Total Factor Productivity among Cities in China: Estimation and … · 2013-04-09 · Total Factor Productivity among Cities in China: Estimation and Explanation Yan Xu yand Shu Yu

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Total Factor Productivity among Cities

in China: Estimation and Explanation

Yan Xu and Shu Yu

The Conference Board and University of Groningen

March 2012

EPWP #EPWP # 12 12 -- 01 01

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Total Factor Productivity among Cities in China:

Estimation and Explanation∗

Yan Xu † and Shu Yu

First draft: August, 2010

This version: March, 2012

Abstract

Based on the stochastic Solow model, we estimate the levels and growth rates of TotalFactor Productivity (TFP) for about 500 cities in China from 1996 to 2007. The averageand weighted average growth rates over these 500 cities are 2.1% and 2.2%, respectively.We find that TFP levels and growth rates are largely different across cities. In orderto explain these differences, this paper investigates into factors that could cause varia-tions in regional TFPs by using panel and cross-sectional analysis. We find that ForeignDirect Investment (FDI) inflows, urbanization, education levels, and government policycould affect TFP to a great extent. These findings would provide insights in policymaking.

Key words: Stochastic Solow model, Total Factor Productivity

∗ This paper was written during our Robert H. McGuckin Fellowship in 2010 at TheConference Board. We thank Bart van Ark, Vivian Chen and Harry Wu for their commentsand helpful suggestions. All remaining errors are ours.†University of Groningen, Faculty of Economics and Business, email: [email protected]

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Contents

1 Introduction 3

2 Literature Review 42.1 Creation, transmission and absorption of knowledge . . . . . . . . . . . . . . 4

2.1.1 Urbanization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.2 FDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Factor supply and efficient allocation . . . . . . . . . . . . . . . . . . . . . . . 52.2.1 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.3 Sectoral structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.4 Resource allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Institutions and invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.1 Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.2 Invariant effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Methodology 83.1 Estimate TFP growth rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2 Estimate TFP Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 Data 9

5 Estimation Results of TFP growth and TFP level 12

6 Determinants of TFP growth rates and levels in China 186.1 Determinants of TFP growth rates . . . . . . . . . . . . . . . . . . . . . . . . 186.2 Determinants of TFP levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

7 Conclusion 25

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1 Introduction

The tremendous economic development of China has attracted much attention. Many discus-sions focus on how Chinese growth affects Western economies (e.g. trade deficits, outsourcingand unemployment). What has largely been lacking, however, is comprehensive analysis ofthe Chinese domestic market. This includes the regional differences in the economic growth,especially in the Total Factor Productivity (TFP) growth.

Many studies suggest that China has a high capital accumulation rate compared to the otherdeveloping economies. However, a large proportion of output cannot be explained by thenumber of inputs used in production. Such residual is captured by TFP which is determinedby how efficiently and intensively the inputs are used in production process. This proportioncould be considerable, so the issue is important in many senses. As is shown in the landmarkarticle by Solow (1957), long-run growth in income per capita in an economy with an aggre-gate neoclassical production function must be driven by growth in TFP. Therefore, growthof TFP provides society with an opportunity to increase the welfare of people. According toYoung (1995), the average TFP growth rates for Hong Kong, Singapore, Korea, and Taiwanwere 2.3%, 0.2%, 1.7%, and 2.1% respectively during the year 1966 to the early 1990s. Onaverage, this accounts for 20% to 25% of the GDP growth. However, using results of existingliteratures, Crafts (1998) find that TFP growth used to contribute approximately 40% to60% of GDP growth in OECD countries in the 1950s and 1960s when these economies wereenjoying fast growth. It also shows China’s TFP growth rate during the period 1984 to 1994was 4.6%, which means approximately 42% of the Chinese GDP growth comes from the TFPgrowth. However, the central question asked by investors is whether China still enjoys suchfast growth of TFP in the recent decade. Therefore, the first aim of this paper is to find outthe TFP growth rates for cities in China during the period from 1996 to 2007, and to analyzethe average TFP growth over the cities during this period.

Another problem with regard to China’s development is the persistent and widening incomegap among regions. At the beginning of economic reform twenty years ago, the investmentwas largely concentrated in the costal areas, with the non-coastal areas’ investment laggingbehind. In particular, rising per-capita income in the 10 coastal provinces has outstrippedgrowth in the interior, so that between 1978 and 1993 the coast/non-coast ratio of mean GDPper capita grew from 2.53 to 2.82, or 11 percent. However, in 2007, the coast/non-coast ratioof mean GDP per capita fell back to 2.51. The non-coastal regions’ average growth rate ofGDP per capita in 2007 is 20%. Compared to 19% in coastal provinces, it is one percentagepoint higher. Therefore, another two crucial questions are raised here. First, whether theuneven development across the regions in China is correlated to the uneven growth of TFP?Second, during the period after 1993, whether some non-coastal regions were catching up andwhere exactly they were? With estimated TFP levels and growth rates, we will analyze thedistribution of TFP levels and growth among the cities to see whether TFP gap existed andhow it changed during 1996 to 2007 among the cities.

In fact, we find out there are large differences in both TFP levels and TFP growth ratesamong cities. In order to explain these differences, this paper tries to find out determinantfactors of regional TFP by using panel (for TFP level) and cross-sectional analysis (for TFPgrowth). These determinants suggest areas for policymaking. For example, investment in

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human capital would enhance the absorptive capacity, which in turn, facilitates technologytransfer. Improvements in the transportation could make production materials and finalgoods transport faster to the destination. Moreover, allowing foreign capital could bring bet-ter management and production technology to the local factory.

The paper is structured as follows. The second section provides a review of previous studieson TFP determinants. Then, the third section illustrates the methods for estimation. Sec-tion 4 describes the datasets adopted in this study. In the fifth section, we will show thevarious estimation results based on different assumptions, and we will compare them to theresults from previous studies. The determinant factors are tested in section 6. Finally, someconcluding remarks are provided in the last section.

2 Literature Review

In the neoclassical framework, two main sources contribute to economic growth: factor accu-mulation and total factor productivity (TFP) growth. Concerning China’s economic growth,a strand of literature (such as, Kim and Lau (1994)) highlights the effect of capital and laborinputs. They illustrate that China’s high growth rate is mainly caused by rapid capital accu-mulation and vast labor-force participation. Meanwhile, another strand of emerging literature(e.g. Fischer (1993)) highlights the role of productivity in determining China’s development.According to Fischer (1993)’s estimation, China’s TFP growth rates during 1961-1988 werethe highest in East Asia. Regarding China’s regional disparity in economic development,Fleisher and Chen (1996) found inferior factor productivity was the main reason for the lag-ging performance in China’s non-coastal provinces.

The main driver of China’s regional disparity at the city-prefecture level still remains inquestion. If the slow economic growth in some prefecture-cities is caused by low produc-tivity, heavy investment may not be the optimal solution. In this section, studies on TFPdeterminants will be reviewed and specific applications to China will be made. We groupdeterminants under consideration into three different categories: 1) Creation, transmissionand absorption of knowledge; 2) Factor supply and efficient allocation; and 3) Institutionsand invariants. Although some determinants fit in more than one group, we will only discusseach determinant once.

2.1 Creation, transmission and absorption of knowledge

Knowledge has a direct effect on TFP. Both new discoveries and the understanding andimitation of previous discoveries have positive effects on TFP. The former suggests the linkagebetween R&D and knowledge generation and its impact on TFP (i.e Abdih and Joutz (2005),Furman and Hayes (2004), and Chanda and Dalgaard (2003)). The latter is more related tolocal absorptive capacities and efficient technology diffusions.

