1); and the correlation between the change in non-employment and the change in the average wage across sectors, corr((N0t − N0t−1), (wt − wt−1)). We search over values of Γ using a combination of ne grid search and coordinate descent search, which works better than second-derivative Newton-Raphson or quasi-Newton methods in a case like ours with a discretized state space.
of the mobility costs C e and C u . This strategy follows the conditional choice probability (CCP) approach of Hotz and Miller (1993). More details about the SMM estimation including the estimation of η and ν are in on-line Appendix A.
Results are reported in Table 2. Standard errors for the estimates are computed analytically, as in Bloom (2009). The estimated capital adjustment costs are sizeable and signicantly dierent from zero (panel A). We estimate a xed cost γ 1 = 0.038. This is a substantial cost since it implies that the xed cost of adjustment is about 3.8 percent of the average plant-level capital value.
The estimated coecient for the quadratic adjustment cost parameter ( γ 2 ) equals 0.18. Using the quadratic adjustment cost function and a steady state investment rate equal to the depreciation rate 12 In Panel C of Table 2, we report the parameters of the wage process. They support the conjecture that wages follow an AR(1) and that they make a discrete (positive or negative) jump of an order of magnitude between 0 and

Trade Shocks and Capital Adjustment
We now use the model and the estimated parameters to simulate the dynamic implications of tari reductions in the presence of imperfect capital mobility. Since the distinctive feature of our paper is the introduction of capital adjustment in models of labor frictions, we focus our discussion and simulations to illustrate the patterns of responses in sectoral capital, employment and wages that are the consequence of investment frictions.
In order to assess the impact of an unexpected cut in taris, we create a stationary economy and shut down all aggregate shocks.
13 To do this, we work with permanent unforeseen price changes that occur at time t = 1. We allow for rm-specic productivity shocks A ijt given by (16), but we close down the aggregate productivity shocks, that is, we set b t = b ∀t in (15). In the initial stationary equilibrium, at time t = 0, rms are subject to Markov productivity shocks that create individual uctuations in investment, employment and output, while workers are subject to utility shocks that create labor mobility. At the aggregate level, however, labor allocations, wages, capital, output, and rm distributions are constant in the initial stationary equilibrium. At time t = 1 there is a permanent elimination of taris that triggers dynamic responses. After a transition period, the economy converges to a new stationary equilibrium, at time T . Shutting down other price shocks and aggregate productivity shocks allows us to isolate the eect of a pure trade shock. We use the model parameters to solve for the initial stationary equilibrium, the transition period, and the new stationary equilibrium, jointly for rms and workers.

The Consequences of a Tari Cut in Textiles
We begin the analysis by exploring the impacts of a reduction in prices due to tari cuts. The motivation to use tari reductions as a source of price shocks is to link our work to the trade reforms literature. We also study price hikes below, for example due to increases in trade protection as a result of the recent waves of protectionism. Using tari data from Brambilla, Galiani and Porto (2018), we report in Table 3 the average sectoral tari in place in Argentina during 1994Argentina during -2000 (the period spanned by our data). There is a fair degree of protection, with average taris of 19.4 percent in textiles, 13.9 percent in food and beverages, 14.2 percent in metals, 14.1 percent in other manufactures, and 11.6 percent in minerals. The tari on capital goods is also fairly high, 12.3 percent.
Our benchmark simulation is the full elimination of taris on textiles. We chose textiles because it is the most heavily protected sector of the economy and because this simulation allows us to document in a neat way the generic dynamic responses of the economy to a tari cut. For a small country and homogeneous goods, we have that p jt = p * jt (1 + τ jt ) and, consequently, the impact of the elimination of taris on prices is given by d ln p jt = −τ jt /(1 + τ jt ). As a result, such a cut in taris would bring textiles prices down by 16.2 percent. The other taris and prices of traded goods remain unaected, while the price of the non-traded goods responds in equilibrium.  Table 4. All the results in the paper are very robust to the Leontief production function assumption. Indeed, a Cobb-Douglas specication delivers very similar results both qualitative and quantitatively.
The immediate implication of lower textile prices is a decrease in protability for rms in the sector. Textile rms want to contract. However, capital and employment are predetermined and do not respond initially (i.e., at t = 1). 14 The nominal wage in the textile sector goes down proportionately to prices due to the decrease in the value of the marginal product of labor. But lower textile prices imply a decline in the price index that brings up real wages in all sectors. In addition, the price of non-traded goods declines by 1.36 percent because of the negative income 14 Note that investment at t becomes productive capital in t + 1. In consequence, while there is an investment response in the rst year of the shock, the capital stock remains at the steady state level for one period before adjusting.

