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Real Exchange Rates and Current Account Imbalances in an Economy With Excess Supply of Labor Jiandong Ju Justin Yifu Lin Qing Liu University of Oklahoma &Tsinghua University (jdju@@ou.edu) World Bank (justinlin@@worldbank.org) Tsinghua University (liuqing@@sem.tsinghua.edu.cn) This version: January 2011 (Very Preliminary. Please don’t circulate!) Abstract The Balassa-Samuelson theory suggest a long run trend of a real appreciation for a fast growing country. In this paper, however, the empirical evidences we established for Chinese economy do not seem to follow such a prediction: China experienced little real appreciation in recent years while keeping rapid growing. To explain for the seemingly abnormal data pattern, we extend the standard model by incorporating two features: Excess supply of labor and structural change. We demonstrate in the model that real depreciation is not necessarily incompatible to the higher TFP growth in a developing country, which is in sharp contrast to the prediction of the Balassa-Samuelson effect. The two features we introduced are the key to generate the results. While the existence of excess labor supply depresses the rise in the wage, factor reallocation across sectors will drive up prices of some factors and push down prices of others. If the non-traded goods sector uses intensively those factors with falling prices, the aggregate prices falls, and hence there is real depreciation during rapid growing period. Interestingly, our model can account for other data patterns we evidence for Chinese Economy, such as Current account surplus, large migration from rural area to industry, and income inequality between skilled labor and unskilled labor. JEL Classifications: F41, F32. Keywords: Real Exchange rates; Current account imbalance; Excess supply of labor; Structural change. 1. Introduction (To Be Complete!) Given such an inconsistency of long run trend of real exchange rate and the coincidence of large trade imbalance during recent year, here emerge the questions such as ”Whether RMB is deliberately under-valued to promote export in China?” or ”Whether an appreciation of RMB is the way to alleviate the global imbalance?”. Some commentators have tried to explain this puzzle by attributing it to government manipulation of the exchange rate that holds the value of the Chinese currency artificially low. This argument is controversial, as it attributes a long-standing imbalance to a nominal rigidity, without explaining why the peg of the nominal exchange rate did not trigger an adjustment of the real exchange rate through inflationary pressure. Our paper is organized as follows. Section 2 describes some empirical evidence of transition of China since 1980. Sector 3 presents a static model to highlight the role of excess supply of labor and structural change. Sector 4 describes the full dynamic model and characterizes the equilibrium. A discussion of robustness of our results as well as the policy implication of our model is included in section 5. Section 6 concludes. 2. The Transition of Chinese Economy: Empirical Evidence Over the last thirty years, China has undergone a remarkable economic transformation which involves some unique features for a fast growing developing country. In this section, we document empirically the main features of Chinese economy during its transition since 1980’s. 1. Higher TFP growth in exporting sectors than in importing sectors China has maintained a high growth rate, nearly 10% per year, over the last thirty years, which still remains a miracle to many researchers as well as policy makers. If we decompose the aggregate TFP growth by sectors, the technology improvement across sectors follows the prevailing pattern of a fast growing country, i.e., the traded goods sector grows relatively faster than non-traded goods sector. Moreover, we compared the average TFP growth rate in exporting sectors to that in importing sectors and generically, the exporting sectors are growing relatively faster than importing sector. [Insert Table and Figure 1 here] 2. Large migration of unskilled labor from rural area to urban industry 1 During the transition period of China, we observe a large amount of reallocation of labor across sectors. A remarkable fact is the large scale migration of unskilled labor from rural area to