HIAS-E-83

Wage Markdowns and FDI Liberalization
Yi Lu(a) , Yoichi Sugita(b) and Lianming Zhu(c)(a) School of Economics and Management, Tsinghua University, China(b) Graduate School of Economics, Hitotsubashi University, Japan(c) Institute of Social and Economic Research, Osaka University, Japan

March, 2019

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Wage Markdowns and FDI Liberalization⇤
Yi Lu†

Yoichi Sugita‡

Lianming Zhu§

January 31, 2019

Abstract
This paper examines whether foreign direct investment (FDI) liberalization
reduces firms’ monopsony power in labor markets. We estimate firm-level wage
markdown, wage over marginal revenue of labor, from China’s production dataand identify the causal effect of FDI liberalization on wage markdown, using
China’s regulation changes upon its accession to the World Trade Organization.
Large and productive firms, state-owned firms, exporters, and foreign firms set
narrower wage markdowns. FDI liberalization widened wage markdowns anddecreased labor income share in value-added. These findings are contrast to classical monopsony theory based on concentration but consistent with modern theory based on search friction.
Keywords: Foreign direct investment, Monopsony, Wage, Search, Firm heterogeneity
We thank comments from Arnaud Costinot, Anna Gumpert, Hiroyuki Kasahara, Daiji Kawaguchi,
Kohei Kawaguchi, Lin Ma, Tomohiro Machikita, Kensuke Teshima, Miaojie Yu, Xiwei Zhu, and participants at Hitotsubashi conferences, Sogang-HSE, Keio U, IDE-JETRO, APTS, SWET, JISE meetings,
GRIPS, PKU-HSE, U Tokyo, Diatobunka U, Nankai U and Chukyo U. We gratefully acknowledge
financial supports from JSPS Kakenhi (26220503, 17H00986, 18K12769 and 15H05728).
†
School of Economics and Management, Tsinghua University, China.
(E-mail:luyi@sem.tsinghua.edu.cn)‡
Graduate School of Economics, Hitotsubashi University, Japan. (E-mail: yoichi.sugita@r.hitu.ac.jp)§
Institute of Social and Economic Research, Osaka University, Japan.
(E-mail:lianmingzhu@iser.osaka-u.ac.jp)⇤

1

Introduction

Globalization has the potential to limit firms’ market power by increasing competition.
Liberalization of imports increases competition among sellers in goods markets, andliberalization of inward foreign direct investment (FDI) increases competition among
buyers in factor markets. Although trade and FDI have played equally important roles
in globalization, the literature has almost exclusively investigated the competition effect of trade liberalization on goods markets.12 The competition effects of FDI liberalization on factor markets has attracted relatively little attention.
This paper examines the effect of inward FDI liberalization on domestic firms’monopsony power in labor markets. Our study is motivated by recent research in labor
economics highlighting firms’ monopsony power in labor markets.3 Employer concentration, worker’s non-monetary preference for jobs and worker’s search friction makelabor supply curves to firms less elastic and allow firms to capture monopsonic rents
by setting wages lower than the marginal revenue of labor (MRL). Wage markdown,
the gap between wages and the MRL, determines not only the efficiency gains of FDI
liberalization but also the distribution of FDI’s gains to local workers. When foreign
firms enter, local firms lose their employees and increase MRL. If wage markdown isconstant, the wages at local firms should increase as much as the MRL increases, butwhen wage markdown is variable, the wage increase could be larger or smaller thanthe MRL increases.
We develop an empirical framework for analyzing the effect of inward FDI liberalization on wage markdown at domestic firms. We estimate firm-level wage markdown
from Chinese manufacturing production data. Our estimation method is inspired by
the price markup estimation by De Loecker and Warzynski (2012). Assuming thatfirms are price takers with respect to materials, we express wage markdown as a for1

For instance, during the 1990–2017 period, worldwide sales by foreign affiliates and worldwide
exports have grown by roughly the same proportion (around 500%) (UNCTAD, 2018).
2
See Tybout (2003), De Loecker and Goldberg (2014) and Van Biesebroeck and De Loecker (2016)
for surveys of the literature.
3
See, e.g., Manning (2003; 2011) and Ashenfelter, Farber, and Ransom (2010) for surveys.

2

mula relating wage expenditure, material expenditure, the revenue (or output) elasticity of labor, and the revenue (or output) elasticity of materials. We obtain the input
expenditures from data and the output and revenue elasticities by estimating gross output production functions in a recent non-parametric method by Ghandi, Navarro andRivers (2017). This method can be applied with typical production data available formany countries. We identify the causal effect of FDI liberalization on wage markdowns using variations in China’s regulation on FDI inflow upon its accession to theWorld Trade Organization (WTO).
A main advantage of our framework is that it imposes no assumptions about labormarket structure and the functional form of labor supply curves to individual firms.
Such generality is crucial for our purpose. Theoretical predictions about the effect of
FDI liberalization on wage markdowns are generally ambiguous and depend on labormarket structures and the functional form of labor supply curves.4 If one estimates
wage markdown from a structural model, the choice of a specific model and functional
forms might result in assuming the sign of FDI’s competition effect a priori. Our
framework can avoid that potential pitfall.
We apply our framework to firm-level Chinese manufacturing production dataspanning 1998 to 2007. In that period, Chinese labor markets generally lacked institutions protecting workers from firms’ monopsony power (Gallagher, Giles, Park andWang, 2015). Employment without formal written contracts was common. Collective
bargaining and strikes were prohibited. Workers often had to accept wages unilaterally set by employers. In 2008, right after our sample period, China introduced a Labor
Contract Law which improved worker protection. The estimated wage markdowns are
consistent with this background. First, employers ubiquitously exercise monopsony
powers. There are wage markdowns for 88% of the firms in our sample and the median firm pays only 25% of the MRL in wages. Second, markdowns are narrower
for firms known for offering well-paying jobs, or “good jobs” in China: in particular
4
In Appendix A2, we consider three canonical models of labor monopsony and shows that the signof FDI’s competition effect on wage markdown depends on the choice of model and functional form.

3state owned enterprises (SOEs), foreign-owned firms, and exporters. Finally, narrow
markdowns are associated with high productivity and large employment. These patterns tend to contradict the concentration theory of monopsony according to which itis large firms that exercise monopsony power, but they are consistent with the search
frictional theory whereby high productivity firms offer higher wages to attract moreworkers.
Our second contribution is to estimate the causal effect of FDI liberalization on
wage markdowns. Following Lu, Tao and Zhu (2017), we utilize plausibly exogenous relaxation of China’s regulations on FDI inflow upon its WTO accession at theend of 2001 where China liberalized 112 of its 424 four-digit manufacturing industries. Following Topalova (2010) and Autor, Dorn and Hanson (2013), we map thisindustry-level FDI liberalization into county-level exposure to FDI liberalization basedon county’s initial employment across industries. We then conduct a simple differencein-differences estimation of county’s exposure to FDI liberalization on firm-level wage
markdowns with firm fixed effects and year fixed effects. To address potential endogeneity, we control for (1) county’s initial employment structure; (2) other policy reforms such as trade liberalization on output tariffs, input tariffs, and external tariffs,
state owned enterprises reforms (SOE reforms), special economic zones; (3) interindustry effects through vertical FDI linkages.
The estimation results are contrasting to the conventional wisdom. FDI liberalization induced the entry of foreign employers and enhanced competition among employers as expected. The conventional wisdom predicts that wage markdowns at incumbent
firms would then narrow, but instead they actually widened. In a county with the meanlevel of exposure to FDI liberalization, incumbent firms reduced employment by 2.9%
and increased MRL by 4.3%, as theory predicts. If wage markdown were constantas in traditional models, wages should have increased by the same 4.3%, but in fact
they fell by 0.3% on average. The wage markdown therefore widened by 4.6%. Of
course, the average wage in China grew steadily during this period. Precisely speaking,firms in counties with high exposure to FDI liberalization increased wage at almost the4same rate as firms in other counties, despite that the formers had labor shortage andincreased MRL. A weighted regression using initial employment as weight shows thatwage markdown for an average worker at incumbent firms expanded by 11.2 %. The
economic gain of FDI inflow distributed to local workers is substantially smaller thanthe prediction of traditional models featuring constant wage markdown.
The expansion of wage markdown after FDI liberalization also contributes to a decline in labor income share in manufacturing value-added. We decompose changes inlabor income shares in value-added of each firm to changes in four components: wage
markdowns, price markups, labor elasticity and value-added revenue share. Then, we
estimate the impact of FDI liberalization on each component and calculate its impacts
on labor income share in value-added of the manufacturing sector. At the individual
firm-level, a firm in a county with mean exposure to FDI liberalization reduced labor
income share by 4.9%. Most of the effect comes from increases in firm’s market power
in labor and good markets. Wider wage markdown accounts for 84% of the effect,
while wider price markup accounts for 17%. At the aggregate level, FDI liberalization
brought 9% of the decline in aggregate labor income share in the manufacturing sector
during 2001–2007. Wage markdown expansion accounts for 68% of the FDI effect.
Finally, we provide a theoretical explanation for our two main findings: (1) large
and productive firms set narrower wage markdown; (2) FDI liberalization expands
average wage markdown at incumbent firms. These two findings are contrast to aclassical Cournot oligopsony model where employer concentration creates monopsony power, but they are consistent with a canonical model of search frictional monopsony by Burdett and Mortensen (1998) where workers search on the job. Burdett andMortensen (1998) have demonstrated that large and productive firms may set narrower
wage markdown to employ more workers and to earn profits from output markets. Our
new finding is that when foreign firms with high productivity enter after FDI liberalization, the majority of domestic firms may expand their wage markdowns except
for very high productive firms who can compete on wages with foreign firms. The
intuition is simple. When foreign firms that pay higher wages enter, a marginal wage
5

increase by a domestic firm leads to fewer additional workers than before because sucha marginal wage increase is insufficient to compete with high wage by foreign firms.
In other words, those domestic firms that pay lower wage than foreign firms now faceless elastic labor supply curves and widen wage markdown accordingly. On the other
hand, for very productive firms that can pay higher wage than some of foreign entrants,
a marginal increase in wage leads to more additional workers. Thus, these firms face
more elastic labor supply curves and narrow wage markdown. We have confirmed
this prediction about the heterogeneous change in wage markdown. We found thatthe top 19% of firms in terms of initial TFP before liberalization reduced their wage
markdowns, while other firms increased them.
Related literatureThis paper contributes to the empirical literature on the effectof international competition on firm’s market power. To our knowledge, our study isthe first to empirically examine the effect of FDI liberalization on firm’s monopsony
power in labor markets. The literature has mostly focused on the impact of trade liberalization on price markups. Empirical studies using micro-level data include those of
Levinsohn (1993), Harrison (1994), Krishna and Mitra (1998), Konings, Van Cayseele
and Warzynksi (2001), Chen, Imbs and Scott (2009), De Loecker, Goldberg, Khandelwal and Pavcnik (2016), and Feenstra and Weinstein (2016). Another strand of
the literature conducts general equilibrium analyses such as those of Holmes, Hsu andLee (2014), Edmond, Midrigan and Xu (2015), and Arkolakis, Costinot, Donaldson
and Rodriguez-Clare (2018). Among these studies, our study closely follows the spiritof De Loecker et al. (2016) where the authors estimate price markups without imposing assumptions about market structure and functional forms and investigate the effectof import liberalization by India. De Loecker et al. (2016) found that import liberalization of final goods narrows output price markups (after controlling for the effect ofimport liberalization of intermediate goods). We found that FDI liberalization expands
wage markdowns.
There is large literature about the impact of FDI on wage levels in host countries6

(see Javorcik, 2013 and Hale and Xu, 2016 for surveys). The literature commonly findsthat foreign firms pay higher wages than domestic firms (e.g., Aitken, Harrison and
Lipsey, 1996; Heyman, Sjoholm and Tingvall, 2007). Several studies find the entry of
foreign firms increases the wages paid by other firms in the labor market, including in
China (e.g., Feenstra and Hanson, 1997; Hale and Long, 2011). Our focus is different.
Our question is not whether wages increase or not, but whether wages increase as muchas the MRL increases.
The current paper is related to recent research in labor economics estimating firmlevel labor supply elasticities and monopsony power. Dal Bó, Finan and Rossi (2013),
Falch (2010), Matsudaira (2014), Naidu, Nyarko and Wang (2016), and Staiger, Spetz
and Phibbs (2010) estimate industry-level average markdowns. Dobbelaere, Kiyota
and Mairesse (2015) and Dobbelaere and Kiyota (2018) classify industries in whichfirms exercise labor monopsony. Naidu, Nyarko and Wang (2016) is the closest to thecurrent paper. The authors analyze the impact of an expansion of immigrant workers’
outside options on (industry-level) wage markdowns, while we examine the effect ofincreased competition among employers induced by FDI liberalization.
The rest of the paper is organized as follows. Section 2 presents our estimation
framework of wage markdowns. Section 3 discusses our data and China’s FDI liberalization. Section 4 report empirical results. Section 5 concludes the paper.