19
shock and the consequent lower aggregate demand. The net eect on the real wage in textiles is, however, a decline of 15.04 percent. Real wages instead increase by 1.45 percent in the other tradable sector. In the non-traded sector, there is only a very mild increase in real wages of 0.06 percent. This is because of two opposing eects: lower prices reduce the CPI but the decrease in the output price of non-tradables reduces nominal wages on impact.
In the following periods textile rms disinvest to adjust their stock of capital and workers ow out of the sector attracted by higher real wages elsewhere. Capital and employment gradually decline until they converge to a new steady state level. In the full tari elimination simulation, the capital stock in textiles decreases by 9.41 percent initially (Year 2 15 In the long-run, the annual welfare loss of a textile worker escalated to 1.5 percent, while the loss for other workers is slightly below 1 percent.

Overshooting of Real Wages
The responses of the economy to a trade shock (and more generally to price shocks) is very rich and complex. This is because our model features costs of adjusting both capital and labor in a multi- ). An important nding of our paper is that capital adjustment, though costly and imperfect, prevents this overshooting of real wages. To illustrate this more clearly, we compare the behavior of our model, with both capital and labor imperfections, with a model that features imperfectly mobile labor but xed capitalthe most common environment in the literature.
Following a full tari cut in textiles, we solve the model assuming a constant capital stock in all sectors during the transition and we compute the evolution of wages and employment.  Table 4). The dashed line depicts the dynamic responses of real wages for the xed-capital model. Comparing these two models, there are striking dierences. In both models, because capital and employment are predetermined, the real wage declines on impact in Year 1. However, while real wages continue to decline in the benchmark model, they increase in the xed-capital model. This is the typical overshooting in xed-K models. As explained, the tari shock creates wage dierences that induce workers to move out of sector 2. When rms can adjust the capital stock in response to a negative tari shock, the capital stock shrinks. As a result, labor productivity further declines and, in fact, this eect dominates the increase in the marginal product of labor created by the outow of workers. In the end, real wages continue to drop. By contrast, when the capital stock is xed, labor productivity increases in the sector as workers are displaced during the transition and, as a result, real wages recover. This mechanism is mild in our simulation for textiles (but it might not be in other cases). To see this, note that the real wage in the new steady state of the xed-K model is 13.93 percent lower. Compared to the initial decline of 15.04 percent, this implies a recovery of roughly 1 percentage point. Moreover, the transition is much shorter, 3-4 years only. 16 It is important to note that whether wage overshooting occurs or not depends on the interaction between the capital adjustment costs relative to the labor adjustment costs. This is because the labor market response depends on the speed and magnitude of disinvestment relative to the speed and magnitude of the outow of workers. If, in a given sector, a trade shock can trigger a suciently large exodus of workers, then the longer run recovery of real wages that is distinct to recent frictional models of trade such as Artuc, Chaudhuri and McLaren (2010) or Artuc, Lederman and Porto (2015) could be preserved. To explore this, we simulate a model with reduced C in which we set the labor 16 The role of capital adjustment in impeding the overshooting of real wages is also present in the other sectors.
However, these eects are very small in our current setting and are thus not shown to ease the exposition. mobility costs to US levels from Artuc and McLaren (2015). This simulation delivers a response of real wages that is represented by the dotted line in Figure 2. The overshooting, which is mild in the xed-K model and the estimated mobility costs, become much sharper when C is lower. Given the size of the shock, this higher labor mobility induces a suciently large outow of labor to actually compensate for the declining capital stock. In the new steady state, real wages would decline by Dix-Carneiro (2014) corroborates that, as expected, wages respond negatively to an adverse trade shock in the short-run but that, along the transition, these responses can become attenuated or amplied. There is also solid reduced-form evidence showing that the long-run wage responses can be larger than the short-run eects (Dix-Carneiro and Kovak, 2017). The results of our paper, based on a full structural estimation, put these intuitions into context and quantitatively elucidate how capital and labor market frictions interact in shaping them.

