Policy Research Working Paper 9775
Patterns of Labor Market Adjustment to Trade
Shocks with Imperfect Capital Mobility
Erhan Artuc
Irene Brambilla
Guido Porto
Development Economics
Development Research Group
September 2021
Policy Research Working Paper 9775
Abstract
This paper explores how different investment frictions responses. This happens as textile firms disinvest during the
affect the patterns of responses of labor markets to tariff transition. This paper also shows that the reduction of tariffs
cuts. To investigate these patterns, this paper formulates on capital inputs boosts investment and real wages across
a multi-sector dynamic model featuring capital and labor sectors. This paper assesses the nature of capital adjustment
adjustment costs that is fitted to Argentine data. Counter- costs, including fixed, convex, and irreversibility costs in
factual simulations of a tariff decline in the textile sector are determining these patterns of labor market responses to
used to show that capital adjustment can create long-run trade reforms.
responses of real wages that are larger than the short-run
This paper is a product of the Development Research Group, Development Economics. 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://www.worldbank.org/prwp. The authors may
be contacted at at eartuc@worldbank.org; irene.brambilla@econo.unlp.edu.ar; or guido.porto@depeco.econo.unlp.edu.ar.
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
Patterns of Labor Market Adjustment to Trade Shocks
with Imperfect Capital Mobility*
Erhan Artuc Irene Brambilla
Guido Porto
The World Bank Dept. of Economics Dept. of Economics
DECRG UNLP UNLP
JEL Codes: F1; J21; J62; E22.
Keywords: Trade shocks, capital adjustment, labor mobility, labor market dynamics.
*
The authors thank seminar participants at Carlos III, Di Tella, FREIT, LACEA-TIGN, La Plata, Penn State,
Princeton, Pompeu Fabra, San Andres, Syracuse, Temple, Illinois-UC, and the World Bank. The authors have
beneted from discussions with N. Bloom, R. Dix-Carneiro, J. Eaton, B. Eyigungor, B. Kovak, J. McLaren, B.
Rijkers and J. Rodrigue. The Editor and the referees provided excellent comments to improve the paper. The views
in this paper are the authors' and not those of the World Bank and its aliated organizations, or those of the
Executive Directors of the World Bank or the governments they represent, or any other institution. Research for this
paper has been supported in part by the Knowledge for Change Program, the Multidonor Trust Fund for Trade and
Development, and the Strategic Research Program of the World Bank. Porto also gratefully acknowledges support
from the r4d program on Employment funded by Swiss National Science Foundation and the Swiss Development
Cooperation.
Development Economics Research Group, The World Bank. email: eartuc@worldbank.org
Universidad Nacional de La Plata, Departamento de Economia, Calle 6 e/ 47 y 48, 1900 La Plata, Argentina.
email: irene.brambilla@econo.unlp.edu.ar
Universidad Nacional de La Plata, Departamento de Economia, Calle 6 e/ 47 y 48, 1900 La Plata, Argentina.
email: guido.porto@depeco.econo.unlp.edu.ar
1 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' sector-
specic 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
1994-2001. 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.
3
This feature is shared by the trade model of Artuc, Chaudhuri and McLaren (2010) but it is a major dierence
with the capital adjustment costs models of Cooper and Haltiwanger (2006) and Bloom (2009) in which wages are
exogenous.
3
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 com-
plex 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), Caliendo, Dvorkin
and Parro (2019) and others.
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.
1.1 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
5
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.
2 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 optimiz-
ing 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 τjt so that domestic prices
are pjt = p∗
jt (1+τjt ). In the non-tradable sector, prices are endogenously determined in a competitive
domestic market. Wages are determined endogenously in each sector as well.
2.1 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
αL αK Mijt
(1) Yijt = min (b0
jt Aijt )Lijt Kijt , ,
vM
where Yijt is output, Lijt is labor, Kijt is the capital stock, and Mijt is materials. The variables
b0
jt and Aijt are sector-level and rm-level productivity shocks, respectively. Both are Hicks-neutral
in the three inputs. The parameters αK and αL are the Cobb-Douglas output elasticities and vM
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
αK αL
(2) Πijt = pjt b0
jt Aijt (1 − vM )Kijt Lijt − wjt Lijt ,
where wjt is the sector wage and pjt the sector domestic price including taris. Notice that the price
and productivity shocks enter instantaneous prots multiplicatively. We combine the two sector-
level shocks into one prot shock, denoted by bjt = pjt b0
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 (Aijt ), since this is a perfect competition model and all rms face the same price. We treat
the sector-level prot shock bjt as a single random variable, and we assume that Aijt and bjt follow
two independent time-invariant rst-order Markov processes. As in Cooper and Haltiwanger (2006),
we assume that the prot shock bjt 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.
Calculations from IO tables from Argentina for the year 1997 show that materials sourced from
own-sector account for 75 percent of all materials for food and beverages, 59 percent for textiles, 80
percent for metals, 26 percent for minerals, and 70 percent for other manufacturing industries. To
assess the xed proportions technology assumption, we present an alternative specication with a
Cobb-Douglas technology in on-line Appendix B. The qualitative conclusions of the paper remain
unchanged.
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 (Kijt , Aijt , bjt , wjt ). Let µjt 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
1/(1−αL )
αL bjt
(3) N d (bjt , wjt , µjt ) = (1 − vM ) AK αK µ(dK × dA).
(K,A) wjt
We now turn to the dynamic problem. Firms choose gross investment Iijt 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
(4) G(Kijt , Iijt ) = γ1 Kijt 1[Iijt = 0] + γ2 (Iijt /Kijt )2 Kijt +
+ pb (1 + τK )Iijt 1[Iijt > 0] + ps Iijt 1[Iijt < 0],
where 1[Iijt = 0], 1[Iijt > 0] and 1[Iijt < 0] are indicator variables that are equal to one when
investment is non-zero, strictly positive, and strictly negative, respectively.
The rst term captures xed adjustment costs, which are paid whenever investment or disin-
vestment take place. Fixed costs are independent of the investment level in order to capture non-
convexities and increasing returns to the installation of new capital.
5 The second term captures the
quadratic adjustment costs. These are variable costs that increase with the level of the investment
rate (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 pb (1 + τK ), which includes the tari on imported capital goods τK , and selling
price ps of capital so that pb > ps .