2

Empirical Framework

2.1

Wage markdown measurement

Assume that firm j produces output Yjt at time t with the gross production function:
Yjt = Fjt (Ljt , Kjt , Mjt ) exp (!jt )(1)

where Ljt is labor, Kjt is capital, Mjt is materials and !jt is total factor productivity.
Assume that firms are price takers of materials and that the first order condition for
7

profit maximization with respect to materials holds:@Rjt @Fjt= PjtM@Yjt @Mjt(2)

where Rjt (Yjt ) = Pjt (Yjt )Yjt is a firm’s revenue as a function of its output Yjt ,Pjt (Yjt ), is an inverse demand function and PjtM is the price of materials. From (2), themarginal revenue of labor is then@Rjt @Fjt
M RLjt ⌘= PjtM@Yjt @Ljt

✓

@Fjt
@Mjt

◆ 1

@Fjt
.
@Ljt

(3)

The wage markdown ⌘jt , the ratio of wage to MRL, which can be simplified from
(3) aswjt⌘jt ⌘=M RLjt@F✓M

wjt Ljt
PjtM Mjt

@F

◆

M
✓jt
=
L
✓jt

✓

wjt Ljt
PjtM Mjt

◆ ˜M
✓jt
,
✓˜L

(4)

jt

L

jt
M
L
where ✓jt
⌘ @Mjtjt Yjtjt and ✓jt⌘ @Ljtare the output elasticities of materials andjt Yjt
@R
M
@R L
jt
jt
labor, respectively; ✓˜M ⌘and ✓˜L ⌘ jt jt are revenue elasticities of ma-

jt@Mjt Rjt

jt@Ljt Rjt

terials and labor, respectively. The ratio of the revenue elasticities equals the ratio of
@R

@R

@F

the output elasticities because of the chain rule @Zjtjt = @Yjtjt @Zjt
. A firm’s total wage
jt
payment wjt Ljt and total material purchases PjtM Mjt are available from typical production datasets. Revenue and output elasticities can be estimated from production
data by applying production function estimation techniques.
Wage markdown can be interpreted as a measure of a firm’s monopsony power.
The profit maximization problem with respect to labor can be expressed as:
max Rjt (Yjt )Ljt

wjt (Ljt )Ljt s.t. (1)(5)

where wjt (Ljt ) is the inverse labor supply function that the firm faces. The first ordercondition simplifies wage markdown as
⌘jt =

"jt
 1.
"jt + 18

(6)

w

where "jt ⌘ w0 (Ljtjt )Ljt
jt

0 is the elasticity of the labor supply curve that firm j faces.

When a firm is a price taker in the labor market, "jt = 1, wages equal the MRL
and the wage markdown is one. When "jt is finite, i.e., the firm-level labor supply

curve to firm j is upward sloping, a firm sets its wage lower than its MRL. Noticethat smaller ⌘jt represents greater monopsony power. In the following, “wide” and“narrow” markdown express large and small monopsony power, respectively.

2.2

Discussion

Generality about market structure and functional forms

The formula (4) is gen-eral about output and labor market structures and functional forms of demand andsupply functions. Its derivation uses only the first order condition for materials (2). It
does not impose any assumption about how wages and employment are determined.
The firm-level inverse demand function Pjt (Yjt ) is consistent with all the major models of imperfect competition, and it allows various types of firm heterogeneity. When
we interpret measured wage markdown we additionally assume that firms choose theirlabor following (5). The inverse labor supply function wjt (Ljt ) represents a reduced
form relationship between wages and employment that is consistent with various models of imperfectly competitive labor market including search, bargaining, wage posting, etc.5 Although in problem (5) a firm chooses employment, it is straightforward toderive the same formula (4) from an equivalent problem where a firm chooses its wage
level instead.
The generality of this formulation about labor market structure and functional
forms is crucial for the study of FDI liberalization on wage markdown. Theoreticalpredictions about the effect of FDI liberalization on domestic firm’s wage markdowns
vary among models depending on their functional form. In Appendix, we examine
three canonical models of labor monopsony: the Cournot oligopsony model of employer concentration (e.g. Naidu et al. 2016), the Logit model of job differentiation
5

For instance, Mortensen (2009), among others, has derived an upward-sloping inverse supply curvein a model in which a firm and workers bargain as Helpman and Itskohi (2008) have proposed.

9(e.g. Card, Cardoso, Heining and Klein, 2018), and the Burdett-Mortensen model ofworker’s on the job search. The Cournot model predicts that FDI liberalization usually
narrows wage markdown, while the other two models can predict that FDI liberalization widens wage markdown of domestic firms even with standard functional forms
and parameters. This disagreement of prediction across models poses a challenge to
our empirical study. If one estimates wage markdown from a structural model, thechoice of a specific model may determine the sign of FDI’s competition effect a priori.
The generality of the formula (4) does not, however, imply that its implementation
is free from assumptions. The estimation of revenue and output elasticities requires
some assumptions about data generating process and market structure. We choose
an estimation method which is general about labor market structure and where theproduction function and labor supply curve are non-parametric.
The De Loecker-Warzynski price markup formula Our wage markdown estimation can be regarded as an application of price markup estimation by De Loecker andWarzynski (2012) (DLW price markup, hereafter). The generality of our markdown
estimation about market structure and functional forms originates from the same virtueof the DLW price markup. Consider the following alternative derivation of (4). From
@Rjt /@Yjt = M Cjt where M Cjt is marginal cost, wage markdown can be expressed
as
⌘jt =

wjt
⇣

M Cjt

@Fjt
@Ljt

⌘ = µjt

L
↵jt
,
L
✓jt

L
where µjt ⌘ Pjt /M Cjt is the output price markup and ↵jt⌘ wjt Ljt /Rjt is the wage

payment share in revenue. If the firm is a price taker of materials, the DLW formulaMMM
estimates price markup as µjt = ✓jt/↵jt
where ↵jt
⌘ PjtM Mjt /Rjt is material expen-

diture share in revenue. Substituting this markup into the above equation yields wage
markdown formula (4).

An important difference from the DLW markup formula is the data requirement.

10Strictly speaking, the DLW markup formula requires output elasticities, while ourwage markdown formula can be computed with either revenue elasticities or output
elasticities. A typical production dataset reports only firm revenue without output
price information. It is a common practice to use firm revenue as a proxy for output
and to estimate revenue elasticities instead of output elasticities.6 Our wage markdown formula can be implemented with a typical production dataset without output
price information.
Monopsony power for materials As in the DLW markup, our markdown formularequires firms to be price takers with respect to materials. If a firm holds monopsonyPMpower in materials, it charges the material price markdown jt ⌘ @Rjt jt@Fjt  1. Then,@Yjt @Mjt(4) reduces to ⌘jt / jt , labor monopsony power relative to material monopsony power.
That will underestimate labor monopsony power (and overestimate ⌘jt ). However, material monopsony is less likely to cause a major problem in our analysis. First, buyers
usually hold monopsony power because sellers cannot easily find alternative buyers.
This difficulty is particularly acute for workers who cannot easily move across labormarkets and find buyers for their labor compared with sellers of materials. This isespecially applicable in China where migration across regions are restricted while materials are freely tradable across regions. Second, as will be shown below, our estimatesindicate significant labor monopsony, so there is little scope for underestimating labormonopsony. Finally, we use regional variations in exposure to FDI liberalization to estimate its effect on wage markdowns specifically because workers are not fully mobile
across regions. On the other hand, since materials are tradable goods, the variations inmaterial monopsony are more likely to be evident across industries rather than acrossregions. Thus as long as our region-level treatment is exogenous to regional industry
structure (the identification assumption), our regression will consistently estimate thecausal effect of FDI liberalization on wage markdown.
6

Klette and Griliches (1996) and De Loecker and Warzynski (2012) discuss how to estimate output
elasticities with such datasets.

11

Heterogeneous labor While we have considered the case that firms employ homogenous labor, firms normally employ workers of several skill types and set different
wage markdowns for different skill types. If the wage and employment for each skill
type can be observed as data, the formula (4) can easily be extended to measure wage
markdown by type s of worker ⌘ s by replacing wjt Ljt , ✓˜L , and ✓L with the correjt

jt

jt

sponding variables for each type s worker.
Typical production datasets like the one we use usually report only firm’s total labor input without skill level breakouts. But even then, our markdown measure is still
informative about a firm’s monopsony power because workers’ skills increase boththe numerator (wages) and the denominator (MRL) simultaneously. To see this, suppose that workers of different types are perfectly substitutable. That is, the production
P s sfunction includes labor L⇤jt in an efficiency unit such that L⇤jt = s ⌫jt
Ljt where Lsjtsis type s labor and ⌫jt
is a skill converter. As we show in Appendix, in this case, asfirm sets identical markdown for all types, ⌘jt = ⌘jt
for all s since they are perfectly

substitutable. Our markdown formula (4) then correctly measures the firm’s wage
markdown. Even when workers of different types are imperfectly substitutable, ourmarkdown measure(4)◆is the average markdown weighted by output elasticities such
✓
s
P
✓jt
s
s
that ⌘jt = s P ✓s0 ⌘jt
where ✓jt
is the output elasticities of type s workers.
s0

jt

Non-profit maximizing firms

Profit maximization may not be the objective forsome firms such as state-own enterprises (SOE), firms in public sectors, and non-profit
organizations. In China, SOE firms are large employers and often considered to caremore about employment than about maximizing profits (e.g., Berkowitz, Ma and Nishioka, 2017). Suppose an SOE j seeks to maximize ⇡jt + j Ljt where ⇡jt is profits andj > 0 is a weight for employment. Our formula (4) correctly estimates such an SOE’s
SOEwage markdown ⌘jt
since the first order condition for materials remains in the same

form as (2). However, the relationship between wage markdown and labor supply elasticities changes. In the Appendix, we show that the wage markdown of SOE firms is

12

then
SOE
⌘jt
⌘

wjt
=
M RLjt✓"j"j + 1

◆

0
@

1

w

1
⇣

"j
"j +1

1

⌘A >

✓

"j
"j + 1◆.

(7)

If SOEs and private firms face similar labor supply elasticities, the SOEs would be
expected to charge narrower wage markdown than the private firms.

2.3

Production Function Estimation

We estimate gross production function using a nonparametric estimation method byGandhi, Navarro and Rivers (2017) (hereafter GNR). The literature of production function estimation has developed to cope with an endogeneity problem that firm’s input
choices may be correlated with unobservable total factor productivity (TFP). A series of seminal papers by Olley and Pakes (1996), Levinsohn and Petrin (2003) and
Ackerberg, Caves and Frazer (2015) have developed the so-called proxy approach using firm’s factor usages as a proxy for TFP. Although the proxy approach can validly
estimate value-added production function, GNR recently show that it is difficult toapply for that of gross output production function. When a standard set of assumptions for the proxy approach is satisfied, the gross output production function is not
non-parametrically identifiable using either the proxy approach or the dynamic panel
GMM approach.
GNR proposes an alternative method that additionally estimates the first order condition for materials (2). To utilize the first order condition, GNR’s method has to specify output market structure, though it is still general about the labor market structureand non-parametric about production function and labor supply curve. Since output
markups potentially affect wage markdowns, we use GNR’s method for a monopolistic competitive output market where firms charge time-varying output markups (GNR,
Appendix O5-4) and where markups can respond to FDI liberalization. Following
De Loecker (2013), we also allow the stochastic process of productivity to depend on
characteristics of the firms, industries and regions. Appendix A2 explains our imple-

13

mentation of GNR’s method in detail.

2.4

Impacts of FDI liberalization

2.4.1

FDI regulation in China

In December 1978, the then leader of China, Deng Xiaoping, initiated an open door
policy to promote foreign trade and investment. It dramatically altered the situation
which had prevailed under rigid central planning. Before 1978, China hosted almost no
foreign-invested enterprises, but during the 1980s, a series of laws on FDI and implementation measures were introduced.7 Foreign-invested enterprises enjoy preferential
policies in terms of taxes, land use, and other matters, often in the form of policies for
special economic zones. They have been expected to bring advanced technologies andmanagement know-how to China and to promote China’s integration into the world
economy. As a result of these laws and implementation measures, China experienced
rapid growth in FDI inflows from 1979 to 1991 (Figure 1). After Deng Xiaoping tooka tour of Southern China in the spring of 1992 to revive a slowing economy, the FDI
inflows to China grew even faster, reaching US$ 27.52 billion in 1993.
Most significantly, the policies designated certaining industries in which FDI would
be encouraged or discouraged. In June 1995, the central government published a Catalogue for the Guidance of Foreign Investment Industries (hereafter, the Catalogue).
There were modifications made in 1997, but it became the government’s unique guideline for regulating FDI inflows. Specifically, the Catalogue classified products into
four categories: (i) those where FDI was supported, (ii) those where FDI was permitted, (iii) those where FDI was restricted, and (iv) those where FDI was prohibited.
Importantly, the guideline was implemented uniformly nationwide. The central gov7

In July 1979, a “Law on Sino–Foreign Equity Joint Ventures” was passed to attract foreign direct
investment. In September 1983, the “Regulations for the Implementation of the Law on Sino–Foreign
Equity Joint Ventures” was issued by the State Council of China; it was revised in January 1986, December 1987, and April 1990. In April 1986, the “Law on Foreign Capital Enterprises” was enacted. In
October 1986, “Policies on Encouragement of Foreign Investment” was issued by the State Council ofChina.