Trade Shocks and the Nature of Capital Adjustment
We model capital frictions in a complex way, which includes xed, convex, and irreversibility costs.
We do this because the nature of the capital adjustment costs function plays an important role in the way the economy responds to trade shocks. To show why our complex structure of capital adjustment costs matters, we compare the evolution of the economy in two experiments. One is our benchmark case with full tari cuts in textiles, which is a negative shock to the sector. The other is the opposite case of a positive shock to the textile sector (for example due to tari protection).
To get the comparison right, we set the price increase equal to the negative of the price decline in 23 the benchmark simulation.
The results are in Table 5. What emerges from this exercise is an intriguing asymmetry between the negative shock and the positive shock (of equal size). Concretely, the positive shock triggers a proportionately larger response of the capital stock than the negative shock. Moreover, this asymmetry is stronger in the short-run and it partially dilutes during the transition. In the benchmark, the initial decline of K is 9.4 percent. In the opposite positive shock, the increase is 12.72 percent.
The positive shock thus triggers a response of K that is 35 percent higher in Year 2. It is 20 percent higher in Year 3, 12 percent higher in Year 4, and 9 percent higher in the steady state. This can be seen clearly in Figure 3, which shows the evolution of the capital stock in the positive shock (solid line) and the mirrored (changed sign) benchmark response (dashed line), which is how a positive symmetrical response would look like. The gap between these two responses starts wide at Year 2 and decreases slowly after that.
The reason for the asymmetry is the nature of the capital adjustment costs. There are convex costs of investment, which provide incentives to smooth (dis)investment over time. There are also xed costs and irreversibility costs of investment. At the rm level, these costs operate in the opposite direction to convex costs, providing an incentive to concentrate (dis)investment in one period and remain inactive in others. At the aggregate level, however, xed costs and irreversibility costs together with rm heterogeneity generate a gradual reaction to a trade shock. Consider now a positive price shock, which gives rms incentives to invest if they are productive enough (relative to their capital stock). Because idiosyncratic productivity uctuates over time and is heterogeneous across rms, rms react to the price shock sequentially upon receiving idiosyncratic shocks and contributing to a gradual increase in the aggregate capital stock. The outcome of this process is the solid black line in Figure 3.
When faced with a negative price shock, rms decide to disinvest if they are not productive enough (relative to their capital stock). However, when the optimal choice is to disinvest, rms have the option of (partially) adjusting capital automatically via depreciation. Depreciation is a free way to reduce capital. As a result, the disinvestment decision is smaller and the capital stock decreases proportionately less. This type of asymmetry cannot be created by a model with xed capital. It cannot either be the result of a model with a simpler structure of capital adjustment costs, such as convex costs alone or ad-hoc specications as in Dix-Carneiro (2014).
The fact that the capital stock in the sector reacts proportionately more to a positive shock than 24 to a negative (and equal) shock, especially in the short-run, has similar implications for employment and real wages. In Table 5, we show that the more pronounced response of capital raises real wages and employment proportionately more in the positive shock as well. These asymmetries are much stronger in the short-run than in the long-run as expected. In fact, note that the asymmetric response is real wages disappears eventually in steady state.
Qualitatively, these results suggest that in the presence of a complex structure of capital adjustment costs, the economy can respond dierently to positive than to negative shocks and to shocks of dierent sizes. In the simulations, these dierences are large enough to warrant attention in the assessment of trade shocks.

The Consequences of Tari Cuts on Capital Goods
In this section, we explore the implications of tari cuts on capital goods. In our model, we assume capital goods can be imported at given international prices plus any taris, as in Rho and Rodrigue The results are presented in Figure 4 which shows the evolution of capital (panel a), real wages (panel b) and employment (panel c). For each variable, we reproduce on the left the responses following a reduction of textile taris (as in Figure 1). We then perform two simulations. In the rst one, we only allow the textile sector to import capital at the lower prices. These results are reported on the center panel of Figure 4. In the second experiment, we assume the tari cuts on capital apply to all sectors. These results are on the right panel.
A lower price of capital goods for textile rms dampens the disinvestment caused by the loss of output protection during the transition. The total capital stock declines only by about 10 percent, compared to about 25 percent in the benchmark experiment. The speed of adjustment is slightly faster. The initial decline in real wages (15.4 percent) is the same in the two scenarios, because L and K are predetermined at t = 1. However, the additional decline in real wages observed in the benchmark disappears, to a large extent. Instead of a long-run decline of 20 percent, real wages decline by about 16 percent. This is because, while rms disinvest less, workers are still being displaced to other sectors at the same time. In the end, the marginal product of labor does not decrease by much. The responses of employment are attenuated: there is a smaller contraction of employment in textiles (again, because the capital stock is higher than in the benchmark) and a consequent smaller expansion of the other sectors, including non-employment. We can conclude that while the textile sector suers from the loss of tari protection, the opportunity for cheaper investment helps cushioning some of the negative impacts. This eect is not strong enough in our case to overdo the consequences of the tari de-protection on nal goods so that there is no wage overshooting. But the magnitudes are sizeable nevertheless.
The impacts of the liberalization of capital import tari across all sectors (right panel of Figure   4), are as follows. A lower price of capital goods creates investment incentives in other traded manufactures as well as in non-traded sectors. The magnitudes are large, between 15-17 percent depending on the sector. This is important for various reasons. Real wages in these sectors increase by much more than before (up to 5 percent in other traded goods). This attracts more workers from the textile sector, which thus shows a higher decline in employment. Finally, the expansion of the non-textile sectors absorbs unemployed workers. More specically, while non-employment increases with the reduction in output taris in textiles, it instead declines by more than 1 percent when capital goods taris are removed as well.

