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THE QUARTERLY JOURNAL OF ECONOMICS

Vol.CXXIV November2009Issue4

MISALLOCATION AND MANUFACTURING TFP

IN CHINA AND INDIA?

C HANG-T AI H SIEH AN

D P ETER J.K LENOW

Resource misallocation can lower aggregate total factor productivity(TFP).We use microdata on manufacturing establishments to quantify the potential extent of misallocation in China and India versus the United States.We measure sizable gaps in marginal products of labor and capital across plants within narrowly de?ned industries in China and India compared with the United States.When capital and labor are hypothetically reallocated to equalize marginal products to the extent observed in the United States,we calculate manufacturing TFP gains of30%–50%in China and40%–60%in India.

I.I NTRODUCTION

Large differences in output per worker between rich and poor countries have been attributed,in no small part,to differ-ences in total factor productivity(TFP).1The natural question then is:What are the underlying causes of these large TFP dif-ferences?Research on this question has largely focused on dif-ferences in technology within representative?rms.For example, Howitt(2000)and Klenow and Rodr′?guez-Clare(2005)show how large TFP differences can emerge in a world with slow technology ?We are indebted to Ryoji Hiraguchi and Romans Pancs for phenomenal research assistance,and to seminar participants,referees,and the editors for

comments.We gratefully acknowledge the?nancial support of the Kauffman Foun-dation.Hsieh thanks the Alfred P.Sloan Foundation and Klenow thanks SIEPR for?nancial support.The research in this paper on U.S.manufacturing was con-ducted while the authors were Special Sworn Status researchers of the U.S.Census Bureau at the California Census Research Data Center at UC Berkeley.Research results and conclusions expressed are those of the authors and do not necessarily re?ect the views of the Census Bureau.This paper has been screened to ensure that no con?dential data are revealed.chsieh@https://www.wendangku.net/doc/481293088.html,,pete@https://www.wendangku.net/doc/481293088.html,.

1.See Caselli(2005),Hall and Jones(1999),and Klenow and Rodr′?guez-Clare (1997).

C 2009by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

The Quarterly Journal of Economics,November2009

1403 at University of Virginia on October 12, 2012 https://www.wendangku.net/doc/481293088.html,/ Downloaded from

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diffusion from advanced countries to other countries.These are models of within-?rm inef?ciency,with the inef?ciency varying across countries.

A recent paper by Restuccia and Rogerson(2008)takes a dif-ferent approach.Instead of focusing on the ef?ciency of a repre-sentative?rm,they suggest that misallocation of resources across ?rms can have important effects on aggregate TFP.For example, imagine an economy with two?rms that have identical technolo-gies but in which the?rm with political connections bene?ts from subsidized credit(say from a state-owned bank)and the other?rm (without political connections)can only borrow at high interest rates from informal?nancial markets.Assuming that both?rms equate the marginal product of capital with the interest rate,the marginal product of capital of the?rm with access to subsidized credit will be lower than the marginal product of the?rm that only has access to informal?nancial markets.This is a clear case of capital misallocation:aggregate output would be higher if capital was reallocated from the?rm with a low marginal product to the ?rm with a high marginal product.The misallocation of capital results in low aggregate output per worker and TFP.

Many institutions and policies can potentially result in re-source misallocation.For example,the McKinsey Global Institute (1998)argues that a key factor behind low productivity in Brazil’s retail sector is labor-market regulations driving up the cost of la-bor for supermarkets relative to informal retailers.Despite their low productivity,the lower cost of labor faced by informal-sector retailers makes it possible for them to command a large share of the Brazilian retail sector.Lewis(2004)describes many similar case studies from the McKinsey Global Institute.

Our goal in this paper is to provide quantitative evidence on the potential impact of resource misallocation on aggregate TFP. We use a standard model of monopolistic competition with het-erogeneous?rms,essentially Melitz(2003)without international trade,to show how distortions that drive wedges between the marginal products of capital and labor across?rms will lower ag-gregate TFP.2A key result we exploit is that revenue productivity (the product of physical productivity and a?rm’s output price) should be equated across?rms in the absence of distortions.To the extent revenue productivity differs across?rms,we can use it to recover a measure of?rm-level distortions.