14

Figure 1: Foreign Direct Investment (Realized) (1979-2007)

Figure 1: Foreign Direct Investment (realized)
800
700
600
500
400
300
200
100
0

Foreign direct investment (realized) (Unit: USD 100 million)

Datasource:Note:
China
Foreign
Economic
Statistical
Yearbook(various
years)The data
on foreign
direct investment
are obtained
from China
Foreign
Economic Statistical
Yearbook (various years).

ernment prohibited discretional policies on FDI entry by regional governments.8
During the negotiations to join the WTO, China was asked to open itself up for
trade and FDI. After China’s entry into the WTO in November 2001, its central government substantially revised the Catalogue in March 2002 and relaxed FDI regulation
to illustrate its commitment to WTO rules.9 In this study we exploit the plausibly exogenous relaxation of FDI regulations upon China’s WTO accession at the end of 2001
to identify the FDI liberalization effect.
2.4.2

Locality-event DD approach

While FDI liberalization is nation-wide, firms are likely to exercise monopsony power
within local labor markets. Following Topalova (2007) and Autor, Dorn and Hanson
8

On May 4, 1997, the State Council issued the Termination of Unauthorized Local Examination andApproval of Commercial Enterprises with Foreign Investment, which forbid the location discretions
about FDI entry regulations.
9
There was another minor revision of the Catalogue in November 2004. The National Development
and Reform Commission and the Ministry of Commerce jointly issued fifth and sixth revised versionsof the Catalogue in October 2007 and December 2011, beyond the period studied.

15

(2013), we apply a locality-event difference-in-differences (DD) approach based on
local labor market-level exposure to FDI liberalization. We use county as a unit oflocal labor market. That roughly corresponds to the US commuting zones used byAutor, Dorn and Hanson (2013).
We first map industry-level FDI liberalization into local labor market-level exposure to FDI liberalization. The industrial activity varies substantially among counties
before China’s WTO accession, so the sudden FDI regulation changes upon WTO
accession impact the counties differently based on their initial employment structures. The county-level exposure to FDI liberalization F DIct is constructed as a local
employment-weighted average of FDI regulation changes:
LIBc ⌘

X Lcs1998s

Lc1998⇥ Liberalizeds and F DIct ⌘ LIB c ⇥ P ost2002t ,(8)

where s represents a four-digit manufacturing industry; Liberalizeds is an indicatorof whether inward FDI is liberalized for industry s; P ost2002t is a dummy variableindicating the post-WTO period, i.e., P ost2002t = 1 if t

2002, and 0 if t  2001;

and Lcs1998 /Lc1998 is industry s’s share of employment in county c in 1998, the initial
year of the sample period. The denominator Lc1998 also includes employment in nonmanufacturing sectors. By construction, F DIct takes its minimum value of zero if thecounty had no initial employment in liberalized industries and its maximum value one
if all the county’s initial employment is in liberalized industries.
The local labor market DD estimation has the following specification:ln ⌘jct = ↵j + ↵t + F DIct + X0ct

+ "jct ,(9)where j, c, and t represent firm, county and year, respectively. ↵j is the firm fixed
effect, controlling for all time-invariant differences across firms. Since most firms inthe sample do not change their location, the firm fixed effects also control for all timeinvariant difference among the counties such as geography, etc; ↵t is the year fixed
effect controlling for any annual shocks common to the counties such as business cy16

cles, monetary policies, exchange rate shocks, etc; and "jct is the error term. To isolate
the effect of FDI regulation changes, we control for a vector of industry characteristics Xct (to be explained later) that may affect the outcome. To deal with potential
heteroskedasticity and serial autocorrelation, the standard errors are clustered at thecounty level. The coefficient of interest

captures the impact of county’s exposure to

FDI liberalization on wage markdown at an average firm. Since firms are heterogenous in employment size, the effect on wage markdown to an average worker might bedifferent. We therefore also conduct a weighted regression using employment share in2001 as weights.
A crucial identification assumption about

in equation (9) is that conditional on

the covariates, the regressor of interest is uncorrelated with the error term, i.e.,
E ["jct |F DIct , ↵j , ↵t , X0ct ] = E ["jct |↵j , ↵t , X0ct ] .

(10)Since the variations in F DIct stem from variations in county’s initial employment
structure, one concern is that a county’s initial employment structure may be correlated with unobserved time-varying county-level characteristics that affect wage markdowns. To address this concern, we include three sets of control variables in vector
Xct . The first set of control variables is county’s initial employment composition. We
include interactions between year dummies and the share of employment in each of
15 sectors in county’s total employment in 1998.10 The second set of control variables captures other on-going policy reforms around the time of FDI liberalization.
First, to control for the effects of tariff reductions by China and its trading partners
after China’s WTO accession, we include county-level exposure to output tariffs, input
10

The 15 sectors are 1. farming, forestry, animal husbandry and fishery; 2. mining and quarrying;
3. manufacturing; 4. production and supply of electric power, gas and water; 5. construction; 6.
geological prospecting and water conservancy; 7. transport, storage, postal and telecommunication
services; 8. wholesale and retail trade and catering services; 9. finance and insurance; 10. real estate;
11. social services; 12. health care, sports and social welfare; 13. education, culture and the arts, radio,
film and television; 14. scientific research and polytechnical services; and 15. governments agencies,
party agencies and social organizations.

17

tariffs, and external tariffs imposed by foreign countries.11 Second, the restructuring
and privatization of SOEs is another important policy reform in the early 2000s. To
control for any differences in the SOE reforms across counties, we include county’s
share of SOEs in the total employment. Third, China set up special economic zones toattract foreign direct investment. We include an indicator for whether or not a county
is in a special economic zone. Finally, county’s exposure to FDI liberalization might
be magnified by inter-industry vertical linkages. We therefore include county-level
exposures to FDI liberalization in backward and forward industries as the third set ofcontrol variables.

3

Data

Panel Data on Industrial Firms The first dataset used in this study comes from theAnnual Survey of Industrial Firms (ASIF), conducted by the National Bureau of Statistics of China for the 1998–2007 period.12 The surveys cover all of the state-owned
enterprises (SOEs) and non-SOEs with annual sales exceeding 5 million Chinese yuan(about US$827,000). The number of firms covered in the surveys varies from approximately 162,000 to approximately 270,000. Though the title of ASIF includes “firms”,
all information is reported on the firm-province level, so that the dataset is closer to a
11
The tariff data for HS-6 products are obtained from the World Integrated Trade Solution (WITS). By
mapping HS-6 products to ASIF 4-digit industries through the concordance table published by China’s
National Bureau of Statistics, we are able to calculate simple average output tariff at the industry level.
The input tariff is constructed as a weighted average of the output tariff, using the share of the inputs inthe output value from the 2002 China’s Input-Output Table as the weights. The export tariff is measured
as a weighted average of the destination countries’ tariffs on China’s imports, using China’s imports
from each destination country as the weight. County’s exposure to each tariff are calculated as a local
employment-weighted average of the tariff as in (8).
12This is the most comprehensive and representative firm-level dataset in China, and the firms surveyed contribute the majority of China’s industrial value-added. The dataset has been widely usedby economic researchers in recent years, including Lu, Lu, and Tao (2010), Brandt, Van Biesebroeck,
and Zhang (2012), and Khandelwal, Schott, and Wei (2013). In 2003, a new classification system forindustry codes (GB/T 4754-2002) was adopted in China to replace the GB/T 4754-1994 system that
had been used from 1995 to 2002. To achieve consistency in the industry codes over the period studied(1998–2007), we use the concordance table constructed by Brandt, Van Biesebroeck, and Zhang (2012).

18

plant-level dataset in contrast to the firm-level datasets in other countries.13 The dataset
includes the basic information about each plant, such as its identification number, ownership structure, and industry affiliation, and the financial and operating information
extracted from accounting statements, such as sales, employment, intermediate inputs,
and the total wage bill, from which we construct variables for production function
estimation. The total wage bill is measured as the sum of firm’s wage bills and supplementary compensation such as bonuses and insurance.14
Data on China’s FDI Regulations

We classify each 4 digit industry into liberalized

industries and non-liberalized industries, following Lu, Tao and Zhu (2017). We use
the Catalogue to obtain information on FDI regulation changes of each industry upon
China’s WTO accession at the end of 2001. Using the Catalogue for year t, we classify
the products into four groups and assign an index of FDI regulation Regst for products that could take one of four values: (ii) the supported products Regst = 1 where FDI
was supported; (ii) the permitted products Regst = 2 where FDI was permitted; (iii)the restricted products Regst = 3 where FDI was restricted; (iv) the prohibited products Regst = 4 where FDI was prohibited. Products not mentioned in the Catalogue
are classified into the permitted category.
We then compare the 1997 and 2002 versions of the Catalogue and identify products into three groups: (i) liberalized products
no change products

Regs ⌘ Regs1997

Regs = 0; (iii) regulated products

13

Regs2002 > 0; (ii)Regs < 0. Finally, we ag-

According to Article 14 of the Company Law of the People’s Republic of China, however, fora company to set up a plant in a region other than its domicile, “it shall file a registration application with the company registration authority, and obtain the business license.” For example, Beijing
Huiyuan Beverage and Food Group Co., Ltd. has six plants, located in Jizhong (Hebei Province),
Youyu (Shanxi Province), Luzhong (Shandong Province), Qiqihar (Heilongjiang Province), Chengdu(Sichuan Province), and Yanbian (Jilin Province). Our data set accordingly counts them as six different
observations belonging to six different regions.
14
To convert the nominal values of output and input into real terms, we use industry-level ex-factory
price indices for sales, and input price indices for intermediate inputs. Both price indices are provided
by Brandt, Van Biesebroeck, and Zhang (2012). The real capital stock is constructed using the perpetualinventory method proposed by Brandt, Van Biesebroeck, and Zhang (2012). Specifically, we first calculate firm’s real capital stock in its founding year. Then we use firm’s fixed investment with depreciation
rate of 9% to calculate its real capital stock in each year. The investment deflator is provided by Perkins
and Rawski (2008).

19

Table 1: FDI entry after liberalization
(1)

(2)

(3)

1998–2001 2002–2007 Change (%)
Panel A. Foreign equity share
Treatment

0.043

0.077

79.07

Control

0.069

0.104

50.72

Treatment

0.131

0.161

22.78

Control

0.192

0.208

8.48

Panel B. Share of number of foreign firms

Note: the treatment (control) group refers to counties with high (low) FDI
liberalization exposure in the initial year. Foreign equity share in Panel A andshare of number of foreign firms in Panel B calculated over the pre-WTO 1998–
2001 period, the post-WTO 2002–2007 period, and their percentage changes,
respectively.

gregate the changes in FDI regulation from the Catalogue’s product level to the ASIF
industry level. The aggregation process leads to four possible scenarios: (i) FDI encouraged industries where all of the products are either liberalized or not changed; (ii)no change industries where all of the products are unchanged; (iii) FDI discouraged industries where all of the products are either more tightly regulated or unchanged; and(iv) mixed industries where some products are liberalized and others become moreregulated. Among the 424 4-digit industries, 112 are FDI encouraged industries, 300
are no-change industries, 7 are FDI discouraged industries and 5 are mixed industries.
We define an indicator of liberalized industries in (8) as follows: Liberalizeds = 1 if
industry s belongs to encouraged industries and Liberalizeds = 0 otherwise.
Using information of county-level employment, we construct the county-level exposure to FDI liberalization F DIct . Its summary statistics are as follows: mean 0.32
with a standard deviation 0.21. The median falls at 0.28, the 25th percentile at 0.18,
and the 75 percentile at 0.43. Table 1 shows FDI entry after the liberalization, comparing counties with above-mean exposure to FDI liberalization (the treatment group)and those with below-mean exposure (the control group). The treatment group showsa greater increase in FDI entry.