Extensive Margin Adjustments
The responses of labor market outcomes and investment to sector shocks are the aggregation of rm-level responses and as such they depend on the distribution of rms. In our baseline model aggregate responses only have an intensive margin dimension, as we do not consider rm turnover.
However, there is a large literature on industry dynamics that argues that entrants and exiters are systematically dierent from incumbents (Dunne, Roberts and Samuelson, 1988;1989;Jovanonic, 1982;Hopenhayn, 1992). Firm entry and exit can amplify or reduce the impact of aggregate shocks and have persistent consequences on capital accumulation, employment and wages over time (see Clementi andPalazzo, 2016, andSedlacek, 2020). In this section we explore how aggregate responses change when we add an extensive margin in the domestic market. 17 17 There is a vast literature of selection into export markets based on heterogeneous rm characteristics starting with Melitz (2003). This literature is based on rms that produce dierentiated varieties and face a downward sloping 26 We adopt a simple specication that allows for entry and exit. In this section we provide a brief description, while more details are discussed in on-line Appendix B. In each period there is a xed mass of potential entrants in each sector j that face a stochastic iid sunk cost of entry given by F 0 . Upon entry rms receive a draw of productivity (A) and initial capital (K ) from a distribution µ 0 . Firms start operating in the following period after entry and from then on their productivity and capital evolve in the same manner as for incumbent rms. We augment the Markov process of productivity to include an absorbing state of exit. The Markov process is a mixture model.
With probability ζ, productivity A evolves according to the Markov process in the baseline model without exit, and with probability (1 − ζ) the rm falls into an absorbing state of A = 0 and exits the market. To introduce a simple selection mechanism into the exit process, we further assume that only rms with idiosyncratic productivity below the 75th percentile face the possibility of falling into the absorbing state.
In every period the entry equilibrium is dened by a cuto in the sunk cost of entry F 0 . Let V 0jt denote the expected value prior to entry in sector j, integrated over draws of initial productivity and capital stock. The expected value V 0jt is the same for all rms. Firms enter as long as their draw of F 0 is lower than the expected value prior to entry. The equilibrium mass of entrants in sector j, n 0jt , is given by where H is the cdf of the cost of entry.
The expected value V 0jt varies across periods according to state variables b jt and w jt . Equilibrium sector wages further depend on labor allocations, N jt , distributions of active rms, µ jt , and the mass of active rms, which we denote with n jt . When there is a negative sector shock due to a tari reduction, the expected rm value decreases and fewer rms enter. This in turn reduces the number of active rms in the market, n jt . A reduction in the number of active rms leads to a decrease in labor demand and wages, which in turn drives up the rm expected value again. In the post-shock stationary equilibrium the number of active rms is lower than prior to the shock. demand curve. Exporting allows rms to grow and increase revenue and prots after paying export participation costs. By contrast, in our model products are homogeneous and rms face an innitely elastic demand. This setting does not lend itself to the introduction of export participation costs and decisions. Moreover, at the rm level, the possibility of exporting does not play a role on labor demand, investment, and the decision to enter into the domestic market.
In a stationary equilibrium, the expected value prior to entry and the number of active rms in the market are constant over time, while there is rm turnover with an equal number of entrants and exiters.
To simulate aggregate responses to tari shocks we use our previous estimates for the baseline model parameters, including capital adjustment costs, labor mobility costs, production function coecients, and the stochastic evolution of shocks. We calibrate the distribution of the sunk costs of entry and the distribution of entrants and dropouts to match exit rates and relative size of rms from Dunne, Roberts and Samuelson (1988).
We summarize the main implications of the extensive margin of adjustment by comparing the evolution of capital, real wages and employment in the Textile sector in the baseline model and in the extended model with entry and exit. The results are in Table 6. The negative short-run response of the capital stock is much larger when we allow for exit and entry. The negative tari shock reduces protability in the sector, there is less entry than exit (during the short-run), and capital is consequently destroyed more quickly. With this additional margin of adjustment, the aggregate capital stock declines by 40 percent more on-impact (Year 2) and by 14 percent more along the rst ve years of the transition to the steady state. In the long-run, the decline in the steady state capital stock is only 2 percent larger. There is a more pronounced decline in labor, too. The higher rate of exit accounts for a 2 to 3 percent lower level of employment in the sector in the short-run and a 5 percent lower employment in the long-run. Finally, there is a correspondingly larger decline in real wages, which is more pronounced in the long-run (6 percent larger decline) than in the short-run (2 to 4 percent). To sum up, with entry and exit, the adjustments are sharper than in the baseline, especially in the short-run.

Conclusions
We 0.827 Tauchen-Hussey approximation P (b t = high|b t = low) 0173 Tauchen-Hussey approximation Notes: list of estimates and source of each parameter value. Standard errors in parenthesis.
Notes: table shows the capital adjustment cost and labor mobility cost parameters; utility function parameters; wage stochastic process parameters; and the empirical and simulated moments. Standard errors in parenthesis. Source: Taris τ j (in percent) are from Brambilla, Galiani and Porto (2018). Price changes are computed as −τ j /(1 + τ j ). The change in the prices of the non-traded goods comes from the simulations. Notes: Simulation of the transitional dynamic responses of capital, real wages, employment and producer and worker welfare following the full elimination of taris on the textile sector. Notes: Simulation of the transitional dynamic responses of capital, real wages and employment in the benchmark case (full elimination of taris on textiles) and in a positive shock scenario with positive benchmark price changes (price changes with changed sign).