urban industry. The migrant workers, most of which are unskilled labor, occurred at 1978 with the amount of 200 Million, and has surged up to 14,533 Million in 2009. The mobilization of labor from rural area provides excess supply of unskilled labor to industry, which contribute to the persistent growth of Chinese economy. [Insert Figure 2 here] 3. Income inequality between skilled labor and unskilled labor The economic transition of China has been accompanied by increasing income inequality, especially the wage inequality between skilled labor and unskilled labor. Using the Chinese Urban Household Survey Data (1988-2009), we compute the average real wage for skilled workers and unskilled workers. We can observe a clear difference in the real wage between skilled workers and unskilled workers, and the average real wages of the two groups even diverge in recent years. 14000.0000 12000.0000 10000.0000 8000.0000 W‐unskilled 6000.0000 W‐skilled 4000.0000 2000.0000 0.0000 [Insert Figure 3 here] 2 4. Large amount of accumulation of foreign surplus Chinese economy become more and more integrated into the world economy during its development. The share of international trade in GDP grows from less than 20% in early 80’s to nearly 70% in recent year. Along with the economic integration of China with the world is the huge trade imbalance observed in the international trade, which is growing even faster in recent years. As demonstrated in Figure 4, the current account surplus (exports minus imports) of China is averaged at approximately $5 billion per annum in early 80’s; while after the year of 2001 when China obtained its WTO accession, the annual average of their trade imbalance increases sharply; till 2008, China’s current account surplus has amounted to as high as 426.1 billion U.S. dollars. At the mean while, China also holds huge foreign reserve, which has reached to around 2400 billion U.S. dollars in 2009. Such a huge trade imbalance has become a major political and economic issue between China and its trading partners, and it also initiated a series of policy debates as well as academic controversies. Current Account Balance 450000 400000 350000 300000 250000 200000 150000 100000 50000 0 ‐50000 [Insert Figure 4 here] Figure of Foreign Reserves [Insert Figure 5 here] 5. No persistent real appreciation observed during the period of rapid growing It is well documented that countries with rapidly expanding economies tend to have more rapidly appreciating exchange rates, which is also called as the Balassa—Samuelson effect. Given the fact of maintaining a high growth rate over a long period in China, a persistent real appreciation should be expected. The data pattern we observed in China, however, 3 does not follow the prediction of Balassa-Samuelson theory. As demonstrated in Figure 6, the real exchange rate did appreciate for a couple of years in early 80’s, but it has stayed rather stable since the year of 1990. Then, it comes the puzzle why China does not experience a persistent real appreciation as most other countries do? Is it because China deliberately keeps its currency under-valued to promote export? Our model described in following section will offer an explanation for such questions. Real Effective Exchange Rate 350 300 250 200 150 100 50 0 [Insert Figure 6 here] 3. A Static Model In this section, we set up a static model to reveal the main channel that we focus on in this paper. To highlight the role of the two important features of the transition of China, excess supply of labor and structural change, we start with the standard two-sector model. 3.1. Two-sector Economy: A Benchmark Consider a small open economy which consists of two sectors, where one sector produces the traded goods and the other produces non-traded goods. The technology applied in the two sectors are described as follows: ; = 1− (3.1) = 1− ; (3.2) where denotes for labor used in sector , for capital used in sector and is TFP in sector , = ( for traded goods sector and for non-traded goods sector). Following the literature, we assume , i.e., the non-traded goods sector uses labor relatively more intensively than the non-traded goods sector. 