20

4

Empirical Results

4.1

Wage Markdowns and Firm Characteristics

Table 2 reports summary statistics on estimated revenue elasticities for each 2 digit
industry. The substantial heterogeneity on elasticities within industries confirms theadvantage of using a flexible production function. Overall, the estimated elasticities
look reasonable. They are positive for most industries. Although the estimated capitalelasticities are relatively small, this pattern has been observed in previous studies ofChinese firms using different estimation methods (e.g., Lu and Yu, 2015). It is thus
the feature of the Chinese data rather than an artifact of the estimation method. We
dropped three industries with negative median labor elasticities, which would imply
negative wage markdowns. We also exclude the tobacco industry, which is heavily
regulated.
Table 3 reports firm-level wage markdowns and output price markups. First ofall, labor monopsony is ubiquitous in Chinese manufacturing industries. Column (1)reports median wage markdowns for each 2 digit industry. In our sample, 88% of
the firms set wage markdowns smaller than one, and the median wage markdown for
the entire sample is 0.25. Columns (3) and (4) report price markups. The medianmarkup in the entire sample is 1.06, which is reasonably close to previous estimates ofindustry average markups ranging from 0.825 to 1.372. Lu and Yu (2015) make thoseestimates from the same dataset but with different methodology. Third, Columns (5)and (6) report median markdowns weighted by firm’s employment, which suggests themarkdown of an average worker. The weighted median markdown of 0.35 is slightly
larger than the simple median of 0.25, suggesting that small employers exercise greatermonopsony power. Finally, firm-level wage markdowns are heterogenous both acrossand within industries. Many industries show substantial heterogeneity in markdowns
within industries.
Our estimates of wage markdown are comparable to estimates previously studied. Sokolova and Sorensen (2018) collect 700 labor supply elasticity estimates for21

Table 2: Production Function Estimation
Revenue Elasticity With Respect to …
Labor

Capital
(4)

(5)

(6)

Obs.

(1)

(2)

Industry

Median(p25, p75)

Median (p25, p75) Median (p25, p75)

Food processing

0.35(0.24, 0.46)

0.29(0.22, 0.37) 0.69

(0.64, 0.73) 129,975

Food manufacturing

0.32(0.21, 0.42)

0.35(0.25, 0.45) 0.67

(0.63, 0.71) 52,333

Beverage manufacturing

0.46(0.27, 0.62)

0.36(0.24, 0.50) 0.63

(0.59, 0.68) 35,865

Textile industry

0.17(0.09, 0.25)

0.27(0.20, 0.33) 0.74

(0.70, 0.77) 170,353

Garments & other fiber products

0.24(0.19, 0.28)

0.18(0.13, 0.23) 0.70

(0.66, 0.75) 97,194

Leather, furs, down & related products

0.28(0.24, 0.31)

0.21(0.14, 0.27) 0.72

(0.68, 0.76) 48,522

Timber processing, bamboo, cane,palm fiber & straw products

0.19(0.17, 0.22)

0.22(0.17, 0.28) 0.71

(0.67, 0.74) 44,491

Furniture manufacturing

0.21(0.18, 0.23)

0.17(0.13, 0.21) 0.71

(0.67, 0.74) 23,656

Papermaking & paper products

0.27(0.15, 0.37)

0.29(0.22, 0.38) 0.73

(0.7, 0.75)

61,096

Printing industry

0.27(0.24, 0.30)

0.72(0.55, 0.90) 0.66

(0.6, 0.71)

43,597

Cultural, educational & sports goods

0.21(0.19, 0.24)

0.20(0.14, 0.25) 0.73

(0.69, 0.76) 26,550

Petroleum processing & coking

0.29(0.18, 0.40)

0.30(0.23, 0.40) 0.71

(0.67, 0.75) 17,977

Raw chemical materials & chemical products

0.29(0.22, 0.35)

0.41(0.31, 0.53) 0.71

(0.67, 0.74) 149,424

Medical & pharmaceutical products-0.13(-0.21, -0.05)

0.45(0.36, 0.55) 0.61

(0.57, 0.66) 43,060

Chemical fiber

0.52(0.38, 0.65)

0.33(0.24, 0.47) 0.76

(0.73, 0.79) 10,304

Rubber products

0.01(-0.01, 0.03)

0.30(0.22, 0.39) 0.71

(0.68, 0.74) 24,205

Plastic products

0.40(0.35, 0.43)

0.40(0.29, 0.51) 0.73

(0.69, 0.76) 94,307

Nonmetal mineral products

0.12(-0.6, 0.85)

0.30(0.13, 0.47) 0.69

(0.65, 0.72) 175,768

Smelting & pressing of ferrous metals

0.06(0.03, 0.10)

0.29(0.22, 0.36) 0.74

(0.70, 0.77) 49,354

Smelting & pressing of nonferrous metals

0.00(-0.03, 0.03)

0.30(0.22, 0.38) 0.75

(0.70, 0.78) 36,339

Metal products

0.21(0.14, 0.28)

0.40(0.30, 0.50) 0.72

(0.69, 0.76) 109,990

Ordinary machinery

1.20(1.00, 1.37)

0.26(0.17, 0.35) 0.71

(0.68, 0.74) 153,252

Special purpose equipment

0.56(0.53, 0.59)

0.42(0.30, 0.53) 0.67

(0.63, 0.72) 85,860

Transport equipment

0.13(0.09, 0.17)

0.46(0.33, 0.58) 0.67

(0.6, 0.73)

Electric equipment & machinery-0.06(-0.08, -0.04)

0.33(0.24, 0.41) 0.73

(0.69, 0.76) 120,020

Electronic & telecommunications equipment

0.31(0.20, 0.40)

0.51(0.36, 0.65) 0.67

(0.62, 0.73) 67,530

Instruments, meters, cultural &office equipment

0.07(0.04, 0.11)

0.40(0.29, 0.51) 0.65

(0.60, 0.70) 29,001

Other manufacturing(3)

Materials(7)

98,891-0.22 (-0.25, -0.19) 0.22 (0.16, 0.27) 0.71 (0.66, 0.75) 39,526
Note: The table reports median, 25 percentile (p25) and 75 percentile (p75) of revenue elasticities with respect to labor,
capital, and materials and the number of observations for each two digit level industry.

22individual firms using 38 articles published from 1977 to 2018. According to theirreport on directly estimated 700 elasticities, the distribution of wage markdowns implied by (6) is that the median wage markdown is 0.52 with a 5% to 95% intervalof [ 0.04, 0.80]. Our estimated median markdown of 0.25 falls within the range ofpast estimates. Although it is lower than the median of previous estimates, that seems
reasonable because the majority of past estimates are computed using data from developed countries which have better institutions protecting workers than those in China
during our sample period.
Table 4 examines correlations of wage markdowns with firm characteristics, reporting the regression of wage markdown on logged TFPR in Column (1), on employment
in Column (2), on dummy variables indicating state-ownership and foreign ownershipin Column (3), and on a dummy variable indicating whether a firm is an exporter inColumn (4). These regressions all include year fixed effects, with firm fixed effects
included in Columns (1) and (2), and 4-digit industry fixed effects and county fixed
effects in Columns (3) and (4). TFPR is revenue-based TFP (Foster, Haltiwanger, andSyverson, 2008), the residuals of revenue unexplained by inputs that may include not
only physical TFP but also all positive shocks to firm revenue. Because such shocks
tend to increase MRL, we use TFPR in this analysis.
Those firms that have narrower markdowns are considered to offer “good jobs” inChina. They are high productivity firms, large employers, state-owned firms, foreignowned firms and exporters. SOEs and foreign firms set 49% and 7% narrower markdowns, respectively, than domestic private firms. The SOEs’ narrower markdowns are
consistent with (7)—SOEs care about employment as well as their profits.
Although those associations presented in Table 4 do not necessarily imply causality, the associations indicating that large and productive firms exercise less monopsony
power might appear strange in view of classic monopsony theory of employer concentration predicting that a large firm will exercise monopsony power. They are, however,actually consistent with modern monopsony theory (Burdett and Mortensen, 1998) inwhich it is search friction that creates monopsony. Firms with high productivity pay
23Table 3: Wage Markdowns and Price Markups
Wage Markdowns

Price Markups

Wage Markdowns(Weighted)

(1)

(3)

(5)

(2)

(4)

(6)

Industry

Median (p25, p75) Median(p25, p75) Median (p25, p75)

Food processing

0.09(0.04, 0.22)

1.38(1.34, 1.43)

0.22(0.09, 0.6)

Food manufacturing

0.22(0.1, 0.48)

1.07(1.04, 1.1)

0.43

(0.19, 0.99)

Beverage manufacturing

0.14(0.06, 0.33)

1.13(1.11, 1.18)

0.32(0.13, 0.78)

Textile industry

0.45(0.27, 0.73)

1.05(1.03, 1.07)

0.32(0.2, 0.49)

Garments & other fiber products

0.48(0.32, 0.71)

2.95(2.85, 3.02)

0.45(0.29, 0.66)

Leather, furs, down & related products

0.34(0.17, 0.56)

1.02(1.01, 1.05)

0.59(0.33, 1.14)

Timber processing, bamboo, cane,palm fiber & straw products

0.31(0.17, 0.52)

1.15(1.13, 1.17)

0.45(0.25, 0.8)

Furniture manufacturing

0.36(0.22, 0.56)

1.20(1.19, 1.21)

0.40(0.26, 0.58)

Papermaking & paper products

0.21(0.11, 0.42)

1.02(1.01, 1.03)

0.37(0.18, 0.89)

Printing industry

0.38(0.22, 0.66)

1.17(1.15, 1.17)

0.45(0.27, 0.75)

Cultural, educational & sports goods

0.48(0.29, 0.77)

1.06(1.05, 1.08)

0.82(0.47, 1.55)

Petroleum processing & coking

0.12(0.05, 0.28)

1.04(1.02, 1.08)

0.30(0.12, 0.86)

Raw chemical materials & chemical products

0.17(0.08, 0.38)

1.07(1.04, 1.09)

0.56(0.22, 1.31)

Chemical fiber

0.08(0.03, 0.16)

1.02(1.01, 1.04)

0.18(0.08, 0.46)

Rubber products

5.33(3.24, 9.83)

7.36(7.23, 7.5)

6.18

(3.57, 12.03)

Plastic products

0.16(0.09, 0.29)

1.02(1.02, 1.03)

0.28(0.15, 0.53)

Nonmetal mineral products

0.09(0.03, 0.25)

1.01(1, 1.03)

0.15(0.06, 0.44)

Smelting & pressing of ferrous metals

0.63(0.39, 1.02)

7.86(7.67, 8.12)

0.52(0.33, 0.76)

Smelting & pressing of nonferrous metals

1.60(0.82, 3.26)

1.03(1.01, 1.05)

2.85(1.42, 6.81)

Metal products

0.36(0.21, 0.56)

1.00(0.98, 1.02)

0.28(0.16, 0.45)

Ordinary machinery

0.07(0.03, 0.12)

1.04(1.02, 1.07)

0.14(0.07, 0.32)

Special purpose equipment

0.15(0.08, 0.26)

1.03(1, 1.07)

0.21(0.12, 0.35)

Transport equipment

0.74(0.4, 1.3)

5.46

(5.24, 5.74)

0.90(0.46, 1.57)

Electronic & telecommunications equipment

0.30(0.17, 0.52)

4.41(4.31, 4.6)

0.19

(0.1, 0.35)

Instruments, meters, cultural & office equipment

1.38(0.95, 2.13)

1.09(1.04, 1.14)

1.72(1.15, 2.59)

All industries

0.25(0.1, 0.55)

1.06(1.02, 1.19)

0.35(0.17, 0.7)

Note: The table reports median, 25 percentile (p25) and 75 percentile (p75) of wage markdown, those of output
price markup, and those statistics weighted by firm employment of wage markdown.

24

Table 4: Wage Markdown and Firm Characteristics
Log wage markdown

(1)

(2)

Log TFPR

0.047

(3)

(4)

(0.003)Log employment

0.278(0.003)

State owned dummy

0.489(0.005)

Foreign owned dummy

0.070(0.004)

Export dummy

0.04(0.003)Firm fixed effects

X

X

County fixed effects

X

X

Industry fixed effects

X

X

X

X

Year fixed effects
Observations

XX

1,308,875 1,292,740 1,235,508 1,235,508

Note: Standard errors are clustered at the firm level in parentheses.

25

higher wages, hire more workers and produce more output than firms with low productivity. In Section 5, we will show that wage markdown and employment can be bothincreasing in productivity.
Table 5 reports the regressions of logged wage markdown on county characteristics
in 2000 together with log county’s GDP per capita: on college graduate shares in
population in Column (1), on manufacturing employment shares and SOE employment
shares in manufacturing in Column (2), on the Herfindahl-Hirschman Index (HHI) of
manufacturing employment in Column (3), and on county income per capita in Column(4). Wage markdown is narrower in counties with more college graduates, with moremanufacturing and SOE employment, and with high concentration.
These results are also consistent with the job search theory. First, it may be easierfor college graduates than others to change employers than for less educated workers, giving them lower search costs and wider outside options. If so, firms would set
narrower markdowns for college graduates who have more elastic labor supply. Second, manufacturing firms and SOEs are considered to offer attractive jobs in China.
In counties with plenty of such jobs, workers’ better outside options may limit firms’monopsony power. Third, the positive relationship between wage markdown and the
HHIs is at odds with the concentration theory, but not necessarily with the job searchtheory. Concentration usually plays no role in job search models, which often features
a continuum of infinitely many firms. These patterns are robust after controlling forcounty GDP per capita.

