The Balassa-Samuelson e ect in a developing country

Transcription

1 The Balassa-Samuelson e ect in a developing country Karine Gente y I wish to thank two anonymous referees, M. Aloy, P. Bacchetta, B Decreuse, J. De Melo, M. Devereux, M. Leòn Ledesma and participants to OLG seminars in Marseilles for their helpful comments. The usual disclaimer applies. y CEDERS, University of Aix-Marseilles II, 14 avenue Jules Ferry, Aix-en-Provence, FRANCE, Tel : , Fax : , kgente@univ-aix.fr. 1

2 Abstract Some Asian countries experience small real exchange rate appreciations or even a real depreciation despite a fast growth in tradable productivity. A keycharacteristic of these countries is that they are constrained on capital in ows. Is the Balassa-Samuelson theory still valid in those countries? Are there other factors likely to explain real exchange rate (RER) changes? To address these questions we develop a two-sector model in which a small open economy faces a constraint on capital in ows. In this setting, the RER does not only depend on productivity but also on other factors like the rate of time preference, the age dependency ratio or the level of the external constraint. A calibration of the constrained economy model seems to match at least qualitatively empirical evidence for China, Hong Kong, Indonesia, Malaysia, Thailand and Singapore between 1970 and Key-words: Real exchange rate; capital in ows constraint; overlapping generations; productivity shock. Classi cation J.E.L.: E39; F00; F20. 2

3 1 Introduction How does the real exchange rate (RER) react to changes in factor productivity? The usual answer to this question hinges on Balassa (1964) and Samuelson (1964) analyses. They analyze the RER determination in a two-sector economy - tradable and non-tradable goods- with international capital mobility and perfect factor mobility between sectors. They obtain two main conclusions. First, the RER is fully determined by the supply side of the economy. Second, an increase in tradable productivity leads to a real appreciation. The traditional Balassa-Samueslon (BS) theory is often considered as relevant to explain the real appreciation experienced by developing countries. However, most of the time in such countries, international factor mobility is imperfect because foreign investors require risk premia. The empirical evidence is not always in accordance with the BS analysis. Surveying the empirical papers, Section 2 shows that the BS theory works for OECD countries and especially for Japan. Nevertheless, in developing countries the growth in tradable productivity seems unable to explain the RER appreciation. Some Asian countries experience small RER appreciations or even a RER depreciation despite a fast growth in tradable productivity. Considering these controversial empirical results, this article aims at studying the RER reaction to a tradable productivity shock when key-characteristics of developing countries are taken into account. In particular, what would happen if a risk premium was explicitly spelled out, that is if capital was not perfectly mobile? Would the Balassa Samuelson theory still be valid? Are there any factors other than productivity likely to explain RER changes? To address these issues, this article deals with the case of a developing country which faces a constraint on capital in ows 1. We build an OLG model as Obstfeld and Rogo (1996) where it is assumed that for exogenous reasons - such that political risk or high in ation for example - the developing country under study can only borrow up to a given amount of capital on the world market. In this setup, we introduce a two-sector/two- 3

4 factor structure and investigate the RER reaction to a rise in tradable productivity. The model encompasses both the constrained case where the domestic interest rate exceeds the world interest rate, and the traditional BS case, where the domestic and world returns on capital converge. In the constrained case, the RER results from supply and demand mechanisms: it depends not only on growth but also on preferences and age pyramid. As in the BS case, the rise in tradable productivity leads to a new factor allocation between sectors. This partial equilibrium mechanism a ects the returns on each factor: the domestic interest rate increases while the wage decreases. Hence, unlike the BS case, the rise in tradable productivity lowers aggregate demand through these factor returns changes and the RER may depreciate. Several theoretical papers have already explained that the RER departs from the level predicted by the BS analysis. Grafe and Wyplosz (1997) and Mahbub Morshed and Turnovsky (2004) introduce an imperfect allocation of factors between sectors, whereas Devereux (1999) considers that the PPP on tradable does not hold due to the existence of a distribution sector. Considering imperfect labor mobility, Grafe and Wyplosz (1997) show that transition countries require a real appreciation - exogenous - to promote economic growth. Thus, the BS e ect is reversed: the rise in tradable productivity, endogenous, is a reaction to the real appreciation. Mahbub Morshed and Turnovsky (2004) introduce intersectoral adjustment cost on capital in a dependent economy. Out of the steady state, the model explains the RER dynamics 2 from both supply and demand factors as public spending for example. Nevertheless, in the long-run, the BS analysis holds: an increase in tradable productivity always leads to a real appreciation. Finally, Devereux (1999) considers three di erent sectors: the tradable one, the non tradable one and the distribution services sector where monopolistic competition is assumed. Due to the existence of the distribution sector, the nal goods price of traded 4