4 There is no friction in this economy. Capital is mobile internationally and labor is mobile domestically. So the model is set up in a standard two-sector framework. We pick the traded goods as the numeraire and its price is normalized to 1, and use to denote the price of non-traded goods. Define = as the capital-labor ratio in sector . Then, the following conditions must be satisfied if both sectors are operated: = ( ) −1 = ( ) −1 (3.3) = (1 − ) ( ) = (1 − ) ( ) (3.4) where is the return to capital and is the wage to labor. Above equations just say that the return to a factor should equal to its marginal product, and the free mobility of factors guarantees the factor price equalization across sectors. Note that = ∗ in a small open economy, which is taken as an exogenous variable in the model. Therefore, ( ) can be pinned down by above 4 equations. i.e., the prices are independent of the demand side! The model can be solved easily. First obtain the capital-labor ratio in the traded-goods sector from equation (3.3) and (3.4) = µ ¶ 1 1− ; (3.5) then, = (1 − ) ( ) ⎡ = ⎣ 1 − 1 − µ 1 1− ¶ µ 1− ¶ 1− ; 1 1− (3.6) ⎤ ( ) ⎦ 1 ; (3.7) Therefore, the relative price of non-traded goods is 1− − ( ) 1− 1− ; = where = ( ) ( ) −1 1− ³ (3.8) 1− 1− ´ −1 , which is a positive constant. Let = log ( ) ; = log ( ) ; = log ( ) ; ̂ = log () Equation (3.8) can be rewritten as: = 0 + 1 − − − + ̂ 1 − 1 − (3.9) 5 The aggregate price is proportional to 1 : = ( ) ( )1− = ( )1− (3.10) Given the assumption that the non-traded goods sector uses labor-intensive technology, i.e., ≥ and ≥ , we can obtain the result that ≥ 0. Thus, we should expect the real appreciation when there is TFP growth and the grow is biased toward the labor-intensive non-traded goods sector. This is indeed the Balassa-Samuelson effect in a standard two-sector model. 3.2. Two-sector Economy with Excess Supply of Labor Underlying the Balassa-Samuelson effect is the wage linkage across sectors. The technology improvement in the traded goods sector increases the marginal product of labor for workers in the sector, and push up real wages. Since wages are equalized across sectors because of labor mobility, the wage in non-traded goods sector also increases, and hence push up the price for nontraded goods. As the result, there is real appreciation along with the TFP growth. Note that the rise in wage is the key channel to generate the Balassa-Samuelson effect in the Benchmark model. Such a channel might be insignificant since we observe abundant supplies of ”surplus labor” from rural areas during the transition period in China. To investigate the role of abundant labor supply, we introduce the excess supply of labor into the Benchmark model. Now consider an economy with similar environment as previous section, but with abundant supplies of ”surplus labor” from rural areas. We assume an exogenous minimum wage level, min . Therefore, the equilibrium for this economy is characterized by equation (3.3) and (3.4), and two additional constraints: ≥ min ; (3.11) + ≤ ; (3.12) where is total labor supply in this economy. We focus on the case that the labor supply constraint (3.12) do not bind. i.e., + and = min . Now the real interest rate will be determined endogenously, and in equilibrium, capital-labor ratio in each sector and factor prices are given by ∙ min = (1 − ) 1 ¸ 1 (3.13) We will drive the relation in next section. 6 1 = ( ) = ∙ min (1 − ) ¸1− 1 (3.14) min 1 − (3.15) Then, we can obtain the price of the non-traded goods, ( ) = 1 where 1 = (3.16) 1− 1 "(min ) (1− ) 1− 1 1− (1− ) # 0. Consider a similar scenario where there is technology improvement in the traded goods sector. From equation (3.16), it is clear that the price of non-traded goods will increase, and hence a real appreciation follows. The intuition is straightforward: Though the wage of labor is depressed to the minimum level, the technology improvement drives up the demand for capital, which pushes up the real interest rate, leading to an increase in the price of the non-traded goods. Note that the effect of technology improvement on is ambiguous if all sectors are growing at the same rate, given non-traded goods sector is labor intensive. This result is different from the benchmark model where real appreciation is possible in the case where = . Therefore, introducing ”Surplus Labor” into the benchmark model does does generate new effect on real exchange rates, but a weaker version of Balassa-Samuelson effect still exists. 