International trade, productivity in open economies

If private …rms face unfavorable discriminations relative to SOEs and they are a muchlarger presence in the tradable sector than the non-tradable sector in other words, if theprivileged

THE UNIVERSITY OF CHICAGO

INTERNATIONAL TRADE, PRODUCTIVITY AND GROWTH IN OPEN ECONOMIES

A DISSERTATION SUBMITTED TOTHE FACULTY OF THE DIVISION OF THE SOCIAL SCIENCES

IN CANDIDACY FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

DEPARTMENT OF ECONOMICS

BYHUA CHAI

CHICAGO, ILLINOISJUNE 2013

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To my dear wife Yayun Pan and daughter Deborah Erya Chai

TABLE OF CONTENTS

LIST OF FIGURES vi

LIST OF TABLES vii

ACKNOWLEDGMENTS viii

ABSTRACT ix

1 CHAPTER I REAL EXCHANGE RATE UNDERVALUATION AND RESOURCE ALLOCATION IN CHINA: THEORY 1

1.1 Introduction 1

1.2 A Simple Model 5

1.2.1 Basic Setup 6

1.2.2 Equilibrium with Capital Account Policies 7

1.2.3 TFP E¤ect 9

1.2.4 Equilibrium with Sectoral Subsidies 10

1.2.5 Short-Run Analysis 11

2 CHAPTER II REAL EXCHANGE RATE UNDERVALUATION AND RESOURCE ALLOCATION IN CHINA: QUANTITATIVE EXPLORATION 16

2.1 A Quantitative Model 16

2.1.1 The Environment 16

2.1.2 Distortions 18

2.1.3 Equilibrium 19

2.1.4 General Equilibrium E¤ects 23

2.2 Quantitative Analysis 24

2.2.1 Estimating Distortions 25

2.2.2 Observables and Parameters 27

2.2.3 Results 29

2.3 Conclusion 33

3 CHAPTER III INTERNATIONAL TRADE AND TECHNOLOGY DIFFUSION: A MODEL OF LEARNING-BY-EXPORTING 34

3.1 Introduction 34

3.2 Model 36

3.2.1 Technology and preference 36

3.2.2 Learning and technology di¤usion 37

3.2.3 Evolution of the technology frontier 41

3.2.4 Equilibrium 42

3.3 A Numerical Example 46

3.4 Conclusion 47

A APPENDIX FOR CHAPTER I AND CHAPTER II 49

A.1 Proof of Proposition 1 49

A.2 Deriving equilibrium conditions in "changes" 49

A.3 Equilibrium with sectoral subsidies 51

A.4 Algorithm for Solving the Quantitative Model 53

B APPENDIX FOR CHAPTER III 54

C FIGURES 55

REFERENCES 63

LIST OF FIGURES

3.1 Equilibrium Dynamics 48

C.1 Private Firms’Share of Industry Sales 55

C.2 Private Firms’Share of Industry Value-Added 56

C.3 Private Firms’Share of Industry Fixed Investment 57

C.4 Shares of Domestically-Funded Fixed Investment by Industry 58

C.5 Results of Varying Trade Balance 59

LIST OF TABLES

2.1 Estimated Distortions at Sector Level 26

2.2 Results without Distortions 29

2.3 Results with Distortions 30

2.4 Alternative Parameter Values 30

2.5 Results with Average Distortions 31

3.1 Parameter Values 47

3.2 Steady State 47

I am deeply grateful to my main advisor and the chair of my thesis committee, ProfessorSamuel Kortum, for his invaluable advice and guidance, and continual support and encour-agement I am also deeply indebted to Professor Robert Lucas and Professor Ralph Ossa,for their patience and generous help since even before the beginning of this thesis project

to its completion I also thank Nancy Stokey, Thomas Chaney, Chang-Tai Hsieh, ZhengMichael Song, and Kerem Cosar for their extremely helpful comments and suggestions atvarious stages of this project

I am also grateful to all the fellow students in the International Economics WorkingGroup at the University of Chicago, whose kind support, open discussions and constructivecriticisms have bene…ted my research greatly and prepared me better for the job market Ialso thank my loving wife for being so considerate, tolerant and supportive Without herhelp in every possible way, the completion of this dissertation would have been much moredi¢ cult