On-line Appendix: Estimation Details
This appendix provides more details on the estimation procedures introduced in section 3 of the paper. We estimate the parameters related to the rm and worker decision problems using Argentine data. We combine a panel of rms with a panel of workers.
A.1 Data

Firm data
The estimation of the rm problem requires panel data with detailed information on the investment decision of rms. In particular, to t the capital adjustment cost model, we need data on purchases of new capital as well as on sales of installed capital. We use the Encuesta Industrial Anual (EIA, or Annual Industrial Survey), which meets these requirements. We express all monetary variables in real terms using dierent deators. For wages we use the consumer price index; for investment, capital and intermediate inputs we use the general level wholesale price index; and for revenue, sales and prots a wholesale price index at a four digit level of disaggregation according to the ISIC classication.
To construct the real investment series, we generate an initial measure of the real capital stock at the plant-level and then complete the series using the perpetual inventory method according to the rule K ijt+1 = (1 − δ)K ijt + I ijt . Real investment is dened as I ijt = E ijt − S ijt , where E ijt is real gross expenditures on capital equipment, and S ijt is real gross retirements of capital equipment.
Since our dataset does not contain information on the book value of capital, we approximate the initial capital stock of the rm as the average across years of the ratio between the amount of capital depreciation declared by the rm and the estimated depreciation rate. We deate our measure of initial capital stock by the general level of the wholesale price index. We use depreciation rates estimated by the Bureau of Economic Analysis (BEA) as described before. Our depreciation rates include both in-use depreciation (which reects declines in the eciency of the asset because of aging or wear and tear) as well as retirements or discards (which reects, for example, obsolescence).

Labor force survey
The estimation of the parameters of the workers' problem requires panel data on workers' sector of employment and wages or non-employment status. We use the panel sample of the Encuesta

A.2 Estimation of the technology parameters Production function parameters
We postulate a production function which is Leontief in materials M ijt and a Cobb-Douglas index of capital K ijt and labor L ijt . To estimate the Cobb-Douglas production function coecients on labor and capital, we follow the regression approach of Ackerberg, Caves and Frazer (2015). It is important to note that the structural assumptions of the estimation method are compatible with our own structural model. We use value of production (Y ijt ) on the left-hand side, capital (K ijt ) and labor (L ijt ) on the right-hand side, and following the Leontief specication of the production function we exclude materials from the regression at this stage. The regression equation for this stage takes the form where is a combination of productivity shocks and measurement error in output. The equation reects the contribution of labor and capital to output and is therefore conceptually a value-added production function (given the Leontief specication), even though total value of production is on the left-hand side. See Ackerberg, Caves and Frazier (2015). We use the predetermined variables K ijt , K ijt−1 and L ijt−1 as instruments. Standard errors are computed from 500 bootstrap replications.
The labor coecient α L is 0.619 and the capital coecient α K is 0.283. Both are statistically signicant. These results are comparable to those obtained by Pavcnik (2002) for Chile.
We calibrate the unit input requirement for materials v M by computing the mean of M ijt /Y ijt across rms. The estimated value for the unit input requirement is 0.41. As a robustness exercise we In the model of section 2 we further assume that rms source intermediate inputs from their own sector of production only. This assumption is key for the viability of the estimation procedure as it allows us to treat rms in all sectors symmetrically. It is based on the notion that sectors are aggregate enough so that products are suciently dierent within a same sector, but related through the production chain. For example, the main material in the production of shirts is fabric, and both shirts and fabrics are products within the textile sector. As a back-of-the-envelope test of the assumption we compute coecients for own-sector sourcing from the input-output Stochastic process for sector and rm-level shocks Firms face sector-level prot shocks b jt , that include shocks to aggregate productivity and to prices, and rm-level shocks A ijt . We assume that b and A follow AR(1) stochastic processes given by with b jt+1 ∼ N (0, σ 2 b ) and a ijt+1 ∼ N (0, σ 2 a ). We further assume that the shocks b jt are independent across sectors and the shocks A ijt are independent across rms. Since b jt and A ijt are not observable, we infer them from data on operating prots as follows. From the denition of instantaneous prots we can write the combination of sector-level and rm-level protability shocks as Let x ijt denote the product of the rm and sector level shocks, with x ijt = b jt A ijt . We compute the right-hand size of (17) from data (π ijt , K ijt , w jt ) and the estimates from the previous step (α L , α K , v M ). This gives us estimates for x ijt . To estimate the A parameters, we rst compute deviations of x ijt from sector-year means (to get rid of b jt ) and then regress this on one lag (no constant) To estimate the b parameters we compute the sector-year means of x ijt and run the regression using the means, at the sector-year level In Table 1 in the paper, we report ρ a = 0.902, σ 2 a = 0.118, b = 0.318, ρ b = 0.777, and σ 2 b = 0.044.