5 commodities contains non-traded elements. As in the BS theory, faster tradable productivity growth leads to a rise in the price of non-traded goods. However, the domestic price of the traded goods - which is a combination of the (exogenous) world price of tradable goods and the price of the distribution services - may decrease. This fall in the domestic price of traded goods generates a fall in the RER despite higher productivity growth in the traded sector. Devereux (1999) provides thus an explanation of the real depreciation experienced by Asian countries. The constrained economy we develop is an alternative: a rise in tradable productivity may theoretically lead to a real depreciation too. However, the theoretical global e ect of a rise in tradable productivity remains indeterminate. A calibration of the model shows that the RER still appreciates after a rise in tradable productivity but less than predicted by the BS theory. In this way, the Balassa-Samuelson e ect remains valid in a constrained economy but productivity is not the only determinant of the RER. Some other factors have to be considered when the country is constrained on capital in ows. When we consider the high growth rates and the fall in age dependency ratios, keycharacteristics of Asian countries during these last thirty years, the Balassa-Samuelson e ect is partly o set: the RER experiences a small appreciation or even a depreciation. The model seems to match empirical evidence at least qualitatively for China, Hong Kong, Indonesia, Malaysia, Thailand and Singapore between 1970 and Among this literature, the model we present in the next section departs from the standard BS analysis considering that the world capital markets are imperfect. Section 2 surveys the empirical literature. Section 3 introduces the model, the temporary equilibrium and the steady state. Section 4 presents the impact of a rise in tradable productivity in a general case compared with the special BS issue and confront the model to empirical evidence. Section 5 provides some conclusions. 5

6 2 Empirical literature We review brie y the BS analysis before surveying the empirical literature. Empirical evidence o ers little support to the BS theory, especially in developing countries. The BS analysis states that an increase in tradable productivity leads to a RER appreciation when there are both perfect international capital mobility and perfect intersectoral factor mobility. Consider a two-sector static economy. Assume that production in the tradable and in the non-tradable sectors resulting from two neoclassical production technologies, respectively F and H, using two inputs, labor L, and capital K. Both inputs are perfectly mobile between the two sectors provided that K T + K N = K (1) L T + L N = L (2) where K i and L i, i = T; N, are the quantities of capital and labor used by sector i. Let k i K i =L i be the capital intensity of sector i and l i L i =L be the share of labor demand allocated to sector i. The mobility of factors implies k T l T + k N l N = k (3) l T + l N = 1 (4) We adopt the following intensive notation for production f (k T ) F (k T ; 1), h (k N ) H (k N ; 1). Let also R be the relative price between non-traded and traded goods: R P N =P T. Pro t maximization and competition among rms imply that production factors are paid their marginal product a T f 0 (k T ) = Ra N h 0 (k N ) (5) a T [f (k T ) k T f 0 (k T )] = Ra N [h (k N ) k N h 0 (k N )] (6) where a T (resp. a N ) denotes tradable (resp. non-tradable) productivity. 6

7 These conditions lead to a factor allocation which only depends 3 on the relative price between the non-tradable and the tradable good: k N k N (R; a T ; a N ), k T k T (R; a T ; a N ) : Perfect international capital mobility implies a T f 0 (k T (R; a T ; a N )) = r (7) where r is the world interest rate. Di erentiating (7), we nally get _R R = _a T a T _a N a N (8) with 4 > 1 when the tradable sector is capital intensive 5 i.e., when k N < k T ; an assumption we consider satis ed hereafter. According to equation (8), the BS theory points out that faster growth in tradable productivity a T leads to a rise in the relative price of the nontraded goods. We review hereafter the econometric tests of equation (8). The empirical literature usually proceeds in two stages. First, the linkage between the logarithm of the e ective RER q t and the relative price between non tradable and tradable goods, log R = p N p T, where p N (resp. p T ) is the logarithm of the price index of the sector non-tradable (resp. tradable), is tested. Second, the relationship between the RER and the productivity spread between sectors is tested. Let the aggregate price index for the home country be a combination of the prices of the two types of goods: p t = (1 ) p Nt + p T t, where 2 (0; 1) denotes the share of traded goods in the price index. The global price index for the foreign country stands for p t = (1 ) p Nt +p T t. Let s t be the logarithm of the exchange rate, de ned as the foreign currency price of domestic currency. Using the de nition of the RER, q t s t +p t p t, the relationship between the RER and the relative prices between non-tradable and tradable goods is q t = (s t p T t + p T t ) + (1 ) [(p Nt p T t ) (p Nt p T t)] (9) As a rst step, the PPP on tradable goods is tested, that is s t = p T t p T t : If the PPP on tradable holds, the RER is highly correlated with the di erence between the relative price between non-traded and traded goods in domestic and foreign countries. The evidence is 7