4.2

FDI Liberalization

The DD estimation results are presented in Table 6. In addition to firm and year fixed
effects, we step-wisely include a set of controls as elaborated in the previous section.
The inclusion of these controls allows us to isolate the effect of FDI liberalizationfrom other confounding factors such as the potential endogenous selection of openup industries and other on-going policy reforms. Specifically, we include interactions
between year dummies and county’s initial sectoral employment share in Column (2).
26

Table 5: Wage Markdown and County Characteristics in 2000
Log wage markdown
College graduates share

(1)

(2)

(3)

(4)

2.638

4.764

(0.185)(1.517)

Manufacturing employment share

(5)

0.909

1.315

(0.065)(0.155)

0.686

0.355

(0.036)(0.052)

SOE emp share

Manufacturing employment HHI

0.347

0.549

(0.087)
County GDP per capita(6)(0.107)-0.030 -0.154

0.015(0.032) (0.030) (0.030)
Province fixed effects
Industry fixed effects
Observations

X

X

X

X

X

X

X

X

X

X

X

X

85,955 89,863 89,929 45,704 47,286 47,286

Note: Standard errors are clustered at the county level in parentheses.

Interactions between year dummies and other policy controls are additionally included
in Column (3). Backward and forward FDI are added in the estimation reported inColumn (4), which is our benchmark estimation.
The estimated coefficients of our regressor of interest, F DIct , are consistently negative and statistically significant at the 1% level. The negative coefficients indicatethat the wage markdowns are wider and incumbent firms exercise greater monopsony
power in counties more exposed to FDI liberalization. To see the economic magnitude, we rely on the estimates in column (4) and in Table 6 and the mean value 0.32
of F DIct at the county level. A firm in an average county decreases wage markdownby 4.6%(' 14.5% ⇥ 0.32). As our sample covers 6 years after the FDI regulation
changes, it can be translated into a 0.8%(' 4.6%/6) drop annually.

Columns (5) and (6) in Table 6 conduct robustness checks. Column (5) adds aninteraction term of F DIct and a dummy on whether the year is 2001, one year before
FDI liberalization. That is to check whether wage markdowns changes in anticipation

27

Table 6: FDI Liberalization and Wage Markdowns
Log wage markdown
FDI Liberalization
FDI Liberalization ×Year2001 dummy
Initial employment struture(1)(2)-0.230 -0.151(0.038) (0.035)

X

Other policy controls(3)-0.138(0.034)(4)-0.145(0.034)(6)-0.145(0.034)(7)-0.351(0.069)X(5)-0.161(0.038)-0.046(0.033)
X

X

X

X

X

X

X

X

X

Vertical FDI controls
X
X
X
X
Ownership controls
X
Weighted by 2001 employment
X
Firm fixed effects
X
X
X
X
X
X
X
Year fixed effects
X
X
X
X
X
X
X
Observations
970,416 970,416 970,416 970,416 970,416 970,416 469,466
Note: Standard errors are clustered at the county level in parentheses. Initial employment structure
include interactions between year dummies and county's employment share of 16 sectors in 2001.
Other policy controls include: (1) county's exposures to tariffs (output tariffs, input tariffs, andtariffs by foreign countries); (2) the share of state-owned enterprises among firms in a county, (3)a dummy variable indicating whether a county is a special economic zone or not. Vertical FDI
controls include county's exposure to FDI liberalization in backward and forward industries.
Ownership control includes FIE dummy and SOE dummy. Column (7) reports weighted regression
with employment in 2001 being the weight.

of the FDI liberalization. The coefficient of the interaction term is close to zero andstatistically insignificant, which indicates there is no expectation effect. Column (6)includes SOE and foreign-invested enterprise dummies to control for firm’s ownership
structures and that produces virtually no change.
Our baseline regression estimates the effect of FDI liberalization on an averagefirm. To see the effect on an average worker, Column (7) conducts a weighted regression that uses firm’s employment in 2001 as the weight. The coefficient becomes larger
than the unweighted estimates. In an average county with mean FDI exposure, wage
markdown for an average worker expands by 11.2%(' 35.1% ⇥ 0.32).

Figure 2 plots yearly effects of FDI liberalization. We estimate a regression withbaseline covariates in Column (4) of Table 6 and the interaction terms of LIBc in (8)and year dummies instead of F DIct . Figure 2 reports the coefficients of the interaction terms with 95% confidence intervals. The negative effect of FDI liberalization
becomes stronger in later years. It suggests that the discrepancy between wages and28

Figure 2: Yearly Effects of FDI Liberalization on Wage Markdown

-.4

-.3

-.2

-.1

0

.1

Yearly effects on log wage markdowns

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

Note: the solid line expresses the coefficients of interaction terms of FDI liberalization and year dummies in the regression of log wage markdown with main regressors. The dashed lines expresses 95%
confidence intervals.

MRL did not occur as a short-run adjustment process. It is a long run transition processfrom one equilibrium to another. Furthermore, it is apparent that in the pre-WTO period, the coefficients are stable around zero, which suggests that with our main control
variables, counties highly exposed to FDI liberalization and other counties show quite
similar trends. This alleviates the concern that our treatment and control groups are
systematically different ex ante, lending support to our DD identifying assumption.
Next we investigate the mechanism behind the expansion of wage markdown. Because our dataset records firm-level wages, we obtain each individual firm’s MRL
as the ratio of wages to wage markdown. Theories commonly predict that the entry of foreign firms makes incumbent firms lose employees and increases their MRL.
Columns (1) and (2) of Table 7 regress log employment and log MRL as a dependent
variable on the main regressors in Column (4) of Table 6 and find evidence confirming this prediction. In an average county, incumbent firms reduced employment by
2.9%('

9.0% ⇥ 0.32) and increased their MRL by 4.3%(' 13.3% ⇥ 0.32). If wage

markdown is constant as in traditional models of FDI, workers should receive as much29

as the increase in MRL. However, Column (3) regresses log wages on the same regressors, and it shows that the actual wage change was close to zero or even slightly negative. In an average county, wages at an average firm fell by 0.38%('
By construction, the coefficient
coefficient

1.2% ⇥ 0.32).

from the wage markdown regression is equal to thefrom the wage regression in Column (3) minus the coefficientfrom theMRL regression in Column (2). Note that the small coefficient in Column (3) does not
imply that wages were stable over the period. Instead, during 2001–2007, the average
wages grew steadily at an average annual growth rate of 12%. Column (2) thus implies that firms with high exposures to FDI liberalization increased their wages onlyat the same speed as the national average even though they faced labor shortages andincreases in MRL.
One might think that the wage stagnation is due to a drop in labor quality at incumbent firms. Wages might decrease relative to estimated MRL if high skilled workers
move to new foreign firms and incumbent firms replace them with workers with low
skills paying them lower wages. Column (4) checks this hypothesis by investigating
the effect of FDI liberalization on the firm-specific component of TFPR (TFPRC),
which removes industry-level demand shocks from TFPR. Since we do not control forlabor quality when estimating the production function, a fall in labor quality should bereflected in a fall in TFPRC. The fact that the impact of FDI liberalization on TFPRC
is small and insignificant does not support the hypothesis.

4.3

Labor Income Share in Manufacturing Value-added

The labor income share of GDP has been declining over the past decades in many countries (e.g. Karabarbounis and Neiman, 2014). The Chinese economy shows a similar
trend: in our dataset, labor income share in the aggregate manufacturing value-added
declined from 0.26 to 0.19 during 1998–2007.15 There is active ongoing research into
15
The labor share in this dataset is smaller than those for other countries. Even if there is a systematic
underestimation of labor shares, our DD estimation is still valid as long as the pattern of underestimation
is not correlated with our treatment variable.

30

Table 7: Decomposition and Mechanism

Dependent variables:
FDI liberalization

(1)

(2)

(3)

(4)

Log Employment

Log MRL

Log wages

Log TFPRC-0.0900.133-0.012-0.010(0.031)(0.034)(0.022)(0.055)Initial employment structure

X

X

X

X

Other policy controls

X

X

X

X

Vertical FDI controls

X

X

X

X

Firm fixed effects

X

X

X

X

Year fixed effects

X

X

X

X

970,416

970,416

970,416

970,416

Observations

Note: Standard errors are clustered at the county level in parentheses. Initial employment
structure include interactions between year dummies and county's employment share of
16 sectors in 2001. Other policy controls include: (1) county's exposures to tariffs (output
tariffs, input tariffs, and tariffs by foreign countries); (2) the share of state-owned
enterprises among firms in a county, (3) a dummy variable indicating whether a county is a
special economic zone or not. Vertical FDI controls include county's exposure to FDI
liberalization in backward and forward industries.

the causes of the labor share decline. Two candidates often mentioned are technological changes and a rise in firm’s market power in goods markets. In the study of thelatter candidate, for instance, Autor, Dorn, Katz, Patterson and Van Reenen (2017)
investigate labor income share and industry concentration; De Loecker, Eeckhout andUnger (2018) examine output price markups following De Loecker and Warzynski(2012). These studies focus on firm’s market power in good markets, but not in labormarkets.
In theory, a rise in firm’s monopsony power in the labor markets also contributes
to a decrease in labor income share. As we show in Appendix, firm j’s labor income
share in value-added can be decomposed as:ln

wjt Ljt= ln ⌘jt
V Ajt

Lln µjt + ln ✓jt

ln

V Ajt
Pjt Yjt(11)

L
where ⌘jt is the wage markdown, µjt is the output markups, ✓jt
is the labor elasticityof the gross production function, and V Ajt /Pjt Yjt is the share of valued-added in to31

Table 8: FDI Liberalization and Labor Income Share
Dependent variables:

Log Labor Share Log Markdown Log Markup Log Labor Elasticity Log VA share
(1)
(2)
(3)
(4)
(5)
FDI Liberalization-0.175-0.147
0.030
0.003
0.000
(0.043)(0.037)(0.015)(0.018)(0.026)
Initial employment structure
X
X
X
X
X
Other policy controls
X
X
X
X
X
Vertical FDI controls
X
X
X
X
X
Firm fixed effects
X
X
X
X
X
Year fixed effects
X
X
X
X
X
Observations
848,738
848,738
848,738
848,738
848,738
Note: Standard errors are clustered at the county level in parentheses. Initial employment structure include
interactions between year dummies and county's employment share of 16 sectors in 2001. Other policy
controls include: (1) county's exposures to tariffs (output tariffs, input tariffs, and tariffs by foreign countries);(2) the share of state-owned enterprises among firms in a county, (3) a dummy variable indicating whether acounty is a special economic zone or not. Vertical FDI controls include county's exposure to FDI liberalization
in backward and forward industries.

tal sales. Equation (11) shows that wider wage markdowns and wider price markups
both tend to decrease labor income share. We have already seen that FDI liberalization
tend to widen wage markdowns. This raises a question of how much FDI liberalization decreases labor income share by increasing firm’s monopsony power in the labormarket.
Table 8 examines the impact of FDI liberalization on firm-level labor income sharein value-added and its four components in (11). The logs of labor income share andeach component in (11) are regressed on the same set of covariates as in (9) and thefixed effects. Each column reports the coefficients of F DIct . The decomposition in(11) indicates that the coefficient in Column (1) should equal that in Column (2) minus
Column (3) plus Column (4) and minus Column (5). First of all, FDI liberalization
decreases labor income share in value-added. With a mean F DIct of 0.32, a firm in
an average county reduces labor income share by 5.6% ' 17.5 ⇥ 0.32. The change
in wage markdown in Column (2) accounts for 84% of the effect, and the change in
output markup in Column (3) for 17%. Columns (4) and (5) suggest that technology
played little systematic role.
To see the aggregate economic magnitude, we conduct a simple counter-factual
analysis about the aggregate labor income share in the manufacturing sector. We first32

run the regressions in Table 8 including interaction terms of LIBc and year dummies for the post-liberalization period. Based on the estimates, we calculate counterfactual labor income shares and the four components without FDI liberalization, i.e.
LIBc = 0, for each firm and each year. We assume that FDI liberalization does notchange firm’s value-added share in the industry. We then calculate the counter-factual
aggregate labor income share in the manufacturing sector under two scenarios. In
scenario 1, all four components in (11) are counter-factual ones without FDI liberalization; in scenario 2 all components except the markdown in (11) are counter-factual.
Figure 3 shows these two scenarios with actual data. The figure shows that FDI liberalization may not be the main cause of the decline in labor income share, but it seems toaccelerate the declining trend. From 2001 to 2007, the aggregate labor income sharedeclined by 23.5% (5.6 points) from 0.242 to 0.185 in data. The counter-factual labor income shares would be 0.207 in scenario 1 and 0.202 in scenario 2. While FDI
liberalization reduced the labor income share by 9% (2.2 points), the expansion of
wage markdown alone reduced it by 7% (1.5 points). These rough estimates should be
carefully interpreted, but they suggest that FDI liberalization accelerated the decline inlabor income share by expanding wage markdowns.