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. Propor-
tionality 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 pro-
duction 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 and Haltiwanger (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:
(5) V (Kijt , Aijt , Λjt ) = max {π (Kijt , Aijt , bjt , wjt ) − G(Kijt , Iijt ) +
Iijt
βEt V (Kijt+1 , Aijt+1 , Λjt+1 )},
where π are maximized instantaneous prots, G is the cost of adjusting the capital stock, Λjt is a
set of aggregate state variables, β ∈ (0, 1) is a discount factor, and Et 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, bjt , and sector wages, wjt . 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 (Kijt , Aijt , Λjt ), and an optimal capital stock for next period given by K (Kijt , Aijt , Λjt ).
Aggregating over next period's capital stock Kijt+1 and the rst order Markov distribution of
idiosyncratic shocks Aijt+1 , we obtain next period's rm distribution µjt+1 .
2.2 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 measure ¯
N and indexed
by . A worker that is employed in sector j receives a wage wjt , 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 ηj , 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 u0t = η 0 (Dvorkin, 2014).
10
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 Cjk . The mobility cost is assumed to
be Cu when moving in or out of non-employment, Ce when moving across production sectors, and
zero when workers remain in their current sector. Formally
(6) Cjk = Cu 1 [k = 0 ∨ j = 0, k = j ] + Ce 1 [k = 0 ∧ j = 0, k = j ] ,
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 φj 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
wjt
(7) u jkt = + η j − Cjk + ε kt ,
Pt
where Pt 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 func-
tion, by integrating the expected discounted value of sector j over the distribution of idiosyncratic
J φh
6 xh
Utility prior to optimization with respect to consumption is u jkt = J
h=1
h + η j − Cjk + ε kt , where xh denotes
h=1
(φh )φ
J h
consumption of good h and φ = 1. Optimizing with respect to x we obtain the indirect utility function (7)
h=1
with a price index given by log P = J h
h=1 φ log ph .
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
wjt
(8) W j (Λjt ) = + η j + E max −Cjk + ε kt + βEt W k (Λjt+1 ) ,
Pt k
where Eε 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 state variables in the decision are the current sector of employment j and the vector of
aggregate variables Λjt . Variables in Λjt are vectors of wages and prot shocks in all sectors, wt
and bt . Like rms, workers form expectations about future wages following a linear prediction rule.
Let mjk be the probability of choosing k conditional on being in j. Under the extreme value
distributional assumption mjk takes the usual multinomial logit form
1
jk exp −Cjk + βEt W k (Λjt+1 ) ν
(9) m (Λjt ) = J
.
1
exp (−Cjk + βEt W h (Λjt+1 ))) ν
h=1
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 mjk (Λjt )Njt , where Njt 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
(10) Nkt+1 (Λjt ) = mjk (Λjt )Njt + mkk (Λkt )Nkt .
j =k
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
J
wjt 1
W j (Λjt ) = + η j + ν log exp −1i=j C + βEt W h (Λjt+1 ) .
Pt ν
h=1
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
jk
probabilities m and for labor supply in equation (10).
12
Regarding aggregate consumption, with Cobb-Douglas preferences aggregate expenditure in each
good is a xed share φj of total income, given by the sum of total labor income and prots net of
adjustment costs across all sectors.
2.3 Equilibrium
We start by discussing equilibrium in labor markets. At time t workers dene their sector of em-
ployment for time t + 1. This implies that at time t, sector labor supply is xed at the current labor
allocations, given by Njt (equation 10). Sector labor demand is given by equation (3). The prede-
termined allocations together with labor demand determine equilibrium wages across sectors. Labor
demand is shifted by sector-level prot shocks bjt and the distribution of rms µjt . Consequently,
we can write equilibrium wages as function of current state variables
(11) wjt = wj (bjt , µjt , Njt ).
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 as-
sumed 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
(12) log wjt+1 = a1 + ρw log wjt × D1jt+1 +
w
(1 − a2 ) log wjt × D2jt+1 + (1 + a3 ) log wst × D3jt+1 + jt ,
where
w 2 ) and where D
∼ N (0, σw is an indicator variables that is equal to one when the sector
jt 1jt+1
shocks bjt and bjt+1 are both high or both low; D2jt+1 is equal one when the sector shocks bjt and
bjt+1 switch from high to low; and D3jt+1 is equal to one when the sector shocks bjt and bjt+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 (D1 = 1),
wages follow an AR(1) with correlation coecient ρw . When instead there are changes in aggregate
conditions (D2 =1 or D3 = 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 Aijt and worker-specic utility shocks ε t , but there are no aggregate prot shocks bjt . 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.
3 Estimation
In this section we discuss the estimation of the model structural paramters. We use two sources of
data from Argentina. The rst is the Encuesta Industrial Anual (EIA, Annual Industrial Survey),
from INDEC. This is a panel of rms spanning the period 1994 to 2001, with information on
investment, disinvestment, employment, revenue, production and materials. The second source of
data is the Encuesta Permanente de Hogares (EPH, Permanent Household Survey), a standard labor
force survey with a panel component, also from INDEC. It spans the period 1996 to 2006 and has
information on sector of employment (or non-employment) and wages. We use the panel component
of the survey to compute movements of workers across sectors. Firms and workers are aggregated
into 6 sectors: food and beverages; textiles, apparel and leather; nonmetallic minerals; primary
metals and fabricated metal products; other manufactures; and non-traded goods. Workers are
further grouped into non-employment. We refer the reader to on-line Appendix A for more details
14
on the data.
3.1 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 = (γ1 , γ2 , γ3 ; Ce , Cu ). 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 φj 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 αL and αK are 0.619 and 0.283, both statistically signicant. The input requirement
for materials vm 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, bjt and Aijt follow independent AR(1)
processes with correlation coecients ρb , ρa , variance of the innovation terms
2
σb and
2,
σa 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
15
constant.
For the rm-level shocks we estimate a correlation coecient of ρa = 0.902 and a variance for
the innovation term of
2 = 0.118.
σa For the sector-level shocks we estimate a constant of b = 0.318, a
correlation coecient of
2 = 0.044.
ρb = 0.777, and variance of σb Once we have the AR(1) parameters
we discretize the state space for Aijt and bjt and compute their Markov transition matrices following
the approximation of Tauchen-Hussey. We dene an 8-point grid for Aijt and two values for bjt ,
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.
3.2 Adjustment cost parameters
We now turn to the estimation of the vector of adjustment cost parameters Γ = (γ1 , γ2 , γ3 ; Ce , Cu ).