8 mixed. First, empirical evidence assembled by Engel (1993), Lapham (1995), Engel and Rogers (1996), and Knetter (1997) show that there are large deviations from the law of one price for many traded goods in disaggregated price data. Engel (1999) shows that the variance of changes in the international relative price of traded goods - i.e., the rst term of equation (9) - account for 90% of the overall variance of RER changes in variance decompositions of RER on the USD exchange rate against currencies of high-income countries. Nevertheless, Engel said that the evidence (...) suggests that the relative price of non-traded goods has little importance for understanding US RER movements over the short and medium-run. This conclusion points out that in the long-run we should follow Engel (1996) since his results show that the second term of equation (9) accounts for about half of the variance of the RER. Moreover, evidence suggests that the rst component of equation (9) is small for developing countries. Second, using a database of 13 OECD countries between 1960 and 1993, Canzoneri et al. (1999) conclude that the null hypothesis of no mean reversion can be rejected on panel data. Finally, Betts and Kehoe (2001) show, using bilateral RER of 52 countries between 1980 and 2000, that the relative price of non-traded goods and the RER are closely related. The relative price of non-tradable goods accounts for one third of all real exchange rate uctuations and is higher when trade intensity between countries increases or when the RER has low variability. However, these controversial results legitimate to think that in the long-run, especially in developing countries, relative price of non-tradable goods and RER are closely related and deviations from PPP seems to be temporary, resulting from monetary phenomena. In our theoretical model we will use a real OLG model which enables us to focus on a long-run horizon. Hence, in the next section the RER is assumed to be the relative price of the non-tradable good R - a rise in R means a real appreciation. According to (8), the relative price of non-traded goods should re ect the productivity spread between sectors and countries q t = (1 ) [(a T a N ) (a T a N)] (10) 8

9 The second step of most econometric analysis consists of estimating a long-run relationship between RER and productivity spread. According to Ito et al. (1999), real exchange rates and growth are positively correlated in Japan, Korea, Taiwan, Hong Kong whereas the correlation remains negative for Indonesia, Thailand, Malaysia, Philippines and China. Hong Kong, Taiwan and Singapore combine a high growth rate and a small appreciation. There is a consensus that, in Japan, the BS theory holds ( "It is well known in the literature that the postwar Japanese record has been a prime example of the BS hypothesis (Ito an al., 1999) "). For other Asian countries except China, Singapore, Taiwan and Thailand, Chinn (2000a) nds that the productivity explains RER only when public spending and oil prices are taken into account. Chinn (2000b) nds with a panel data test that the RER requires around 5 years to converge to the level predicted by BS. In contrast, there is no mean reversion considering only time series data. Finally, Canzoneri et al. (1999) provide similar results on OECD countries. To sum up, the BS theory seems to be empirically validated on panel data while it cannot be when tested on time series. All these empirical papers suggest that except for Japan there is no consensus on the validity of the BS theory. Moreover, productivity spread seems to provide a better explanation for RER changes in developed countries. In developing countries, especially for China, capital markets are not fully liberalized and recent changes in the structure of exports lead to an imperfect intersectoral labor mobility. Hence, the t of the BS theory to explain RER changes seems to be very poor. The model we present in the next section departs from the standard analysis by considering that the world capital markets are imperfect. Equation (7) does not hold and hence, there is a gap between the world and domestic returns on capital. 3 The model The model is a variant of the small open economy overlapping generations model of Obstfeld and Rogo (1996) in which we introduce two production sectors. 9

10 3.1 Individuals The economy consists of a sequence of two-period lived individuals. In the second period of his life, each individual gives birth to 1 + n others so that the per period rate of population growth is n. At time t, each generation consists of N t identical individuals who make decisions concerning consumption and savings. Intertemporal preferences of an individual belonging to generation t are represented by U (c t ; d t+1 ) = ln c t + (1 ) ln d t+1 (11) where c t and d t+1 are respectively composite consumption when adult and composite consumption when old; 2 (0; 1) denotes individuals thrift. Let x = c; d denote individual consumption at each period of life, x N and x T be respectively the spending allocated to non-traded and traded goods. Instantaneous preferences are de ned according to: u (x T ; x N ) = x T x 1 N, 0 < < 1 (12) As in Section 1, the relative price of the non-traded good in terms of the traded good R is the real exchange rate. Following Obstfeld and Rogo, the small economy faces a constraint on capital in ows B t+1 N t w t (13) where B t+1 denotes the net foreign assets of the domestic country in terms of traded goods and > 0 is the proportion of the wage bill 6 (N t w t ) the domestic country can borrow. The consequence of this assumption is that the domestic return on capital may be higher than the world one. During the rst period of life, individuals o er labor inelastically and distribute their earnings w t among own consumption spending t c t and savings t c t + (1 + n) k t+1 + (1 + n) b t+1 = w t (14) 10