2.In terms of the resulting size distribution,the model is a cousin to the Lucas(1978)span-of-control model. at University of Virginia on October 12, 2012 https://www.wendangku.net/doc/481293088.html,/ Downloaded from

MISALLOCATION AND TFP IN CHINA AND INDIA1405 We use this framework to measure the contribution of re-source misallocation to aggregate manufacturing productivity in China and India versus the United States.China and India are of particular interest not only because of their size and rela-tive poverty,but because they have carried out reforms that may have contributed to their rapid growth in recent years.3We use plant-level data from the Chinese Industrial Survey(1998–2005), the Indian Annual Survey of Industries(ASI;1987–1994),and the U.S.Census of Manufacturing(1977,1982,1987,1992,and1997) to measure dispersion in the marginal products of capital and labor within individual four-digit manufacturing sectors in each country.We then measure how much aggregate manufacturing output in China and India could increase if capital and labor were reallocated to equalize marginal products across plants within each four-digit sector to the extent observed in the United States. The United States is a critical benchmark for us,because there may be measurement error and factors omitted from the model (such as adjustment costs and markup variation)that generate gaps in marginal products even in a comparatively undistorted country such as the United States.

We?nd that moving to“U.S.ef?ciency”would increase TFP by30%–50%in China and40%–60%in India.The output gains would be roughly twice as large if capital accumulated in re-sponse to aggregate TFP gains.We?nd that deteriorating alloca-tive ef?ciency may have shaved2%off Indian manufacturing TFP growth from1987to1994,whereas China may have boosted its TFP2%per year over1998–2005by winnowing its distortions.In both India and China,larger plants within industries appear to have higher marginal products,suggesting they should expand at the expense of smaller plants.The pattern is much weaker in the United States.

Although Restuccia and Rogerson(2008)is the closest prede-cessor to our investigation in model and method,there are many others.4In addition to Restuccia and Rogerson,we build on three

3.For discussion of Chinese reforms,see Young(2000,2003)and The Economist(2006b).For Indian reforms,see Kochar et al.(2006),The Economist (2006a),and Aghion et al.(2008).Dobson and Kashyap(2006),Farrell and Lund (2006),Allen et al.(2007),and Dollar and Wei(2007)discuss how capital continues to be misallocated in China and India.

4.A number of other authors have focused on speci?c mechanisms that could result in resource misallocation.Hopenhayn and Rogerson(1993)studied the im-pact of labor market regulations on allocative ef?ciency;Lagos(2006)is a recent effort in this vein.Caselli and Gennaioli(2003)and Buera and Shin(2008)model inef?ciencies in the allocation of capital to managerial talent,while Guner,Ven-tura,and Xu(2008)model misallocation due to size restrictions.Parente and at University of Virginia on October 12, 2012 https://www.wendangku.net/doc/481293088.html,/ Downloaded from data

结论

资源配置失调导致了很大的损失

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papers in particular.First,we follow the lead of Chari,Kehoe, and McGrattan(2007)in inferring distortions from the residu-als in?rst-order conditions.Second,the distinction between a ?rm’s physical productivity and its revenue productivity,high-lighted by Foster,Haltiwanger,and Syverson(2008),is central to our estimates of resource misallocation.Third,Banerjee and Du?o(2005)emphasize the importance of resource misallocation in understanding aggregate TFP differences across countries,and present suggestive evidence that gaps in marginal products of cap-ital in India could play a large role in India’s low manufacturing TFP relative to that of the United States.5

The rest of the paper proceeds as follows.We sketch a model of monopolistic competition with heterogeneous?rms to show how the misallocation of capital and labor can lower aggregate TFP. We then take this model to the Chinese,Indian,and U.S.plant data to try to quantify the drag on productivity in China and India due to misallocation in manufacturing.We lay out the model in Section II,describe the data sets in Section III,and present po-tential gains from better allocation in Section IV.In Section V we try to assess whether greater measurement error in China and

India could explain away our results.In Section VI we make a ?rst pass at relating observable policies to allocative ef?ciency in China and India.In Section VII we explore alternative explana-tions besides policy distortions and measurement error.We offer some conclusions in Section VIII.

II.M ISALLOCATION AND TFP

This section sketches a standard model of monopolistic com-petition with heterogeneous?rms to illustrate the effect of re-source misallocation on aggregate productivity.In addition to differing in their ef?ciency levels(as in Melitz[2003]),we assume that?rms potentially face different output and capital distortions.

We assume there is a single?nal good Y produced by a repre-sentative?rm in a perfectly competitive?nal output market.This ?rm combines the output Y s of S manufacturing industries using Prescott(2000)theorize that low-TFP countries are ones in which vested interests block?rms from introducing better technologies.

5.See Bergoeing et al.(2002),Galindo,Schiantarelli,and Weiss(2007),Alfaro, Charlton,and Kanczuk(2008),and Bartelsman,Haltiwanger,and Scarpetta (2008)for related empirical evidence in other countries. at University of Virginia on October 12, 2012 https://www.wendangku.net/doc/481293088.html,/ Downloaded from

MISALLOCATION AND TFP IN CHINA AND INDIA1407 a Cobb-Douglas production technology:

(1)Y=

s=1

Yθs s,where

s=1

θs=1.

Cost minimization implies

(2)P s Y s=θs PY.

