1 Non-traded goods and the real exchange rate

Transcription

1 University of British Columbia Department of Economics, International Finance (Econ 556) Prof. Amartya Lahiri Handout #3 1 1 on-traded goods and the real exchange rate So far we have looked at environments where all goods are traded. In reality a number of goods in open economies are not traded at all, i.e., they are non-traded goods. In such environments even if the law of one price holds for all traded goods, there would be changes in the relative price of goods and services due to changes in demand and supply conditions within the small open economy that we have been considering. Hence, relative prices and the cost of living would be di erent in di erent countries. Since the data show big di erences in costs of living across countries as well as big changes in them, over time, introducing a non-traded goods sector and studying the behavior of the real exchange rate the ratio of national price levels is the goal of this lecture. We continue to assume that this is a small open economy perfectly integrated with the rest of the world in both capital and goods markets. However, we now assume that there are two goods: tradables and non-tradables. Consumers derive utility from consuming both goods. As before, we consider a representative agent economy. The household receives an endowment y T of the tradable good and y of the non-tradable good every period. The international price of the tradable good is constant and normalized to unity (without loss of generality). The tradable good is the numeraire. We will use p to denote the relative price of non-tradables in terms of the tradable good. Hence, this is the inverse of the real exchange rate. A rise in p is a real exchange rate appreciation while a fall in p will be referred to as a 1 camartya Lahiri. ot to be copied, used, or revised without explicit permission from the copyright owner. 1

2 real exchange rate depreciation. Utility function: 1X t u(c T t ; c t ); (1) t=0 where c i t denotes consumption of good i where i = T; ; and 2 (0; 1) is the subjective discount factor. Flow budget constraint: B t+1 + c T t + p t c t = RB t + y T t + p t y t ; (2) where B t is the (net) stock of an internationally-traded bond (denominated in terms of the importable); R is the (constant and exogenously-given) gross world real interest rate. Intertemporal budget constraint: For future reference, we can also determine the household s lifetime budget constraint by using the ow constraint (2). As before, this yields: 1X t=0 t 1 R c T t + p t c t y T t p t y t = RB0 (3) First order conditions: Consumers maximize (1) subject to a sequence ow budget constraints given by (2) for given b 0. First-order condition is: Combining equations (4) and (5) gives u T (c T t ; c t ) = Ru T c T t+1; c t+1 : (4) u (c T t ; c t ) u T (c T t ; c t ) = p t (5) u (c T t ; c t ) u c T t+1; c t+1 = R p t (6) 2

3 The rst condition is standard it says that with access to perfect capital markets and with R = 1, the household should equalize the marginal utility of tradable consumption over time. ote however that this no longer implies that consumption of tradables must be constant over time. In particular, if consumption of non-tradables changes then so must c T in order to keep marginal utility from tradable consumption unchanged. The second condition is new. It says that at an optimum the household should equate the marginal rate of consumption substitution between non-traded and traded good to the relative price of non-tradables. Equation (6) governs the optimal evolution of the marginal utility of non-tradables. This condition shows that the relevant real interest rate for determining the time pro le of marginal utility from non-tradable consumption is not R but rather it is R pt. This de nes the domestic real interest rate: Market clearing: R d R p t (7) The demand and supply of tradable goods must equal each other period by period. Hence, c t = y t : (8) Resource constraint: Substituting equation (8) into equation (3), we get the economy s intertemporal resource constraint: Current account: 1X t c T t = RB 0 + t=0 1X t yt T (9) t=0 The current account follows from combining (2) and (8): B t+1 B t = rb t + y T t c T t : (10) 3

4 Equilibrium relations: Substituting equation (8) into the rst-order conditions gives u T (c T t ; yt ) = u T c T t+1; yt+1 (11) Lastly, equation (6) in equilibrium reduces to u (c T t ; y t ) u T (c T t ; y t ) = p t (12) u (c T t ; yt ) = u c T t+1; yt+1 p t where we have used our standard assumption R = 1. It should be clear from the rst condition above that the path of c T will depend on the path of the non-traded endowment y. In particular, if u T > 0 then c T and y will tend to comove. In general, one can use equations (11) to determine the time path of c T given a path for yt and an arbitrary c T 0 : This information can then be combined with the resource constraint (9) to solve for c T 0. Equation (12) then determines the complete time path of the real exchange rate. Perfect foresight equilibrium path: We will assume throughout that endowment of both goods is constant over time; that is, yt T = y T and yt = y for all t 0. Moreover, assume that u(c T ; c ) is homothetic. Hence, u (c T t ; yt ) c T u T (c T t ; yt ) = { t ; { 0 > 0. c t Moreover, the constancy of the endowment path implies that consumption of both goods must be constant over time. Hence, the resource constraint implies c T = rb 0 + y T while homotheticity combined with (12) gives rb0 + y T p = { 4 y

5 Moreover, this is a stationary economy which jumps to its steady state instantaneously. A couple of features of this economy are worth noting. First, higher y T implies a higher (or more appreciated) real exchange rate. By symmetric logic, a higher supply of non-tradables implies a more depreciated real exchange rate. Second, economies with higher relative supply of tradables to non-tradables will have higher price levels. ote that since the price of traded goods is the same for all countries, the only source of di erences in the price level across countries is the price of non-traded goods. 1.1 Temporary supply shock We now consider environments where there are temporary shocks as opposed to the permanent shocks that we analyzed above. Temporary shocks are likely to generate external imbalances. Hence these shocks facilitate an analysis of the relationship between the real exchange rate and external imbalances. In particular, we want to know whether the real exchange rate is likely to depreciate during times when the economy is running an external imbalance or will the opposite happen. To carry out this analysis, we simplify our framework marginally. Assume that preferences are separable, i.e., u(c T ; c ) = log c T + log c Separability implies that the rst-order conditions are now given by c T t = c T t+1 y t+1 y t p t = ct t y t = p t where we have substituted in the market clearing condition for non-traded goods. Hence, c T must be constant throughout. The time path of p will thus depend solely on the time path of the non-traded endowment. We set initial assets to zero. Hence, in the initial steady state c T = y T, c = y ; and p = y T =y. Suppose now at date t = 0 there is an unexpected decline in both y T and 5