Recall that γ1 , γ2 and γ3 are the capital adjustment parameters: the xed cost, the convex cost and
the irreversibility cost. On the worker side, Ce and Cu 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 Iijt 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 em-
ployment 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 ), (w t − w t−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.
16
of the mobility costs Ce and Cu . This strategy follows the conditional choice probability (CCP) ap-
proach 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 γ1 = 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 (γ2 ) equals 0.18. Using the
quadratic adjustment cost function and a steady state investment rate equal to the depreciation rate
(I/K = δ = 0.0991), the estimated parameter implies an adjustment cost relative to the average
plant-level capital of 0.175 percent. Finally, our estimate of the transaction costs (γ3 = 0.840)
implies that resale of capital goods would incur a loss of about 16 percent of its original purchase
price.
11
The estimates of the labor mobility costs are in panel B of Table 2. The SMM estimates are
Ce = 3.72 and Cu = 4.22. The estimated variance is ν = 2.63. All our estimates are statistically
signicant. On average, a worker wishing to switch sectors would pay a mobility cost equivalent to
3.72 times his annual wage earnings. Instead, a worker moving from non-employment to employment
would pay a higher cost of 4.22 times the annual wage. These estimated costs are high, revealing
large labor friction in Argentine labor markets. Our estimates are lower than those reported in
Artuc, Chaudhuri, and McLaren (2010) for the U.S., where the average moving cost is around
6.565, and ν is 1.884. Allowing for job quality terms η, Artuç and McLaren (2015) estimate more
modest C, ranging from as low as 0.99 to as high as 1.54 (with ν =0.257), also for the U.S. Finally,
estimating a comprehensive model that allows for worker heterogeneity with Brazilian data, Dix-
Carneiro (2014) nds median mobility costs ranging from 1.4 to 2.7, which are smaller than ours
(though Dix-Carneiro's estimates show large dispersion across the population).
12
11
Our estimates of capital adjustment cost parameters for Argentina can be directly compared with those in Cooper
and Haltiwanger (2006) for the U.S. as we use the same specications. Cooper and Haltiwanger (2006) estimate
US US
comparable xed costs (γ1 = 0.039), but lower quadratic adjustment costs (γ2 =0.049) and lower irreversibilities
US
(γ3 = 0.975). This implies that capital is more exible in the U.S. than in Argentina, especially in terms of the
irreversibility cost of investment. These dierences, as well as the magnitudes of the estimates, are, however, sensible
and plausible. Bloom (2009) reports larger values for the partial irreversibility cost, with capital reselling losses
of 42.7 percent, and for the quadratic adjustment cost parameter (0.996). The xed cost parameter γ1 , which is
estimated in terms of annual sales (instead of average capital), is 1.1 percent. Note that these results are not directly
comparable to ours because of some dierences in specication.
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
17
Table 2 also shows the empirical and simulated moments, which match well. More details about
the SMM estimator as well as an assessment of identication and predictive power are given in
on-line Appendix A.
4 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 Aijt given by (16), but
we close down the aggregate productivity shocks, that is, we set bt = 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.
4.1 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
1 when there are (positive or negative) shocks.
13
Note that aggregate shocks are needed in the estimation of the structural parameters in order to build simulated
moments that match moments computed from real data. Whereas for the simulation of a given price shock, random
aggregate shocks are not needed and a stationary equilibrium is a better framework to study the patterns of adjustment
of endogenous variables.
18
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 1994-2000
(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 pjt = p∗
jt (1 + τjt ) and, consequently, the impact of
the elimination of taris on prices is given by d ln pjt = −τjt /(1 + τjt ). 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.
Figure 1 illustrates the mechanics of the impacts on capital (panel a), real wages (panel b) and
employment (panel c). Note that, in the model, imperfect factor mobility creates cross-industry
spillover eects. To show these general equilibrium responses, we consider impacts on other tradables
(for simplicity of exposition we group the four non-textile traded sectors using employment weights)
and on the non-tradable sector. In each panel, the solid line corresponds to textiles, the dashed
line to other tradables, and the dotted line to non-tradables. The magnitudes of the responses are
given in 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), by 14.62 percent in Year
3, and by 25.47 percent in the new steady state; 95 percent of the transition is covered in 9 years.
Employment decreases by 2.91 percent in Year 2, 3.90 percent in Year 3, and 4.64 percent in the
new steady state; convergence of employment is faster than of capital, covering 95 percent of the
transition in 5 years.
The dynamic adjustment of capital and labor has implications for factor returns during the
transition. After the on-impact decline in the real wage in textiles of 15.04 percent at the time
of the shock, it continues declining gradually. By Year 2, the decline is 17.25 percent, then 18.45
percent in Year 3; in the new steady state, real wages are 20.32 perc-ent lower than in the initial
equilibrium. This is due to the joint investment and employment decisions that determine the
evolution of capital and labor in the sector.
There are general equilibrium eects on other traded goods sectors. The initial higher real wages
in the non-textile manufacturing sector attract workers and employment expands by 0.59 percent
(Year 2), 0.77 percent (Year 3) and 0.91 percent in the new steady state. There is a very minor
response of the capital stock, which increases only by 0.09 percent initially and by 0.57 percent in
steady state. These changes in capital and employment imply a gradual but slight reduction in real
wages during the transition. In non-textile manufacturing, while real wages increase by 1.45 percent
in Year 1, the long-run increase is of 1.20 percent (with respect to the initial steady state). Unlike
what happens in textiles, there is a very slight overshoot of the real wage in these sectors.
There are general equilibrium eects on the non-traded sector as well. As shown above, real
wages remain essentially unchanged (with an increase of only 0.06 percent in Year 1). Employment
increases but the magnitudes are almost negligible. In addition, because of lower non-traded prices,
protability in these sectors is eroded and this triggers disinvestment during the transition. For
20
example, in the new steady state, employment increases by only 0.34 percent, while the capital
stock declines by 1.34 percent. In the end, this decreases labor productivity and wages in the
sector. In the new steady state, real wages are slightly lower with a reduction of 0.39 percent.
Finally, there is an eect on non-employment. As the textile sector shrinks because of the loss of
tari protection, some of the displaced workers are absorbed by the other traded sectors as well as
the non-traded sectors. Some others end up in non-employment, which increases steadily but only
slightly during the transition: non-employment grows by 0.29 percent in Year 2, by 0.41 percent in
Year 3 and by 0.53 percent in the new steady state.