3.3. Three-Sector Model with ”Surplus Labor” To further break down the channel of the Balassa-Samuelson effect. Now consider an economy with 3 sectors: two traded goods sectors and one non-traded goods sector, with production functions described as follows: 1−1 −1 ; (3.17) 1−2 −2 ; (3.18) 1 = (1 1 )1 1 1 1 2 = (2 2 )2 2 2 2 1− ; = (3.19) where denotes for skilled labor, for unskilled labor and for capital, with = 1 2 and denoted for the two traded goods sectors and one non-traded goods sector, respectively. Let denote for the real return to capital, unskilled wage and skilled wage, respectively. We normalize the price of goods 1, and use 2 to denote for the price for the other traded 7 goods and for the non-traded goods. We keep the assumption that both capital and labor are mobile across sectors. Thus, the following conditions has to be satisfied in an equilibrium when all sectors are operated: ³ = (1 − ) ´− ³ = 2 (1 − 2 − 2 ) (2 )2 2 ³ = 1 (1 )1 1 ³ = ³ = 1 (1 )1 1 ´1− ³ 1 1 ´1− ´− ³ 1 1 ³ = (1 − 1 − 1 ) (1 )1 1 ´− ³ 2 ´− 1 ´1− 1 2 ´− 2 ´− ³ ³ = 2 2 (2 )2 2 ³ = 2 2 (2 )2 2 1 1 ´1− ³ 2 ´− ³ 2 2 ´− 2 1 (3.20) ´− 2 ´1− 2 (3.21) (3.22) We still focus on an economy with excess labor supply. Here it turn out to be the case that unskilled-labor supply constraint does not bind, and therefore = min in equilibrium. Then, the capital-labor ratio can be derived from (3.20) - (3.22) 1 = 1 − 1 − 1 min 1 (3.23) 2 = (1 − 2 − 2 ) min 2 (3.24) = 1 − min ; (3.25) and the real interest rate is determined by: µ = 0 where 2 = ¶ 1 2 (1−2 )2 −(1−1 )1 ; 1 h 2 2 (1−1 −1 ) 2 (2 ) h 1 (1−2 −2 ) Therefore, as long as 1 (1 ) 1−2 2 − (3.26) 1− 2 (1−2 −2 ) 1− 1 (1−1 −1 ) 1−1 1 i i 1 2 1 1 (min ) 1 1 2 2 − 0. 0 and ∆1 ∆2 , the real interest rate will fall. Given the price of non-traded goods is a function of interest rate and wage of unskilled labor, = (min ). A fall in interest rate may lead to a fall in and a real depreciation. One scenario that above result could occur is that 1 = 2 and 1 2 , i.e., the traded goods sector 1 uses labor-intensive technology and the traded goods sector 2 uses capital-intensive technology. Then, a technology improvement which is biased toward to sector 1 will lead to a real depreciation. 8 4. Current Account Dynamics: A Small Open Economy The setup discussed above is simple and only involves the supply side of the economy. It can be used to analyze the long-run trend of real exchange rate. However, since the demand side is kept out of the picture, such a framework, as interesting as it is, cannot be used to analyze the current account dynamics. In this section, we extend previous static model to a dynamic framework, and develop a theory of economic transition consistent with the empirical facts documented in the previous section. 4.1. Household The economy is inhibited by a continuum of identical and infinitely lived household that can be aggregated into a representative household. There are 3 goods available in this economy, two of which are traded goods (denoted by goods 1 and 2) and the other goods (denoted by goods 3) are non-traded goods. The representative household can consume all three goods, though the goods are not perfect substitutes. In particular, we assume the consumption index, , is aggregated by consumption of the three goods through a Cobb-Douglas function described as follows2 : 1 −2 ; (1 2 3 ) = 11 22 1− (4.1) where 1 2 ∈ (0 1) are the expenditure shares. We choose goods 1 to be the numeraire and the prices of goods 2 and goods 3 are 1 and 2 , respectively. We can derive the aggregate price, , which is given by = (2 )2 ( )(1−1 −2 ) (4.2) Suppose the expenditure on consumption is in period . Then, the optimal consumption of the 3 goods must follow the following rule in any period : 1 1 = 1 (4.3) 2 2 = 2 (4.4) = (1 − 1 − 2 ) ; (4.5) 2 The consumption index can choose more commonly-used CES function with no qualitative changes in the main results. We use Cobb-Douglas function to simplify the algebra. 