11 where k t+1 is the whole capital stock per young agent in terms of traded goods and b t+1 = B t+1 =N t+1 the net foreign assets per young. The price of the tradable good is normalized at unity. We denote the composite consumption good by x x T x1 N with x = c; d to specify the same preferences among the two goods at each life period and t the consumer price index. National savings can be held into two forms, capital stock and net foreign assets. Since the returns on these stocks are di erent, the agents choose both the amount of their savings s t and its allocation between the two assets. To take into account this arbitrage, we assume following Obstfeld and Rogo that the constraint on capital in ows works at the microeconomic level. This assumption means that banks cannot lend more than w t to each individual at the world market interest rate r. Agents know both the world and domestic returns on capital. A spread between these two returns is a new potential source of income for them: they can borrow from the world market to lend on the domestic market and realize a capital gain. When old, individuals are retired and consume the proceeds of their savings according to t+1 d t+1 = 1 + rt+1 d (1 + n) kt+1 + (1 + r) (1 + n) b t+1 (15) The domestic return on capital is the market interest rate rt+1 d whereas the world return r is xed according to the small open economy assumption. The maximization program of an individual born in period t solves in two steps. First, the individual chooses t c t and b t+1 to maximize life-cycle utility (11) under the budget constraints (14), (15) and the capital in ows constraint b t+1 w t 1 + n (16) Second, he shares his consumption spending (x) between the two goods x N and x T to maximize instantaneous utility (12) under the spending constraint x = Rx N +x T. Hence, the allocation of total consumption spending between the two goods at each period is x T = x Rx N = (1 ) x 11

12 where the price index is = () R 1, with () (1 ) 1. Young and old agents consumption functions are rt+1 d r t c t = w t (1 + n) b 1 + rt+1 d t+1 t+1 d t+1 = (1 ) 1 + rt+1 d wt rt+1 d r (1 + n) b t+1 (17) (18) Individuals consume a proportion of their life-cycle income during the rst period of life and the remaining when old. Life-cycle income consists of the wage w and the capital gain they may realize borrowing at world rate r to invest in domestic capital whose return r d is higher than r. 3.2 Production Sectors The production side is the same as in Section 2. Investment transforms instantaneously a unit of tradable good in a unit of installed capital: K t+1 = I t and capital fully depreciates after one period. The allocation of factors between sectors is de ned by (5) and (6). This means that k N and k T depend only on RER whereas the allocation of labor depends both on capital intensity and RER. Hence, k N k N (R) and k T k T (R), while l N l N (k; R) and l T l T (k; R). From (3), (4), (5) and (6), the optimal factor allocation satis es dk N dr = a T f R 2 a N h 00 (k N k T ) dk T dr = Ra N h f 00 a T (k N k T ) (19) (20) N =@k S 0 if k N S k T N =@R > 0. When the tradable sector is capital intensive, a real appreciation leads to an increase in both capital intensities k N and k T whereas labor moves from the traded to the non-traded sector. These factor movements re ect that a real appreciation makes the non-tradable sector more attractive. Assuming perfect intersectoral mobility, the returns on capital r d a T f 0 (k T (R)) = r d (R) and labor w a T [f (k T (R)) f 0 (k T (R)) k T (R)] = w (R) only depends on the RER R. 12

13 We depart from the BS theory by assuming that there is a constraint on capital in ows and thus equation (7) may not hold. Hence, factor movements a ect both returns on factors and hence agents income. 3.3 The temporary equilibrium in the constrained case We study the temporary equilibrium in the case where the capital in ows constraint binds. This creates a gap between domestic and world returns on capital. This gap - in accordance with risk premia phenomenon - re ects that developing countries do not have access to perfect international capital markets: the return on domestic capital rt+1 d must be higher than the world market interest rate r to o set bad economic conditions in these countries. The period-t temporary equilibrium conditions are (i) Capital market equilibrium. Given the optimal intersectoral factor allocation k T (R) and k N (R), net foreign assets per capita are given by b t+1 = w (R t) 1 + n (21) Let (R t+1 ) r d (R t+1 ) r 1 + r d (R t+1 ) 1 be the arbitrage premium which depends on the interest rate gap between domestic and world capital markets and on proportion of the wage bill agents can borrow. The higher the higher the capital gain agents realize. Therefore, capital per worker is k t+1 = [1 + (1 + (R t+1 ))] w (R t) 1 + n (22) (ii) Labor market equilibrium. The inelastic labor supply N t is equal to the labor demand L t. Given the capital market equilibrium, the wage w equalizing labor supply and demand is de ned by w (R t ) a T [f (k T (R t )) k T (R t ) f 0 (k T (R t ))] (23) (iii) Non-tradable goods market equilibrium. There are N t young agents and 13

