- Email: [email protected]
Is there a J-curve?
Journal
of Monetary
Economics
24 (1989) 53-68.
North-Holland
IS THERE A J-CURVE?* Andrew K. ROSE and Janet L. YELLEN University of California, Berkeley, CA 94720, USA Received June 1987, final version received April 1988
If the response of the value of the trade balance to movements in the real exchange rate is described by a J-curve, then a real depreciation initially worsens a balance of trade deficit, only improving it over time. This paper investigates whether a J-curve can be detected in the last twenty-five years of American data. No statistically reliable evidence of a stable J-curve is detected. The model is checked extensively to support this finding.
1. Introduction
It is commonly believed that the response of a country’s trade balance to movements in its real exchange rate follows a J-curve. According to this view, a currency depreciation improves the balance of trade in the long run, but worsens the trade balance in the short run. The ‘perverse’ initial response occurs if the immediate effect of a depreciation is to raise spending on imports, measured in local currency, by more than any initial increase in export revenues. The trade balance is likely to decline subsequent to a depreciation if export and import volumes adjust slowly to movements in relative prices, but import prices respond quickly to exchange rate changes. This paper examines the question of whether the American trade balance has habitually displayed a J-curve. The major finding is a negative one; the hypothesis of a J-curve can be rejected robustly with American data. We find no convincing evidence that the short-run response of net merchandise trade to real exchange rate movements is perverse, either in bilateral U.S. trade or in *We would like to thank: Pier Ardeni and Matt Lynde for research assistance; William Helkie of the Federal Reserve Board for providing data; and Jeff Frankel, William Helkie, Peter Hooper, Ellen Meade, Dick Meese, Jurg Niehans, Jim Wilcox, a referee, and seminar narticinants at Berkeley and Stanford for comments. The research for this paper was supported by the buggenheim Foundation, the National Science Foundation under arant SES 86-005023. and the Institute for Business and Economic Research of the Universit; of California, Berkeley. This is a condensed version of a working paper with the same title. That paper, as well as our data and programs, are available upon request.
0304-3932/89/$3.5001989,
Elsevier Science Publishers
B.V. (North-Holland)
54
A. K. Rose and J. L Yellen, Is there a J-curve?
aggregate U.S. data. In addition, there is little evidence of a reliable long-run relationship between the U.S. trade balance and the real exchange rate. In section 2 the theory relevant for the empirical work is presented. Section 3 contains a discussion of the modelling approach and some data diagnostics. The econometric technique involves the estimation of a ‘partial’ reduced form equation for the net merchandise trade balance. Tests for unit-roots reveal nonstationarity in the data. Cointegration tests cast doubt on the existence of any underlying stationary relationship between the levels of the real trade balance and its theoretically most important determinants: the real exchange rate, domestic and foreign real income. Section 4 describes the main tests for the existence of the J-curve. Baseline equations are estimated with instrumental variables on bilateral data. No evidence of a J-curve is found. A negative short-run reaction of the trade balance to the real exchange rate is not detected; neither is a long-run positive response. The sensitivity of these results is systematically checked in section 5. A variety of auxiliary assumptions are relaxed, but the statistical rejection of the J-curve is found to be robust. Section 6 uses aggregate data to test for the J-curve. The choice of estimation method is found to influence the results. If OLS is used, weak evidence of a J-curve is detected. However, instrumental variables techniques are shown to be appropriate and reveal no signs of a J-curve. A final section contains a few conclusions.
2. Theory Standard ‘two-country’ models of trade [see, for example, Lindert (1986)] assume that the volume of imported goods demanded by domestic (foreign) residents depends positively on real domestic (foreign) income and negatively on the relative price of imported goods:
D,,,=D,(Y,p,)
and
D,*=D,*(Y*,P,*),
where D, (02) is the quantity of goods imported by the home (foreign) country; Y (Y*) is the level of real income measured in domestic (foreign) output; p, is the relative price of imported goods to domestically produced goods, both measured in home currency; and p,* is the analogous relative price of imports abroad. These equations represent Marshallian demand functions, with relative price and income elasticities expected to be negative and positive in sign, respectively. A number of different approaches have been adopted to analyze the determinants of supply. One simple model postulates a world of perfect competition, where the supply of exportables in each country depends posi-
A. K. Rose and J. L Yellen, Is there
55
a J-curve?
tively on the relative price of exportables:’
(2) where S, and S,* are the supplies of home (foreign) exportables, respectively; p, is the home country relative price of exportables, defined as the ratio of the domestic currency price of exportables, P,, to the domestic price level, P; p,* is analogously defined as the foreign currency price of exportables, P,*, divided by P*, the foreign price level.