Here,P s refers to the price of industry output Y S and P≡

s=1(P s/θs)θs represents the price of the?nal good(the?nal good

is our numeraire,and so P=1).Industry output Y s is itself a CES aggregate of M s differentiated products:

(3)Y s=

M s

i=1

Yσ?1σ

σ?1

The production function for each differentiated product is given by a Cobb-Douglas function of?rm TFP,capital,and labor:

(4)Y si=A si Kαs si L1?αs

Note that capital and labor shares are allowed to differ across industries(but not across?rms within an industry).6

Because there are two factors of production,we can sepa-rately identify distortions that affect both capital and labor from distortions that change the marginal product of one of the factors relative to the other factor of production.We denote distortions that increase the marginal products of capital and labor by the same proportion as an output distortionτY.For example,τY would be high for?rms that face government restrictions on size or high transportation costs,and low in?rms that bene?t from public output subsidies.In turn,we denote distortions that raise the marginal product of capital relative to labor as the capital distor-tionτK.For example,τK would be high for?rms that do not have access to credit,but low for?rms with access to cheap credit(by business groups or state-owned banks).

Pro?ts are given by

(5)πsi=(1?τY si)P si Y si?w L si?(1+τKsi)RK si.

6.In Section VII(“Alternative Explanations”),we relax this assumption by replacing the plant-speci?c capital distortion with plant-speci?c factor shares. at University of Virginia on October 12, 2012 https://www.wendangku.net/doc/481293088.html,/ Downloaded from

这生产函数，三个

整在一起还真比较复杂

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Note that we assume all?rms face the same wage,an issue to which we return later.Pro?t maximization yields the standard condition that the?rm’s output price is a?xed markup over its marginal cost:

(6)P si=σ

1?αs

1?α

s(1+τKsi)αs

A si(1?τY si)

The capital-labor ratio,labor allocation,and output are given by

K si L si =

αs

1?αs

·1

(1+τKsi)

(7)

L si∝Aσ?1

(1?τY si)σ(1+τKsi)αs(σ?1)

(8)

Y si∝Aσ

(1?τY si)σ(1+τKsi)αsσ

(9)

The allocation of resources across?rms depends not only on?rm TFP levels,but also on the output and capital distortions they face.To the extent resource allocation is driven by distortions rather than?rm TFP,this will result in differences in the marginal revenue products of labor and capital across?rms.The marginal revenue product of labor is proportional to revenue per worker:

(10)MRPL si =(1?αS)σ?1

P si Y si

L si

=w1

1?τY si

The marginal revenue product of capital is proportional to the revenue-capital ratio:

(11)MRPK si =αS σ?1

P si Y si

K si

=R1+τKsi

1?τY si

Intuitively,the after-tax marginal revenue products of capital and labor are equalized across?rms.The before-tax marginal revenue products must be higher in?rms that face disincentives,and can be lower in?rms that bene?t from subsidies.

We are now ready to derive an expression for aggregate TFP as a function of the misallocation of capital and labor.We?rst at University of Virginia on October 12, 2012 https://www.wendangku.net/doc/481293088.html,/ Downloaded from

MISALLOCATION AND TFP IN CHINA AND INDIA 1409

solve for the equilibrium allocation of resources across sectors:7

L s ≡M s i =1L si =L (1?α

s )θs /MRPL s

s =1(1?αs )θs /MRPL s

(12)K s ≡M s

i =1K si =K αs θs /MRPK s

s =1αs θs /MRPK s

(13)Here,

MRPL s ∝ M s i =111?τY si P si Y si

P s Y s ,MRPK s ∝

M s i =11+τKsi 1?τY si P si Y si

P s Y s

denote the weighted average of the value of the marginal product of labor and capital in a sector,and L ≡ S s =1L s and K ≡

s =1K s

represent the aggregate supply of labor and capital.We can then express aggregate output as a function of K S ,L S ,and industry TFP:8

(14)Y =S s =1

TFP s ·K αs s ·L 1?αs s θs

To determine the formula for industry productivity TFP s ,it is use-ful to show that ?rm-speci?c distortions can be measured by the ?rm’s revenue productivity .It is typical in the productivity liter-ature to have industry de?ators but not plant-speci?c de?ators.Foster,Haltiwanger,and Syverson (2008)stress that,when indus-try de?ators are used,differences in plant-speci?c prices show up in the customary measure of plant TFP .They stress the distinc-tion between “physical productivity ,”which they denote TFPQ,and “revenue productivity ,”which they call TFPR.The use of a plant-speci?c de?ator yields TFPQ,whereas using an industry de?ator gives TFPR.