4.4

An Explanation: Search Frictional Monopsony

The conventional wisdom suggests that monopsony power increases in firm size andthat competition reduces monopsony power. We have found the exact opposite: large
and productive firms tend to set narrower wage markdowns and FDI liberalization
widens incumbent firms’ wage markdowns. In Appendix, we show that these findings
indeed contrast with a classical Cournot oligopsony model where employer concentration creates monopsony power. However, concentration is not the only reason for
firm’s monopsony power. In this section, we show that these findings are consistent
with modern monopsony theory: a canonical model of Burdett and Mortensen (1998)
where search frictions create monopsony power.
In the Burdett-Mortensen model, workers always search for better jobs even when33

Figure 3: Labor Income Share in Manufacturing Value-added

.18

.2

.22

.24

.26

Manufacturing Labor Income Share

1998

2000

2002

2004

2006

2008

year
Labor Share (Data)
w/o Markdown Change

w/o FDI Liberalization

Note: the solid line expresses labor income share in the aggregate manufacturing value-added in data.
The dashed line expresses counter-factual labor shares without FDI liberalization. The dotted line expresses counter-factual labor shares when FDI liberalization changes other components of labor shares
except wage markdown.

34they are employed, so that workers may accept low wage jobs, hoping to move up toa better job in future. The worker’s search on the job makes the labor supply curvesof individual firms less elastic and allows firms to set wages lower than their MRL.
This logic does not rely on either concentration or firm’s size. Therefore, there is no
guarantee that the entry of foreign firms would make labor supply curves more elastic.
We consider an original formulation of Burdett and Mortensen (1998). There exist
continuums of homogenous workers with mass L and continuums of firms with mass
N . Firms are heterogenous in productivity ' that follows distribution function J(')
with continuous support [b, 'max ]. Firms produce a numeraire good under perfectcompetition for labor and constant returns to scale technology.
The model infinitely repeats the following period game. First, each firm announces
wage offer w that is common for its employees. Second, both employed and unemployed workers meet a new potential employer with Poisson rate . An unemployedworker accepts any offer with wage w higher than unemployment benefit b, while anemployed worker only accepts a higher wage offer than the current wage. Third, firms
produce goods. Fourth, workers leave their jobs with exogenous rate

and become

unemployed. The time discount rate of workers and firms is negligible so that theymaximize their per-period payoffs.
In a steady state, there is a positive relationship between employment and wages,
which represents the labor supply curve to an individual firm:l (w) =

Lk
for w 2 [b, w̄],N [1 + k(1 F (w))]2(12)

where k ⌘ / and F (w) is the distribution function of wage offers. The labor supply
curve is upward sloping because a high-wage firm attracts workers from other firms aswell as prevents its own workers from moving to other firms.
Firms maximize per-period profits, facing labor supply curves (12):wl (w) subject to (12).

max ⇡ (w, ') ⌘ 'l (w)
w

35

(13)

Supermodularity @ 2 ⇡(w, ')/@w@' > 0 implies that the equilibrium wage is increasing in productivity, w0 (') > 0. The lowest wage is equal to the unemployment benefitb = w(b). This positive sorting of wage and productivity implies that the wage distribution agrees with the productivity distribution: F (w (')) = J(') for all '.
We obtain equilibrium wage markdown as:⌘(') = 1

✓

'

b
'

◆

L̄(')
,
L(')

where L(') = l(w(')) ⌘ N [1+k(1Lk J('))]2 is an equilibrium employment at firm withRs
productivity ' and L̄(') ⌘ '1 b b L(s)ds is the average employment among firms

with productivity lower than '. Wage markdown increases and narrows when L(')/L̄(')
increases. This is intuitive, because a firm increases wages to attract workers fromlower productive firms which set lower wages. Markdown can increase or decrease
with productivity, depending on the productivity distribution J. For instance, whenk'
J (') = ' is uniform, ⌘ (') = 1+kfor ' > 0. In this case, larger and more productive

firms set narrower markdowns, as we found in the data.
Inward FDI affects wage markdown by changing the productivity distribution offirms in the labor market. There is a robust empirical finding that foreign-owned firms
are more productive and pay higher wages than domestic firms. Following these stylized facts, we model inward FDI liberalization as the entry of foreign firms with productivity support ['Fmin , 'Fmax ] and 'Fmin > b. Inward FDI liberalization affects markdown by shifting productivity distributions to the right. We establish the following
proposition.
Proposition 1. There exists a productivity threshold '¯ > 'Fmin such that domestic
firms with productivity '  '¯ widen wage markdown after FDI liberalization.
The intuition is simple. Consider an incumbent firm with ' < 'Fmin and how many
additional workers it can employ by marginally increasing wages. The marginal wage
increase cannot attract workers from foreign firms and the increase leads to fewer additional employment than before. In other words, the labor supply curve to the firm36

becomes less elastic. From (6), a fall in labor supply elasticity implies an expansionof wage markdown. Due to strategic complementarities, domestic firms with slightly
higher productivity than 'F also reduce wages and expand wage markdown because
less productive firms reduce wages. Therefore, the threshold '¯ is larger than the productivity threshold 'Fmin of foreign firms.
Proposition 1 is silent about domestic firms with higher productivity than someforeign entrants. In the case of uniform distribution, we have a clear-cut result. Let
J0 (') = ' for ' 2 [0, 1] be the productivity distribution of incumbent firms andb = 0. FDI liberalization is an exogenous entry of foreign firms with mass N ⇤ andwith a uniform productivity distribution with support ['Fmin , 1] where 'Fmin > 0.
Proposition 2. In the case of uniform distribution, there exists a threshold productivity'¯ 2 ('Fmin , 1) such that a domestic firm with productivity ' > b widen wage markdown
if ' < '¯ and narrows if ''.
¯For productive domestic firms with ' > ',¯ a marginal wage increase can attract
workers from foreign firms as well as domestic firms. This neck-to-neck competition
with foreign firms makes the labor supply curve to those firms more elastic. It therefore narrows their wage markdowns. Notice that the threshold is higher than 'Fmin .
Thus it is possible to make a case that in terms of productivity, only the top few firms
narrow their wage markdowns and the rest of firms expand them. To our knowledge,
Propositions 1 and 2 are new findings in the literature.
To bring Propositions 1 and 2 to data, we investigate whether the effect of FDI
liberalization on wage markdowns is heterogeneous across firms with different initial
productivity. Table 9 reports the results, including interaction terms of F DIct andinitial TFPR before 2002. Column (1) reports a baseline result for the sample where
initial TFPR is available. Column (2) reports a result with interactions with log initial
TFPR. Column (3) adds a squared log initial TFPR and its interactions. Consistent
with the model’s prediction, markdown widend more among firms with low initial
TFPR. There is a threshold initial TFPR such that firms with higher TFPR than thethreshold narrow wage markdown and firms with lower TFPR expand. Using Column
37

Table 9: Heterogeneous Effects of FDI Liberalization on Wage Markdowns
Log Wage Markdown

(1)

(2)

(3)

FDI Liberalization-0.124-0.260-0.256(0.035)(0.058)(0.061)

FDI Liberalization × loginitial TFPR

0.053

0.073

(0.017)(0.024)

FDI Liberalization × loginitial TFPR 5-0.006(0.007)

Post2002 × log initial TFPR

-0.009-0.033(0.006)(0.008)Post2002 × loginitial TFPR 5

0.008(0.002)

Initial employment structure

X

X

X

Other policy controls

X

X

X

Vertical FDI controls

X

X

X

Firm fixed effects

X

X

X

Year fixed effects

X

X

X

Observations

531,038 531,038 531,038

Note: Standard errors are clustered at the county level in parentheses.
Initial employment structure include interactions between year dummies
and county's employment share of 16 sectors in 2001. Other policy
controls include: (1) county's exposures to tariffs (output tariffs, input
tariffs, and tariffs by foreign countries); (2) the share of state-owned
enterprises among firms in a county, (3) a dummy variable indicating
whether a county is a special economic zone or not. Vertical FDI
controls include county's exposure to FDI liberalization in backward andforward industries.

(3), the threshold is approximately 3.72 ' 0.242/0.065, which is positioned at the 81st
percentile of log initial TFPR. In sum, a vast majority of low productive firms widened

wage markdowns, while a few high productive firms narrowed them. On average, wage
markdowns are estimated to have widened.

5

Conclusion

Recent empirical research in labor economics and industrial economics has documented that firms exercise market power in labor markets as well as in product markets.
38This paper has developed an empirical framework to examine whether FDI liberalization reduces firm’s monopsony power in labor markets by increasing competition. In
contrast to the conventional wisdom and a fact that trade liberalization usually reduces
firm’s monopoly power, FDI liberalization increases firm’s monopsony power on average. This finding is consistent with modern monopsony theory where the source ofmonopsony power is search friction rather than concentration.
Whether our finding can be applied to other countries is an open question. During
our data period China’s weak protection of worker’s rights is common in other developing countries. An interesting question is whether better labor market institutions that
reduce worker’s search costs can mitigate the negative effect of FDI liberalization on
monopsony power. Our estimation method of wage markdowns can be applied for typical firm-level production data in many other countries. Such international comparison
is left for future research.

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[40] Manning, Alan. 2011. “Imperfect competition in the labor market.” in David Cardand Orley Ashenfelter (eds). Handbook of Labor Economics, vol. 4B: 973–1041.
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[43] Sokolova, Anna and Todd Sorensen. 2018. “Monopsony in labor markets: A
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Handbook of International Trade: 388–415.

44Online Appendix (Not for Publication)
A1 Derivations
A1-1. Wage markdown in state-own enterprises
SOE firm’s maximization problem with respect to labor is:
max Rjt (Yjt )Ljt

wjt (Ljt )Ljt + Ljt .

The first order condition implies thatM RLjt ⌘@Rjt
0= wjt (Ljt ) + wjt(Ljt )Ljt@Ljt
1= wjt 1 +.
"jt wjt✓◆
✓◆
1 + "jt
"jt
= wjt
1
.
"jt
wjt 1 + "jt

The wage markdown is thenwjt=
M RLjt✓"jt"jt + 1

◆

1

wjt

✓

"jt
1 + "jt◆

1.

A1-2. Heterogenous Labor
Imperfectly substitutable case Suppose there are S types of workers and firm j’s
production function is Yjt = Yjt L1jt , ..., LSjt , Kjt , Mjt , !jt where Lsjt is type s laborssinput. Firm j pays wage wjt
with markdown ⌘jt
for type s labor.
s
wjt
s
⌘jt
= @Rjt @Y jt@Yjt @Lsjt

=

✓

s s
wjt
Ljt
M
Pjt Mjt1◆ ˜M✓ s s ◆ M
✓jt
wjt Ljt ✓jt=,s
PjtM Mjt ✓jt
✓˜s
jt

@R S
@Y Sjts ssswhere wjt
Ljt is the wage expenditure for type s. ✓˜jt
⌘ @Sjtjt Rjtjt and ✓jt⌘ @Sjtarejt Yjtthe revenue and output elasticities of type s labor, respectively.

P
In our data we can observe only total employment Ljt = s Lsjt and total wage
P s spayments wjt Ljt = s wjt
Ljt . To calculate output elasticities of total employmentL✓jt, we assume that a firm maintains the current skilled ratio:

dLsjt
dLjt
= s .
Ljt
Ljt
L
Then, ✓jt
becomes

L
✓jt
=

=

dYjt LjdLj Yjt!
X @Yjt dLsjt Ljt@Lsjt dLjt Yjt!
X @Yjt Lsjt Ljt=@Lsjt Ljt Yjts
X @Yjt Lsjt=
@Lsjt Yjt
s
X
s
=
✓jt
.
s

s

From these relationships, our markdown measure (4) becomes a weighted average ofskilled wage markdown and unskilled wage markdown sinceM
wjt Ljt ✓jt
PjtM Mjt ✓jt✓P s s ◆M✓jt
s wjt LjtP
= Ms
Pjt Mjts ✓jt◆✓ s s ◆ M
sX ✓ ✓jt
wjt Ljt ✓jt
P=ss
PjtM Mjt ✓jt
s ✓jt
s
✓
◆
X
✓s
s
P jt s ⌘jt
=
.
✓
s jt
s

⌘jt =

2

(14)

Perfectly substitutable case

An interesting special case is when skill types are per-fectly substitutable. The production function includes labor L⇤jt in an efficiency unit:
Yjt = Yjt L⇤jt , Kjt , Mjt , !jt and L⇤jt =

X

s s
⌫jt
Ljt

s

s
where Lsjt is the amount of type s labor and ⌫jt
is a skill converter that can vary across⇤firms and time. Let wjt
be the wage for an efficiency unit. Perfect substitutability thenimplies that
s
s ⇤
wjt
= ⌫jt
wjt and@Yjt
s @Yjt
= ⌫jt
.
s
@Ljt
@L⇤jt

Therefore, wage markdown against type s labor becomes
s
wjt
s
⌘jt
⌘ @Rjt @Yjt =@Yjt @Lsjt

s ⇤
⌫jt
wjt

⇤
wjt
⇤
=
⌘ ⌘jt
.
@Rjt @Yjt@Rjt @Yjt

s⌫jt@Yjt @L⇤jt@Yjt @L⇤jt

Then, from equation (14), our markdown measure ⌘jt equals to this common mark⇤down ⌘jt.