14 N t 1 old agents. Hence, the equilibrium on the non tradable goods market is (1 ) (N t t c t + N t 1 t d t ) = R t Y N (k t ; R t ) (24) where consumption spending is given by equations (17) and (18) and Y N (k t ; R t ) a N l N (k t ; R t ) N t h (k N (R t )) : Equation (22) describes the allocation of savings between the two assets. It o ers a rst dynamic relationship between RER and capital intensity. Using (21), (23) and (24), with consumption spending given by (17) and (18), we get a second dynamic relationship between RER and capital intensity: (1 + (R t+1 )) w (R t ) n (1 + (R t)) 1 + r d (R t ) w (R t 1 ) = a Nl N (k t ; R t ) R t h (k N (R t )) 1 (25) Given K 0, and L 0, the dynamic system made of equations (22) and (25) yields the paths of the two variables k t and R t. Then, given B 0, equation (21) determines the path of the current account. 3.4 Steady state in the constrained case The country faces a credit constraint 7 and, even in the long-run, the domestic return on capital is higher than the world return i.e., the arbitrage premium remains positive. Thus, solving long-run steady state is equivalent to nding (k ; R ) such that where y N k = w (R ) 1 + n [1 + (1 + (R ))] (CA) R y N (k ; R ) = w (R ) (1 + (R )) n 1 + rd (R ) (NM) Y N =N t is the non-tradable production per worker. Equation (CA) is the long-run capital accumulation condition. It de nes an increasing locus between k and R since dw=dr > 0 and dr d =dr < 0. Equation (NM) is the long-run non-tradable market clearing condition. The slope of the corresponding locus is ambiguous. Hereafter, we assume that there exists a unique steady-state (k ; R ). This implies the slope of (NM) is lower than the slope of (CA) in (k ; R ). Formally, consider the function 14

15 ( 1 ; 2 ) such that 1 (k; R) = k 2 (k; R) = Ry N (k; R) 1 w (R) [1 + (1 + (R))] (26) 1 + n w (R) (1 + (R)) n 1 + rd (R) (27) The steady-state solves (k ; R ) = 0. Let J denote the Jacobian matrix of function evaluated in equilibrium. We assume for uniqueness that 8 det J > 0 2 (k ;R R h a N 1 (k ; R (28) k N k T The key-characteristic of this economy is the presence of in equations (26) and (27) With a constraint on capital in ows, equation (7) does not hold and the level of the RER depends not only on sectoral productivity spread but also on the rate of time preference, the rate of population growth, and the share of non-tradable goods in consumption. A fall in the domestic rate of time preference leads to higher savings, higher wealth and higher non-tradable consumption, entailing a real appreciation. A fall in the share of traded goods in consumption leads to a rise in the consumption of non-traded good and hence to a RER appreciation. A fall in the rate of population growth n means that population is getting older. Since young agents save and old agents consume the proceeds of their savings, a fall in n leads to a rise in non-tradable good consumption and hence a RER appreciation. This model provides thus new potential sources of RER appreciation. Indeed, in such a constrained economy, demographic transition going together with development may lead to a real appreciation. At the opposite to the Balassa-Samuelson analysis, the sectoral productivity growth is not here the only determinant of the long-run RER. This model enables to understand why empirical studies are sometimes forced to take into account other determinants of the RER like public spending 9 to validate the Balassa-Samuelson e ect. We could also argue that Hong Kong, Taiwan and Singapore experienced only a small real appreciation despite a high growth rate because changes in tradable productivity when together with changes in n or. Figure 1 plots the age dependency ratios for some 15

16 Asian countries. Hereafter we will always refer to these countries because according to Ito and Symansky (1999), the BS analysis does not hold (see Section 2). It depicts a decreasing trend for all countries. This fall in the age dependency ratio comes from a rising size of the working age population, resulting from an increasing participation of women in the labor market. The model we develop suggests that the fall in n tends to depreciate the RER. This depreciating e ect may have partly o set the real appreciation generated by growth. [INSERT Figure1 Here] Does this empirical evidence explain the real depreciation experienced by China, Indonesia, Malaysia and Thailand despite the rise in productivity? What becomes in such an economy the Balassa-Samuelson e ect? 4 An increase in tradable productivity In this section, we study the steady-state e ects of a tradable productivity increase. First, we show the BS analysis may not always hold in the constrained economy (CE). Second, we calibrate the model to show that even if underlying mechanisms are very di erent to those pointed out by the Balassa-Samuelson analysis, the RER still appreciates when the country is credit constrained. Finally, we show that the CE model matches empirical evidence when we consider both growth and a fall in the age dependency ratio. 4.1 Theoretical e ects To highlight the dependency vis-à-vis a T, let w w (R ; a T ), r d r d (R ; a T ), (R ; a T ), k i k i (R ; a T ), l i l i (k ; R ; a T ), i = N; T, and y N y N (k ; R ; a T ). We =@a T < d =@a T > =@a T > N =@a T < 0 if k N < k T. The RER reaction to an increase in tradable productivity is given by dr da T = 1 det J R a N 2 (k N k T ) (1 T (29) 16