2.1.1 Urbanization

According to Isaksson (2007), agglomeration leads to changes in the stock of knowledge.As argued by Krugman (1991), there are externalities via agglomeration. Among them,those positive externalities include forward and backward linkages and knowledge spillovers.

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Through agglomeration in urban areas, cities with productive variety will emerge, which willexpedite knowledge spillover via horizontal and vertical linkages. Glaeser and Shleifer (1992)find a lack of productive variety has a strong negative effect on growth. At the same time,urban economies, which are spurred by productive variety, promote economic growth. Theirfindings are further confirmed by a strand of literature so called urban growth literature, suchas Combes (2000) for France and Cainelli and Lupi (1999) for Italy.

In order to test whether the level of population agglomeration in an urban area has a positiveor a negative effect on TFP growth, we use the ratio of urban population over prefecture pop-ulation as an index. If we find a robust positive effect, it implies that the positive externalitiesbrought by agglomeration are dominant in promoting economic growth at the prefecture-citylevel through TFP growth. On the contrary, a robust negative effect from urbanization levelson TFP growth indicates that the urbanization level in China has reached a point wherethe negative externalities caused by agglomeration are slowing down TFP growth in China’sprefecture-cities.

2.1.2 FDI

Foreign direct investment (FDI) is commonly included to explain TFP (i.e.Granr and Isaks-son (2002), Haskel and Slaughter (2002), and Keller (1998)), since it embodies the latesttechnology in production and management. As Griffith and Simpson (2003) suggest, FDI canaffect either the level of TFP or its growth via two mechanisms: 1) the introduction of foreigntechnologies, and 2) an increase competition in the domestic market. Thus, FDI could be asource of technology diffusion between the world and China. In recent years, foreign-fundedenterprises (FFE) in China have shown more interest in the domestic market (Graham andWada, 2001). Based on Ahn (2001)’s arguement that in reality it is not innovation inputper se that counts for productivity but the actual use of innovation output. The presence ofFFEs which produce more innovation-embodied products will enhance the local productivity.

While many studies find a positive effect of FDI on China’s regional development, Lemoine(2000) argues that foreign direct enterprises in China generate little in terms of technologytransfer and/or integrating domestic Chinese enterprises into global production structures.Moreover, Aitken and Harrison (1999) show a negative effect of FDI on TFP in Venezuela,since foreign-owned firms attract most of the skilled workers and deprive domestic firms oftheir service. Both Hanson (2001) and Gorg and Greenaway (2002) support their argument.

Based on the previous literature, we expect FFEs could impose a positive effect on the TFPgrowth. Due to China’s specific situation, there is another type of enterprise funded byHongkong or Taiwan, which is superior to Domestic-funded enterprises but inferior to FFEsin terms of technologies and management capabilities. Thus, we expect them to have a smallerpositive effect than FFEs.

2.2 Factor supply and efficient allocation

In this section, we take a selective view and focus on human capital (education) and infrastruc-ture availability (roads and financial institutions). Concerning efficient resource allocation,we discuss the role of sector allocation in achieving TFP growth.

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2.2.1 Education

Concerning education, a distinction between higher education and basic education would benecessary, since the former matters more for carrying out technological innovation (Romer(1990)) while the latter is more relevant to the adoption of foreign technology. However,according to Miller and Upadhyay (2000) and Miller and Upadhyay (2002), education levelsare negatively associated with TFP growth at low-income level of countries; while the effectsturn to be positive concerning to the countries with middle or high income levels. In addition,the positive effect of employee training is shown by Bartel (1992) and Barrett and O’Connell(1999). Although higher education and basic education foster TFP via different channels, wehypothesize that both secondary and higher education have a positive effect on local TFPlevels and growth.

2.2.2 Infrastructure

The role of infrastructure on TFP is to increase resources and enhance the productivity ofprivate capital. Although investment in infrastructure is also counted as public capital for-mation, infrastructure appears to have a direct effect on TFP (Isaksson (2007)). Based on astudy of 28 developing countries for the period 1981 to 1991, Dessus and Herrera(2000) findinvestment in infrastructure is associated with long-term GDP growth. Although Fleisherand Chen (1997) find that investment in infrastructure has a moderate rate of return in TFPgrowth, we cannot rule out the possibility that it may have a positive effect on TFP growth byattracting foreign direct investment and retaining university graduates. However, as Fernald(1999) points out that investment in infrastructure may depend on the level of income andis endogenous in explaining TFP. In terms of causality, Fernald (1999) is able to show thatroad network growth causes productivity growth, but not the other way around.

There is a line of literature stressing the role of financial institutions in TFP growth. Asargued by Isaksson (2007), in developing countries where sophisticated financial systems areabsent, firms have to rely on retained earnings of investment on technology upgrade or foregothe opportunity. By including measures of financial repression and development in estimatinggrowth equations, Roubini and Sala-Martin (1991) confirms the relationship between financialdevelopment and growth.

For hypotheses falling in this category, we consider the following three: 1) more access tofinancial institutions leads to higher TFP levels and growth rates (the value of outstandingloans can be used as a measure of financial access); 2) availability of transportation system(i.e. railway and paved roads) has a positive impact on TFP; 3) availability of communicationsystems (i.e.telephone lines) boosts TFP.

2.2.3 Sectoral structure

Chen and Dahlman (2003) show that the structure of an economy, especially the agriculturaland nonagricultural composition, could greatly influences TFP. Bloom and Malaney (1999)find a part of income growth in East Asia is due to economic structural change, from agri-culture to manufacturing. Another study in this line, Dessus and Herrera (2000), suggeststhat countries specializing in high-tech industries will experience faster TFP growth and leavecountries specializing in low-tech industries behind.

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By using ratios of different sectors’ GDP over total GDP, we would like to find out howthe composition of production activities in Chinese prefecture-cities affect their TFP growth.We expect productivity in the primary sector (agriculture) would be lower than productivityin the other sectors. Thus, a larger agriculture sector would be negatively associated withTFP; while a larger secondary or teriay sector would be positively associated with TFP.

2.2.4 Resource allocation

Research on the causes of large TFP differences normally focuses on differences in technologywithin representative firms ( e.g. Howitt (2000)). A recent study by Restuccia and Rogerson(2008) takes a different approach and tests whether misallocation of resources across firms canhave significant effects on aggregate TFP. Assuming two firms have identical technologies, onefirm (domestic-funded) with political connections can gain access to subsidized credit whilethe other firm has to suffer from high financial costs. When each firm’s marginal productof capital is equal to its interest rate, the firm with political connections would have lowermarginal product than the firm without political connections. In this case of capital misallo-cation, TFP will rise if capital flows more to firms without political connections. Hsieh andKlenow (2007) provide quantitative evidence that resource misallocation has a detrimentalimpact on aggregate TFP. They find that by moving to the efficiency level of resource allo-cation in the United States, TFP in China could increase by 30-40 percent.

Based on the previous literature, we expect the dominance of Domestic-funded enterprises ina region may lead to favorable policies and inefficient resource allocation. Thus, there will bea negative impact on TFP. In combination with the previous section on FDI, we conjecturethat the ownership structure of the economy is associated with TFP.

2.3 Institutions and invariants

In this section, we discuss the role of geopolitical forces in determining TFP. First, we studythe policy instruments local governments can utilize in fostering TFP. Then, determinantsthat are connected with some deeper determinants (i.e. geography), which are invariant overtime, will be discussed. The latter group of determinants can affect TFP via geography,culture, institutions and policies.