A1.3 Labor share decomposition@R

Using the first order condition for profit maximization @Yjtjt = mcjt , MRL can be
simplified as@Rjt @Fjt@Yjt @Ljt@Fjt= mcjt@Ljt✓◆
mcjt @Fjt Ljt Pjt Yjt=
Pjt @Ljt Fjt
Ljt
◆
L ✓
✓jt Pjt Yjt
=
µjt
Ljt

M RLjt =3

The labor income share in value-added then becomes✓◆
wjt Ljt
M RLjt= ⌘jt Ljt
V Ajt
V Ajt
◆
L ✓
⌘jt ✓jt Pjt Yjt
=
.
µjt
V Ajt

A2 FDI liberalization in canonical monopsony models
A2.1 Employer concentration
The concentration of employers (e.g. company towns) is a classic reason that firms
face upward sloping labor supply curves. Consider Cournot oligopsony as a canonicalmodel. There are N firms and each firm j decides employment Li , taking other firm’s
employment as given. Let LA be the aggregate employment and w(LA ) be an inverseA)labor supply curve to the industry with elasticity "A ⌘ ww(L
0A )LA > 0. Let R('i , Li ), 'i ,Li and sj ⌘ Lj /LA be firm j’s revenue, productivity, employment and employment
share, respectively. Firm j’s profit maximization problem can then be written as
max R('i , Lj )

w

Lj

X
j

Lj

!

Lj

The first order condition leads to wage markdowns⌘j ="j"A /sj= A.
"j + 1" /sj + 1

(15)

Thus, the elasticity of labor supply to an individual firm "j = "A /sj depends on
industry-level labor supply and the firm’s employment share.
Cournot oligopsony conforms with the conventional wisdom. First, equation (15)implies that when we compare two firms j and k, ⌘j > ⌘k if and only if sj < sk . Thus,
large employers exercise greater monopsony power and exhibit wider markdowns thansmall employers. In a typical case where @ 2 R/@'@L > 0, employment increases in4

productivity. Thus, monopsony power increases in productivity. Second, equation (15)implies a limit theorem for Cournot oligopsony. When the number of firms increases
toward infinity and "A is finite, each firm’s employment share approaches zero andmarkdowns converge to one as in a perfectly competitive labor market. This limit
theorem contributes to the conventional wisdom that new entrants such as those after
FDI liberalization reduce incumbent firm’s monopsonic power and narrows their wage
markdowns.16

A2.2. Job Differentiation
In a goods market, a firm may face a downward-sloping demand curve because of
product differentiation. Similarly, a firm may face an upward-sloping labor supply
curve because of job differentiation. That is, workers may have preferences for jobs’
non-monetary characteristics so that a wage cut does not necessarily lead to losing
all of the employees. As a canonical model, we consider a logit model (e.g., Card,
Cardoso, Heining and Klein, 2018). There are N firms that produce a homogenous
numeraire good from labor and constant returns to scale technology. A worker n receives net utility Unj = ln vj (wj ) + "nj from working at firm j, where wj is firm j’s
wage. The second term "nj is the worker’s utility from non-monetary characteristics
of working at firm j, and it independently follows the Gumbel distribution. There isa continuum of workers with mass L, and workers are homogenous except "nj . By
standard arguments (McFadden, 1973), a labor supply supply curve to firm j becomes
Lj (wj ) =vj (wj )PN

k=1 vk (wk )

!

LA ,

(16)

where N is the number of firms and LA is the aggregate labor supply. Let R('i , Li ),'i , Li and sj ⌘ Lj /LA be firm j’s revenue, productivity, employment and employment
16

Of course, if new entry is finite, it is theoretically possible that markdowns expands, i.e. "A /sj
decreases, when "A shrinks significantly and offsets a fall in employment shares sj . However, this is
not considered as a typical case.

5share, respectively. Firm j’s profit maximization problem is written as
max R('j , Lj (wj ))wj

wj Lj (wj ) subject to (16).

In a typical case where @ 2 R/@'@L > 0, wage is increasing in productivity. Thus,
more productive firms offer higher wages to hire more workers. Since the elasticity oflabor supply is "j = j (wj ) (1⌘j =sj ), wage markdown is"jj (wj ) (1 sj )=,"j + 1j (wj ) (1 sj ) + 1(17)

where j (w) ⌘ vj0 (wj )wj /v(wj ) is the elasticity of vj and sj ⌘ Lj /LA is firm j’s
employment share.

In the logit oligopsony model, wage markdown is determined by the curvature ofmonetary utility as well as by concentration. When j =  for all j, the logit model
predicts similar results to Cournot oligopsony. First, equation (6) implies that when wecompare two firms j and k, ⌘j > ⌘k if and only if sj < sk . Larger and more productive employers exercise greater monopsony power and exhibit wider markdowns thansmaller and lower productive employers. FDI liberalization will shrink the wage markdowns of incumbents by decreasing their employment shares. When j (wj ) can varywith the wage, these predictions become ambiguous. When N is large and the market
becomes monopsonically competitive, "j = j (wj ) holds and wage markdowns are
determined solely by the curvature of the monetary utility j . Therefore, it is theoretically possible that FDI liberalization widens wage markdowns of incumbents.

A2.3 An equilibrium of the Burdett-Mortensen modelThis section presents calculations for obtaining an equilibrium in the Burdett-Mortensen
model which are omitted from the main text.
Labor supply curve

A stationary steady state requires the size of unemployed work-ers and that of each wage group to be stable overtime, which implies the following two
6

conditions:(1u)L = uL,

F (w)uL = [ + (1F (w))] NZ wl (t) dF (t) for all w on the support of F (w),

b

(18)

where u is unemployment rate, N is the number of firms in this labor market, l (w)is the employment in a firm that offers wage w, and F (w) is the distribution of wage
offers among firms. The first equation represents the size of unemployed workers.
The inflow into unemployment on the left-hand side equals the outflow from unemployment on the right-hand side. The second equation is the inflow and the outflow
into a group of employed workers who currently receive wages lower than w. The
left-hand side expresses that a mass uL of unemployed workers join this group withprobability F (w). The right-hand side expresses that workers in this group with sizeRw
N b l (t) dF (t) leave the group either because of being unemployed with rate or
moving to better-paying job with rate (1F (w)).

A celebrated result by Burdett and Mortensen (1998) is that F has a continuous
support [b, w̄] for some w̄ > b. See their paper for a formal proof. The intuitionis that if the support is [b, w0 ] [ [w1 , w̄] and w1 > w0 with a gap, a firm setting w0

can disproportionally increase employment and profits by infinitesimally increasing
its wage to w0 + ". Differentiating (18) by w, we obtain a positive relation between
employment and wage in a steady state:l (w) =

Lk
for w 2 [b, w̄],N [1 + k(1 F (w))]2(19)

where k ⌘ / .
Equilibrium wage markdown We obtain an equilibrium as follows. Substituting
F (w (')) = J(') into the labor supply curve, we obtain equilibrium employment of7

firm with productivity ':Lk.
N [1 + k(1 J('))]2

L(') = l(w(')) =(20)

By applying the envelop theorem for ⇡ (') in (13), we obtain ⇡ 0 (') = L ('). Integrating and setting ⇡(b) = 0 yields the profit function⇡ (') =Z '⇡ 0 (x) dx + ⇡(b)b

Z 'L (x) dx

= ('b)L̄(')

=

b

where
L̄(') ⌘

1
'

b

Z '

(21)

l (s) dsb

may be interpreted as a weighted average of employment among firms with productivity lower than '. From the above, we obtain⇡(') = ('w('))L(') = ('b)L̄(').

Then, we obtain the markdown ⌘(') ⌘ w (') /' as
w (')
'
✓
'
=1

⌘(') =

=1
=1

b

◆

'
Z '✓

L̄(')
L(')

1
1 + k(1' b
1 + k(1R'f (s)dsbf (')'

wheref (') ⌘

✓

J('))
J(s))

1
1 + k(1 J(s))
8

◆2

ds
(22)

◆2

.

Uniform distribution case Define#(') ⌘

1
'

Z '✓
0

1 + k(1
1 + k(1

J('))
J(s))

◆2

ds and v ⌘

k
.
1+k

Then, it follows that1
# (') =
'
=
=
=
=
=

(v

Z '✓
0

')

'
(v
'
')
'
(v

')

v

'
'
v

')
s)
1

2 
2 

0

1

v

◆2

ds

ds
s)2
◆0
1
ds.
v s

(v
2 Z '✓
0')(v

1 + k(1
1 + k(1
2 Z '

1
v

'
'

v(v

')

.

We obtain the markdown function⌘ (') = 1

# (') =

'
k
=
'.
v
1+k

Proof for Proposition 1 Definef0 (s)
a(s) ⌘=
f1 (s)✓

1
1⇢J1 (s)⇢J0 (s)◆2where ⇢ ⌘ k/(1 + k).We first prove the following lemmas.
Lemma 1. If a0 (s)0 for all s  ', then ⌘1 (') < ⌘0 (').

Proof. Under the condition, it holds thatR'bf0 (s)ds=
f0 (')

R'b

R'
R'a(s)f1 (s)ds
a(') b f1 (s)ds
f1 (s)ds<= b.
a(')f1 (')a(')f1 (')
f1 (')
9Thus, ⌘1 (') < ⌘0 (') from (22).
Lemma 2. If ' is lower than productivities of all foreign entrants, then a0 (s)0 for

all s 2 (b, '].
Proof. Under the condition, the share of low productive firms decreases: j0 (s) > j1 (s)and J0 (s) > J1 (s) for all s  '. Then,0a (s) = 2a(s)1/2= 2a(s)1/2⇢j1 (s)(1⇢ (j0 (s)⇢J0 (s)) + ⇢j0 (s)(1 ⇢J1 (s))(1 ⇢J0 (s))2
j1 (s)) (1 ⇢J1 (s)) + ⇢2 j1 (s)(J0 (s)(1 ⇢J0 (s))2J1 (s))> 0.
(23)

Proof for Proposition 2
Proof. Let N0 = N and N1 = N + N ⇤ be the mass of firms before and after liberalization. In the uniform case, J0 (s) = s andJ1 (s) =

where

8
>
< s
>
:1

0
= N
< 1 and ✓ ⌘ (1N1

j0 (s) = 1 andj1 (s) =From (23),for ' 2 [0, 'Fmin ]✓(1s)

a )/ (1
8
>
<

>
:✓

for ' 2 ['Fmin , 1],a) > 1. Then, their densities become

for ' 2 [0, 'Fmin ]for ' 2 ['Fmin , 1].

8hi><2a(s)1/2 ⇢(1 )2 > 0(1 ⇢s)a0 (') =hi>: 2a(s)1/2 ⇢(✓ 1)(1 2 ⇢) < 0(1 ⇢s)
10for ' 2 (0, 'Fmin )for ' 2 ('Fmin , 1).