17 We know from the uniqueness condition (28) that the determinant of the Jacobian matrix J is positive 1 =@a T T 0 when k N S k T, 2 =@a T remains indeterminate. An increase in tradable productivity may lead to a RER depreciation when k N < k T 2 =@a T < 0. In the BS case, the arbitrage premium vanishes, since according to equation (7) domestic and world returns on capital converge, we have = 0: As a result, an increase in tradable productivity always gives rise to a RER appreciation. Indeed, the rise in a T leads to a real appreciation d =@R < d =@a T > 0 and r d = r: The main di erence between the constrained economy (CE) and the BS case is that equation (7) does not hold. Hence, in the CE the arbitrage premium is positive because there is a gap between domestic and world returns on capital. As a result, R is not fully determined by the supply side. It depends, as k does, on both supply and demand variations. Consequently, we recover in the CE the BS e ect on factor movements, but the RER reaction depends on additional demand e ects due to changes in factor returns. On the supply side, as in the BS case, an increase in tradable productivity leads to a new factor allocation: capital and labor move from the non-traded to the traded sector exerting a negative e ect on non-traded good production. On the demand side, the domestic return on capital r d increases while the wage w decreases. These changes in factor returns a ect the demand for non-tradable goods. The mechanisms are the following: - a fall in w reduces the agents income and the amount the country can borrow on the world capital market. - a rise in r d increases the arbitrage premium and hence the capital gain agents can realize from borrowing at r and lending to domestic rms at r d ( > 0): Let the consequences of this rise in r d (drop in w) on consumption spending be the positive interest rate e ect (negative wage e ect). The negative wage e ect lowers savings and the amount the country can borrow. Finally, the global capital intensity k is reduced and =@k < 0 the supply of non-traded goods may increase as the capital stock 17

18 decreases. Through equation (29), the global long-run e ect on the RER depends both on these supply and demand variations. It follows the RER may depreciate when non-tradable production nally increases and non-tradable consumption decreases, or when the fall in non-tradable production exceeds the fall in non-traded goods demand. Nevertheless, the global e ect of such a productivity shock remains theoretically indeterminate. Hereafter, we illustrate it using a calibration exercise. 4.2 Calibration We calibrate the model assuming Cobb-Douglas production functions. Let the production functions be f (k T ) = (k T ) and h (k N ) = (k N ). Table 1 reports the value of parameters used in the calibration. [INSERT Table 1 Here] We assume as in Mahbub Morshed and Turnovsky (2004) that the productivity is higher in the traded sector and that half of consumption is spent on non-traded good. We choose the elasticities of substitution between labor and capital for the two sectors to match empirical evidence 10 : 40% of total output 11 is traded with 37% of labor being employed in that sector. With = 0:2 and = 0:65; the tradable sector is capital intensive and we have l T = 35:98% whereas Y T =Y is 12 56%: If each period represents 25 years, r = 0:37 means that the world real interest rate is about 1:25% per year. In accordance with Beine et al. (2001), let be 0:5 to have a domestic rate of time preference of around 3:7%. The choice of a numerical value for parameter n is motivated by the following gures. [INSERT Table 2 Here] Table 2 collects the age dependency ratios (the ratio of dependents to working age population) in some developing countries. To be consistent with these gures, the dependency ratio 13 should be around 63% (so that n ' 0:58). Assuming that each generation lives 25 years, n = 0:6 corresponds to a rate of population growth about 1:9% a year. 18

19 Finally, the key-parameter of our model is : First, indicates the capacity for a country to borrow from the rest of the world. Second, is a determinant of agents income as it measures the magnitude of arbitrage premia. From (21), the constraint is binding. Thus, we evaluate the parameter on the basis of = B=(0:75Y ) with 0:75Y the labor income share of GDP 14. Figure 2 shows that very often 0:3 [INSERT Figure 2 Here] As increases, the long-run domestic return on capital converges to the world return on capital. Indeed, the higher ; the higher the life-cycle income and non-tradable consumption, the more appreciated the RER. When the tradable sector is capital intensive, the domestic return on capital is a decreasing function of : Thus, there exists > 0 such that r d = r: When < the country is credit constrained and the RER results from demand and supply on non-tradable goods. Otherwise, we recover the Balassa-Samuelson (BS) case and the RER only depends on productivity spread between sectors. In this calibration, > 4:9. [INSERT Table 3 Here] Table 3 gives the reaction of the long-run RER in the traditional BS case - that is with perfect capital mobility ( = 0)- and in the CE - that is r d (R) > r ( > 0)- after a 30% increase in tradable productivity. I reported domestic interest rates and wages too to check that r d i > r i = 0; 1 is always ful lled. Let 0 denote the initial steady state and 1 the steady state with a higher tradable productivity. We could notice that the domestic interest rate shows very low uctuations 15 while the wage increases. A rise in a T exerts a positive direct e ect and a negative indirect e ect (through the rise in k T ) on r d : Since, the rise in a T leads to an increase in tradable production the wage increases even if the domestic interest rate is constant. We observe that the behavior of the RER is very similar in the CE case and in the BS setting. Hence, the presence of a credit constraint does not a ect the qualitative result: the RER still appreciates after a productivity shock. Nevertheless, this real appreciation 19

