An Application of the Melitz Model to Chinese Firms

• Published date: 01 August 2013
• Author: Tao Zhang,Guoqiang Tian,Churen Sun
• DOI: http://doi.org/10.1111/rode.12045
• Date: 01 August 2013

An Application of the Melitz Model to

Chinese Firms

Churen Sun, Guoqiang Tian, and Tao Zhang*

Abstract

When the Melitz model is implemented in practice, the industrial productivity distribution is often assumed

to be of Pareto form. In this case, a fundamental relationship κ>σ− 1 must hold to guarantee the conver-

gence of the industrial average productivity, where κis the concentration degree of the industrial produc-

tivity Pareto distribution and σis the substitution elasticity across varieties in the industry. This paper

estimates the concentration degrees of the Pareto distribution in industrial productivity and industrial sub-

stitution elasticities using firm-level data of 40 Chinese manufacturing industries between 1998 and 2007.

However, the paper shows that the above fundamental assumption κ>σ− 1 does not hold for nearly all the

industries for Chinese firm-level data. An explanation is proposed as a result of the distorted firm size and

productivity for Chinese characteristics.

1. Introduction

The Melitz model developed in Melitz (2003),1has become a stepstone in the “new”

new trade theory and many other fields.2Among the many extended versions of the

Melitz model there is one that assumes that industrial productivity follows a Pareto

distribution Gl(θ), which we call “the Melitz–Pareto model,” whose form is as follows

G

bb

l

l

k

l

l

θθθ

()

=−

()

≥

⎧

⎨

⎪

⎩

⎪

1

0

,

,else

(1)

where klis the concentration degree, and bl>0 is the lower bound of productivity

distribution.

Many classic literatures adopt this form of productivity distribution in the practical

application of the Melitz model, such as Antras and Helpman (2004, 2006), Di

Giovanni et al. (2011), Ottaviano (2011). However, an assumption that kl+1>σl

must be made under this assumption,3where σlis the substitution elasticity among

varieties in industry l. Though it is clearly indicated that there are other ex-ante distri-

butional assumptions,4say Gamma distribution, the applicability of Pareto distribu-

tion in the Melitz model still need great attention in developing countries, in our case,

China. This paper investigates whether the assumption of productivity Pareto distri-

* Sun (corresponing author) and Zhang: Shanghai Institute of Foreign Trade, No. 1900, Wenxiang Road,

Songjiang, Shanghai, China. Tel: 86-13482207010; E-mail: sunchuren@gmail.com. Tian: Department of

Economics, TexasA&MUniversity, College Station, TX 77843, USA. The research is funded by the Key

Research Base of Humanities and Social Science of Shanghai Municipal of Higher Education (Institute of

International Business, Shanghai Institute of Foreign Trade). Sun gratefully acknowledges financial support

from Project supported by the National Natural Science Foundation of China (Grant No. 71273167),

Project supported by General research for Humanities and Social Sciences from Chinese Ministry of Edu-

cation (Grant No. 09YJCZH074) and Innovation Program of Shanghai Municipal Education Commission

(Grant No. 10YS168). Zhang gratefully acknowledge financial support from National Natural Science Fund

Projects (Grant No. 118DZD003).

Review of Development Economics, 17(3), 494–509, 2013

DOI:10.1111/rode.12045

© 2013 John Wiley & Sons Ltd

bution in the Melitz model can be applied to Chinese firms. Evaluating whether this

assumption holds is important for the validity of the Pareto pre-assumption, especially

because of the wide use of this model.

By comparing the estimates of above two parameters (kland σl) using Chinese

firm level data, this paper shows that in most cases, kl(estimated to be around 1) is

much smaller than σl(ranging from 3 to 8) and concludes that the assumption that

kl+1>σldoes not hold and, the ex-ante Pareto distribution assumption cannot be

verified with Chinese firms. Our empirical finding suggests that there are necessary

pre-examinations for countries with imperfect competition market and distorted

firm productivity, such as China. Other distributions of industrial productivity shall

be considered when applying the widely applied Melitz analytical framework to

these countries.

Our paper relates to many existing literatures. First, the stylized facts of k1+1>σl

are valid in many empirical studies (mainly based on developed countries). For

instance, the estimates of klare 8.28, 3.60, and 4.87 in Eaton and Kortum (2002),

Bernard et al. (2003), and Eaton et al. (2011), respectively. All these estimates are for

the US firms. Our estimate of klis close to 1 which is very low when compared with

the above mentioned studies. Second, the literature has established that the power

law exponent is close to 1, a phenomenon known as Zipf’s Law, which implies that

approximately, kl=σl− 1. In Di Giovanni et al. (2011), which our paper follows

closely, the estimates of the power law exponent for French exporting and

nonexporting firms separately are both close to 1. However, this inconsistence from

the literature does not mean that the results in this paper are wrong. Instead, it is sug-

gestive that China might have a different distribution function than those in devel-

oped countries, which needs to be carefully evaluated. To clarify our argument, this

paper estimates exporting and nonexporting firms’ (including all 40 industries) prod-

uctivity and sales distributions with different total-factor productivity (TFP) measure-

ment methods. It is robust that the estimates of klare close to unity across different

methods and sectors. This result is quite essential since if klis close to unity, it is

almost certain that kl+1>σlcannot hold since σlis estimated greater than two in

most literature. Further, consistent with the estimates of kl, the estimates of the

power law exponent are all around 0.4. Since the power law exponent is kl

l

σ

−1, this

result indicates that kl+1>σlcannot hold in China’s case. The results that most of

the estimates for me estimated power law exponent being lower in absolute value

among exporting firms compared with the nonexporting ones are also consistent with

di Giovanni et al. (2011).

Our strategy of realizing the Melitz–Pareto model is as follows. First, we estimate

the production function of each industry (using four micro-econometric approaches,

namely the pooled ordinary least square (OLS), Olley–Pakes (OP), Levinsohn–

Petrin (LP), and firm fixed-effect model (FE)) based on the firm-level data from

1998 to 2007. Second, we compute each firm’s productivity, and then estimate indus-

trial productivity Pareto distribution, accordingly. Note that the size distributions of

both nonexporting and exporting firms under the productivity Pareto distribution

are also Pareto ones and their parameters are functions of parameters of those of

industrial productivity distribution. Third, we estimate parameters of these size dis-

tributions. Comparing these estimations with the parameters of the Pareto distribu-

tion of industrial productivity yields the substitution elasticities of varieties and fixed

production cost. Combining the results obtained above shows that kl+1<σlfor all

industries.

AN APPLICATION OF THE MELITZ MODEL 495

© 2013 John Wiley & Sons Ltd