Financial support from the University of Chicago Social Science Fellowship, the IMF Scholarship for Advanced Studies, and the Margaret G Reid Memorial Fund Disser-tation Fellowship are gratefully acknowledged All remaining errors within this dissertationare my own

This thesis studies aggregate productivity and growth of developing countries in open economieswith access to international trade with a focus on China It is divided into three chapters.Chapter 1 argues that real exchange rate undervaluation improves resource allocation inthe Chinese economy The gain in allocative e¢ ciency results from two institutional features

of China’s "state capitalism": (1) State-owned enterprises (SOEs) are generally favored

by the government over private …rms; (2) Private …rms dominate the tradable sector, whileSOEs retain strong presence in the non-tradable sector These facts jointly point to potentialresource misallocation between the tradable and the non-tradable sectors Real exchange rateundervaluation mitigates this misallocation by raising the relative price of tradable goods,inducing resources to be reallocated toward the tradable sector Foreign exchange reserveaccumulation is a major instrument used by the Chinese government to keep a competitivereal exchange rate

To make quantitative assessments of this policy, in chapter 2 I develop a two-sector Kortum model of international trade with two types of …rms and type-and-sector speci…cdistortions I estimate distortions from Chinese industry-level data, and calibrate the model

Eaton-to match aggregate trade ‡ows and secEaton-toral spending data for the year 2007 Quantitativeresults suggest that reserve accumulation depreciates the real exchange rate by a moderate4%, compared to a reference point with balanced trade, and the resulting improved resourceallocation raises China’s real GDP in 2007 by 1% I show that alternative policies thatcan also generate real undervaluation, such as a moderate consumption subsidy on tradablegoods, could deliver positive TFP e¤ects without the need for a high trade surplus

Chapter 3 is a theoretical exploration of how international trade facilitates internationaltechnology di¤usion In particular, it formalizes the notion of "learning-by-exporting" byembedding learning in an Eaton-Kortum type trade model with Bertrand competition Ex-porting …rms can learn from international best practices at an endogenously chosen learningintensity The model is able to generate the so-called "catch-up growth" where an econ-

omy with relatively backward technologies exhibits faster growth rate than more advancedeconomies due to the opportunities to engage in international trade and learning However,its growth slows down as the technology gap narrows, reducing gains from learning and alsothe endogenous learning intensity.

CHAPTER 1 CHAPTER I REAL EXCHANGE RATE UNDERVALUATION AND RESOURCE ALLOCATION IN CHINA: THEORY

1.1 Introduction

Much of the existing research suggests that the real exchange rate of China’s currency hasbeen undervalued for a substantial part of the last decade.1 If these beliefs are true, whatwould be the implication for resource allocation in the Chinese economy? In textbook models,real exchange rate undervaluation distorts domestic relative prices and leads to misallocation

of resources This paper argues that the reverse is true in China, where real undervaluation ofthe RMB acts as a second-best measure to correct pre-existing misallocation in the Chineseeconomy and hence improves resource allocation

This argument is based on two observations regarding institutional features of the Chineseeconomy The …rst observation is the contrasting industry concentrations of China’s privatesector and the public sector Private …rms in China dominate the tradable sector Figure C.1shows private enterprises’share of industry sales in twenty-eight 2-digit tradable industries.Private …rms contribute more than 80% of industry sales in all but a few industries Overall,the private sector accounts for more than 90% of sales in tradable industries Figure C.2 andFigure C.3 look at two di¤erent measures –private …rms’share of industry value added anddomestic …xed investment respectively The patterns are almost identical to …gure 1 Thelandscape is drastically di¤erent when we look at the non-tradable sector Figure C.4 plotsthe share of domestic …xed investment of state-owned enterprises (SOEs) and the privatesector in non-tradable industries.2 For most of these industries, the state sector accounts

1 Estimates of the extent to which the RMB is undervalued in the 2000s vary from "small" to as high as 50% See Cheung, Chinn and Fujii (2010) for a survey of di¤erent estimation approaches and results This paper neither takes a stand regarding nor depends on what the correct estimate is.