2.3.1 Policies

As Chen and Xu (2008), Bao and Woo (2002), and Ho and Li (2010) suggest, there are manypolicies that can affect China’s urban economic growth and regional disparity. In case ofChina, two policies have attracted much academic attention: one is Special Economic Zones(SEZ), four of which were established around 1980; and the other is Open Coastal Cities, 14of which were chosen around 1984. Both policies aim to attract foreign direct investmentsand gain access to international markets. As proven by a series of studies (i.e. Hao (1999),Bosworth and Chen (1995), and Schor (2004)), integration into the international market isstrongly and positively associated with TFP growth. Thus, we expect cities related to thetwo policies mentioned above have high TFP levels and growth.

Meanwhile, we also consider the fiscal policy of the local government (i.e. fiscal autonomy and

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revenue) and expect cities with higher government expenditures to have higher TFP levels andgrowth. This policy perspective is associated with the effect of investment in infrastructureon TFP.

2.3.2 Invariant effects

Among the existing literature about China’s growth, convergence clubs are often found to beimportant in the process. Some of these studies focus on the Coastal-Noncoastal disparity(Fleisher and Chen (1997), Hall and Jones (2008), and Ying (2003)) while others illustrateCoast-Middle-West geo-economic zones (Brun and Renard (2002), Yao and Zhang (2001), andTian and Chen (2010)). The regional effects can be analyzed via two layers: geo-economiceffects and policy effects.

At the prefecture-city level, there are more than 2000 units. Those prefecture-cities differin culture, geographic composition, and local dialects. These underlying elements are fixedover time and connected with their geographic locations. Since they can influence regionalTFP, we divide the whole nation into 6 regions and hypothesize the existence of geo-economiceffects. Meanwhile, the regional development strategies decided by Chinese central govern-ment tends to be different among these 6 big regions.

Moreover, using Chinese city-level data from 1990 to 2006, Chen and Xu (2008) apply theCore-Periphery model and find a border effect of administrative boundaries among Chineseprovinces. The existence of the border effect limits inter-city agglomeration and preventssome big cities’ growth by influencing their surrounding areas. Thus, provincial dummies areused to test the border effects, since governments at the provincial level have a certain levelof autonomy in regional fiscal policies and budgets related to infrastructure investments.

3 Methodology

3.1 Estimate TFP growth rate

Consider a set of cities, i = 1, 2, . . . , N , over a number of years, t = 1, 2, . . . , T . Output in eachcity, Yit, is produced by physical capital, Kit and labour force, Lit, through a Cobb-Douglasproduction function

Yit = AitKαit(Lit)

1−α, 0 < α < 1 (1)

where Ait represents technology and endowment while capital stock is given by

Kit = Ii,t−1 + (1− δ)Ki,t−1, (2)

where δ is the rate of depreciation. Investment, Iit = sitYit, and the saving rate, sit, is timevarying in each city.

The stochastic process determined technology and employment are

logAit = ai0 + git+ uait, (3)

uait = ρaiuai,t−1 + εait, |ρai ≤ 1| (4)

logLit = li0 + nit+ ubit (5)

ubit = ρbiubi,t−1 + εbit, |ρbi ≤ 1| (6)

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where the initial TFP is defined as ai0 and its growth rate is defined as gi; the initial laborforce is defined as li0 and its growth rate is defined as ni

We denote the logarithm of per-capita output, log(Yt/Lt) by xt. After the simplification(see the Appendix B), we could obtian the esimtaion models as follows:

xit − xt = (ci − c) +α

1− α(lsi,t−1 − lst−1) + (gi − g)t+ uit − ut (7)

uit − ut = λ(ui,t−1 − ¯ut−1) + vit − vt (8)

where ln(s) are denoted by ls for short and ci is a constant term (see the definition in AppendixB). The regression yields estimates of ci− c and gi− g, etc. To obtain estimates of ci, gi, andµi we also need to estimate the aggregate equations

xt = c+α

1− αlst−1 + gt+ ut (9)

ut = λut−1 + vt (10)

Estimates of ci and gi can now be recovered from those of ci − c and gi − g in equation (7).

3.2 Estimate TFP Level

We estimate the TFP growth rate with 6 approaches of employment.

To estimate Ai0, we made several assumptions:(i) The α is the average value from year 1996 to 2007 (The Conference Board, Total

Economy Database, Labor Share). That is 0.5319.(ii) The depreciation rate δ is the depreciation rate of China, that is 0.09.(iii) The curvature rate h is assumed to be zero as in the traditional model.(iv) We use average population growth rate from year 1996 to 2007 as the labor growth

rate.

ci = αi0 −α

1− αlog(ni + gi + δ − hi)−

αhi1− λi

(11)

We use the formula:αi0 = ci +

α

1− αlog(ni + gi + δ) (12)

andAi0 = eαi0 . (13)

4 Data

Data used in this study come from two statistical year books. Both are published by ChinaStatistics Press. The first one is the China City Statistical Yearbook(1997-2008), from whichwe obtain the data at the city level. The second one is the China Statistical Yearbook(1997-2008), from which we obtain the ratios of 15 to 64-year-old people to the total population.

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The source of data is from the National Bureau of Statistics of P. R. China. We use the dataat the prefecture city level.

Real GDP

We adjust the norminal GDP from City Year Books by the CPI. City level CPI is avail-able for 36 cities. Then the provincial level CPIs are applied to the remaining cities.

Number of Employees

The number of employees cannot be obtained directly from the datasets available. In or-der to estimate this variable, we propose six approaches. Later, we will refer to them as“Approach 1” to “Approach 6” for short.

• Approach 1: National ratio

The data we obtain from City Yearbook is “total population at year-end (in 10,000persons)”. First, we adjust the total population to the the total employment by

Total Number of Employment = Total Population× Number of Employees of China

Total population of China.

• Approach 2: City employment data

Use the employment data in China City Yearbook directly.

• Approach 3: Province employment ratio approach

Similar to the national ratio approach, we have

Total Number of Employment = Total Population× Number of Employees of Province

Total population of Province.

• Approach 4: Province average urban employment

We have data of urban population for each province from 2005 to 2007, and employmentfor each province from 1996 to 2007. For year 2005 to 2007 the ratios of employmentcould be obtained by

r1 =Employment Province Urban/Population Province Urban

Employment Province/Population Province. (14)

Taking average of the three years we have r1. Then we obtain the total employment foreach city by

Total Number of Employment = Total Population×r1×Number of Employees of Province

Total population of Province.

• Approach 5: City urbanization adjustment (-0.31)

Since there’s no urban population for each province from 1996 to 2004, we have to usethe (urban/ total GDP) for each province as the indicator of urbanization. It is definedby

r2 = logEmployment Province

Population Province(15)

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and

r3 = logGDP Primary Sector Province

Total GDP Province. (16)

We run a regression using the fixed effect model

r2t = α1r2,t−1 + α2r3t + logGDPt−1 +Di + εit (17)

The coefficient in front of r3 indicates percentage changes in urbanization level will leadto α2 percentage change in employment. The estimated coefficient is -0.31. Thus, theemployment of each city is obtained by

Total Number of Employment = Employment Approach3 (18)

− 0.31× (GDP Primary Sector City

Total GDP City− r3)/r3.