We can also calculate changes in welfare for producers and workers. Because of lower prices,
textiles rms lose value instantaneously and this becomes exacerbated as rms disinvest: the initial
decline in producer welfare is 16.91 percent, while the long-run decline is 25.73 percent. Producer
welfare increases in other traded sectors, because of relative price changes, and it declines in non-
traded sectors, because of the direct eect of the taris on non-traded prices. The evolution of
worker welfare is more complex. Since workers can change sectors at any time period, welfare in
one sector aects workers in all sectors. Thus, the changes in worker welfare in all sectors tend
to be highly correlated with each other, unlike producer welfare (Artuc, Chaudhuri and McLaren,
2010). Therefore, the change in worker welfare does not resemble the change in real wages or in
employment. Initially, annualized worker welfare decreases in all sectors, by 1.38 percent in textiles,
and around 0.9 percent in other sectors.
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.
4.2 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-
sector economy. The labor market frictions create inter-industry wage dierences and, as we have
shown, the interplay of capital and labor mobility jointly determine employment and investment
decisions, which in turn aect the real returns to factors of production. We know from the literature
what the role of labor mobility costs with xed capital is: the overshooting of real wages (Artuc,
Chaudhuri and McLaren, 2008; Artuc, Chaudhuri and McLaren, 2010; Artuc, Lederman, and Porto,
15
The welfare metrics of workers are the value functions deated by the price index, annualized and reported
relative to average annual wage. In addition, we distribute the tari revenue back to the workers uniformly. 1.38
percent decline means a welfare loss equivalent to a loss of 1.38 percent of average wage every year.
21
2015; Dix-Carneiro, 2014). 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.
Figure 2 plots the responses of the real wage in the textile sector. The solid line depicts real
wage dynamics for the benchmark model with imperfect mobility of both labor and capital (from
Figure 1, panel b, and 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.
22
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
9.15 percent. Compared with the initial drop of 15.04 percent, this implies an overshooting of real
wages of almost 6 percentage points.
These ndings have relevant implications for the interpretation of some of the results recently
found in the literature. Our structural model with market frictions shows that tari reforms can
actually have long-lasting impacts and that the patterns of adjustment, especially in the long-run,
strongly depend on the nature of capital adjustment costs. In a setting with xed capital, while
tari cuts positively correlate with wage changes in the short-run, this correlation can become
negative in the long-run. In models with capital adjustment costs, tari changes positively correlate
with wage changes not only in the short-run but possibly also in the long-run. The notion that
capital adjustment costs can play a role is discussed in Dix-Carneiro (2014). Using ad-hoc imperfect
capital adjustment rules, he shows that sluggish capital responses can aect the wage dynamics.
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.
4.3 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 asym-
metry 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 adjust-
ment 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.
4.4 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
(2016)see Eq. (4). With an average tari on capital goods of 12.3 percent, the elimination of
taris would cause the price of capital to decline by 10.9 percent. This experiment allows us to
explore the implications for the labor market of reductions in input tarisa prevalent topic in
the literature. In particular, Argentine rms heavily rely on imported capital to build their capital
stock and, thus, trade liberalization of capital goods can induce sizeable rm responses. To this
end, we study the evolution of the economy following a joint elimination of output taris in textiles
and input taris on capital goods.
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
25
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.
4.5 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 and Palazzo, 2016, and Sedlacek, 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
F0 . Upon entry rms receive a draw of productivity (A) and initial capital (K ) from a distribution
µ0 . 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 F0 . 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 F0 is lower than the expected value prior to entry. The equilibrium mass of entrants in
sector j , n0jt , is given by
V 0jt
(13) n0jt = H (dF0 ),
0
where H is the cdf of the cost of entry.
The expected value V 0jt varies across periods according to state variables bjt and wjt . Equilib-
rium sector wages further depend on labor allocations, Njt , distributions of active rms, µjt , and
the mass of active rms, which we denote with njt . 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, njt . 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.
27
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.
5 Conclusions
We have developed a structural dynamic general equilibrium model of trade and the labor market
with factor adjustment costs. Firms make intertemporal investment decisions facing capital ad-
justment costs that include xed costs, convex costs and investment irreversibility costs. Workers
choose employment sector based on equilibrium intersectoral wage dierences and labor mobility
costs. These costs include various labor market frictions such as imperfections in ring and hiring
workers as well as specic utility shocks. The model features general equilibrium eects, articulating
both the product and the labor market, in a multisector economy. This allows us to analyze the
28
interplay between trade shocks and factor adjustment costs. We have tted our model to household
survey panel data and plant-level panel data from Argentina and recovered measures of the adjust-
ment frictions faced both by workers and rms. Using the structural parameters, we have simulated
the response of the model, both of rms and workers, following a tari cut episode.
Our paper combines labor market frictions with a complex model of capital adjustment costs,
which few papers do. This matters for the patterns of responses of investment, employment and
wages. Following a tari cut in textiles, factor market frictions amplify the labor market responses
so that the long-run responses of real wages are larger than the short-run responses. There is no
overshooting of real wages, as in xed capital models. Our results suggest that the cost of adjusting
capital is a fundamental driver of these patterns. After losing protection, real wages decline on
impact. Moreover, as rms disinvest in response to the negative trade shock, labor productivity
continues to decline during the transition, and real wages further decline as the economy approaches
the new steady state. The results are also consistent with the recent ndings in the empirical trade
literature, notably those reported by Dix-Carneiro and Kovak (2017). By combining capital and
labor adjustment costs, our analysis complements the growing literature on the role of factor market
frictions in shaping the way employment and labor adjust to the elimination of taris.
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32
Figure 1
Tari Cuts in Textiles
Capital, Real Wages, Employment
(a) Capital (b) Real Wages
.05
.05
0
0
-.05
-.05
-.1
-.1
-.15
-.15
-.2
-.25
-.2
-2 0 5 10 15 -2 0 5 10 15
Year Year
Textiles Other Traded Textiles Other Traded
Non-traded Non-traded
(c) Employment
.01
0
-.01
-.02
-.03
-.04
-.05
-2 0 5 10 15
Year
Textiles Other Traded
Non-traded Unemployment
Notes: responses of capital (panel a), real wages (panel b) and employment (panel c) to a full elimination of taris on
textiles. Simulation results from estimated structural model. In each panel, the solid black line represents the textile sector,
the gray dashed line represents the non-textile manufacturing sector, and the gray dotted lines represents the non-traded
sector. The solid gray line in panel c corresponds to non-employment.