7.To derive K s and L s we proceed as follows:First,we derive the aggregate demand for capital and labor in a sector by aggregating the ?rm-level demands for the two factor inputs.We then combine the aggregate demand for the factor inputs in each sector with the allocation of total expenditure across sectors.8.We combine

the aggregate demand for capital and labor in a sector,the

expression for the price of aggregate industry output,and the expression for the price of aggregate output. at University of Virginia on October 12, 2012

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The distinction between physical and revenue productivity is vital for us too.We de?ne these objects as follows:9

TFPQ si =A si =Y si

K αs si (w L si )1?αs

TFPR si =P si A si =P

si Y si

K αs si (w L si )1?αs .

In our simple model,TFPR does not vary across plants within an industry unless plants face capital and/or output distortions.In the absence of distortions,more capital and labor should be allocated to plants with higher TFPQ to the point where their higher output results in a lower price and the exact same TFPR as at smaller https://www.wendangku.net/doc/481293088.html,ing (10)and (11),plant TFPR is proportional to a geometric average of the plant’s marginal revenue products of capital and labor:10

TFPR si ∝(MRPK si )αs (MRPL si )1?αs ∝(1+τKsi )αs

1?τY si .

High plant TFPR is a sign that the plant confronts barriers that raise the plant’s marginal products of capital and labor,rendering the plant smaller than optimal.

With the expression for TFPR in hand,we can express indus-try TFP as

(15)TFP s =??M s i =1 A si ·TFPR s TFPR si

σ?1??1

σ?1

,where TFPR s ∝(MRPK s )αs (MRPL s )1?αs is a geometric average of the average marginal revenue product of capital and labor in the sector.11If marginal products were equalized across plants,TFP would be ˉA s =( M s i =1A σ?1si )1

σ?1.Equation (15)is the key equation we use for our empirical estimates.Appendix I shows that we would arrive at an expression similar to (15)if we assumed a Lucas span-of-control model rather than monopolistic competition.9.To crudely control for differences in

human capital we measure labor input as the wage bill,which we denote as the product of a common wage per unit of

human capital w and effective labor input L si .10.TFPR si =σσ?1 MRPK si αS αs MRPL si w (1?αS ) 1?αs = R αS αs 11?αS 1?αs (1+τKsi )αs 1?τY si .11.TFPR s = R αS M s i =1 1+τKsi

1?τY si · P si Y si P s Y s αs

11?αS M s i =1 11?τY si P si Y si P s Y s 1?αs

. at University of Virginia on October 12, 2012

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MISALLOCATION AND TFP IN CHINA AND INDIA 1411

When A (≡TFPQ)and TFPR are jointly lognormally dis-tributed,there is a simple closed-form expression for aggregate TFP:

(16)log TFP s =1σ?1log M s i =1A σ?1si

?σ2

var (log TFPR si ).

In this special case,the negative effect of distortions on aggregate TFP can be summarized by the variance of log TFPR.Intuitively ,the extent of misallocation is worse when there is greater disper-sion of marginal products.

extent of misallocation as long as average marginal revenue prod-ucts are unchanged.Our Cobb-Douglas aggregator (unit elastic demand)is responsible for this property (an industry that is 1%more ef?cient has a 1%lower price index and 1%higher demand,which can be accommodated without adding or shedding inputs).We later relax the Cobb-Douglas assumption to see how much it matters.

Second,we have conditioned on a ?xed aggregate stock of capital.Because the rental rate rises with aggregate TFP ,we would expect capital to respond to aggregate TFP (even with a ?xed saving and investment rate).If we endogenize K by invoking a consumption Euler equation to pin down the long-run rental rate R ,the output elasticity with respect to aggregate TFP is

1/(1? S s =1αS θS ).Thus the effect of misallocation on output is

increasing in the average capital share.This property is reminis-cent of a one-sector neoclassical growth model,wherein increases in TFP are ampli?ed by capital accumulation so that the output elasticity with respect to TFP is 1/(1?α).

Third,we assume that the number of ?rms in each industry is not affected by the extent of misallocation.In an Appendix available upon request,we show that the number of ?rms would be unaffected by the extent of misallocation in a model of endogenous entry in which entry costs take the form of a ?xed amount of labor.12

12.We

assume entrants do not know their productivity or distortions before expending entry costs,only the joint distribution of distortions and productivity

from which they will draw .We also follow Melitz (2003)and Restuccia and Roger-son (2008)in assuming exogenous exit among producers.Unlike Melitz,however, at University of Virginia on October 12, 2012

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III.D ATA S ETS FOR I NDIA,C HINA,AND THE U NITED S TATES

Our data for India are drawn from India’s ASI conducted by the Indian government’s Central Statistical Organisation.The ASI is a census of all registered manufacturing plants in India with more than?fty workers(one hundred if without power)and a random one-third sample of registered plants with more than ten workers(twenty if without power)but less than?fty(or one hundred)workers.For all calculations we apply a sampling weight so that our weighted sample re?ects the population.The survey provides information on plant characteristics over the?scal year (April of a given year through March of the following year).We use the ASI data from the1987–1988through1994–1995?scal years.The raw data consist of around40,000plants in each year.