• Approach 6: City urbanization adjustment (0.208)

It is basically the same as Approach 5, but the logGDPt−1 is dropped out of the regres-sion. Consequently, the sign of the coefficient changes. The model to estimate coefficientis

r2t = α1r2,t−1 + α2r3t +Di + εit. (19)

The estimated coefficient is 0.208, and the number of employees are obtained by

Total Number of Employment = Employment Approach3 (20)

+ 0.208× (GDP Primary Sector City

Total GDP City− r3)/r3.

Investment

In the City Year Book we have the data “Total Investment in Fixed Assets (in 10,000 yuan)”.We need to adjust this value to the “Newly increased Fixed Assets (10,000 yuan)”, becausethis value tells us how much fixed capital is formed in a given year that can be used in pro-duction in the next year.

• Year 2004-2007

We have the “Rate of Fixed Assets Put into Use” for each province reported by ChinaStatistical Yearbook 2005-2008. This rate is,

Newly increased F ixed Assets

Total Investment in F ixed Assets. (21)

• Year 1996-2003

There are four categories of Total Investment in Fixed Assets: Investment in CapitalConstruction, Investment in Innovation, Investment in Real Estate, and other Invest-ment. We have the Newly Increased Fixed Assets of the first two categories of invest-ment from 1996 to 2003 for each province, and the total Newly Increased Fixed Assets

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of China.

First, we get the ratio of

Newly Increased F ixed Assets in first two categories of China

Newly Increased F ixed Assets of China(22)

Then, divide the sum of Newly increased Fixed Assets in the two categories by thatratio to get the Newly increased Fixed Assets for each province.

Finally, using the same method for years 2004-2007, we get the Rate of Fixed As-sets Put into Use for each province. With the total investment in fixed assets of eachcity, we get the newly increased fixed assets for each city.

5 Estimation Results of TFP growth and TFP level

We estimate by applying the model in Section 3. The estimated average growth rate of TFP,g = .021 with a p-value 0.000. This result is quite close to those obtained by Lee and Smith(1997). Their estimated average growth rate for 102 countries is 0.01768, for an intermediategroup of 61 countries it is 0.02230, and for 22 OECD countries it is 0.02760. A summary ofChina’s TFP studies is presented in Table 3.

The estimated TFP growth rates and levels by Approaches 3 and 4 for some cities are pre-sented in Table 1 and 2. The estimation results of the other approaches are presented in theAppendix A.

The results are a bit weaker than those obtained by Fleisher and Chen (1997) at provincelevel. For example, they have TFP growth rates for Beijing, Tianjin, Hebei province, andGuangdong province as 0.05, 0.039, 0.067, and 0.095, respectively. Their estimation period isfrom 1978 to 1993. It may be due to different estimation methods and/or different estimationperiods. However, if we take a look at the other studies during the recent years, our resultsare closer and more reasonable.

Before we start explaining the spatial variation of TFP in China, we would like to com-pare the results generated from the six employment adjustment methods stated previously.First, we found TFP growth rates generated using city employment data directly have thelowest correlations with the results generated by other methods (in comparison with othermethods). Meanwhile, using the provincial employment ratio and provincial employment leveladjusted by the urban employment ratio both produce growth rates that are highly consistentwith results obtained using other methods.

Next, we consider the TFP levels at the beginning and at the end of our sample period. Wetest whether they are largely different from their means. After going through both parametric(t-test) and nonparametric (sign-test) tests, using city employment data directly appears todeliver much better results than other methods. Among all adjustment methods, using theprovincial employment ratio is the only one that does not deliver upper/lower-biased results.Moreover, the provincial employment ratio does not cause too many extreme values (SeeTable 4). Thus, we suggest to use the provincial employment ratio.

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city name city code growth rate TFP level 96 TFP level 07

Beijing 110000 0.012 155.32 176.75Tianjin 120000 0.051 154.45 271.30

Shijiazhuang 130100 0.015 151.06 177.66Taiyuan 140100 0.016 164.40 196.77Hohhot 150100 0.062 129.91 257.41

Shenyang 210100 0.034 174.39 253.44Dalian 210200 0.026 184.83 245.71

Changchun 220100 0.028 157.09 213.07Harbin 230100 0.033 141.48 203.61

Shanghai 310000 0.007 225.73 244.26Nanjing 320100 0.035 184.15 270.25

Hangzhou 330100 0.007 181.86 196.94Ningbo 330200 0.019 169.37 207.68Hefei 340100 0.058 115.17 217.86

Fuzhou 350100 0.007 182.52 197.96Xiamen 350200 0.018 257.99 313.10

Nanchang 360100 0.028 150.43 204.14Jinan 370100 0.002 184.95 189.29

Qingdao 370200 0.032 162.69 230.43Zhengzhou 410100 0.027 140.53 189.92

Wuhan 420100 0.010 206.84 230.28Guangzhou 440100 0.033 218.76 314.82Shenzhen 440300 0.031 448.17 629.88Nanning 450100 -0.009 139.03 125.69Haikou 460100 -0.034 233.63 160.76

Chongqing 500000 0.026 95.65 126.64Chengdu 510100 0.027 144.16 193.23Guiyang 520100 0.021 126.57 159.41

Xi’an 610100 0.006 134.51 143.85Xining 630100 0.009 118.88 131.52

Urumichi 650100 0.021 169.48 212.90AVE 0.021 174.32 222.15

Table 1: Province employment ratio approach (1996-2007)

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Beijing 110000 0.012 164.72 187.08Tianjin 120000 0.051 174.41 306.03


Shenyang 210100 0.034 195.72 284.14Dalian 210200 0.026 207.26 274.97




Fuzhou 350100 0.007 210.24 227.17Xiamen 350200 0.017 297.15 359.88

Nanchang 360100 0.028 167.24 226.61Jinan 370100 0.002 225.49 229.95




Xi’an 610100 0.006 151.24 161.31Xining 630100 0.009 116.06 128.08

Urumichi 650100 0.021 141.53 177.89AVE 0.021 197.64 252.06

Table 2: Province average urban employment approach (1999-2007)

14

Table 3: Summary of China TFP Studies

Methods obs < 0 obs > .10

growth rate1 5 0growth rate2 1 45growth rate3 59 1growth rate4 60 1growth rate5 33 5growth rate6 87 1

Table 4: Number of extreme values in estimated growth rates

15

By using the model in Section 3.1, we could obtained λ, gi, and ci. Then, we could esti-mate the initial level of TFP ai0 using equation (12), with additional assumptions about thepopulation growth rate ni and the depreciation rate δ. In general, if we would like to obtainthe level of TFP, some of the assumptions could be very strong.

The distribution of TFP growth rates and levels estimated by Approach 3 are presentedin Figure 1 to Figure 3. We classify the cities into five groups according to the percentiles oftheir TFP growth rates and levels. The higher the value the warmer color will be. That is,dark green is the first percentile, and followed by light green, yellow, organe and red as thesecond, third, fourth and fifth percentile group.

Figure 1: Distribution of China TFP Growth Rate

The east coast China had a higher TFP growth rate compared to other regions. Along thecoastline, the northen part of Yang Zi River grew faster than the southen part. In Guangdongprovince, Peal River Delta enjoyed high TFP growth as well. However, this only happens ina few cities such as Guangzhou, Shenzhen and Zhuhai. In North China, there were lots ofred spots, indicating high TFP growth rate in that region.

If we look at the TFP levels in 1996, we would find a group of red spots along the coastof China. It is similar to the TFP levels in 2007. However, a few cities in North China joinedthe fifth percentile group in 2007 with their high TFP growth rates. Besides, we notice thatHainan Province had a high TFP level in both 1996 and 2007, but it had a very low TFPgrowth rate.