33
Figure 2
Real Wage Overshooting in Textiles
0
-.05
-.1
-.15
-.2
-2 0 5 10 15
Year
Model Fixed Capital
Low Labor Mobility Cost
Notes: real wage responses in the textile sector. The solid black line corresponds
to the benchmark model with capital adjustment costs; the dashed gray line corre-
sponds to a xed-K model; the dotted gray line corresponds to a model with capital
adjustment costs and lower labor mobility costs (set to U.S. values from Artuc and
McLaren, 2015).
Figure 3
Asymmetric Response of the Capital Stock
Positive and Negative Price Shocks in Textiles
.25
.2
.15
.1
.05
0
-2 0 5 10 15
Year
Positive shock Negative shock (mirror)
Notes: evolution of the capital stock in the positive shock (solid line) and the
mirrored (changed sign) benchmark response (dashed line).
34
Figure 4
Tari Cuts in Textiles & in Capital Goods
Capital, Real Wages, Employment
(a) Capital
Benchmark Liberalization K---textiles Liberalization K---all sectors
.05 .1 .15 .2
.05 .1 .15 .2
.05 .1 .15 .2
-.25 -.2 -.15 -.1 -.05 0
-.25 -.2 -.15 -.1 -.05 0
-.25 -.2 -.15 -.1 -.05 0
-2 0 5 10 15 -2 0 5 10 15 -2 0 5 10 15
Year Year Year
Textiles Other Traded Non-traded Textiles Other Traded Non-traded Textiles Other Traded Non-traded
(b) Real Wages
Benchmark Liberalization K---textiles Liberalization K---all sectors
.05
.05
.05
0
0
0
-.05
-.05
-.05
-.1
-.1
-.1
-.15
-.15
-.15
-.2
-.2
-.2
-2 0 5 10 15 -2 0 5 10 15 -2 0 5 10 15
Year Year Year
Textiles Other Traded Non-traded Textiles Other Traded Non-traded Textiles Other Traded Non-traded
(c) Employment
Benchmark Liberalization K---textiles Liberalization K---all sectors
.01
.01
.01
0
0
0
-.01
-.01
-.05 -.04 -.03 -.02 -.01
-.02
-.02
-.03
-.03
-.04
-.04
-.05
-.05
-2 0 5 10 15 -2 0 5 10 15 -2 0 5 10 15
Year Year Year
Textiles Other Traded Textiles Other Traded Textiles Other Traded
Non-traded Unemployment Non-traded Unemployment Non-traded Unemployment
Notes: responses of capital (panel a), real wages (panel b) and employment (panel c) to a full elimination of taris on textiles
(benchmark), to a full elimination of taris in textiles and in capital goods in the textile sector (Liberalization K textiles),
and to a full elimination of taris in textiles and in capital goods in all sector (Liberalization K all sectors). Simulation results
from estimated structural model. In each panel, the solid black line represents the textile sector, the gray dashed line represents
the non-textile manufacturing sector, and the gray dotted lines represents the non-traded sector. The solid gray line in panel c
corresponds to non-employment.
35
Table 1
Estimates of Structural Parameters
Parameter Estimate Description
Discount factor β 0.95 Predetermined
Depreciation rate δ 0.0991 Computed from BEA and rm data
Expenditure shares
Food and beverages 0.313 National accounts
Textiles and apparel 0.052 National accounts
Minerals 0.025 National accounts
Metals 0.025 National accounts
Other manufactures 0.211 National accounts
Non-traded goods 0.374 National accounts
Production function parameters
αL 0.619 ACF regression
(0.036)
αK 0.283 ACF regression
(0.029)
vm 0.410 Computed from rm data
(0.003)
Stochastic processes of shocks A and b
ρa 0.902 AR(1) regression
(0.008)
2
σa 0.118 AR(1) regression
(0.00009)
b 0.318 AR(1) regression
(0.156)
ρb 0.777 AR(1) regression
(0.116)
2
σb 0.044 AR(1) regression
(0.00011)
P (bt = high|bt = high) 0.827 Tauchen-Hussey approximation
P (bt = high|bt = low) 0173 Tauchen-Hussey approximation
Notes: list of estimates and source of each parameter value. Standard errors in parenthesis.
36
Table 2
Estimates of Labor and Capital Adjustment Costs
Estimates
Estimate Std. Error Description
A) Capital Adjustment Costs
Fixed Cost γ1 0.0379 (0.008) SMM
Quadratic Cost γ2 0.178 (0.016) SMM
Irreversibility Cost γ3 0.84 (0.057) SMM
B) Labor Mobility Costs
Ce 3.72 (0.48) SMM
Cu 4.22 (0.26) SMM
Utility parameters
variance ν 2.63 (0.395) CCP within SMM
η1 0 Normalized
η2 0.049 (0.233) CCP within SMM
η3 0.411 (0.280) CCP within SMM
η4 0.543 (0.286) CCP within SMM
η5 0.255 (0.202) CCP within SMM
η6 0.671 (0.348) CCP within SMM
η0 0.232 (0.307) CCP within SMM
C) Wage Process
a1 0.027 Simulated
ρw 0.943 Simulated
a2 0.410 Simulated
a3 0.623 Simulated
σw 0.017 Simulated
Moments
Empirical Simulated
Corr(I, I−1 ) 0.145 0.163
Corr(I, A) 0.046 0.048
N egative spike 0.014 0.004
Corr(w − w, N − N ) 0.313 0.301
Corr(N0 , N0,−1 ) 0.887 0.828
Corr(N0 − N0,−1 , w − w−1 ) 0.101 0.071
Notes: table shows the capital adjustment cost and labor mobility cost parameters; utility func-
tion parameters; wage stochastic process parameters; and the empirical and simulated moments.
Standard errors in parenthesis.