9 Note that we impose perfect-forsight assumption since the main focus in this paper is on the long run trend of real exchange rate. Then, the representative household’s preference over consumption can be summarized by ∞ X ( ) (4.6) =0 where is described by consumption index (4.1). The households own all factors of production, capital, skilled labor, and unskilled labor, and rent the factors to firm in a competitive market. To simplify the analysis, we consider a fixed labor supply, = ̄ for unskilled labor and = ̄ for skilled labor, in the text. The households have access to international capital market and hold foreign asset +1 to smooth consumption. There is financial frictions in this economy in the sense that trade in foreign bonds is subject to a small portfolio adjustment cost, 2 ¡ +1 − ̄ ¢2 (denominated in units of traded goods 1), where ̄ is the steady state level of net foreign asset. The costs for adjusting international bond holdings reflect not only the narrowly defined transaction costs such as the bid-ask spread, but also costs associated with information asymmetry. In addition, it can be understood as a short hand for (not explicitly modeled) risks associated with cross-country differences in legal system, culture, and currencies. The budget constraint and capital accumulation equation faced by the representative household is given by + + +1 + ¢2 ¡ +1 − ̄ = + + + (1 + ∗ ) 2 (4.7) (1 − ) + = +1 (4.8) ³ ´ where is the capital depreciation rate, is the investment in period , and are the factor prices for skilled labor, unskilled labor and capital, respectively. ∗ is the world interest rate, which is taken as given in our small open economy setup. The first order conditions with respect to +1 and +1 give the following intertemporal optimization conditions £ ¡ 0 ( ) 1 + +1 − ̄ 0 ( ) = 0 (+1 ) ¢¤ = 0 (+1 ) 1 + ∗ +1 1 − + +1 ; +1 (4.9) (4.10) 10 Equation (4.9) is the standard Euler equation, which say that the marginal cost of reducing 1 unit of consumption today should equal to the marginal benefit of extra future consumption. Equation (4.10) gives the optimal investment rule. Using (4.9) and (4.10), we immediately obtain ¡ ¢ 1 + +1 − ̄ = 1 + ∗ ; 1 − + +1 (4.11) Equation (4.11) is the optimal foreign asset holding condition. The level of foreign asset holding in each period depends on the difference between domestic real interest rate and world interest rate. Households would like to choose to hold more foreign assets if they expect higher return on foreign assets. 4.2. Production The production setting is similar to the three-sector model with ”surplus labor” in previous static setup. There are 3 sectors producing good 1, 2, 3, using following technology: 1−1 −1 ; (4.12) 1−2 −2 ; (4.13) 1 = (1 1 )1 1 1 1 2 = (2 2 )2 2 2 2 1− = ; (4.14) Goods 1 and 2 are traded goods, and goods 3 are non-traded goods. We assume sector 1 are using a unskilled-labor intensive technology and sector 2 are using capital-intensive technology. In particular, 1 = 2 and 1 2 , i.e., the intensity of skilled labor in the two traded goods sectors are the same. ( = 1 2 ) measures TFP in each sector, and technology is assumed to be skilled labor augmented. We assume that the non-traded goods sector does not use skilled labor3 . The conditions for optimal allocation of factors across sectors are given by (3.20)-(3.22). 4.3. Equilibrium In equilibrium, free trade in traded goods sector leads to price equalization across countries in every period. That is = ∗ = 1 2 (4.15) 3 This assumption is not essential for our main results. We can allow skilled labor to enter into the production function of non-traded goods, as long as the non-traded goods sector applies unskilled labor intensive technolodgy. 11 where ∗ is taken as exogenously given in the small open economy setup. Then the factor prices and capital-labor ratio in each sectors can be derived as (The detailed derivation of the results is summarized in Appendix): Factor prices: = min ; = µ 1 1 min ; 1 1 = 0 where 2 = (4.16) (4.17) ¶ 1 2 (1−2 )2 −(1−1 )1 ; 1 h 2 2 (1−1 −1 ) 2 (2 ) h (4.18) 1− 2 (1−2 −2 ) 1− 1 (1 ) 1 (1−1 −1 ) Capital labor ratios in each sectors: 1 (1−2 −2 ) i i 1 2 1 1 (min ) 1 1 2 2 − 0. 1 = 1 − 1 − 1 min 1 (4.19) 2 = (1 − 2 − 2 ) min 2 (4.20) = 1 − min ; (4.21) 1 2 ⎡ ³ ⎢ 1 1 = 1 ⎣ ⎡ ´1− ⎤ 1 1 min ⎢ 2 2 = 2 ⎣ ³ 2 min ⎥ ⎦ 1 ; (4.22) ´1− ⎤ 1 2 ⎥ ⎦ 1 (4.23) Once we obtain factor prices and capital-labor ratios in each sector, we can solve the factor allocation using following resource constraints 1 1 + 2 2 = ; (4.24) 1 1 = 1 1 = 1 ; (4.25) 2 2 = 2 2 = 2 ; (4.26) = ; (4.27) 12 1 + 2 = ̄ (4.28) and goods market clear conditions: = i.e., (1 − 1 − 2 ) = (4.29) ¡ ¢2 where = + +(1 + ∗ ) − − +1 − 2 +1 − ̄ , which is the expenditure on consumption in period . To interpret our results, let’s focus on equation (4.18) and (4.11). Since 1 = 2 and 1 2 , a technology