16

Figure 2: Distribution of China TFP Level in 1996

Figure 3: Distribution of China TFP Level in 2007

17

6 Determinants of TFP growth rates and levels in China

In this section, we are going to explore the determinants of TFP growth rates and lev-els in China at the prefecture-city level. As metioned in the section of literature review,we have the following categories of hypotheses (with variables in the brackets): 1)Sectoralstructure (Primary Sector, Secondary Sector and Tertiary Sector); 2)Ownership structure(Domestic-Funded Enterprises, HTM-Funded Enterprises, and Foreign-Funded Enterprises);3)Urbanization (Urban); 4)Education (HighEdu std, HighEdt inst, SecEdu std, SecEdu inst);5)Infrastructure (Loan pc, Railway, Paved roads, Telephone); 6)Policies (SEZ 80, SEZ 84,Gov exp); and 7)Regional effects (Region i, Prov i). Hypotheses concerning FDI and resourceallocation is grouped into one heading: ownership structure. We further include Populationand RGDPpc to take the scale effect into consideration. See Table A5 in the Appendix A fordetailed description of the variables.

6.1 Determinants of TFP growth rates

To identify the determinants of TFP growth, we estimate the annual TFP growth for 1996-2007 using the provincial employment ratios. For explanatory variables, their values are takenfrom the initial year, 1996, if those are available. For those that are unavailable, the valuesfrom the first year provided by China City Statistical Yearbooks is used.

As stated above, we have seven groups of hypotheses to test. Thus, we first regress eachvariable in those groups one by one upon the TFP growth rate (Gi). Variables that turn outto be significant in each (sub)category are reported in Table 5 from Column(1) to Column(6).Then, we redo the regression with variables that are most significant in each subcategoryand the scale effects, and then take the general-to-specific approach. Model with remainingsignificant variables are shown in Column(7). We further redo the model in Column(8) withregional dummies and put remaining significant variables in Column(9). In the last Column,we report the model with provincial dummies.

The OLS regression results fall largely in line with our hypotheses. Cities with economiesmore dependent on the primary sector do have a lower TFP growth rate. Meanwhile, a size-able secondary sector bring a higher TFP growth rate to the city. However, the size of thetertiary sector do not show any impact on cities’ TFP growth rates. The reason might bethat the tertiary sector has a negligible size in the base year of our sample period.

When concerning ownership structure, the results are a bit counter-intuitive. Dominanceof Domestic-funded enterprises leads to a higher TFP growth rate while enterprises fundedby HK, Taiwan, or Macau drag cities’ TFP growth rate downwards. Moreover, FFEs do notinfluence TFP growth rate significantly. These foundings seem to question the hypothesisthat non-domestic-funded enterprises bring advanced technologies to China and boost tech-nology diffusion. However, one possible interpretation is that the positive coefficient beforeDomestic-funded enterprises shows the technology diffusion process. Although Domestic-funded enterprises were using outdated technologies in 1996, they were adopting more ad-vanced technologies during our sample period. So far, we cannot draw any clear conclusionabout the relationship between ownership structure and TFP. To fully test this hypothesis,we have to consider the regression results of TFP levels.

18

VA

RIA

BL

ES

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Pri

mary

Sec

tor

-0.0

0019

1**

-2.0

81S

econ

dar

yS

ecto

r0.

0002

68**

0.000

264*

*0.

000

344*

**0.0

002

11**

2.25

02.

439

3.158

2.078

Dom

esti

c-F

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ded

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ses

0.01

35**

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0**

2.10

32.2

97

HT

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ded

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ses

-0.0

285*

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.060

Gov

exp

0.004

90**

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209*

**0.

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0.024

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2.3

20

6.22

15.9

23

10.

32

SE

Z80

-0.0

252*

*-0

.0285

***

-0.0

252*

**-0

.023

4***

-2.0

28

-2.9

74

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08

-2.9

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rban

0.0

064

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0.0

109

***

0.0

101

***

2.254

4.171

3.841

RG

DP

pc

-0.0

184*

**-0

.020

6***

-0.0

185

***

-5.0

05-6

.217

-6.3

32

Pop

ula

tion

0.0

027

5**

2.070

Con

stant

0.0

223***

0.00

590

0.00

637

0.02

01**

*-0

.0148

0.018

8***

-0.0

0740

0.0

424*

*-0

.0461

**8.

809

1.11

71.

102

17.3

5-0

.985

11.8

9-0

.280

2.331

-2.3

05

Ob

serv

atio

ns

233

233

235

235

282

282

233

233

233

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are

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019

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012

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0.313

0.389

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are

0.0

151

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0.04

360.

008

660.

012

30.

292

0.362

0.591

Tab

le5:

Est

imat

ion

Res

ult

sfo

rT

FP

Gro

wth

Det

erm

inants

Note

:R

ob

ust

t-st

ati

stic

sare

rep

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din

seco

nd

row

s.“*

”,“*

*”,

“***

”den

ote

sign

ifica

nt

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the

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ecti

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nal

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ies

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Col

um

n(8

)w

hil

ep

rovin

cial

du

mm

ies

are

incl

ud

edin

Colu

mn

(9).

Bot

har

eom

itte

dfo

rb

revit

y.

19

Urbanization level and the level of higher eduction are found to be insignificant, while localgovernments’ fiscal expenditure is positively related with the city’s TFP growth rate. Thisfinding suggests the government’s role in determining the city’s development path via promot-ing TFP. However, no indicators for infrastructure are found to be significant. Neither accessto a railway system nor bank loans matter individually for TFP growth. Interestingly, we findcities that have SEZs in 1980s to have a lower TFP growth rate. It might suggest that thesecities had their TFP spurs in the 1980s while 1996-2007 is a period for other cities to catch up.

When we reached the model in Column(7), we found Primary Sector, Domestic-Funded En-terprises, SEZ 80, and Gov exp have their previous signs and remain significant when otherexplanatory variables are included. Furthermore, some scale effects, Population and RGDPpc,turn out to be significant. The negative sign for RGDPpc suggests the convergence effect thatcities with lower economic development levels catch up via higher TFP growth rates. Mean-while, the positive coefficient before Population indicates the agglomeration of people speedsup TFP growth, possibly via needs for diversity of service and technology diffusion. More-over, the hypothesis that urbanization level facilitates TFP growth is supported here. In theperiod 1996-2007, centripetal forces that can trigger pure external economies and a variety ofmarket scale effects are apparently in action.

After regional effects are included in Column(8), Domestic-Funded Enterprises and Popu-lation become insignificant, which suggest the distribution of Domestic-Funded Enterprisesand population follows a certain regional pattern. Moreover, F-test statistics show that thoseregional dummies are jointly significant at the level of one percent. Although the coefficientsfor those dummies are not reported due to brevity reasons, they indicate the TFP growthrate has the following rank among regions:

Northwest < SouthCentral < North < Northeast < Southwest < East

In Column(9), all provincial dummies are included and are jointly significant at the 1 per-cent level. Thus, there is indeed some border-effect in determining TFP growth rate at theprefecture-city level. Moreover, results do not change much from the model in Column(8),which shows the robustness of our results.