2 Sales and value added data are not available at the industry level for the non-tradable industries, except for a few of them.

for a much higher share in investment Even in industries where its share of investment islower than private …rms, the state sector tends to hold a signi…cant portion In terms ofaggregate sales of non-tradable industries, private …rms and SOEs split the market roughlyhalf-and-half according to my estimates.3

The second observation is China’s "state favoritism", a term that summarizes the variouspreferential treatments SOEs get from the government regarding access to credit, marketentry, legal protection, etc Boyreau-Debray and Wei (2005) document that Chinese banks –mostly state-owned –o¤er easier credit to SOEs Song and Wu (2011) …nd that small, private

…rms without political connection in east China face unfavorable capital market conditions

A recent World Bank report (2012) points out that in many key sectors of the Chineseeconomy, SOEs are protected by barriers that discourage entry from the private sector.Details of this aspect of "capitalism with Chinese characteristics" are also documented inHuang (2008) As a result, there may exist misallocation of resources between the privatesector and the state sector Dollar and Wei (2007) report that even after a quarter of acentury of reforms, state-owned …rms still have signi…cantly lower returns to capital thannon-state …rms Brandt, Tombe and Zhu (2010) …nd that almost all of the within-provincedistortions in China can be accounted for by the misallocation of capital between the stateand non-state sectors

If private …rms face unfavorable discriminations relative to SOEs and they are a muchlarger presence in the tradable sector than the non-tradable sector (in other words, if theprivileged state sector concentrates in non-tradable industries), then it is plausible that thetradable sector might be subject to more severe distortions than the non-tradable sector.This would result in potential cross-sector resource misallocation: too few resources areallocated to the tradable sector relative to optimum, while too many are allocated to thenon-tradable sector As a result, undervaluation of the real exchange rate, by raising the

3 Adding funded investment doesn’t signi…cantly change the pattern The amount of funded investment is small compared to domestic sources, especially in the non-tradable sector.

foreign-relative price of tradable goods, may improve the allocative e¢ ciency of the economy byinducing resources to ‡ow from the non-tradable sector to the tradable sector.

Of course, the real exchange rate is not a policy variable in itself It is a relative pricedetermined in equilibrium How then is real exchange rate undervaluation achieved? Gov-ernments have a variety of instruments at their disposal to in‡uence the level of the realexchange rate Capital account intervention is probably the most notable tool used by theChinese government Jeanne (2012) shows how accumulation of foreign exchange reserves,together with restrictions on private international capital ‡ows, lead to the real undervalu-ation of China’s currency.4 To illustrate the e¤ects of such policies on resource allocationand aggregate total factor productivity (TFP) in the Chinese economy, I develop a simplestatic small open economy model with a tradable sector and a non-tradable sector Reserveaccumulation requires an increase in trade surplus, which is modeled as an outward transfer

of tradable goods To sharply model the two aforementioned observations, I assume thatthe tradable sector is subject to distortions in the form of a tax, while the non-tradablesector is not I show that real depreciation through reserve accumulation induces resources

to be reallocated toward the tradable sector, which mitigates misallocation and improvesaggregate productivity of the economy

In order to evaluate the magnitude of resource reallocation induced by real ation, particularly through reserve accumulation, and its e¤ects on aggregate productivity,

undervalu-I develop a quantitative two-sector Ricardian model of international trade based on Eatonand Kortum (2002) and Alvarez and Lucas (2007) I introduce two types of …rms into theframework –private and state-owned –which compete with each other in both the tradableand the non-tradable sectors Domestic …rms are subject to type-and-sector speci…c distor-tions on output, capital and labor These distortions are estimated with disaggregated datausing an approach similar to that of Hsieh and Klenow (2009) The model is calibrated to

4 China has accumulated more than 3 trillion dollars of o¢ cial foreign reserves by late 2011 –more than 50% of its GDP (data source: People’s Bank of China)

match aggregate trade ‡ows and sectoral spending data for the year 2007 Massive reserveaccumulation translates into a huge trade surplus I study the e¤ects of real undervaluationusing counterfactual "appreciation" (rebalancing) experiments where the Chinese govern-ment adjusts its stock of foreign reserves to eliminate the trade surplus and to appreciatethe real exchange rate.