A.3 SMM estimator
The adjustment costs parameters are given by the vector Γ = (γ 1 , γ 2 , γ 3 ; C e , C u ), which we estimate by simulated method of moments (SMM). The SMM estimator is based on comparing a vector of empirical moments computed from rm and worker actual data, denoted by Ψ, with moments computed from rm and worker simulated data, denoted by Ψ s (Γ). The simulated moments depend on the parameters Γ through the investment policy function and the employment transition probability policy function, given that the moments are based on rm-lelve investment and labor allocations across sectors. The estimator for the adjustment costs minimizes the weighted distance between the empirical and simulated moments. Formally, where Ω is the optimal weighting matrix.
The estimation procedure involves iterating over possible values of Γ. At each iteration there are two steps: (i) we solve Bellman equations and policy functions for rms and workers for a discretized state space; (ii) we draw a Markov chain of aggregate shocks b jt and simulate an equilibrium path for the endogenous variables from which we compute the simulated moments and the distance function.
The problem is computationally challenging. Some model assumptions have been made to keep the estimation tractable. In the case of rms, we assume symmetry across production sectors and input sourcing within sector. This allows us to solve only one rm Bellman equation and rm policy function instead of one for each sector. In the case of workers we cannot treat the sectors symetrically. We need to solve seven worker Bellman equations (one for each production sector and one for non-employment) in order to compute the transition probabilities across sectors.
We therefore follow a dierent modelling strategy to reduce the state space by assuming that idiosyncratic shocks are iid and follow a type-I extreme value distribution. In the case of rms, on the other hand, we allow for autoregressive shocks.
To further reduce the state space, we take advantage of the fact that several aggregate state variables enter the rm and worker problems solely through wages, which are an endogeneous variable from the point of view of the equilibrium of the economy but an exogenous variable from the point of view of rms and workers. Following Krusell and Smith (1998) and Lee and Wolpin (2006) we impose an ad-hoc stochastic process for wages that workers and rms use in computing expected values (equation 12).
Finally, we reduce the SMM to iterating through the capital and labor mobility cost parameters Γ. This keeps the estimation more tractable, and the minimization of the distance function more precise and reliable. We estimate the production technology parameters prior to the SMM, as described above, and the worker utility function parameters as a linear function of Γ within the SMM. More details on the estimation of the utility function parameters are given below.
We discretize the state variables to construct grids. We discretize capital K with a grid of 150 points, and wages w with a grid of 50 points. Aggregate shocks b take two values, high and low.
Idiosyncratic shocks take 8 values. We approximate the transition probability matrices of b and A with the method of Tauchen-Hussey, and the transition matrix for w from the stochastic evolution given by equation (12). To compute the distance function (20)  Estimation of worker utility parameters ν and η The vector of sector employment quality η and the variance of the idiosyncratic utility shocks ν can be estimated as a linear function of the mobility cost parameters C e and C u . The estimation strategy for η and ν is based on Hotz and Miller (1993) and the ensuing CCP-estimator literature.
In the trade literature, a similar approach is utilized by Artuc and McLaren (2015) and Caliendo, Opromolla, Parro and Sforza (2020).
Given the extreme value distribution of ε, from the ex-ante value function (8) and the conditional choice probabilities (9), we can write the ex-ante value function as a function of the probability of staying in the initial sector of employment as We can also write the dierence in expected continuation values between sectors k and j as a function of the dierence in choice probabilities of switching to k or staying in j as Combining these two results, we get This is an Euler equation that can be estimated conditional on C e and C u with a linear regression, from actual data, as in Artuc, Chaudhuri and McLaren (2010), by allowing for a disturbance term ω t+1 which captures the innovation in the stochastic process of wages, unforeseen at time t. The employment quality parameters η are the coecients on sector dummy variables (sector 1 is normalized to zero). Since there is a potential correlation between real wage dierences across 18 Lee and Ingram (1991) show that the inverse of the variance-covariance matrix of the actual moments is a consistent estimator for the optimal weighting matrix. We use 1,000 bootstrap replications on actual data to generate the variance-covariance matrix of the actual moments.
sectors and the disturbance term ω t+1 because this includes unexpected shocks to wages, we follow Artuc, Chaudhuri and McLaren (2010) and use past wage dierences as an instrument. Given the assumptions of the labor choice model, past wage dierences should be uncorrelated with shocks at t + 1. The key identication assumptions for this IV to work are that i) the idiosyncratic shocks ε are iid shocks; ii) the state of the economy evolves as a Markov process. The Markov assumption is straightforward.