The domestic relative price of imports can be expressed as p,=E.P,*/P=(E.P*/P).(P,*/P*)=q.pp,*,
(3)
where E is the nominal exchange rate, defined as the domestic currency price of foreign exchange; and q is the real exchange rate, defined as q = E. P*/P. Analogously to (3), the relative price of imports abroad is Pt = PJ4.
(4)
In equilibrium, quantities transacted and the relative prices of exported goods in each country are determined by the two equilibrium conditions: D,,, = S,*
and
D*=S m
(5)
X’
The value of the home country’s balance of trade in real (domestic output) terms, B, is the value of net exports in domestic currency divided by P: B=p;D,*--q.p,*.D,,,.
(6)
In the presence of capital flows, B need not equal zero. Eqs. (l)-(5) can be solved for the levels of domestic imports and exports and the relative price ratios, p, and p,*, as functions of q, Y, and Y*. Accordingly, B can be written as a ‘partial reduced form’ (i.e., an equation derivable from a set of partially solved structural equations): B = B(q,
Y, Y*).
(7)
In this paper, eq. (7) is treated as the equation of interest. The estimated empirical equations are essentially log-linear approximations to (7) augmented by a ‘suitable’ number of lags, a constant, and a ‘well-behaved’, ‘small disturbance term to represent ‘unimportant’ omitted factors. ‘Many models of imperfectly competitive similar to (7) below; see Mann (1986).
import
supply lead to a ‘reduced
form’ equation
for B
56
A.K. Rose and J. L. Y&n,
Is there n J-curve?
The effect of a depreciation of the real exchange rate on the real balance of trade depends on the sign of the partial derivative of B with respect to q in (7). This effect is positive if the ‘Bickerdike-Robinson-Metzler (BRM) condition’ is satisfied [Dornbusch (1975)]; in the case of initially balanced trade and infinite supply elasticities, this reduces to the well-known Marshall-Lerner condition. Using the notation of our model, the Bickerdike-RobinsonMetzler condition is
-q.D,;p.~[(1-1).&*/(~+&*)1
‘0.
where q(v*) and E (E*) denote the absolute values of the price elasticities of demand and supply respectively at home (abroad). Estimating this partial derivative in both the long and short run is the primary objective of this paper. A J-curve is defined as the combination of a negative short-run derivative with a positive long-run derivative. The question posed - under what circumstances does a real depreciation improve the real trade balance in the long run but worsen it in the short run? - is distinctly partial equilibrium in nature.’ A typical J-curve scenario runs as follows: the initial effect of a depreciation is to raise the domestic prices of imported goods, because prices of export goods are sticky in sellers’ currencies. Thus q rises while p, and p_,? remain fixed in (6). There is only a small immediate impact on the volume of trade flows [i.e., D,,, and D,* in (6) change little]. Therefore, the value of exports ( P,~. D,*) rises only slightly, while the value of imports (q .p: . D,* ) rises substantially due to the increased cost of an unchanged quantity of imports. Consequently, the balance of trade in real terms deteriorates in the short run. Naturally, this argument is predicated on the assumption of a large export supply elasticity and a low short-run import demand elasticity. As time passes, the increased price of imports eventually diminishes import volume; export volume and value also increase over time because the price elasticity of foreign import demand is larger in the long run than in the short run. Thus, although the depreciation has an initially negative impact on the real trade balance. the effect is reversed over time, leading to a cumulatively positive effect; thus the short-run response is ‘perverse’. The graph of the response of the trade balance over time to a once-and-for-all real depreciation, resembles a ‘J’ tilted to the right. The prevailing view appears to be that a J-curve exists; the perverse effect is thought to have a duration of about a year [e.g., Dornbusch and Krugman (1976) and Krugman and Baldwin (1987)]. ‘The theoretical model consisting of (l)-(6) is not complete; in a full general equilibrium. y. Y. and Y* are also endogenous. If the exchange rates are endogenous. it is not apparent that the BRM condition provides the answer to any interesting question [Dombusch (1975)].