The variables in the ASI that we use are the plant’s industry (four-digit ISIC),labor compensation,value-added,age(based on reported birth year),and book value of the?xed capital stock. Speci?cally,the ASI reports the plant’s total wage payments, bonus payments,and the imputed value of bene?ts.Our measure of labor compensation is the sum of wages,bonuses,and bene?ts.

In addition,the ASI reports the book value of?xed capital at the beginning and end of the?scal year net of depreciation.We take the average of the net book value of?xed capital at the beginning and end of the?scal year as our measure of the plant’s capital.We also have ownership information from the ASI,although the own-ership classi?cation does not distinguish between foreign-owned and domestic plants.

Our data for Chinese?rms(not plants)are from Annual Sur-veys of Industrial Production from1998through2005conducted by the Chinese government’s National Bureau of Statistics.The Annual Survey of Industrial Production is a census of all nonstate ?rms with more than5million yuan in revenue(about$600,000) plus all state-owned?rms.The raw data consist of over100,000?rms in1998and grow to over200,000?rms in2005.Hereafter we often refer to Chinese?rms as“plants.”

The information we use from the Chinese data are the plant’s industry(again at the four-digit level),age(again based on we do not have overhead costs.Because of the overhead costs in Melitz,some ?rms exit after spending entry costs but before commencing production,thereby creating an endogenous form of exit that truncates the left tail of the productivity distribution.We leave it as an important topic for future research to investigate the impact of distortions on aggregate productivity and welfare through endogenous entry and exit. at University of Virginia on October 12, 2012 https://www.wendangku.net/doc/481293088.html,/ Downloaded from

MISALLOCATION AND TFP IN CHINA AND INDIA1413 reported birth year),ownership,wage payments,value-added,ex-port revenues,and capital stock.We de?ne the capital stock as the book value of?xed capital net of depreciation.As for labor com-pensation,the Chinese data only report wage payments;they do not provide information on nonwage compensation.The median labor share in plant-level data is roughly30%,which is signif-icantly lower than the aggregate labor share in manufacturing reported in the Chinese input-output tables and the national ac-counts(roughly50%).We therefore assume that nonwage bene?ts are a constant fraction of a plant’s wage compensation,where the adjustment factor is calculated such that the sum of imputed ben-e?ts and wages across all plants equals50%of aggregate value-added.We also have ownership status for the Chinese plants. Chinese manufacturing had been predominantly state run or state involved,but was principally private by the end of our sample.13 Our main source for U.S.data is the Census of Manufactures (CM)from1977,1982,1987,1992,and1997conducted by the U.S.Bureau of the Census.Be?tting its name,the census cov-ers all manufacturing plants.We drop small plants with limited production data(Administrative Records),leaving over160,000

plants in each year.The information we use from the U.S.Cen-sus are the plant’s industry(again at the four-digit level),labor compensation(wages and bene?ts),value-added,export revenues, and capital stock.We de?ne the capital stock as the average of the book value of the plant’s machinery and equipment and struc-tures at the beginning and at the end of the year.The U.S.data do not provide information on plant age.We impute the plant’s age by determining when the plant appears in the data for the?rst time.14

For our computations we set industry capital shares to those in the corresponding U.S.manufacturing industry.As a result,we drop nonmanufacturing plants and plants in industries without a close counterpart in the United States.We also trim the1% tails of plant productivity and distortions in each country-year to make the results robust to https://www.wendangku.net/doc/481293088.html,ter we check robustness to adjusting the book values of capital for in?ation.

13.Our data may understate the extent of privatization.Dollar and Wei(2007) conducted their own survey of Chinese?rms in2005and found that15%of all ?rms were of?cially classi?ed as state owned but had in fact been privatized.

14.For plants in the Annual Survey of Manufactures(ASM),we use the annual data of the ASM(starting with the1963ASM)to identify the plant’s birth year.For the plants that are not in the ASM,we assume the birth year is the year the plant?rst appears in the quinquennial CM minus three years. at University of Virginia on October 12, 2012 https://www.wendangku.net/doc/481293088.html,/ Downloaded from

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IV .P OTENTIAL G AINS FROM R EALLOCATION

To calculate the effects of resource misallocation,we need to back out key parameters (industry output shares,industry cap-ital shares,and the ?rm-speci?c distortions)from the data.We proceed as follows:

We set the rental price of capital (excluding distortions)to R =0.10.We have in mind a 5%real interest rate and a 5%depreciation rate.The actual cost of capital faced by plant i in industry s is denoted (1+τKsi )R ,and so it differs from 10%if τKsi =0.Because our hypothetical reforms collapse τKsi to its average in each industry ,the attendant ef?ciency gains do not depend on R .If we have set R incorrectly ,it affects only the average capital distortion,not the liberalization experiment.