37
Table 3
Taris Cuts in Textiles and Price Changes
Tari Price Change
Food & Beverages 13.9
Textiles 19.4 16.2
Minerals 11.6
Metals 14.2
Other Manufactures 14.1
Capital Goods 12.3
Non-Tradables
short-run 1.36
long-run 1.30
Source: Taris τ (in percent) are from Brambilla,
Galiani and Porto (2018). Price changes are com-
j
puted as −τ /(1 + τ ). The change in the prices of
the non-traded goods comes from the simulations.
j j
Table 4
Responses to Tari Cuts in Textiles
Capital, Employment, Real Wages and Welfare
(percent)
Year 1 Year 2 Year 3 Steady State
Capital
Textiles 0.00 -9.41 -14.62 -25.47
Other Traded Goods 0.00 0.09 0.24 0.57
Non-Traded Goods 0.00 -0.62 -0.83 -1.34
Real Wage
Textiles -15.04 -17.25 -18.45 -20.32
Other Traded Goods 1.45 1.21 1.19 1.20
Non-Traded Goods 0.06 -0.19 -0.28 -0.39
Employment
Textiles 0.00 -2.91 -3.90 -4.64
Other Traded Goods 0.00 0.59 0.77 0.91
Non-Traded Goods 0.00 0.20 0.28 0.34
Non-employment 0.00 0.29 0.41 0.53
Producer Welfare
Textiles -16.91 -20.21 -22.00 -25.73
Other Traded Goods 0.82 0.90 0.10 0.11
Non-Traded Goods -1.31 -1.50 -1.57 -1.75
Worker Welfare
Textiles -1.38 -1.44 -1.47 -1.53
Other Traded Goods -0.89 -0.90 -0.91 -0.92
Non-Traded Goods -0.93 -0.96 -0.97 -0.98
Non-employment -0.94 -0.95 -0.95 -0.96
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.
38
Table 5
Tari Cuts or Tari Protection
Asymmetric Responses
Textile Sector
(percent)
Year 2 Year 3 Year 4 Year 5 Year 10 Steady State
Capital
negative shock (1) -9.41 -14.62 -18.08 -20.66 -24.73 -25.47
positive shock (2) 12.72 17.61 20.21 22.84 26.97 27.26
| (2)/(1) | 1.35 1.20 1.12 1.11 1.09 1.07
Real Wage
negative shock (4) -17.25 -18.45 -19.10 -19.62 -20.18 -20.32
positive shock (5) 18.90 19.53 19.61 20.02 20.40 20.34
| (5)/(4) | 1.10 1.06 1.03 1.02 1.01 1.00
Employment
negative shock (7) -2.91 -3.90 -4.27 -4.44 -4.61 -4.64
positive shock (8) 3.18 4.21 4.54 4.69 4.78 4.78
| (8)/(7) | 1.09 1.08 1.06 1.06 1.04 1.03
Notes: Simulation of the transitional dynamic responses of capital, real wages and employment in the bench-
mark case (full elimination of taris on textiles) and in a positive shock scenario with positive benchmark
price changes (price changes with changed sign).
Table 6
Extensive Margin Responses: Entry and Exit of Firms
Textile Sector
(percent)
Year 2 Year 3 Year 5 Year 10 Steady State
Capital
baseline (1) -9.41 -14.62 -20.66 -24.73 -25.47
entry-exit (2) -13.13 -19.70 -23.56 -24.84 -25.94
| (2)/(1) | 1.40 1.35 1.14 1.01 1.02
Real Wage
baseline (4) -17.25 -18.45 -19.62 -20.18 -20.32
entry-exit (5) -17.58 -19.14 -19.96 -20.54 -21.58
| (5)/(4) | 1.02 1.04 1.02 1.02 1.06
Employment
baseline (7) -2.91 -3.90 -4.44 -4.61 -4.64
entry-exit (8) -2.97 -4.01 -4.53 -4.69 -4.92
| (8)/(7) | 1.02 1.03 1.02 1.02 1.06
Notes: Simulation of the transitional dynamic responses of capital, real wages and employment
in the benchmark case and in the extended model with entry and exit. The shock is the full
elimination of taris on textiles.
39
A 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. In the EIA panel, we have data
for the period 1994-2001. The EIA dataset provides information on revenue, value of production,
employment, wages, costs, intermediate inputs, inventory stock, and both gross expenditures and
gross sales of capital.
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 Kijt+1 = (1 − δ )Kijt + Iijt . Real investment is dened as Iijt = Eijt − Sijt , where Eijt is real
gross expenditures on capital equipment, and Sijt 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).
40
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
Permanente de Hogares (EPH, Permanent Household Survey). The database contains information
on individual wages, employment sector, non-employment and other standard variables in labor force
surveys. Part of the EPH is a panel and we can use it to track employment decisions across sector
pairs, across employment and non-employment, and average sector wages. We use the available
panel from 1996 to 2006.
A.2 Estimation of the technology parameters
Production function parameters
We postulate a production function which is Leontief in materials Mijt and a Cobb-Douglas index
of capital Kijt and labor Lijt . 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 (Yijt ) on the left-hand side, capital (Kijt )
and labor (Lijt ) 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
(14) ln Yijt = αL ln Lijt + αK ln Kijt + ijt ,
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 Kijt ,
Kijt−1 and Lijt−1 as instruments. Standard errors are computed from 500 bootstrap replications.
The labor coecient αL is 0.619 and the capital coecient αK 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 vM by computing the mean of Mijt /Yijt
across rms. The estimated value for the unit input requirement is 0.41. As a robustness exercise we
41
Table A1
Intermediate Input Requirements
Firm data Input-output data
Average intermediate input requirement 0.41 0.42
Intermediate inputs sourced from own sector
Food and beverages 0.38
Textiles 0.31
Minerals 0.04
Metals 0.40
Other manufactures 0.36
Source: INDEC. Input-output table for year 1997.
also compute the unit input requirements from an input-output table and we average them across
sectors. The resulting coecient is 0.42. The input-output coecients used in the estimation of the
production function parameters are presented in Table A1. The data come from the IO Tables for
1997 published by INDEC (Instituto Nacional de Estadística y Censos.
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 table. These
are 0.38, 0.31, 0.40, 0.04, and 0.36 for food and beverages, textiles, metals, minerals and other
manufacturing sectors. The own-sector coecients are very close to the calibrated intermediate
input requirement of 0.41 in 4 out of the 5 manufacturing sectors, which implies that the assumption
agrees with the data relatively well, with the exception of the small minerals sector. See Table A1.
Stochastic process for sector and rm-level shocks
Firms face sector-level prot shocks bjt , that include shocks to aggregate productivity and to prices,
and rm-level shocks Aijt . We assume that b and A follow AR(1) stochastic processes given by
b
(15) ln bjt+1 = b + ρb ln bjt + jt+1 ,
a
(16) ln Aijt+1 = ρa ln Aijt + ijt+1 ,
42
with
b 2 ) and
∼ N (0, σb a 2 ).