20 results from a rise in non-tradable demand that overcomes the rise in non-tradable supply. In contrast, in the BS case the real appreciation results only from factor movements between sectors. Figure 3 plots the RER reaction to a 30% rise in a T for di erent levels of the constraint and in the BS case. The level of the constraint is reported near each point while the BS case is depicted by the larger line. [INSERT Figure 3 Here] We observe that a ects the RER reaction to a rise in a T. Indeed, a rise in a T leads to a new factor allocation between sectors. These factors movements do not depend on the level of the credit constraint whereas the long-run global capital intensity k does. According to equation CA, the higher the larger is the negative wage e ect. The more the country can borrow on the international capital market, the larger the fall in k which results from the productivity shock and hence the larger the rise in the production of non-traded good. It follows that the real appreciation is milder when the country is less constrained since the production of non-traded good increases more after a productivity shock. We can notice that the RER appreciation predicted by the CE model even with = 0 remains lower than the RER appreciation predicted by the BS analysis. Finally, the Balassa-Samuelson analysis seems to be still valid in the presence of a credit constraint. However, the CE model suggests that RER changes experienced by Asian countries do not only result from productivity shocks but also from other structural parameters. In the BS case, the RER appreciation could only be explained by a faster growth in tradable productivity. In the CE model, the real appreciation could be explained by a faster growth in tradable productivity or by a fall in the birth rate, a fall in the rate of time preference or a slackening of the credit constraint as suggested by Figure 4. Figure 4 depicts the locus (CA)-(NM) for the mentioned values of the parameters ; and : Long-run RER (R ), such that (CA)=(NM), is on the horizontal axis. [INSERT Figure 4 Here] The lower 16 the more the RER appreciates following a productivity shock. The lower 20

21 the higher the domestic return on capital, the higher the arbitrage premia and so does the life-cycle income. On one side, a lower tends to increase demand on non-tradable goods. On the other side, a lower tends to increase capital accumulation which a ects negatively the non-tradable supply when non-tradable sector is labor intensive. These two e ects imply that the real appreciation is higher for a more stringent constraint. To confront the CE model with empirical evidence, we calibrate the model for Asian countries. We analyze a productivity shock combined with a fall in the age dependency ratio. Results are summarized in Table 4. We refer to the period because we use Ito et al. (1999) data for RER changes. [INSERT Table 4 Here] Table 4 provides some calibrations of the CE model considering the changes in the age dependency ratio. We use a CES utility function U (c t ; d t+1 ) = (1 ) 1 c 1 t + (1 ) (1 ) 1 d 1 t+1, > 0 instead of (11). We examine the two extreme cases for intertemporal elasticity of substitution 1 = 1 and 1 = 0:1. Results are more able to t changes of RER observed between 1970 and 1992 in a CE than in the BS case. The reason is that the real appreciation coming from productivity is partly o set by a fall in the age dependency ratio. In such an OLG model, consumption spending decreases when the share of working agents in total population increases, exerting a depreciating e ect on the RER. 5 Conclusion The analysis above shows that the Balassa-Samuelson (BS) theory must be enriched to explain the real exchange rate (RER) appreciation in developing countries. Indeed, investors on world capital markets require risk premia for developing countries, and capital cannot be considered a perfectly mobile factor. As a result, there is a long lasting stage of development during which the domestic return on capital exceeds the world return and hence the BS analysis does not necessarily hold. 21

22 This article complements the traditional analysis questioning the e ects of an increase in tradable productivity during this stage of development. Since capital is imperfectly mobile, we must consider both supply and demand factors as determinants of the RER. In this way, an increase in tradable productivity involves some additional e ects on the demand side compared to those pointed out by the BS analysis. A calibration of the model seems to match empirical evidence: the RER depreciates or experiences a low appreciation despite high growth rates because the working age population has increased in Asian developing countries since

23 References [1] Balassa B., The purchasing power parity doctrine: a reappraisal, Journal of Political Economy, 72 (1964): [2] Beine B., F. Bismans, F. Docquier and S. Laurent, Life-cycle behavior of US household agents: a nonlinear GMM estimation on pseudopanel data, Journal of Policy Modeling, 23 (2001): [3] Betts C. and T. Kehoe, Real exchange rate movements and the relative price of non-traded goods, Federal Reserve Bank of Minneapolis (2001). [4] Canzoneri M., Cumby R. and B. Diba, Relative labor productivity and the real exchange rate in the long run: evidence for a panel of OECD countries, Journal of International Economics, 47 (1999): [5] Collins S. and B. P. Bosworth, Economic growth in East Asia: Accumulation versus Assimilation, Brookings Papers on Economic Activity, 2 (1996): [6] Chinn M., Before the fall: were East Asian currencies overvalued?, Emerging Markets Review, 1 (2000a): [7], The usual suspects? Productivity and demand shocks and Asia-Paci c real exchange rates, Review of International Economics, 8 (2000b) : [8] Engel C., Accounting for US real exchange rate changes, Journal of Political Economy, 107 (1999): [9], Long-run PPP may not hold after all, NBER WP no. 5646: (1996). [10], Real exchange rates and relative prices - an empirical investigation, Journal of Monetary Economics, 32 (1993): [11] Engel C. and J. H. Rogers, How wide is the border?, American Economic Review, 86 (1996):