improvement in sector 1 will drive down the real interest rate, , according to (4.18). Then, households choose to hold more foreign asset because the relative return to foreign assets increases, according to (4.11). The intuition behind our result is clear: Suppose there is a TFP growth in sector 1. More resources flow into sector 1 because of higher marginal product of factors. As the result, sector 1 expands and more goods 1 are exported, while sector 2 shrinks and more goods 2 are imported. Following Stopler-Samuelson theorem, the wage for skilled labor increases and real interest rate fall. Meanwhile, the wage for unskilled labor does not change because of excess unskilled labor supply. The price of non-traded goods falls since the production of non-traded goods uses intensively the unskilled labor. The economy will experience a real depreciation even though there is TFP growth in traded goods sector, which is in sharp contrast to the Balassa-Samuelson Effect. Our results are consistent with data patterns we documented in previous section: During the fast-growing period, large amount of unskilled labor is reallocated into the industry from the rural area; There is increasing wage inequality during the transition of China; There are a large amount of foreign assets accumulated in China and it keeps increasing in recent years; No persistent real appreciation in China is observed during the rapidly growing period. 4.4. Quantitative Analysis We have focused so far on qualitative predictions of the theory. In this section, we show that a calibrated version of our theory can also account quantitatively for the stylized facts we established in previous section. 4.4.1. Calibration The calibration of our model focuses on matching empirical moments during 1980-2009. Some parameters are calibrated exogenously, and the rest are estimated within the model. 13 For now, we have done a numerical exercise, where the parameters in model is set as: = 096 1 = 06 2 = 02 1 = 2 = 025 = 065 1 = 035 2 = 035 ∗ = 008 ∗2 = 10764 min = 10 = 10 (We will do serious calibration in the next step!) 4.4.2. Computation Method We solve the model using the shooting method. The idea of shooting algorithm is straightforward: Given the initial capital stock, we guess a path of capital accumulation. Once we find a guess that leads to a balanced growth path, then the computation is done. The following algorithm is what we used for computation: 1. Normalize Initial capital stock 0 , and get 0 ; 2. Guess 1 ∈ [1 min 1 max ] where 1 min = 050 1 max = 15 3. Compute factor prices using (4.16)-(4.18), and capital-labor ratio in each sector using (4.19)(4.23) 4. Solve +1 by equation (4.11) 5. Solve (1 2 1 2 1 2 ) using (4.24)-(4.29) 6. Compute using (4.7) 7. Calculate +1 ( ≥ 0) using (4.9) 8. Once we obtained +1 , we can compute +2 using capital accumulation equation 9. If +1 0 1 is too high. Let 1 max = 1 Goto step 3 if +2 0 1 is too low. Let 1 min = 1 Goto step 3 10. if ̃+1 ̃+1 = ̃ ̃ = ̃ and +1 ̃+1 = ̃ = ̃ Convergence is achieved! 14 4.4.3. Results The dynamics of the calibrated economy are illustrated in Figure 7. [Insert Figure 7 here] Here is a summary of our results: 1) Real exchange rate is depreciating during the rapid growing period; 2) Large accumulation of foreign assets and Current account surplus; 3) Diverged real wage between skilled labor and unskilled labor; All these results are qualitatively consistent with the stylized facts we documented. 5. Discussion (To be completed!) 6. Conclusion In this paper we first empirically establish 5 stylized facts about the transition of China. We show that such data patterns are inconsistent with the existing theory. To explain for the seemingly 15 inconsistency, we introduce two new ingredient, which we believe are the important features of Chinese transition, into the standard model. We uncover a new channel that drives the long run trend of real exchange rate, and provide an explanation for the puzzle that China does not seem to experience persistent real appreciation during the rapid growing period. Our model also matches the other stylized facts well. (To be completed!) 16 Appendix A. To be completed! 17 References [1] Blanchard, Olivier J. and Giavazzi, Francesco, Rebalancing Growth in China: A ThreeHanded Approach (November 25, 2005). MIT Department of Economics Working Paper No. 05-32 To be completed! 18