∼ N (0, σa We further assume that the shocks bjt are independent
jt+1 ijt+1
across sectors and the shocks Aijt are independent across rms. Since bjt and Aijt 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
1−αL
πijt −αL αL −αK 1
(17) bjt Aijt = αL wjt Kijt .
1 − αL 1 − vM
Let xijt denote the product of the rm and sector level shocks, with xijt = bjt Aijt . We compute the
right-hand size of (17) from data (πijt , Kijt , wjt ) and the estimates from the previous step (αL , αK ,
vM ). This gives us estimates for xijt . To estimate the A parameters, we rst compute deviations
of xijt from sector-year means (to get rid of bjt ) and then regress this on one lag (no constant)
a
(18) log xijt+1 − log xjt+1 = ρa (log xijt − log xjt ) + ijt+1 .
To estimate the b parameters we compute the sector-year means of xijt and run the regression using
the means, at the sector-year level
b
(19) log xjt+1 = b + ρb log xjt + jt .
In Table 1 in the paper, we report
2 = 0.118, b = 0.318, ρ = 0.777,
ρa = 0.902, σa and
2 = 0.044.
σb
b
A.3 SMM estimator
The adjustment costs parameters are given by the vector Γ = (γ1 , γ2 , γ3 ; Ce , Cu ), 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 com-
puted from rm and worker simulated data, denoted by Ψs (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,
(20) Γ = arg min [Ψ − Ψs (Γ)] Ω[Ψ − Ψs (Γ)]
Γ
43
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 bjt 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) we use the optimal weighting matrix
44
given by the inverse of the variance covariance matrix of [Ψ − Ψs (Γ)].18 We search over values of
Γ using a combination of ne grid search and coordinate descent search, which works better than
second-derivate Newton-Raphson or quasi-Newton methods in a case like ours with a discretized
state space. Standard errors for the estimates are computed analytically, as in Bloom (2009).
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 Ce and Cu . 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
wjt
Wtj = + ηj + β Et Wtj+1 − ν ln mjj
t .
Pt
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
j jk jj
β Et Wtk
+1 − Et Wt+1 = ν ln mt − ln mt + Cjk .
Combining these two results, we get
Cjk β wkt+1 wjt+1 β
Et (ln mjk jj jk kk
t − ln mt ) − β (ln mt+1 − ln mt+1 ) − (β − 1) − − − (ηk − ηj ) = 0.
ν ν Pt+1 Pt+1 ν
This is an Euler equation that can be estimated conditional on Ce and Cu with a linear regression,
from actual data, as in Artuc, Chaudhuri and McLaren (2010), by allowing for a disturbance
term ωt+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.
45
sectors and the disturbance term ωt+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.
19
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 A1 below establishes that the SMM objective function is well-behaved around the solution
and that a minimum is achieved. To show this, we plot the SMM objective function as a function
of one of the adjustment cost parameters while keeping the other four parameters constant at their
solution value. In each panel, the dashed vertical line denotes the solution to the minimization
problem.
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 cor-
relation between investment and protability) identies the xed cost parameter γ1 . The quadratic
2 3
cost parameter (γ ) and the irreversibility parameter (γ ) 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 (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). 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.
46
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 rm-
level 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) we present the distribution of log
employment and prots conditional of dierent percentiles of the rm capital stock. This prediction
corresponds well with the log employment from the rm-level data.
22 We can match the conditional
distribution of prots as well.
21
Wages are normalized with respect to the average wage across sectors and time.
22
In the SMM simulated data, there is a linear relationship between log employment and log capital due to the
homotheticity of the Cobb-Douglas index in the production function.
47
Figure A1
Identication in SMM. Minimization of objective function
(a) Fixed cost γ1 (b) Convex cost γ2
(c) Irreversibility cost γ3 (d) Mobility cost Ce
(e) Mobility cost Cu
Notes: Graph plots the SMM objective function as a function of one adjustment cost parameter keeping the other four
parameters constant at their solution value. The dashed vertical lines denote the solution to the minimization problem.
48
Figure A2
Identication in SMM. Dierence between Empirical and Simulated Moments
(a) Fixed cost γ1 (b) Convex cost γ2
(c) Irreversibility cost γ3 (d) Labor cost Ce
(e) Labor cost Cu
Notes: Each panel shows the dierence between the observed and the simulated moments (squared) as a function of an ad-
justment cost parameter. Moment 2 (the correlation between investment and protability) identies the xed cost parameter
γ . The quadratic cost parameter (γ ) and the irreversibility parameter (γ ) are both identied from the opposing forces of
2 3
moment 1, the serial correlation in investment, and moment 3, the negative spike moment. The labor mobility cost across
1
sectors (C ) 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 ) is identied from the serial correlation in non-employment (moment
e
5) and the correlation between the change in non-employment and in the average wage (moment 6).
u
49
Figure A3
Comparison of empirical data and simulated data
(a) Log employment density (b) Log capital density
.3
.2
.15
.2
density
density
.1
.1
.05
0
0
0 2 4 6 8 5 10 15 20
log employment log capital
Model Data Model Data
(c) Prots density (d) Log employment | K
8
.008
.006
6
log employment
density
.004
4
.002
2
0
0 200 400 600 5 10 15 20
profits K percentiles
Model Data Model Data
(e) Prots | K
400
300
profits
200
100
0
8 10 12 14 16 18
K percentiles
Model 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.
50
Table A2
Comparison of empirical data and simulated data
Wages and employment transition probabilities
Wages Food & Textiles Minerals Metals Other Non Unemp.
beverages manuf. traded
A) Simulated data
Food & Beverages 0.958 0.866 0.023 0.030 0.023 0.029 0.029 0.001
Textiles 0.955 0.023 0.864 0.031 0.023 0.029 0.029 0.001
Minerals 1.039 0.018 0.018 0.902 0.018 0.022 0.023 0.001
Metals 0.959 0.023 0.023 0.030 0.867 0.028 0.029 0.001
Other Manuf. 1.012 0.020 0.020 0.026 0.020 0.891 0.024 0.001
Non-Traded 1.016 0.019 0.019 0.026 0.020 0.023 0.893 0.001
Unemployment 0.086 0.086 0.115 0.087 0.106 0.108 0.413
B) Empirical data
Food & Beverages 0.943 0.717 0.002 0.001 0.005 0.015 0.205 0.059
Textiles 0.953 0.005 0.748 0.000 0.011 0.029 0.123 0.093
Minerals 1.169 0.018 0.025 0.692 0.046 0.087 0.136 0.076
Metals 0.876 0.021 0.024 0.016 0.615 0.170 0.122 0.064
Other Manuf. 1.039 0.007 0.009 0.005 0.041 0.713 0.166 0.062
Non-Traded 1.020 0.008 0.004 0.001 0.003 0.015 0.908 0.061
Unemployment 0.014 0.018 0.002 0.008 0.029 0.374 0.556
Firm Investment
Percentage of Firms
All rms Low-K rms High-K rms
I <0 I =0 I >0 I <0 I =0 I >0 I <0 I =0 I >0
Data 3.87 35.63 60.49 3.85 41.84 54.31 3.90 29.42 66.68
Simulated data 8.45 43.72 47.83 3.25 31.21 65.54 13.65 56.23 30.12
Notes: Comparison of data from EPH (Encuesta Permanente de Hogares, Permanent Household Survey) and from EIA
(Encuesta Industrial Anual, Annual Industrial Survey), and simulated data based on parameter estimates.