Assessment and Goodness of Fit
We end this section with an assessment of the estimation. First of all, note that the observed moments and simulated moments (at the estimated parameters) are well-matched by the SMM.
This can be seen at the bottom of Table 2.  Figure A2 provides more intuition about how the SMM identies these dierent parameters.
Each panel shows the response of the dierence between the observed and the simulated moments (squared) to a dierent adjustment cost parameter. In panel A, we show that moment 2 (the correlation between investment and protability) identies the xed cost parameter γ 1 . The quadratic cost parameter (γ 2 ) and the irreversibility parameter (γ 3 ) are both identied from the opposing forces of moment 1, the serial correlation in investment, and moment 3, the negative spike moment (panels B and C). The labor mobility cost across sectors (C e ) is identied from the serial correlation between the change in wages and the change in employment (moment 4). The mobility cost in and out of non-employment (C u ) is identied from the serial correlation in non-employment (moment 5) and the correlation between the change in non-employment and in the average wage (moment 6). These are shown in panels D and E of Figure A2. 20 19 Note that in this Euler equation the expectation is taken over realizations of all the state variables so that it is consistent with any structure in the economy provided it evolves as a Markov process. In particular, workers expectations are perfectly consistent with our formulation of rm behavior.
20 Note that our model does not match the spikes as well as it does the other moments. This is because the spikes correspond to estimating a percentile of rms located in the tail of the rm distribution, which is much harder to replicate in the simulation of the model than a measure of central tendency such as a mean (or a correlation).
As Figure A2 shows, the moment does however play a crucial role in identifying the trade-os between inaction in investment or smoothing investment faced by rms.

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The model also matches important moments of the data that we did not include in the SMM.
The top panel of Table A2 reports the average sector wage as well as the employment transition probabilities. 21 As it can be seen, the model and the data correspond quite well. We can also assess investment patterns by looking at the direction of investment. In the bottom panel of Table A2, we show the percentage of rms that disinvest (I < 0), the percentage of rms with investment inaction (I = 0), and the percentage of rms that invest (I > 0). We do this unconditionally and for two types of rm: low-capital (below the average capital stock) and high-capital (above the average capital stock). On average, the data and the model also correspond well, and especially so for low-K rms.
To further analyze the goodness of t of the model, we present the comparison of several rmlevel outcomes in Figure A3. Panels (a)-(c) show the kernel density estimates of the distribution of employment, capital and prots using the rm datasolid lineand the simulated data from the SMMdashed line. The densities t well. In panels (d) and (e)  Notes: Each panel shows the dierence between the observed and the simulated moments (squared) as a function of an adjustment cost parameter. Moment 2 (the correlation between investment and protability) identies the xed cost parameter γ 1 . The quadratic cost parameter (γ 2 ) and the irreversibility parameter (γ 3 ) are both identied from the opposing forces of moment 1, the serial correlation in investment, and moment 3, the negative spike moment. The labor mobility cost across sectors (Ce) is identied from the serial correlation between the change in wages and the change in employment (moment 4). The mobility cost in and out of non-employment (Cu) is identied from the serial correlation in non-employment (moment 5) and the correlation between the change in non-employment and in the average wage (moment 6).
49 Figure A3 Comparison of empirical data and simulated data Notes: comparison of rm-level outcomes from rm data (EIA, Annual Industrial Survey) and the SMM simulated data. Panels (a) to (c) present the kernel density estimates of log employment, log capital and prots. Panels (d) and (e) present the mean of log employment and prots conditional on percentiles of the log capital distribution. This appendix provides more details about the extension of the model to include rm entry and exit (Section 4.5); and a robustness exercise in which we assume a Cobb-Douglas production function in labor, capital and materials (instead of our baseline case in which the production function combines materials and a Cobb-Douglas index of labor and capital in xed proportions given by equation 1).

B.1 Firm entry and exit
The extension of the model to study the role of the extensive margin introduces rm entry and exit based on selection. We assume that in every sector and time period there is a continuum of rms with measure one that are waiting to enter. They each take an iid draw of the sunk cost of entry, F 0 , from a Frechet distribution with cdf H and shape parameter h. Firms compare the sunk cost of entry with the expected value prior to learning their productivity and capital, V 0jt . Firms that take a draw of F 0 between 0 and V 0jt enter the market. This rule denes the mass (or number) of entrants, n 0jt , as dened in equation (13). We denote the number of entrants, active and exiting rms with n 0jt , n jt and n xjt . Notice that the expected value at entry, V 0jt , is time-varying outside of a stationary-equilibrium, as rm prots depend on sector shocks and wages, which in turn are also time-varying.
After paying the sunk entry cost F 0 , rms take productivity and initial capital draws (A 0 , K 0 ) from a rm distribution µ 0 . We assume that the distribution of entrants (µ 0 ) is proportional to the distribution of incumbents (µ) and right-truncated on both dimensions (A and K), so that µ stochastically dominates µ 0 and entrants are on average less productive and smaller than incumbents. We arbitrarily truncate the productivity of entrants at the 80th percentile. 23 Firms further need to pay the investment cost to achieve the random initial level of capital, which we assume is not subject to adjustment costs and is equal to the initial level of capital. In period 1, new rms become active rms, with productivity and capital initially drawn from µ 0 . They make their rst decisions regarding employment, production and investment, and are subject to adjustment costs. From period 1 onwards, idiosyncratic productivity evolves according to the Markov process for active rms as in the baseline model without entry and exit.
23 We have experimented with alternative truncation points such as the mean and the median. However, the alternative lower truncation points do not allow us to correctly match the truncation point for capital. We discuss this below.
We dene two groups of rms, according to whether their idiosyncratic productivity A is below or above the 80th percentile, and denote them with Z L and Z K . In each period, rms in the group Z L (low productivity rms) face a probability (1 − ζ) of falling into an absorbing state of A = 0, which means exiting the market as present and future prots become zero. The probability of exit is zero for rms in Z H (high productivity rms). These simplifying assumptions are based on the empirical observations of Dunne et al (1988Dunne et al ( , 1989, who nd that exiting rms are smaller than continuing rms, and in the simulations of Clementi and Palazzo (2016), who estimate close-to-one probabilities of survival for rms with high productivity. The probability of exit introduces a simple mechanism of selection that correlates with productivity. Notice that because the distribution of entrants is truncated at the 80th percentile, all new rms fall into the Z L group and face a positive probability of falling into the absorbing state (1 − ζ). This matches the empirical fact that entrants are more likely to exit than incumbents (Dunne et al, 1988).
In any given period, the probability of being in group Z L , denoted with ρ Lt , is given by The probability of exit, denoted with ρ xt , is ρ xjt = (1 − ζ)ρ Ljt . The number of rms that exit the market is given by n xjt = ρ xjt n jt−1 .
Under these assumptions, the expected rm value prior to entry is given by where the expectation E t is taken over next period's values of sector shocks and wages. The last term corresponds to the required stochastic initial investment drawn from µ 0 . The expected value V 0jt varies across periods according to state variables b jt and w jt . Wages are determined in equilibrium (equation 11). They depend on the current labor allocations between sectors, and on aggregate shocks and rm distributions through labor demand. With the introduction of entry and exit, wages further depend on the mass of active rms, n jt . When there are sector shocks, incentives to enter the market are aected, and equilibrium is restored through changes in number of rms, labor demand, equilibrium wages, and rm prots.
To simulate aggregate responses to tari shocks we use our previous estimates for the baseline model parameters, and calibrate the new parameters to match statistics from Dunne et al (1988).