6.2 Determinants of TFP levels

When concerning the determinants of TFP levels, we are now dealing with a panel settinginstead of a cross-sectional setting as we have done in the previous section. The estimationequation is as follows:

TFPLevelit = α+ βXit−1 + εit

where X is a matrix representing all the explanatory variables described above, and β is thecoefficient vector. In order to avoid the endogeneity problem that could lead to inefficientestimation results, all explanatory variables are used in their lagged values. Moreover, aFixed-Effect (FE) estimator is used since the Hausman test resoundingly rejects that most ofour models can be adequately estimated with a Random-Effect (RE) estimator.

As we have done in the previous section, we start by adding variables in each category one by

20

one into the regression and report those ones that are at least significant at 10 percent levelfrom Column(1) to Column(14) in Table 6.

Constant (1) (2) (3) (4) (5) (6) (7)

Primary Sector -1.427***-9.456

Secondary Sector 1.236***9.388

Tertiary Sector 0.528***2.914

Domestic-Funded Enterprises -60.43***-4.697

Foreign-Funded Enterprises 80.50***5.104

HighEdu std 0.101***7.503

HighEdu inst 13.78***7.572

SecEdu std

Paved roads

Loan pc

SEZ 80

SEZ 84

RGDPpc

Population

Constant 167.3*** 83.55*** 120.9*** 194.3*** 136.6*** 132.6*** 126.4***56.85 14.02 18.92 17.85 105.5 137.1 64.15

Observations 2,855 2,854 2,854 2,021 2,021 2,695 2,371R-squared 0.195 0.129 0.017 0.065 0.099 0.327 0.180

Number of id 281 281 281 281 281 281 274Adj. R-Square 0.194 0.128 0.0168 0.0647 0.0986 0.326 0.180

Table 6: Estimation Results for TFP Growth Determinants

Our hypotheses regarding the sectoral structure are supported by the TFP level regressionmodels. Not only a negative coefficient is found for Primary Sector, but also positive coeffi-cients are found for both Secondary Sector and Tertiary Sector. More precisely, the SecondarySector has a positive impact on TFP levels two times larger than the Tertiary Sector does.

When concerning ownership structure, the results meet all our hypotheses in this category.

21

Constant (8) (9) (10) (11) (12) (13) (14)

Primary Sector

Secondary Sector

Tertiary Sector

Domestic-Funded Enterprises

Foreign-Funded Enterprises

HighEdu std

HighEdu inst

SecEdu std 314.4***3.374

Paved roads 9.526***6.672

Loan pc 22.70***8.633

SEZ 80 132.9**1.999

SEZ 84 65.60***3.113

RGDPpc 30.41***17.23

Population 11.53**2.513

Constant 119.2*** 61.13*** -58.57** 133.7*** 131.4*** -135.3*** 73.08***20.34 5.202 -2.477 50.23 49.39 -8.508 2.762

Observations 2,897 2,854 1,124 3,091 3,091 2,909 2,857R-squared 0.070 0.133 0.282 0.1111 0.1024 0.566 0.014

Number of id 281 281 281 281 281 281 281Adj. R-Square 0.0696 0.133 0.282 . . 0.566 0.0137

Table 6 (Continued): Estimation Results for TFP Growth Determinants

Note: Robust t-statistics are reported in second rows.“*”, “**”, “***”denote significant lev-els at the 10%, 5%, 1% levels, respectively. Fixed estimator is used in all models exceptColumn(11) and Column(12), where RE estimator is used. For RE estimator, R-sq overall isreported.

22

Domestic-funded enterprises now exhibit a strong negative effect on TFP both statisticallyand economically. Although the presence of HTM-funded enterprises show no impact on TFPlevels, FFEs are certainly associated with higher TFP levels. Thus, we partially verified thatthe absence of FFEs’ impact on TFP growth is due to the negligible size of FFEs in the initialyear. Based on the results here and those above, we conclude that non-domestic-funded en-terprises do bring advanced technology and boost the local TFP through technology diffusionvia domestic firms’ adaptation.

Although the urbanization level shows no impact on TFP levels, education at both the higherand secondary level exhibit positive correlations with TFP levels. Student enrollment in thesecondary school is much more significant economically than the enrollment in the higher edu-cation. Meanwhile, the estimation results suggest a positive relationship between the numberof higher education institutions and TFP levels; while such relationship between secondaryschools and TFP levels does not exist.

For the policy indicators, government expenditure does not matter for TFP levels; whileSEZ 80 and SEZ 84 dummies, which can only be estimated with the RE estimator, are asso-ciated with higher TFP levels. It shows that those cities entitled to have SEZs around 1980have much higher TFP levels than cities without them, even much higher than cities thatstarted to have SEZs around 1984.

Although access to a railway system is only significant at the 15 percent level, the availabilityof paved roads is assoicated with higher TFP levels. Despite the positive effect brought bythe transportation system, the number of telephones per capite is irrelevant. Moreover, citieswith more access to the financial system, indicated by outstanding loans, enjoy higher TFPlevels. It is highly possible that more investment in some lagging cities will boost economicgrowth via both capital accumulation and higher TFP. With the remaining two variables,Population and RGDPpc, cities with higher population density and economic developmentlevel are superior in terms of TFP levels.

In the second step, we pick the most significant variable from each (sub)category and addthem together as explanatory variables. When variables from the same (sub)category areequally significant, the one used in finding the determinants for TFP growth rates is chosen.After following a general-to-specific approach, we reached the model in Column(1) of Table7, where only variables that are significant at 10 percent level (or lower than 10 percent level)remain. As the results show, cities with higher TFP levels have the following characteristics:more student enrollment in higher education, higher government expenditure, more popula-tion density and higher economic development.

Since SEZ dummies cannot be estimated with an FE estimator, we redo the model in Col-umn(1) with the RE estimator and show the results with only significant variables in Col-umn(2). With the RE estimator, SEZ dummies and population density do not turn out tobe significant, while a substantial group of domestic-funded enterprises tend to drag the TFPlevels down. The results of HighEdu std and RGDPpc do not differ much from those in Col-umn(1). Moreover, we find financial access, paved roads and urbanization are associated withhigher TFP levels in this setting.

23

VARIABLES (1):FE (2):RE (3):RE (4):RE

RGDPpc 18.71*** 19.78*** 23.02*** 19.48***8.451 6.735 9.040 7.065

Gov exp 0.929* 2.567*** 2.356*** 2.758***1.818 4.195 4.106 4.131

HighEdu std 0.0258*** 0.0145* 0.0185** 0.0132*2.791 1.933 2.313 1.676

Urbanization 55.28*** 59.63*** 53.45***4.265 4.706 4.261

Domestic-Funded Enterprises -13.90*** -14.52*** -13.26**-2.600 -2.691 -2.431

Paved roads 3.021*** 3.169*** 3.001**2.670 2.836 2.492

Loan pc 6.747* 8.317*1.744 1.936

Population 13.42**2.270

Constant -114.3*** -149.9*** -123.2*** -66.16-2.635 -4.717 -4.652 -0.788

Observations 1,089 1,001 1,001 1,001R-squared 0.486 0.7521 0.7464 0.7803

Number of id 281 281 281 281Adj. R-Square 0.484 . . .

Table 7: Estimation Results for TFP Growth Determinants

Note: Robust t-statistics are reported in second rows.“*”, “**”, “***”denote significant levelsat the 10%, 5%, 1% levels, respectively. For RE estimator (Col(2)-(4), R-sq overall is reported.