51
B On-line Appendix: Robustness and extensions
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,
F0 , 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 F0 between 0 and V 0jt enter the market. This rule denes the mass (or number)
of entrants, n0jt , as dened in equation (13). We denote the number of entrants, active and exiting
rms with n0jt , njt and nxjt . 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 F0 , rms take productivity and initial capital draws (A0 , K0 )
from a rm distribution µ0 . We assume that the distribution of entrants (µ0 ) is proportional to
the distribution of incumbents (µ) and right-truncated on both dimensions (A and K ), so that µ
stochastically dominates µ0 and entrants are on average less productive and smaller than incum-
bents. 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 µ0 . 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.
52
We dene two groups of rms, according to whether their idiosyncratic productivity A is below
or above the 80th percentile, and denote them with ZL and ZK . In each period, rms in the group
ZL (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 ZH (high productivity rms). These simplifying assumptions are based on the
empirical observations of Dunne et al (1988, 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 ZL 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 ZL , denoted with ρLt , is given by
(21) ρLjt = µjt (dK × dA).
(A,K )∈ZL
The probability of exit, denoted with ρxt , is ρxjt = (1 − ζ )ρLjt . The number of rms that exit the
market is given by nxjt = ρxjt njt−1 .
Under these assumptions, the expected rm value prior to entry is given by
(22) V 0jt = βζL Et V (A0 , K0 , bjt+1 , wjt+1 )µ0 (dK × dA) − K0 µ0 (dK × dA),
(A,K )∈ZL (A,K )
where the expectation Et is taken over next period's values of sector shocks and wages. The last term
corresponds to the required stochastic initial investment drawn from µ0 . The expected value V 0jt
varies across periods according to state variables bjt and wjt . 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, njt . 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).
53
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 ρx to 0.098 based on the annualized average exit rate in Dunne et al (1988). We compute
the expected value at entry, V0 , 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
(23) Yijt = (b0 αL
jt Aijt )(Lijt ) (Kijt )
αK
(Mijt )αM ,
The variables are dened as before, with aggregate and idiosyncratic productivity shocks b0
jt and
Aijt , and the new parameter αM 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
αL αM 1/(1−αL −αM )
αL αM
(24) πijt = (1 − αL − αM ) b0
jt pjt Ajt K
αK
,
wjt pjt
where the aggregate shocks b0
jt and pjt do not enter multiplicatively. As before, we dene the
combined protability shock as bjt = b0
jt pjt 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.
54
Table B1
Estimates of Labor and Capital Adjustment Costs
Leontief and Cobb-Douglas Production Functions
Estimates Baseline Cobb-Douglas
Fixed Cost γ1 0.0379 0.026
(0.008) (0.005)
Quadratic Cost γ2 0.178 0.163
(0.016) (0.067)
Irreversibility Cost γ3 0.84 0.854
(0.057) (0.096)
Mobility cost across employment sectorsCe 3.72 2.51
(0.48) (0.22)
Mobility cost in or out of non-employment Cu 4.22 4.24
(0.26) (0.20)
Moments Baseline Cobb-Douglas Data
Corr(I, I−1 ) 0.163 0.173 0.145
Corr(I, A) 0.048 0.046
Corr(I, A) 0.044 0.044
N egative spike 0.004 0.002 0.014
Corr(w − w, N − N ) 0.301 0.173 0.313
Corr(N0 , N0,−1 ) 0.828 0.738 0.887
Corr(N0 − N0,−1 , w − w−1 ) 0.101 0.299 0.101
Notes: The baseline column reproduces results from Table 2. The Cobb-Douglas column
shows results under the Cobb-Douglas technology assumption in equation (23).
values of b0
jt and pjt , which we need to input separately into the prot function: log b0
jt = 0.5 log bjt ;
log b0
jt = 0.5 log bjt .
We calibrate the output elasticities αL , αK and αM from the 1997 input-output table for Ar-
gentina. From the rm data we estimate the stochastic process for bjt and Aijt given by equations
(18) and (19). We estimate the adjustment cost parameters Γ = (γ1 , γ2 , γ3 , Ce , Cu ) following the
SMM objective function (20). We rst recompute the second empirical moment, which is the cor-
relation between investment and idiosyncratic shocks Corr(Iijt , Aijt ), as the shocks Aijt need to be
recomputed under the new technology specication.
Table B1 reports the results, both for our baseline Leontief case and the alternative Cobb-
Douglas specication. The estimates of capital and labor adjustment costs are comparable in order
of magnitude under the two technology specications. The moments are also well-matched in the
Cobb-Douglas case, although moments related to labor allocations are a better matched in the
baseline Leontief case.
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.
56
Figure B1
Tari Cuts in Textiles
Capital, Real Wages, Employment
Baseline (left) & Cobb-Douglas (right)
.05
.05
0
0
-.05
-.05
-.1
-.1
-.15
-.15
-.2
-.2
-.25
-.25
-2 0 5 10 15 -2 0 5 10 15
Year Year
Textiles Other Traded Textiles Other Traded
Non-traded Non-traded
.05
.05
0
0
-.05
-.05
-.1
-.1
-.15
-.15
-.2
-.2
-2 0 5 10 15 -2 0 5 10 15
Year Year
Textiles Other Traded Textiles Other Traded
Non-traded Non-traded
.01
.05
0
0
-.01
-.05
-.02
-.1
-.03
-.15
-.04
-.05
-.2
-2 0 5 10 15 -2 0 5 10 15
Year Year
Textiles Other Traded Textiles Other Traded
Non-traded Unemployment 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