As a preliminary exercise, I …rst compute results assuming that there is no distortion

in the Chinese economy "Rebalancing" in this case raises aggregate TFP, con…rming theview that real undervaluation itself is a distortion and causes misallocation in a …rst-bestworld I then perform an analogous exercise, but now with distortions set to their estimatedvalues The results show that restoring trade balance leads to a moderate appreciation ofthe real exchange rate of the RMB by 4:3%; and real GDP goes down by 1:1%: In otherwords, it is as if China experiences 1% gain in aggregate TFP through real exchange rateundervaluation, compared to the reference point with balanced trade Finally, I show thatthe same magnitude of real exchange rate undervaluation can be achieved with very moderatesubsidies on the purchase of tradable goods, without the need for a big trade surplus.This paper is not the …rst one to put forth the view that real exchange rate undervaluationmay improve resource allocation Rodrik (2009) argues that the tradable sector su¤ersdisproportionately from government or market failures, which justi…es real exchange rateundervaluation as a second-best correction of the misallocation between the tradable sectorand the non-tradable sector He discusses possible sources of these distortions, but does notmeasure them In a similar vein, Korinek and Serven (2010), Gala (2007), and Rodrik (1988)base their rationale for real undervaluation on learning externalities or increasing returns thatare supposedly more characteristic of the tradable sector than the non-tradable sector.5 Anempirical di¢ culty with this line of work is that externalities are hard to measure Thispaper is novel in that it traces the misallocation of resources to policy distortions that can

5 Similar hypotheses have been advanced in previous literature on export-led growth (see, e.g Keesing, 1967) For a survey of empirical work in this literature, see Giles and Williams (2000).

be estimated from disaggregated data, thereby enabling quantitative exploration in a generalequilibrium framework.

This paper is also connected to the literature that relates micro-level resource cation to low aggregate total factor productivity in developing countries (See Parente et al2000; Caselli and Coleman 2001; Banerjee and Du‡o 2005; Restuccia and Rogerson 2008;Gancia and Zilibotti 2009; Hsieh and Klenow 2009; and Song et al 2011) While much of thisliterature is concerned with measuring misallocation and quantifying its impact on aggre-gate TFP, less thought is devoted to the question of what can be done about misallocation.This paper tries to identify particular sources of misallocation, and shows that well-targetedpolicies could counter misallocation and enhance aggregate productivity

misallo-This paper uses the same technique popularized by Dekle et al (2007) to calculate generalequilibrium e¤ects of a counterfactual rebalancing scenario They study how relative wages,real wages and welfare would di¤er from the data in a counterfactual world with all currentaccounts balancing While their paper is more of a hypothetical "positive" analysis, thispaper is more of a "normative" analysis in the sense that it asks whether there is a potentialjusti…cation for China’s policy Furthermore, this paper is more focused on China andconsiders more institutional details of the Chinese economy, and hence delivers quantitativelydi¤erent results

The rest of the chapter is organized as follows Chapter 1 presents a simple modeland derives some analytical results as well as extension for short-run analysis Chapter 2develops the quantitative framework and shows how to compute the general equilibriume¤ects It then turns to empirical application and includes description of data, calibration

of parameters, and results

1.2 A Simple Model

In this section, I use a simple model to illustrate how real exchange rate undervaluationinduces reallocation of resources between the tradable and the non-tradable sectors, and

study the resulting e¤ects on aggregate total factor productivity in an economy with tortions I consider two sets of policies that can achieve real exchange rate undervaluation:capital account policies and sectoral subsidies Many assumptions in this section are madefor simplicity and will be relaxed later in the quantitative model.

dis-1.2.1 Basic Setup

Consider a static model of a small open economy with two sectors indexed by m 2 fT; Ng,

a tradable sector (T ) and a non-tradable sector (N ) Labor is the only productive factorand production functions are linear in labor in both sectors:

Ym = Lm:

Total labor force, L; is …xed, and labor is perfectly mobile between sectors I do notassume cross-sector di¤erences in productivity, but relaxing this assumption does not changeany of the qualitative results There are no intrinsic reasons for international trade sincethere is only one tradable good The existence of a tradable sector is to allow for inward andoutward transfers of goods (trade de…cit and trade surplus) Perfect competition is assumed

in both sectors throughout

Utility is de…ned over consumption of both the tradable good and the non-tradable good,with a Cobb-Douglas utility function:

Let the tradable good be the numeraire Denote the price of the non-tradable good in terms

of the tradable good as PN:

There are two types of …rms indexed by 2 fs; pg : state-owned …rms (s) and private

…rms (p) : In light of the two observations described in the introduction, I assume completespecialization: private …rms specialize in the tradable sector, while state-owned …rms spe-

cialize in the non-tradable sector The assumption of complete specialization will be dropped

in the next section I also assume that private …rms are subject to a labor tax at rate > 0;which captures the idea that private …rms are subject to discrimination relative to the statesector Given this assumption, we can drop the ownership type index as it has a one-to-one correspondence with the sector index m and is therefore redundant: All tax revenue isassumed to be rebated to consumers in a lump-sum fashion The pro…t function of a private

…rm (in the tradable sector) is given by:

T = lT (1 + ) wlT;

and the pro…t function of a state-owned …rm (in the non-tradable sector) is similarly givenby:

N = PNlN wlN:Standard pro…t maximization under perfect competition implies that:

1.2.2 Equilibrium with Capital Account Policies

Following Jeanne (2012), I assume that the government can a¤ect the net foreign assetposition through capital account policies –restrictions on private capital in‡ows and out‡ows,

and public accumulation of foreign reserves This immediately implies that the governmentcan a¤ect the size of trade balance as well, because as an accounting identity, trade balance

is equal to the di¤erence between the change in net foreign asset position (current account)and net returns from net foreign asset position.6 Therefore, I treat the trade balance as apolicy variable that can be adjusted by the government, with the understanding that changes

in the trade balance is implicitly associated with capital account policies operating in thebackground

For convenience, I express trade balance, T B; as a fraction of output of the tradablesector, i.e T B = YT:A higher can be shown to be always associated with a higher T B

I restrict the analysis to a situation with trade surplus, i.e > 0:In a static model, a tradesurplus is usually interpreted as a transfer of tradable goods to the rest of the world, orequivalently, as dumping a fraction of tradable goods in the ocean The remaining (1 )fraction of the tradable sector output is supplied to the domestic market

Denote X as total consumption spending, of which a fraction is devoted to the tradablegood The market clearing condition for the tradable good is therefore given by:

The allocation of labor can be readily obtained by inserting equation (1.2) into (1.5):

induc-of the real exchange rate and a lower PN; a depreciation Since PN is …xed in equilibrium,

so is the real exchange rate In other words, a trade surplus only "temporarily" undervaluesthe real exchange rate before its equilibrium level is restored

1.2.3 TFP E¤ect

What is the e¤ect of raising (temporary undervaluation of the real exchange rate) onaggregate productivity? Since the size of the labor force is …xed, the e¤ects on aggregateTFP and on GDP are equivalent.7 GDP can be expressed as the sum of value of sectoraloutputs:

where the coe¢ cient in front of L is the aggregate productivity (TFP) In the absence ofdistortions ( = 0), the above equation reduces to Y = L; which is intuitive since PNwould be equal to one in this case Distortions on private …rms ( > 0) lowers productivityand output because it results in misallocation of labor across sectors: too much labor isallocated to the non-tradable sector while too little to the tradable sector However, thiscan be countered by increasing the trade surplus The above equation clearly shows thatproductivity and output are increasing in ; which is because higher trade surplus results

in a "temporary" undervaluation of the real exchange rate, inducing labor to be reallocatedtoward the tradable sector, thereby correcting the misallocation of labor