24

To estimate the regional effects, the model in Column(3) is repeated with the RE estima-tor and the regional fixed effects. Despite the fact that access to the financial system is nolonger relevant, the results do not change much from those in Column(2). Additionally, theregional dummies are jointly significant at 5 percent level. More important, the TFP leveldistribution exhibits a following regional pattern:

Northwest < Southwest < SouthCentral < North < East < Northeast

Finally, provincial fixed effects are added to Column(3), which is further estimated withthe RE estimator. The remaining significant variables are the same as those ones in Col-umn(4) and do not differ much in coefficients. Moreover, provincial fixed effects are jointlysignificant at 1 percent level, which verifies the existence of border-effect.

7 Conclusion

The stochastic Solow model provides a tight theoretical framework within which the growthprocess can be systematically interpreted and has implications that are rather different fromthe standard deterministic model. With an average growth rate around 2%, our estimationshows that TFP at the city level from 1995 to 2007 did not grow as fast as it did in the periodfrom 1984 to 1994. The empirical analysis in this paper indicates that the TFP growth ratesdiffer a lot among cities in China. We provide a map with high and low TFP growth ratesacross regions. For example, Guangzhou has a growth rate around 3.3%, but Haikou has agrowth rate of -3.4%. Evidence suggests the presence of regional variation in terms of TFPgrowth. We observe lower TFP growth rates in the southwest part of China (see Figure 1);while higher ones in the north. Some cities have high TFP growth rates and low TFP levelsin both 1996 and 2007, while some have low TFP growth rates and high TFP levels in bothyears. Therefore, there is a catching up trend with regard to some cities. In general, thecoastal cities have higher TFP growth rates and TFP levels than the non-coastal cities.

Concerning the determiants of TFP growth rates and levels, we test 7 groups of hypotheses.Evidence supports that transition from agriculture production to secondary-sector produca-tion has brought higher TFP growth and it is also positively correlated with TFP levels.Foreign-funded enterprises are more associated with cities have higher TFP levels; whiledomestic-funded enterprises are more associated with cities have lower TFP levels. However,in terms of TFP growth rate, these two types of enterprises show the exact opposite effects,which may suggest the absorption of advanced technology brought by FDI. In addition, ed-ucation, urbanization and goverment expenditure are positively connected with TFP levels.Infrastructure accessibility, such as paved roads and loans, also positively influences TFP lev-els. Moreover, the empirical results indicate a strong catch-up effect in cities that are laggingbehind in terms of TFP levels at the beginning our sample period.

As a first attempt to analyze China’s TFP at the perfecture-city level, the quality of ourestimation is largely limited by the availablity of data and the quality of data. Although nocausal interpretation can be drawn from our study, it sheds some light on the geographic dis-tribution of TFP levels and growth rates in China. Additionally, it suggests some candidatesfor future studies to find robust TFP determinants in cities of China, such as secondary-sector

25

production levels, education levels, and urbanization levels.

26

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29

Appendix A: Tables


Beijing 110000 0.053 79.67 143.36Tianjin 120000 0.046 87.35 145.28

Shijiazhuang 130100 0.031 77.05 107.87Hohhot 150100 0.079 60.65 145.23

Shenyang 210100 0.052 81.18 144.07Dalian 210200 0.048 89.19 151.50




Fuzhou 350100 0.029 90.56 124.82Xiamen 350200 0.039 129.55 197.92

Nanchang 360100 0.044 72.87 117.70Jinan 370100 0.037 88.02 131.52


Wuhan 420100 0.043 85.75 137.71Guangzhou 440100 0.046 114.69 189.87Shenzhen 440300 0.047 229.13 382.65Nanning 450100 0.006 72.97 77.54Haikou 460100 0.000 100.93 100.47


Xi’an 610100 0.023 68.52 88.64Xining 630100 0.019 63.50 77.86

Urumichi 650100 0.034 78.40 113.88AVE 0.040 87.13 136.66

Table A1: National ratio approach (1996-2007)

30


Beijing 110000 0.069 50.53 108.37Tianjin 120000 0.083 74.13 184.23


Shenyang 210100 0.152 57.24 305.11Dalian 210200 0.080 89.24 214.82




Fuzhou 350100 0.043 111.85 178.88Xiamen 350200 0.048 92.94 157.38

Nanchang 360100 0.083 76.64 191.56Jinan 370100 0.053 96.59 172.12


Wuhan 420100 0.088 68.36 180.08Guangzhou 440100 0.068 96.00 202.33Shenzhen 440300 0.060 115.75 223.29Nanning 450100 0.060 78.77 152.10Haikou 460100 0.223 16.14 187.20


Xi’an 610100 0.046 70.25 116.84Xining 630100 0.093 53.92 149.86

Urumichi 650100 0.065 70.07 142.60AVE 0.078 79.50 181.62

Table A2: City employment data approach (1999-2007)

31


Beijing 110000 0.016 146.74 174.36Tianjin 120000 0.049 159.25 272.19


Shenyang 210100 0.031 164.91 231.41Dalian 210200 0.023 182.36 233.61


Shanghai 310000 -0.003 233.56 227.04Nanjing 320100 0.031 172.08 242.22


Fuzhou 350100 0.005 179.93 189.73Xiamen 350200 0.011 238.98 270.26

Nanchang 360100 0.024 142.59 185.98Jinan 370100 0.004 174.17 181.22




Xi’an 610100 0.003 125.98 130.81Xining 630100 0.008 111.86 121.89

Urumichi 650100 0.015 157.59 186.69AVE 0.018 166.29 205.41

Table A3: City urbanization adjustment approach (-0.31) (1999-2007)

32


Beijing 110000 0.011 238.10 269.84Tianjin 120000 0.037 234.80 353.58


Shenyang 210100 0.012 283.41 324.01Dalian 210200 0.008 286.38 312.42


Shanghai 310000 -0.007 328.07 304.05Nanjing 320100 0.014 288.22 334.47

Hangzhou 330100 -0.001 277.37 274.53Ningbo 330200 0.009 255.83 281.11Hefei 340100 0.039 182.87 279.96

Fuzhou 350100 -0.018 277.85 228.95Xiamen 350200 0.002 416.70 426.47

Nanchang 360100 0.006 239.14 254.12Jinan 370100 -0.011 280.60 249.47


Wuhan 420100 -0.017 310.07 257.08Guangzhou 440100 0.021 361.25 456.39Shenzhen 440300 0.023 755.29 970.06Nanning 450100 -0.039 205.35 134.42Haikou 460100 -0.049 365.62 212.49

Chongqing 500000 0.006 143.37 152.82Chengdu 510100 -0.007 229.46 212.46Guiyang 520100 0.003 197.38 203.26

Xi’an 610100 0.006 211.85 225.36Xining 630100 -0.026 192.67 144.78

Urumichi 650100 0.008 268.96 294.02AVE 0.004 272.65 293.25

Table A4: City urbanization adjustment approach (0.208)(1999-2007)

33

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34

Appendix B: Model Explanations

Consider a set of cities, i = 1, 2, . . . , N , over a number of years, t = 1, 2, . . . , T . Outputin each city, Yit, is produced by physical capital, Kit and labour force, Lit, through a Cobb-Douglas production function

Yit = Kαit(AitLit)

1−α, 0 < α < 1 (23)

where Ait represents technology and endowment while capital stock is given by

Kit = Ii,t−1 + (1− δ)Ki,t−1, (24)

where δ is the rate of depreciation. Investment, Iit = sitYit, and the saving rate, sit, is timevarying in each city. The evolution of capital per effective labor unit,kit = Kit/AitLit, is thengiven by

∆logkit = −∆log(AitLit) + log(si,t−1k−(1−α)i,t−1 + 1− δ). (25)

The stochastic process determining technology and employment are

logAit = ai0 + git+ uait, (26)

uait = ρaiuai,t−1 + εait, |ρai ≤ 1| (27)

logLit = li0 + nit+ ubit (28)

ubit = ρbiubi,t−1 + εbit, |ρbi ≤ 1| (29)

where the initial TFP is defined as aio and its growth rate is defined as gi.