We set the elasticity of substitution between plant value-added to σ=3.The gains from liberalization are increasing in σ,as is explicit in

(16),and so we made this choice conserva-tively .Estimates of the substitutability of competing manufac-tures in the trade and industrial organization literatures typically range from three to ten (e.g.,Broda and Weinstein [2006],Hendel and Nevo [2006]).Later we entertain the higher value of 5for σas a robustness check.Of course,the elasticity surely differs across goods (Broda and Weinstein report lower elasticities for more differentiated goods),so our single σis a strong simplifying assumption.

As mentioned,we set the elasticity of output with respect to capital in each industry (αs )to be 1minus the labor share in the corresponding industry in the United States.We do not set these elasticities on the basis of labor shares in the Indian and Chi-nese data precisely because we think distortions are potentially important in China and India.We cannot separately identify the average capital distortion and the capital production elasticity in each industry .We adopt the U.S.shares as the benchmark because we presume the United States is comparatively undistorted (both across plants and,more to the point here,across industries).Our source for the U.S.shares is the NBER Productivity Database,which is based on the Census and ASM.One well-known issue with these data is that payments to labor omit fringe bene?ts and employer Social Security contributions.The CM/ASM manufac-turing labor share is about two-thirds what it is in manufacturing according to the National Income and Product Accounts,which incorporate nonwage forms of compensation.We therefore scale at University of Virginia on October 12, 2012

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MISALLOCATION AND TFP IN CHINA AND INDIA1415 up each industry’s CM/ASM labor share by3/2to arrive at the labor elasticity we assume for the corresponding U.S.,Indian,and Chinese industry.

One issue that arises when translating factor shares into pro-duction elasticities is the division of rents from markups in these differentiated good industries.Because we assume a modestσof 3,these rents are large.We therefore assume these rents show up as payments to labor(managers)and capital(owners)pro rata in each industry.In this event our assumed value ofσhas no impact on our production elasticities.

On the basis of the other parameters and the plant data, we infer the distortions and productivity for each plant in each country-year as follows:

1+τKsi=

αs

1?αs

w L si

RK si

(17)

1?τY si=

σ?1

w L si

(1?αs)P si Y si

(18)

A si=κs (P si Y si)σσ?1 Kαs

L1?αs

(19)

Equation(17)says we infer the presence of a capital distortion when the ratio of labor compensation to the capital stock is high relative to what one would expect from the output elasticities with respect to capital and labor.Recall that a high labor distortion would show up as a low capital distortion.Similarly,expression (18)says we deduce an output distortion when labor’s share is low compared with what one would think from the industry elasticity of output with respect to labor(and the adjustment for rents).A critical assumption embedded in(18)is that observed value-added does not include any explicit output subsidies or taxes.

TFP in(19)warrants more explanation.First,the scalar is κs=w1?αs(P s Y s)?1σ?1/P s.Although we do not observeκs,relative productivities—and hence reallocation gains—are unaffected by settingκs=1for each industry s.Second and related,we do not observe each plant’s real output Y si,but rather its nominal output P si Y si.Plants with high real output,however,must have a lower price to explain why buyers would demand the higher output. We therefore raise P si Y si to the powerσ/(σ?1)to arrive at Y si. That is,we infer price vs.quantity from revenue and an assumed elasticity of demand.Equation(19)requires only our assumptions at University of Virginia on October 12, 2012 https://www.wendangku.net/doc/481293088.html,/ Downloaded from

1416QUARTERLY JOURNAL OF ECONOMICS

about technology and demand plus pro?t maximization;we need not assume anything about how inputs are determined.Third,for labor input we use the plant’s wage bill rather than its employ-ment to measure L si.Earnings per worker may vary more across plants because of differences in hours worked and human capital per worker than because of worker rents.Still,as a later robust-ness check we measure L si as employment.

Before calculating the gains from our hypothetical liberaliza-tion,we trim the1%tails of log(TFPR si/TFPR s)and log(A si/ˉA s) across industries.That is,we pool all industries and trim the top and the bottom1%of plants within each of the pools.We then recalculate w L s,K s,and P s Y s as well as TFPR s andˉA s.At this

stage we calculate the industry sharesθs=P s Y s/Y.