These results imply that in an economy with severe distortions, aggregate TFP couldpotentially be increased by running a trade surplus But is it optimal to do so from awelfare-maximizing point of view? The static structure has little to say about welfare, asreserve accumulation defers current consumption for future consumption,8 the welfare e¤ect

of which depends on what the optimal saving rate is –a topic beyond the scope of this paper.However, if a huge trade surplus is any cause for concern, it is natural to ask whether realexchange rate undervaluation can be achieved in ways other than reserve accumulation

1.2.4 Equilibrium with Sectoral Subsidies

In this subsection, I show that real exchange rate undervaluation can be achieved by aconsumption subsidy on the tradable good The advantage of this policy is that it doesn’trequire a huge trade surplus I keep the assumption that the government can a¤ect the size

of trade balance In particular, I now assume trade balance is zero, but the analysis goesthrough with an arbitrary level of trade balance

Suppose the government subsidizes consumption of the tradable good at rate tT and

8 In this model, "current" consumption unambiguously falls with a higher trade surplus Consumption

of the non-tradable good falls as output falls in that sector Production of the tradable good increases, but a smaller share of output is left for domestic consumption In the appendix I show that overall a trade surplus lowers consumption of the tradable good.

…nances this subsidy by levying a lump-sum tax Equation (1.3) needs to be rewritten totake into account the impact on the demand for the tradable good:

1.2.5 Short-Run Analysis

The above model essentially features the "long-run" equilibrium as factors can be reallocatedbetween sectors instantly In reality, in the short-run, some factors may be harder to ‡owbetween sectors, e.g capital Here I present a variant of the model presented above withsector-speci…c factors and show that real exchange rate undervaluation could still lead tohigher aggregate productivity in this case Another interesting result of this speci…c-factorsmodel is that the equilibrium real exchange rate now responds to policy

Production in each sector uses labor and sector-speci…c factor Km The productionfunction is Cobb-Douglas with labor share 2 (0; 1) : I normalize the endowment of sector-

speci…c factors to one in each sector The production function is then given by:

Ym = Lm:

Total labor force, L; is …xed, and labor is perfectly mobile between sectors

The pro…t function of a private …rm (in the tradable sector) is given by:

T = lT (1 + ) wlT rTKT;

and the pro…t function of a state-owned …rm (in the non-tradable sector) is similarly givenby:

N = PNlN wlN rNKN:Firms maximize pro…ts by equating their marginal revenue product of labor with after-taxwage rate, which implies

The market clearing condition for the non-tradable good is similarly given by:

answer these questions by examining the TFP e¤ects of real exchange rate undervaluation.Since the size of the labor force is …xed, the e¤ects on aggregate TFP and on GDP areequivalent GDP can be expressed as the sum of value of sectoral outputs:

Y = LT + PNLN:

Rewriting the above equation using equations (1.10) and (1.11), I obtain:

Y = 1wL 1 + LT

Taking log on both sides of the equation yields:

log Y = log w + log 1 + LT

Proposition 1 (The Net E¤ect on TFP) Aggregate TFP is decreasing in the size of the

trade surplus if (1 ) = for 2 (0; 1) : For > (1 ) = ; the aggregate TFP exhibits

a U-shaped pattern: it is decreasing in for 2 (0; ) and increasing in for 2 ( ; 1) ;

Proof See Appendix

As numerical examples, I provide two plots of Y as a function of for a common set ofparameters except the value for :9

1.05 1.10

Y

Case with high

The plot to the left shows that for a small ; Y is decreasing in : When the level ofdistortion is low, gains from reallocation of labor is too small to outweigh the cost associatedwith real undervaluation With a high level of ; as is the case with the plot to the right,the change in Y is not monotonic Y goes down for low levels of before it goes up whengets su¢ ciently large This U-shaped pattern is related to the curvature of the productiontechnology As increases, marginal product of labor (MPL) decreases in the tradablesector The pace of the decrease in MPL is faster when labor stock in the tradable sector isrelatively small, that is, when is small As increases, inducing more labor to be allocated

to the tradable sector, the decrease in MPL slows down Therefore, the negative TFP e¤ectdominates for lower ; and is outweighed by the positive e¤ect when gets bigger Theseresults imply that in an economy with severe distortions, aggregate TFP could potentially beincreased by running a trade surplus But is it optimal to do so from a welfare-maximizingpoint of view?