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The calibration is based on the initial stationary equilibrium. We arbitrarily truncate productivity at the 80th percentile as discussed above. We truncate capital so that the average optimal labor demand of entrants is 25.63 percent of the average labor demand of incumbents. 24 We set the exit rate ρ x to 0.098 based on the annualized average exit rate in Dunne et al (1988). We compute the expected value at entry, V 0 , from equation (22). 25 In a stationary equilibrium the number of entrants is equal to the number of exiting rms. With the number of entrants and the expected value at entry we pin down the distribution of entry costs from equation (13). The shape parameter is h = 1.5961. We then proceed with the simulations of the trade policy shock, which are discussed in the main text.

B.2 Cobb-Douglas production function
In our model we assume that the technology of production is Leontief in materials and a Cobb-Douglas index of labor and capital. This is a convenient assumption so that productivity and price shocks enter multiplicatively into the prot function and can be treated as a single prot shock.
In this section we re-estimate the adjustment cost parameters and simulation results assuming a Cobb-Douglas production function in the three inputs, given by The variables are dened as before, with aggregate and idiosyncratic productivity shocks b 0 jt and A ijt , and the new parameter α M which is the output elasticity of materials. The objective of this exercise is to check whether the qualitative implications of the model remain unchanged under a dierent functional form assumption for the technology of production.
Under the new technology assumptions instantaneous prots are where the aggregate shocks b 0 jt and p jt do not enter multiplicatively. As before, we dene the combined protability shock as b jt = b 0 jt p jt and treat it as a single state variable that follows the AR(1) process in equation (15). We further make the following two assumptions to pin down the 24 Dunne et al report that on average the size of entrants is 25.63 percent of the size of incumbents.
25 In a stationary equilibrium aggregate variables b and w are xed over time and consequently the expectation operator Et is dropped from the equation.  (23).
values of b 0 jt and p jt , which we need to input separately into the prot function: log b 0 jt = 0.5 log b jt ; log b 0 jt = 0.5 log b jt .
We calibrate the output elasticities α L , α K and α M from the 1997 input-output table for Argentina. From the rm data we estimate the stochastic process for b jt and A ijt given by equations (18) and (19). We estimate the adjustment cost parameters Γ = (γ 1 , γ 2 , γ 3 , C e , C u ) following the SMM objective function (20). We rst recompute the second empirical moment, which is the correlation between investment and idiosyncratic shocks Corr(I ijt , A ijt ), as the shocks A ijt need to be recomputed under the new technology specication. 55 Figure B1 reports simulation results of a tari cut in textiles. To facilitate the comparison we reproduce simulation results for the dynamics of capital, wages and employment from Figure   1 in the left panel. Simulations following the Cobb-Douglas specication are in the right panel.
The qualitative results of both models are very similar. Quantitatively, responses are higher in the baseline case, especially for employment, but of similar orders of magnitude. Results are consistent across both specications and do not hinge on a particular specication for the production function. Other Traded Non-traded Notes: responses of capital, real wages and employment to a full elimination of taris on textiles. Simulation results from the baseline Leontief specication for the production technology on the left and from the Cobb-Douglas specication on the right. 57