Figure I plots the distribution of TFPQ,log(A si M1σ?1

s/ˉA

),for

the latest year in each country:India in1994,China in2005, and the United States in1997.There is manifestly more TFPQ dispersion in India than in China,but this could re?ect the differ-ent sampling frames(small private plants are underrepresented in the Chinese survey).The U.S.and Indian samples are more comparable.The left tail of TFPQ is far thicker in India than the

United States,consistent with policies favoring the survival of inef?cient plants in India relative to the United States.Table I shows that these patterns are consistent across years and several measures of dispersion of log(TFPQ):the standard deviation,the 75th minus the25th percentiles,and the90th minus the10th percentiles.The ratio of75th to25th percentiles of TFPQ in the latest year are5.0in India,3.6in China,and3.2in the United States(exponentials of the corresponding numbers in Table II). For the United States,our TFPQ differences are much larger than those documented by Foster,Haltiwanger,and Syverson(2008), who report a standard deviation of around0.22compared to ours of around0.80.As we describe in Appendix II,our measure of TFPQ should re?ect the quality and variety of a plant’s products, not just its physical productivity.And our results cover all indus-tries,whereas Foster,Haltiwanger,and Syverson(2008)analyze a dozen industries speci?cally chosen because their products are homogeneous.

Figure II plots the distribution of TFPR(speci?cally, log(TFPR si/TFPR s))for the latest year in each country.There is clearly more dispersion of TFPR in India than in the United States.Even China,despite not fully sampling small private establishments,exhibits notably greater TFPR dispersion than at University of Virginia on October 12, 2012 https://www.wendangku.net/doc/481293088.html,/ Downloaded from

MISALLOCATION AND TFP IN CHINA AND INDIA 1417

0.1

0.2

0.31/2561/641/161/414

India

00.1

0.2

0.31/2561/641/161/414

China

00.1

0.2

0.31/2561/641/161/414

United States

F IGURE I

Distribution of TFPQ

the United States.Table II provides TFPR dispersion statistics for a number of country-years.The ratio of 75th to 25th percentiles of TFPR in the latest year are 2.2in India,2.3in China,and

1.7in the United States.The ratios of 90th to 10th percentiles of TFPR are 5.0in India,4.9in China,and 3.3in the United States.These numbers are consistent with greater distortions in China and India than the United States.15

15.Hallward-Driemeier,Iarossi,and Sokoloff (2002)similarly report more TFP variation across plants in poorer East Asian nations (Indonesia and the Philippines vs.Thailand,Malaysia,and South Korea). at University of Virginia on October 12, 2012

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1418QUARTERLY JOURNAL OF ECONOMICS

TABLE I

D ISPERSION OF TFPQ

China 199820012005S.D. 1.060.990.9575?25 1.41 1.34 1.2890?10 2.72 2.54 2.44N 95,980108,702211,304India 198719911994S.D. 1.16 1.17 1.2375?25 1.55 1.53 1.6090?10 2.97 3.01 3.11N 31,60237,52041,006United States 197719871997S.D.0.850.790.8475?25 1.22 1.09 1.1790?10 2.22 2.05 2.18N 164,971173,651194,669Notes .For plant i in industry s ,TFPQ si ≡Y si K αs si (w si L si )1?αs

.Statistics are for deviations of log(TFPQ)from industry means.S.D.=standard deviation,75?25is the difference between the 75th and 25th percentiles,

and 90?10the 90th vs.10th percentiles.Industries are weighted by their value-added shares.N =the number of plants.

TABLE II

D ISPERSION OF TFPR

China 199820012005S.D.0.740.680.6375?250.970.880.8290?10 1.87 1.71 1.59India 198719911994S.D.0.690.670.6775?250.790.810.8190?10 1.73 1.64 1.60United States 197719871997S.D.0.450.410.4975?250.460.410.5390?10 1.04 1.01 1.19Notes .For plant i in industry s ,TFPR si ≡P si Y si K αs si (w si L si )1?αs

.Statistics are for deviations of log(TFPR)from

industry means.S.D.=standard deviation,75?25is the difference between the 75th and 25th percentiles,

and 90?10the 90th vs.10th percentiles.Industries are weighted by their value-added shares.Number of plants is the same as in Table I. at University of Virginia on October 12, 2012

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MISALLOCATION AND TFP IN CHINA AND INDIA 1419

00.2

0.4

0.61/81/41/21248

India

00.2

0.4

0.61/81/41/21248

China

00.2

0.4

0.6

1/81/41/21248

United States F IGURE II

Distribution of TFPR

For India and China,Table III gives the cumulative percent-age of the variance of TFPR (within industry-years)explained by dummies for ownership (state ownership categories),age (quar-tiles),size (quartiles),and region (provinces or states).The results are pooled for all years,and are cumulative in that “age”includes dummies for both ownership and age,and so on.Ownership is less important for India (around 0.6%of the variance)than in China (over 5%).All four sets of dummies together account for less than 5%of the variance of TFPR in India and 10%of the variance of TFPR in China. at University of Virginia on October 12, 2012

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1420QUARTERLY JOURNAL OF ECONOMICS

TABLE III

P ERCENT S OURCES OF TFPR V ARIATION WITHIN I NDUSTRIES

Ownership Age Size Region

India 0.58 1.33 3.85 4.71China 5.25 6.238.4410.01Notes.Entries are the cumulative percent of within-industry TFPR variance explained by dummies for ownership (state ownership categories),age (quartiles),size (quartiles),and region (provinces or states).The results are cumulative in that “age”includes dummies for both ownership and age,and so on.