Since a(0) = a(1) = 1 and a(s) is continuous, it holds that a(s) > 1 for s 2 (0, 1).
Thefore, we have ⌘0 (1) < ⌘1 (1) sinceR1bf0 (s)ds=
f0 (1)

R1b

R1
R1
a(s)f1 (s)dsa(1) b f1 (s)ds
f1 (s)ds>= b.
a(1)f1 (1)a(1)f1 (1)f1 (')

From Proposition 1, ⌘0 ('Fmin ) > ⌘1 ('Fmin ). Sinceous, there exists a threshold '¯ such thatR '¯bf0 (s)ds=
f0 (')¯R'b

f0 (s)ds
andf0 (')

R'b

f1 (s)ds
are continuf1 (')

R '¯bf1 (s)ds.
f1 (')¯

A3 Production Function Estimation
Consider the following production function of firm j at time t in the level and log
forms, respectively:
Yjt = F (kjt , ljt , mjt ) exp (!jt + "jt )yjt = f (kjt , ljt , mjt ) + !jt + "jt ,where yjt ⌘ ln Yjt , kjt ⌘ ln Kjt , ljt ⌘ ln Ljt , and mjt ⌘ ln Mjt . Function f ⌘ ln F

takes a flexible form and will be approximated by polynomials below. Terms !jt and"jt are Hicks neutral productivity shocks: "jt is unanticipated to production and i.i.d.
shocks with E["jt ] = 0 including measurement errors; !jt are known to firms whenmaterials mjt and labor ljt are chosen, but unknown when capital kjt (or investment att1) is chosen. In the estimation, f is assumed to be common throughout the 2-digit

industry-level.
Following De Loecker (2011) and GNR, the output market is assumed to be monopolistically competitive in each 4 digit product market. Each firm faces an individual

11demand curve derived from the CES utility function:
Yjt = Ygt✓

Pjt
⇧gt exp( jt )

◆ st

where

t <

(24)

1,

Pjt is firm j’s price, ⇧gt is the product-level (4-digit industry level) price index, Ygt
is product-level demand-shifter andjt is a firm-level demand shifter that is known to

the firm. Following De Loecker (2011) and GNR, the elasticity of demand

st (<

1)

is defined as negative, is specific to a subgroup s of firms, and may vary over time.
This implies that an expected output markup is also subgroup-time specific, thoughrealized markups can vary across firms within subgroups. A subgroup s is obtained by
dividing each 3-digit category into two groups of 4-digit products based on whether or
not they are classified as FDI-liberalized products.17
From the demand function (24), firm’s revenue Rjt = Pjt Yjt becomes
Rjt = Ygtµ
where !jt
⌘

jt +

⇣

1/ st

st +1
st

⌘

µ
⇧t exp "˜jt + !jt[F (kjt , ljt , mjt )]( st +1)/ st ,(25)

!jt is a combined positive shock to firm revenue known toµthe firm at time t. Following De Loecker (2011; 2013), we assume that !jt
follow aµµµMarkov process !jt= h !jt
1 , Wjt 1 +⌘jt where firms with different characteristics

Wjt 1 face different productivity motions, which will be specified below.
Consider the expected profit maximization with respect to materials,
max Ygt
Mjt

1/ st

µ
⇧t exp !jt[F (kjt , ljt , mjt )]( st +1)/ st Ẽ

where Ẽ ⌘ E [exp (˜"jt )] and "˜jt ⌘condition as:✓
17

st + 1
st

◆

⇣

st +1
st

exp ( "˜jt )Theoretically one could allow
obtain stable coefficients.

⌘

PjtM Mjt"jt . Using (25), we obtain the first order

Rjt @F (kjt , ljt , mjt )Ẽ = PjtMF@Mjt

gt to be product-time varying, but the sample becomes too small to12@f (k ,l ,m )M

@F (k ,l ,m )

jt jt
jt
jt jt
jt
By taking the log of both sides, using= Fjt, and denoting
@mjt
@Mjt
⇣PMM ⌘jtM
sjt ⌘ ln ↵jt= ln jtRjt , the first order condition is simplified tosjt = ln✓st + 1st◆+ ln Ẽ + ln

@f (kjt , ljt , mjt )@mjt"˜jt .

@f (kjt ,ljt ,mjt )= exp (µ) Dµ (kjt , ljt , mjt ;@mjtwhere µ is constant to be estimated below and Dµ (kjt , ljt , mjt ; ) is a second order

We approximate output elasticities on materials,
polynomials
Dµ (kjt , ljt , mjt ; ) ⌘
+
where

0+

k kjt +

2mm mjt +l ljt +

kl kjt ljt +m mjt +

2
kk kjt +km kjt mjt +2
ll ljtlm ljt mjt ,⌘ ( 0 , k , l , m , kk , ll , mm , kl , km , lm ) is a vector of parameters.

The estimation consists of two steps. The first step is to estimate

 ✓◆st + 1
sjt = ln
+ µ + ln Ẽ + ln Dµ (kjt , ljt , mjt ; )

"˜jt

st

=

st + ln Dµ(kjt , ljt , mjt ; )

"˜jt

(26)

by non-linear least squares where st is subgroup-year fixed effects and "˜jt is treated as
ˆ an estimate of Ẽ ⌘ E [exp (˜an error term. Using the residuals "ˆ˜jt , we construct Ẽ,"jt )],
by the sample mean of exp("ˆ˜jt ).

Consider the log of the real revenue function deflated by the price index rjt ⌘ln (Rjt /⇧t ) from (25):
rjt =

✓

st + 1st◆f (kjt , ljt , mjt )

1
st

13

µ
ln Ygt + !jt+ "˜jt .

(27))

Substituting

rjt =

⇣

⇣

exp ˆst
Ẽˆ

st +1
st

⌘

⌘

⇣
= exp ˆst⌘
ˆ we obtainµ /Ẽ,
2
4

exp ( µ) f (kjt , ljt , mjt )⇣exp ˆst
Ẽˆ

µ

⌘

3

µ
15 ln Ygt + !jt+ "˜jt .

(28)

Following Klette and Griliches (1996), De Loecker (2010) and GNR, we use the mar⌘P ⇣P
ket share weighted average of deflated revenues ln Ŷgt ⌘ N
R
/
R
jt
j=1
k2Ngt kt rjt
for the product demand shifter ln Ygt , where Ngt is the set of firms that produce positive
output of product g in both t and t 1. Since Dµ (kjt , ljt , mjt ; ) = exp ( µ)@f (kjt ,ljt ,mjt ),@mjt

its integration by mjt leads toexp ( µ) f (kjt , ljt , mjt ) =ZDµ (kjt , ljt , mjt ; )dmjt + exp ( µ) C (kjt , ljt ), (29)where C (kjt , ljt ) ⌘ f (kjt , ljt , mjt )R @f (kjt ,ljt ,mjt )@mjt

dmjt is the constant of the inte-

gration that is a function of kjt and ljt . We approximate C (kjt , ljt ) with second orderpolynomials in kjt and ljt :18
2
2
C (kjt , ljt , ) ⌘ k kjt + l ljt + kk kjt+ ll ljt
+ kl kjt ljt ,where  ⌘ (k , l , kk , ll , kl ) is a vector of parameters.
Using the estimated coefficients ˆ , ˆ , residuals, Ẽˆ from (26) and real revenue r ,stjt

we can construct

Rjt ⌘ rjt
18

it.

⇣ ⌘
exp ˆst ZẼˆDµ (kjt , ljt , mjt ; ˆ )dmjt"ˆ˜jt

Note that C (kjt , ljt ) should not include a constant term because f (kjt , ljt , mjt ) does not contain14

whereZ✓ˆm
2
2
Dµ (kjt , ljt , mjt ; ˆ )dmjt =mjt ˆ 0 + ˆ k kjt + ˆ l ljt +mjt + ˆ kk kjt+ ˆ ll ljt
2◆ˆ mm 2
ˆ km
ˆ lm+
mjt + ˆ kl kjt ljt +kjt mjt +ljt mjt .
322µ
Substituting Rjt and (29) into (28), we obtain !jt
from (28) as a function of µ and :

µ
!jt
= Rjt

⇣
exp ˆstẼˆhi 1Letting ⇢ ⌘ Ẽˆ exp(µ)
and

µ

⌘

C (kjt , ljt , ) +⇣exp ˆstµẼˆ

⌘ln Ŷgt .

µ⌘ ⇢ further simplifies !jt
as a function of ⇢ and :µ!jt(⇢, ) = R̃jt

C˜(kjt , ljt , ) + ⇢ ln Ỹgt

⇣ ⌘⇣ ⌘where R̃jt ⌘ Rjt ln Ŷgt , ln Ỹgt ⌘ exp ˆst ln Ŷgt and C˜(kjt , ljt , ) ⌘ exp ˆst C (kjt , ljt , ).
µThe dynamic motion of !jt
can be written asµµ!jt(⇢, ⇣) = h !jt
1 (⇢, ), Wjt 1 , p , g + ⇠jt .

The control variables Wjt include the following variables on ownerships, trade and
FDI that potentially affect productivity evolution: a dummy indicating the state-owned
enterprises (SOEs dummy), a dummy indicating the foreign-invested enterprises (FIEs
dummy), an export status dummy, output tariffs, input tariffs constructed from an
input-output table, FDI equity shares in the industry (horizontal FDI), FDI equity
shares in the upstream industries (backward FDI), FDI equity shares in the downstream
industries (forward FDI).

p andg are province fixed effects and four-digit industry

15

fixed effects, respectively. We approximate h with the second order polynomialsµh !jt
1 , Wjt 1 , p , g =µp + g + ⇣! !jt 1 + ⇣!!

µ
!jt
1

h
0
h
+ !jt
1 Wjt 1 ⇣ !W + !jt 1

2

2

0
+ Wjt
1⇣ W .

0Wjt
1 ⇣ !!z .

We estimate the parameters as follows. We first choose a given value of (⇢, )µµand regress !jt(⇢, ) on h !jt
1 (⇢, ), Wjt 1 , p , g to obtain ⇠jt (⇢, ) as a functionof (⇢, ). Following De Loecker (2011) and De Loecker and Warzynski (2012), we
assume⇣⌘0
2 2
Mjt ⌘ kjt , ljt 1 , kjt, ljt 1 , kjt ljt 1 , ln Ŷt 1

are pre-determined at time t and orthogonal to the productivity innovation ⇠jt (⇢, ).
Then, we construct six moment conditions E (⇠jt (⇢, )Mjt ) = 0 and estimate six
parameters (⇢, ) by GMM.19

h i 1h⇣ ⌘ i 1Once we obtain (ˆ⇢, ˆ), we first obtain exp(µ̂) = Ẽˆ⇢ˆ
and ̂ = ˆ exp ˆst ⇢ˆ .
Then, we obtain output elasticities ✓ˆL and ✓ˆM . First, material elasticities are obtainedjt

jt@f (kjt ,ljt ,mjt )Mfrom ✓ˆjt== exp (µ̂) Dµ (kjt , ljt , mjt ; ˆ ). Defining ˜i ⌘@mjt

ˆi exp (µ̂), we

obtainM22✓ˆjt= exp (µ̂) ˆ 0 + ˆ k kjt + ˆ l ljt + ˆ m mjt + ˆ kk kjt+ ˆ ll ljt+ˆ mm m2jt + ˆ kl kjt ljt + ˆ km kjt mjt + ˆ lm ljt mjt .
19

For ⇢ to satisfy ⇢ 2 (0, 1), we transform & ⌘ ln

⇣

1 ⇢
⇢

⌘

, estimate & and obtain ⇢ˆ = 1/(1 +exp(ˆ& )). We pick the initial value of (⇢0 , 0 ) as follows. We try 9 different initial values for ⇢0{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9} and choose a case where the objective function is minimized.
For a given ⇢0 , we obtain a vector of initial values 0 as follows. We regress the OLS regression of rj
on the second order polynomials of (kjt , ljt ) and ln Ŷt with controls Wjt 1 , province fixed effects, andfour-digit industry fixed effects. Then, we multiply estimated coefficients of {k, l, k 2 , l2 , kl} by ⇢0 to
obtain 0 , following (27).

16The estimated production function is thenfˆ(kjt , ljt , mjt ) = exp (µ̂)

ZDµ (kjt , ljt , mjt ; ˆ )dmjt + C (kjt , ljt , ̂),✓ˆm2
2
= exp (µ̂) mjt ˆ 0 + ˆ k kjt + ˆ l ljt +mjt + ˆ kk kjt+ ˆ ll ljt
2◆ˆ mm 2
ˆ km
ˆ lm+
mjt + ˆ kl kjt ljt +kjt mjt +ljt mjt
32
2

2
2+ ̂k kjt + ̂l ljt + ̂kk kjt+ ̂ll ljt+ ̂kl kjt ljt .
@ fˆ(kjt ,ljt ,mjt )LThus, the labor elasticities ✓ˆjt=
are obtained as
@ljt

L
✓ˆjt
= exp (µ̂) mjt✓

ˆ lm
ˆ l + 2ˆ ll ljt + ˆ kl kjt +mjt
2KSimilarly, the capital elasticities ✓ˆjt=◆

+ ̂l + 2̂ll ljt + ̂kl kjt .

@ fˆ(kjt ,ljt ,mjt )are obtained as
@kjt

✓
◆
ˆ km
K
ˆ
✓jt = exp (µ̂) mjt ˆ k + 2ˆ kk kjt + ˆ kl ljt +mjt + ̂k + 2̂kk kjt + ̂kl ljt .
2
Once the production function coefficients have been estimated, we can calculate output
LM
elasticities ✓ˆjt
and ✓ˆjt
and estimate wage markdowns by (4). The revenue elasticities⇣ ⌘are obtained by multiplying exp ˆst ⇢ˆ by the output elasticities.
We obtain TFPR as the residual of revenue from inputs, which contains TFP andindustry-level and firm-level demand shifters:ln T F P Rjt ⌘
= rjt

1
st

✓

st + 1◆ln Ygt + jt +
!jt .
st
✓
◆
st + 1f (kjt , ljt , mjt ) "˜jt
st17and its core component TFPRC:
ln T F P RCjt ⌘

jt +

✓

st + 1st= ln T F P Rjt +

◆

1

st

18

!jt
ln Ygt .