Both shocks to technology and labor inputs, uait and ubit allow for the possibility of a unitroot. The technology shock summarizes all the factors that might shift total factor produc-tivity, and the employment shock summarizes the outcome of the interaction between labordemand and supply influences.

We assume a common production function parameter, α, and depreciation rate, δ, but all theother parameters, and in particular the initial endowment, ai0, and the growth rate of TFP,gi, are allowed to differ across cities.

Model Specification Related to Capital

First, we develop the model for a single city and drop the i subscript temporarily. Wefollow the standard procedure which linearizes a deterministic analogue of equation (3), byexpanding it around the steady-state value of the effective capital-labor ratio and then sub-stituting for capital and technology in terms of output to derive a unvariate representationfor output. The difference is that we shall apply this procedure to a stochastic rather than adeterministic growth model.

Using equations (2) and (4) in equation (1) yields

∆logkt = −(n+ g)−∆ut + log(sk−(1−α)t−1 + 1− δ), (30)

35

where ut = uat + ubt is a composite shock. We linearize equation (8) around E[log(k∞)],where kinfty is the random variable that underlies the steady-state distribution of kt. Sincein steady state the expected value of ∆logkt is zero, then taking expectations of equation (8)we also have

n+ g = E[log(sk−(1−α)∞ ) + 1− δ]. (31)

The non-linear terms in equation (9) can be rewritten as

logse−(1−α)log(k∞) + 1− δ, (32)

which is easily established to be a convex function of log(k∞). By Jensen’s inequality

n+ g = E[log(se−(1−α)log(k∞) + 1− δ]= logse−(1−α)E[log(k∞)] + 1− δ + h, (33)

where h is a strictly positive number. The size of h depends on the degree of the curvature ofthe function in equation (9) and the distribution of the shocks. Rewriting euqtion (11), weobtian

E[log(k∞)] =1

1− α[log(s)− log(en+g−h)] (34)

The expansion of the non-linear term in equation (8) around E[log(k∞)] and denote the errorapproximation by ζt yields

log(sk−(1−α)t−1 + 1− δ) = γ − (1− λ)logkt−1 + ζt (35)

where

1− λ =s(1− α)e−(1−α)E[log(k∞)]

se−(1−α)E[log(k∞)] + 1− δ> 0, (36)

andγ = log(se−(1−α)E[log(k∞)] + 1− δ) + (1− λ)E[log(k∞)], (37)

Using equation (12), (1− λ) and γ simplify as:

1− λ = (1− α)[1− (1− δ)e−(n+g−h)], (38)

γ = n+ g − h− [1− (1− δ)e−(n+g−h)][log(en+g−h)− 1 + δ − log(s)] (39)

For small values of n,g, δ, and h,

1− λ ≈ (1− α)(n+ g + δ − h) (40)

γ ≈ (n+ g − h) + (n+ g + δ − h)[logs− log(n+ g + δ − h)] (41)

Model Specification Related to Output

Denote the logrithm of per-capita output, log(Yt/Lt) by xt and log(At) by at. Then theproduction function can be written as

xt = at + αlogkt. (42)

36

Using equations (8) and (13), and assuming the error of approximation is relatively unimpor-tant, we obtain the following relationship for the growth rate:

∆xt = ∆at + α[−(n+ g)−∆ut + γ − (1− λ)xt−1 − at−1

α], (43)

The technology variable (TFP constant) can be eliminated using equation (4) and (5) to get

xt = µ+ (1− λ)gt+ λxt−1 + et, (44)

et = (1− α)∆uat − α∆ubt + (1− λ)ua,t−1, (45)

µt = λg − αh+ (1− λ){α0 +α

1− α[logst−1 − log(n+ g + δ − h)]} (46)

Equation (24) makes it clear that technology and employment shocks have quite differentimpacts on the output process. In particular, even if there is a unit root in the time-seriesprocess for employment, this will not cause a unit root in the output process since the em-ployment shock only appers in equation (24) as a first difference. However, it is not ture forthe technological shock (or TFP shock), and a unit root in the process generating technologyshocks also cause a unit root in the output process.

Estimation Methods

For estimation, we need to reintroduce the distinction between cities, i = 1, 2, . . . , N . Weapply an AR(1) process to remove a possible common factor from the model.

xit = µi + θit+ λixi,t−1 + εit, (47)

where i = 1, 2, . . . , N and t = 1, 2, . . . , T , and

θi = (1− λi)gi, (48)

From equation (25) we have,

µt = λigi − αhi + (1− λi)αi0 +α

1− α[logsi,t−1 − log(ni + gi + δ − hi)]. (49)

To separate the effects of λi and gi, it is convenient to rewrite equation (26) as

xit = ci +α

1− αlogsi,t−1 + gitt+ uit, (50)

uit = λiui,t−1 + εit, (51)

where ci is the deterministic component of initial output,and is defined by

ci = αi0 −α

1− αlog(ni + gi + δ − hi)−

αhi1− λi

(52)

For purpose of estimation, note that

µi = (1− λi)ci + λigi +α

1− αlogsi,t−1. (53)

37

Econometric Considerations: Heterogeneous Panel Data

Under slope heterogeneity, one appropriate estimator is the mean group estimator. A simpleand effective procedure would be to demean the observations before estimation. The demean-ing procedure can be justified in the context of equation (29) if λi = λ, and the cross-sectionaldependence of εit across i can be specified by the two-factor model:

εit = ηt + vit, (54)

where ηt is a time-varing common (stochastic) component, and vit is the country-specificdisturbance term assumed to be independently distributed across i. For this specification, thedemeaned version of equation (26) is given by

xit − xt = (µi − µ) + (θi − θ)t+ λ(xi,t−1 − ¯xt−1) + vit − vt (55)

where xt = N−1N∑i=1

xit, and µ = N−1N∑i=1

µi

It is now easily seen that for large enough N, the demeaned disturbances εit − εt = vit − vtare uncorrelated across i. In the case where εit’s are normally distributed, the errors in thedemeaned regression will also be independently distributed across i, for large N.

It is possible to rewrite equation (34) as

xit − xt = (ci − c) +α

1− α(lsi,t−1 − lst−1) + (gi − g)t+ uit − ut (56)

uit − ut = λ(ui,t−1 − ¯ut−1) + vit − vt (57)

where logs is denoted by ls for short and ci is defined by equation (31). The regression yieldsestimates of ci− c and gi− g, etc. To obtain estimates of ci, gi, and µi we also need to estimatethe aggregate equation

xt = c+α

1− αlst−1 + gt+ ut (58)

ut = λut−1 + vt (59)

Estimates of ci and gi can now be recovered from those of ci − c and bi − g in equation (35).

The above derivations clearly show that the demeaning procedure works exactly when equa-tion (33) holds and λi = λ. However, if λi’s differ across cities, but not markedly so, demeaningbefore estimation can still help remove some of the correlations that may exist across cities.When the growth rates differ, the mean group estimator is appropriate, but the estimate ofthe mean λi across i from this procedure is subject to a downward bias in small samples. Inour caes, we have more than 200 cities, so this problem does not exist.

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