Although it does not ?t well into our monopolistically compet-itive framework,it is useful to ask how government-guaranteed monopoly power might show up in our measures of TFPQ and TFPR.Plants that charge high markups should evince higher TFPR levels.If they are also protected from entry of nearby com-petitors,they may also exhibit high TFPQ levels.Whereas we frame high TFPR plants as being held back by policy distortions,such plants may in fact be happily restricting their output.Still,such variation in TFPR is socially inef?cient,and aggregate TFP would be higher if such plants expanded their output.

We next calculate “ef?cient”output in each country so we can compare it with actual output levels.If marginal products were equalized across plants in a given industry ,then industry TFP would be ˉA s =( M s i =1A σ?1si )1

σ?1.For each industry ,we calculate

the ratio of actual TFP (15)to this ef?cient level of TFP ,and then aggregate this ratio across sectors using our Cobb-Douglas aggregator (1):

(20)Y Y ef?cient =S

s =1??M s i =1

A si A s TFPR s TFPR si

σ?1??

θs /(σ?1).We freely admit this exercise heroically makes no allowance for measurement error or model misspeci?cation.Such errors could lead us to overstate room for ef?ciency gains from better alloca-tion.With these caveats ?rmly in mind,Table IV provides percent TFP gains in each country from fully equalizing TFPR across plants in each industry .We provide three years per country .Full liberalization,by this calculation,would boost aggregate manu-facturing TFP by 86%–115%in China,100%–128%in India,and 30%–43%in the United States.If measurement and modeling at University of Virginia on October 12, 2012

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MISALLOCATION AND TFP IN CHINA AND INDIA 1421

TABLE IV

TFP G AINS FROM E QUALIZING TFPR WITHIN I NDUSTRIES

China 199820012005%115.195.886.6India 198719911994%100.4102.1127.5United States 197719871997%36.130.742.9Notes .Entries are 100(Y ef?cient /Y ?1)where Y /Y ef?cient = S s =1[ M s i =1(A

si A s TFPR s TFPR si )σ?1]θs /(σ?1)and

TFPR si ≡P si Y si K αs si (w si L si )1?αs

.errors are to explain these results,they clearly have to be much bigger in China and India than the United States.16

Figure III plots the “ef?cient”vs.actual size distribution of plants in the latest year.Size here is measured as plant value-added.In all three countries the hypothetical ef?cient distribu-tion is more dispersed than the actual one.In particular,there should be fewer mid-sized plants and more small and large plants.Table V shows how the size of initially big vs.small plants would change if TFPR were equalized in each country .The entries are unweighted shares of plants.The rows are initial (actual)plant size quartiles,and the columns are bins of ef?cient plant size relative to actual size:0%–50%(the plant should shrink by a half or more),50%–100%,100%–200%,and 200+%(the plant should at least double in size).In China and India the most populous col-umn is 0%–50%for every initial size quartile.Although average output rises substantially ,many plants of all sizes would shrink.Thus many state-favored behemoths in China and India would be downsized.Still,initially large plants are less likely to shrink and more likely to expand in both China and India (a pattern much less pronounced in the United States).Thus TFPR increases with size more strongly in China and India than in the United States.The positive size-TFPR relation in India is consistent with Baner-jee and Du?o’s (2005)contention that Indian policies constrain its most ef?cient producers and coddle its least ef?cient ones.16.In India,the variation over time is

not due to the smaller,sampled plants moving in and out of the sample.When we look only at larger census plants the gains are 89%–123%. at University of Virginia on October 12, 2012

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1422QUARTERLY JOURNAL OF ECONOMICS Efficient

Actual

00.050.1

0.15

0.20.251

/5121

/641/

818645

China Efficient

Actual

0.050.1

0.150.2

0.251

/5121

/641/

818645

India Efficient

Actual

00.05

0.10.150.2

0.251

/5121

/641/

818645

United States

F IGURE III

Distribution of Plant Size

Although we expressed the distortions in terms of output (τY si )and capital relative to labor (τKsi ),in Appendix III,we show that these are equivalent to a particular combination of labor (τ?Lsi )and capital (τ?Ksi )distortions.In Appendix III,we also report that more ef?cient (higher TFPQ)plants appear to face bigger distor-tions on both capital and labor. at University of Virginia on October 12, 2012

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