9 The parameters are = 0:5; = 0:5; L = 1:

CHAPTER 2 CHAPTER II REAL EXCHANGE RATE UNDERVALUATION AND RESOURCE ALLOCATION IN CHINA: QUANTITATIVE

EXPLORATION

2.1 A Quantitative Model

To quantitatively evaluate the e¤ects of real exchange rate undervaluation on resource cation and aggregate productivity, I develop a model of international trade based on Eatonand Kortum (2002) and Alvarez and Lucas (2007) As in the simple model, there are twotypes of …rms: private and state-owned In contrast to the simple model where each type of

allo-…rms is assumed to completely specialize in one sector, here both types of allo-…rms are active inthe tradable and the non-tradable sectors in the quantitative model Their relative share ofsectoral output is endogenously determined in equilibrium The small open economy setting

in the simple model is extended to a multi-country structure to account for the e¤ects ofChina’s real exchange rate undervaluation on world prices Other realistic features includemultiple factors of production (capital and labor), a richer set of distortions, iceberg tradecosts and a CES utility function In this chapter, I focus on the "long-run" equilibrium,where all factors can be reallocated across sectors

2.1.1 The Environment

There are N countries indexed by i; and 2 sectors indexed m 2 [T; N] : For concreteness, wecan think of country 1 as China Utility in country i is de…ned over consumption of …nalgoods produced by the two sectors with a CES aggregator:

where !m is the taste parameter, and " is the elasticity of substitution between the tradablesector and the non-tradable sector The ideal price index in country i is given by:

qmi (u) = xim(u) kmi (u) mlmi (u)1 m mzmi (u)1 m;

where m is the share of value-added in output in sector m; m is the value added basedcapital intensity, and zim(u) is the amount of sector m composite good used as inputs inproduction Denote Zmi as the total amount of sector m composite goods used as inputs incountry i, then Zmi = R1

0 zim(u) du: Since sectoral output is divided between consumptionand production, we have Qim = Cmi + Zmi : While capital and labor endowments are …xedand immobile across national borders, they are perfectly mobile across sectors The costdraws, xim(u) ; associated with producing intermediate variety u in sector m country i; arerandom variables They are ampli…ed in percentage terms by 1 In countries j 6= 1; the costvariables xjm(u) are drawn randomly from an exponential distribution with parameter jm:

1 Here I follow the notation in Alvarez and Lucas (2007) The parameter is what Eaton and Kortum (2002) call 1= : In this paper a larger means a larger variance in productivities.

In country 1, each intermediate variety in each sector can potentially be produced by eitherstate-owned or private producers I allow these two types of …rms to draw cost variablesfrom di¤erent distributions In particular, cost variables of type 2 fs; pg producers aredrawn from an exponential distribution with parameter 1;m : Each intermediate variety isproduced by lowest-cost producers in equilibrium Competition between producers of bothtypes (and foreign competitors in the case of the tradable sector) determines the range ofvarieties produced by each type of producers.

Intermediate varieties in the tradable sector are tradable, and subject to iceberg tradecosts: producers in sector m; country i needs to ship dji units of goods so that 1 unit arrives

in country j: Domestic trade is assumed to be costless All factor and goods markets areperfectly competitive

2.1.2 Distortions

Intermediate varieties producers in country 1 (China) are subject to three speci…c distortions, modeled as taxes following Hsieh and Klenow (2009): an output distor-tion y;m ; a capital distortion k;m ; and a labor distortion l;m 2 These distortions are bestrepresented in the pro…t function of a type producer in sector m (suppressing countryindex):

type-and-sector-m(u) = 1 y;m vm(u) 1 + k;m rkm(u) 1 + l;m wlm(u) Pmzm(u) ;

where vm(u) denotes the sales of an intermediate variety u producer of ownership type

in sector m Pro…t equals after-tax sales revenue minus expenditure on capital, labor andmaterials I assume, for state-owned …rms, y;sm = k;sm = l;sm = 0 Therefore, y;pm ; k;pm andl;p

m should be interpreted as distortions on the private sector relative to those on the statesector Tax revenue is rebated lump-sum to consumers