24 [12] Grafe C. and C. Wyplosz, The real exchange rate in transition economies, CEPR Discussion Paper 1773: (1997). [13] Devereux M., Real exchange rate trends and growth: a model of East Asia, Review of International Economics, 7 (1999): [14] Ito T., P. Isard and S. Symansky, Economic growth and real exchange rate: an overview of the Balassa-Samuelson hypothesis in Asia, in Ito Takatoshi, and Anne O. Krueger (ed) Changes in exchange rates in rapidly developing countries: theory, practice, and policy issues, University of Chicago, 1999, pp [15] Jones R. and S. Easton, Factor intensities and factor substitution in general equilibrium, Journal of International Economics, 15 (1983): [16] Kim J. and L. Lau, The Sources of Economic Growth of the East Asian Newly Industrialized Countries, Journal of the Japanese and International Economies, 3 (1994): [17] Knetter M., International comparisons of price-to-market behavior, American Economic Review, 83 (1997): [18] Lapham B. J., A dynamic general equilibrium analysis of deviations from the laws of one price, Journal of Economics Dynamics and Control, (1995): [19] Mahbub Morshed A.K.M. and S. Turnovsky, Sectoral adjustment costs and real exchange rate dynamics in a two-sector dependent economy, Journal of International Economics, 63 (2004): [20] Mendoza E. and K. Smith, Margin calls, trading costs, and asset prices in emerging markets: the nancial mechanics of the sudden stop phenomenon, NBER WP 9286, (2002). [21] Obstfeld M. and K. Rogo, Foundations of International Macroeconomics, Cambridge: MIT Press,

25 [22] Samuelson P., Theoretical notes on trade problems, Review of Economics and Statistics, 23 (1964):1-60. [23] Young A., Accumulation, exports and growth in the high performing Asian economies: a comment, Carnegie-Rochester Conference Series on Public Policy, 40, (1994a): [24], Lessons from the East Asian NICS: A Contrarian View, European Economic Review, 38 (1994b): [25], The Tyranny of Numbers: Confronting the Statistical Realities of the East Asian Growth Experience, Quarterly Journal of Economics, 110 (1995):

26 Notes : 1. Another investigation of a productivity shock with nancial frictions on capital markets is Mendoza and Smith (2002). They do not consider the RER in their one-sector open economy model. 2. In this model, the capital uses non-traded good in order to preserve dynamics without introducing adjustment cost in the capital accumulation. Only the capital reallocation between sectors is costly. 3. This is a general property: Jones and Easton (1983) demonstrate that in a 2x2 structure (2 mobile factor, 2 sectors) with constant returns to scale, returns to factors and factor allocation are not relied on the initial factor endowment. 4. If we consider a Cobb-Douglas example as the one developed in Section 4, then we have = (1 ) (1 ) 1 and > 1 when the tradable sector is capital intensive. 5. According to Ito et al. (1999) the tradable sector is capital intensive in an adavanced stage of development. It could be the case for emerging Asian countries for example. 6. This assumption follows Obstfeld and Rogo. There are two justi cations. First, the international capital market is imperfect and the amount that banks lend to agents is a function of their current income. Since only the young agents can borrow, the constraint depends on the wage. Second, it is easier for lenders to seize labor income than physical capital income. 7. The BS analysis is a special case of this model when the domestic return on capital converges to the world one. 8. This condition is satis ed in the Cobb-Douglas case described in the following section. 9. If we include public spending on non-tradable goods in the model, a rise in public spending would lead to real appreciation. 10. Mahbub Morshed and Turnovsky (2004) used these empirical features for their calibration. 11. Total output is in the model expressed in units of tradable goods: Y = Y T + RY N 26

27 with Y T (k t ; R t ) a T l T (k t ; R t ) N t f (k T (R t )) : 12. The share of traded output is high but seems in accordance with evidence in Asian countries, especially export-oriented. 13. The dependency ratio N t 1 =N t is (1 + n) 1 in such an OLG setting. 14. B corresponds to the Net Foreign Assets (current LCU) and Y to the Gross Domestic Product at market prices (current LCU). 15. We observe r d 1 r d 0 = 1:10 9 : 16. This mechanism holds for : 27