6 y such that yt y remains unchanged. However, both y T and y are expected to return permanently to their original levels at date t = 1. ote that if the shock were permanent then consumption of both goods would jump down permanently at t = 0 and leave the real exchange rate unchanged. In this temporary case however, since c T is constant throughout, it must jump down to its new permanent income level at date 0. Market clearing for nontraded goods implies that c must jump down at date t = 0 and rise back up to its original level at t = 1. What is the e ect of this temporary shock on the real exchange rate? Since y 1 > 1, y0 equation (6) implies that p 0 p 1 > 1. Hence, the real exchange rate must depreciate at date t = 1. To determine the behavior of the real exchange rate at date 0 note that while both y T and y fall equiproportionately, c T falls proportionately less than c. Hence, p 0 rises at date 0, i.e., the real exchange rate appreciates on impact. Since c T falls by less than the fall in y T, there is a trade and current account de cit at date 0 followed by a permanent trade surplus from t = 1 to payo the interest cost of the borrowing at date 0. with an exchange rate appreciation. Hence, in this case, a current account de cit goes hand-in-hand The ip-side of this experiment would suggest that current account surpluses would go hand-in-hand with real exchange rate depreciations. Intuitively, the negative supply shock induces an excess demand for both goods at date t = 0. The economy responds by importing more of the tradable good from abroad. This induces the trade and current account de cit. Supply of the non-tradable good however is in xed supply. To clear this market, consumers must be induced to consume less. This is achieved through an increase in the relative price of non-tradables, i.e., a real exchange rate appreciation. ote that in this experiment there is no sense in which the current account de cit at date t = 0 is being caused by a real exchange rate appreciation. Rather, they are both equilibrium responses to a common output shock. 6

7 2 Sources of real exchange rate uctuations The cross-country data reveals a lot of volatility in the real exchange rate. A literature inspired by the work of Engel (1999) has focused on decomposing the uctuations in the observed real exchange rate into its various components. Start with the basic de nition of the real exchange rate: q = EP P where E is the nominal exchange rate, P is the domestic price level and P is the foreign price level both expressed in terms of their own currencies. Assuming that both the home and foreign countries produce two types of goods, tradables and non-tradables, the price indices can be re-written as P = P T P 1 P = P 1 T P where the subscripts T and denote tradable and non-tradable goods, respectively. and denote the expenditure shares of the tradable good in each country. Using the two price indices, the real exchange rate can be written as q = (EP T ) PT P 1 (EP )1 This, in turn, can be rewritten as P EP q = T P 1 T P PT P T 1 In log terms then, the real exchange rate can be decomposed into rer = fe + p T p T g + f(1 ) (p p T ) (1 ) (p p T )g The term within the rst curly bracket on the right hand side is the relative price of tradables between home and abroad while the second curly bracket gives the ratio of the relative price 7

8 of non-tradable to tradable at home and abroad. E ectively, this expression decomposes the real exchange rate (or di erences in the cost living between home and abroad into the part that comes from variation in the prices of tradable goods across the two countries (when expressed in the same currency) and the part that comes from variations in the relative price of non-tradable goods. The key point to note from the expression above is that if the law of one price holds then there should be no variation in the price of tradable goods across countries, i.e., the rst term in the right hand side above should be zero. Crucially, even if it fails to hold in levels due to transportation and tari s, there is no reason for it vary over time as long as the basic principle of the law of one price holds, an assumption that we have maintained throughout. Hence, under our assumption the only reason for the real exchange rate to deviate from unity and/or time variations in the real exchange rate is the second component, i.e., movements in the relative price of non-tradables. Indeed this has been a key mechanism for understanding real exchange rates in most of the literature that has focused on small economies or developing countries. One of the rst studies to attempt a systematic examination of the sources of real exchange rate uctuations is the study by Engel (1999). In a striking result Engel showed that almost all of the uctuations of the US real exchange rate with other G7 countries was due to uctuations in the price of tradable goods across countries, suggesting that the failure of the law of one price was the key reason underlying real exchange rate volatility. Engel also found the same result for the US-Mexico real exchange rate. These results raised serious issues regarding the empirical plausibility of models that focus on non-traded goods as the main source of real exchange rate variability. Recent work using the same methodology but applying it to developing countries has revealed an interesting contrast between developed and developing countries. Mendoza (2005) examined data for Mexico and found that uctuations in the relative price of non-tradable goods was the more important source of uctuation in the Mexican real exchange rate(relative to uctuations in the relative price of tradable goods). In particular, Mendoza found that 8

9 during periods when Mexico was undertaking explicit exchange rate management, about 70 percent of the real exchange rate variability was due to variability in the relative price of non-tradable goods. In a related study Burstein, Eichenbaum and Rebelo (2005) studied Argentina, Mexico, Korea, Brazil and Thailand and found that in the aftermath of the large nominal exchange rate devaluations, most of the associated depreciation of the real exchange rate was due to changes in the relative price of non-tradables. They also found that the dollar price of tradable goods at the dock didn t change much while the dollar price at the retail changed much more. They interpret this as suggesting that the law of one price held reasonably well but the pass-through of the change to retail prices was slower due to the non-tradable distribution sector and stickiness of those prices. 9