2 A speci…cation of distortions on capital, labor and materials is observationally equivalent.

which is a measure of overall distortion in sector m: Note that for state-owned …rms, 1;sm = 1;

m2 fT; Ng : This term is equal to one in countries other than country 1

I …rst solve for the equilibrium price of the non-tradable sector composite good in country

1, as the result from this exercise helps simplify the analysis of the tradable sector Let

x1N n

x1;pN ; x1;sN o

denote the cost draws of the two types of producers for an arbitrarynon-tradable sector intermediate variety The price of this variety, p1N x1N ; is equal to theunit cost of the lowest cost producer:

p1N (xN) = min x1;pN c1;pN ; x1;sN c1;sN

= BN riN N wi 1 N

N

PNi 1 N min i;pN xi;pN ; xi;sN :

Raising both sides of the above equation to the power of 1= yields:

m as the sectoral technology level as in Alvarez and Lucas (2007) Consequently, almostall standard results of Eaton-Kortum type models apply with minor adaptations.

The price of the non-tradable sector composite good in country i is then:

P2n=1 djn rTn T (wn)1 T T PTn 1 T

1=

n T

Smi;s; which can be calculated as a sum of sales in all markets:

The government sets T B1 = Y1; with the restriction that Y1 PT1Q1T:

A positive (negative) trade balance T Bi > 0 is a trade surplus (de…cit) I view T B1

as a policy variable that can be adjusted by the country 1 government via capital accountpolicies

The share of sector m in aggregate consumption spending in country i; 'im; is derivedfrom the consumer’s problem:

and materials in production, i.e Xmi = Pmi Cmi + Pmi Zmi = Pmi Qim:Substituting Pmi Cmi and

Pmi Zmi using equations (2.5)(2.6)(2.7)(2.8) and (2.9) gives a system of equations:

Xmi = 'im

2

4Xm

1 y;i;m i;m

!Xj

DjimXmj :

To derive factor market clearing conditions, notice that a share m m of the after-taxsales of type producers is used to rent capital, and a fraction (1 m) m goes to thepayroll Therefore,

(1 m) mX 1 y;i;m

1 + l;i;m

i;

mXj

DjimXmj : (2.12)

De…nition 1 An equilibrium is a collection of factor prices wi; ri , such that the linearsystem in Xmi (2.10) and factor market clearing conditions (2.11)(2.12) are satis…ed, where'im is given by (2.9), Pmi and Pi are given by (2.1)(2.2)(2.3), and Dmji is given by (2.4)

2.1.4 General Equilibrium E¤ects

An obvious problem with this system is that it depends on a large set of unknown meters which are di¢ cult to estimate empirically I avoid this problem by rewriting theequilibrium conditions in "changes" using a technique popularized by Dekle et al (2007).These equilibrium conditions can be restated as4

! 1

1 "

(2.14)

^'im =

1 y;i;m i;m

!Xj

ji

mXmj X^mj

35

'im'^imT BiT Bdi+ (1 m) X

1 y;i;m i;m

!Xj

m m i;m

Xj

ji

mXmj X^mj (2.18)

4 For derivation of this system of equations please see the appendix.

where a "hat" denotes the ratio between the counterfactual and factual value of a certainvariable, and

ji m

2.2 Quantitative Analysis

I now apply this framework to quantify the e¤ect of real exchange rate undervaluation cies For this purpose, I …rst estimate distortions, and then obtain data on key observables,and calibrate a small set of parameters

at 4-digit ISIC Revision 3 level of aggregation, applying equations (2.20)(2.21) and (2.22) atthis level I then calculate weighted averages of 4-digit level distortions to arrive at estimatesfor the tradable and non-tradable sectors The weights of a 4-digit industry are its sales,

5 As in Hsieh and Klenow (2009), a critical assumption here is that observed value added does not include any explicit output taxes or subsidies.