A. K. Rose and J. L. Yellen, Is there a J-curve?
57
No theoretical argument leads one to the presumption that the response of the trade balance to an exchange rate perturbation is initially perverse. A set of sufficient conditions consists in two logically separate empirical conditions: low short-run price elasticities of demand for imports both at home and abroad, and a swift response of U.S. import prices to the exchange rate (due, in the theoretical model presented above, to a relatively large foreign export supply elasticity). There is also no theoretical reason why the long-run response of the balance of trade to a real depreciation must necessarily be positive; this occurs only if the BRM condition is satisfied. While the conditions which lead to a J-curve may strike some as realistic, the complement to this set of hypotheses seems equally plausible. In particular, there is evidence [see Mann (1986)] that import prices actually adjust slowly to exchange rate changes, which would undermine the initial negative effect embodied in the J-curve. On balance, the existing empirical literature does not point strongly to either view. Indeed, the paucity of evidence in the academic literature is striking. 3. Methodology and data preliminaries In this section, the methods used in this paper are briefly contrasted with those of other investigators, the data is described, and diagnostic tests for unit-root nonstationarity and cointegration are presented. 3. I. Methodology The vast majority of the existing empirical literature derives the impact of exchange rates on trade by estimating and solving a set of structural supply and demand equations for exports and imports. These equations represent variants of (1) and (2); see, e.g., Hooper and Helkie (1987), Krugman and Baldwin (1987), and Warner and Kreinin (1983).3 The majority of the literature estimates ‘pass-through’ equations as empirical specifications of (2); these typically take the form
Pm= P,(R P*, E, Z,> and
P,* = P,*(P,
P*, E, Z,),
(8)
where Z, is a vector of relevant exogenous variables. These markup equations summarize pricing behavior by firms. The effect of a depreciation can then be 3Many discussions of the J-curve are based on estimates of only a subset of the structural equations. For instance, Spitaller (1980) discusses the short-run effects of a depreciation based on pass-through equations alone, explicitly abstracting from volume effects, while Wilson and Tahacs (1980) assume that export prices in local currencies remain unchanged following a depreciation. For counterevidence concerning the validity of both of these extreme assumptions see Hooper and Helkie (1987) or Krugman and Baldwin (1987).
58
A.K. Rose and J. L. Yellen, Is there a J-cume?
determined by solving the empirical ‘structural’ (volume and pass-through) equations [(l) and (8)] for the ‘reduced form’ corresponding to (7). Using this approach, Krugman and Baldwin’s estimates yield a J-curve with a perverse effect with a cumulative duration of four quarters; the estimates of Artus (1975) and Hooper and Helkie (1987) imply J-curves lasting only one quarter. The analysis in this paper does not distinguish between the price and volume effects of a real depreciation. Rather than solving estimated versions of (1) and (2) eq. (7) is-instead estimated directly. There is only one theoretical restriction that this approach imposes on the estimation process: homogeneity of degree zero in P, P*, and E. This restriction is appropriate in most models; the assumption is later relaxed and tested. To determine the nature of the J-curve, direct estimation of (7) is preferable to the more detailed structural approach prevalent in the literature. The question of interest concerns the dynamic response of the net trade balance, measured in real (domestic output) terms, to movements in the real exchange rate. The answer to this question is directly obtainable from (7) and does not require knowledge of the structural parameters in (l)-(2). We have little confidence that existing volume and pass-through (really demand and supply) equations provide a good approximation to the data generation process.
3.2. Data Most previous studies of the trade balance use extremely aggregated data; this is potentially troublesome for several reasons. If one considers the domestic country to be the U.S. and the foreign country to be the rest of the world (ROW), then to estimate (7) one needs to construct proxies for both ROW income and the American real exchange rate vis-a-vis ROW. In an effort to minimize measurement problems, bilateral data with the other members of the Group of Seven (Japan, Canada, U.K., France, Germany, and Italy) are used for much of the analysis. Trade with the other members of the Group of Seven has played an important role for America throughout the postwar period. Further, if the response of the trade balance to the real exchange rate varies by country with the nature of the trade, there is another benefit from disaggregation. Bilateral data also largely avoids prob!ems associated with petroleum imports and agricultural exports. To compare our methodology with those of previous papers, widely used aggregate data are also exploited. The basic source for the balance of trade data is the IMF’s monthly bilateral merchandise export and import series. These series give the value of U.S. merchandise imports and exports in nominal dollar terms. The dependent variable in our analysis - B, the ‘real’ net merchandise trade balance - is defined as the difference between merchandise exports and imports, measured in current U.S. dollars, deflated by the American GNP deflator. Conceptually, B measures the net merchandise trade balance in units of ‘U.S. output’.
A. K. Rose and J. L. Yellen, Is there a J-curve?
59
Because export and import data is collected both at domestic and foreign borders, there are two measures of trade flows. Both are used below. Logarithms of American and foreign real GNP/GDP are used as demand proxies. The real exchange rate is the log of the product of the nominal bilateral exchange rate, the foreign GNP deflator, and the inverse of the U.S. GNP deflator. As the nominal exchange rate accounts for most movements of the real exchange rate, the results are insensitive to the exact choice of price deflators. Our desire to use GNP measures as both income proxies and as the appropriate price deflators constrained the empirical work to the quarterly frequency. However, the use of monthly data only strengthens the conclusions that are found below. Most of the data spans the first quarter of 1960 through the last quarter of 1985; the Italian data is presently unavailable for the last three quarters of 1985, while the French data spans 1965 through the third quarter of 1985. 3.3. Tests for unit-roots and cointegration Given the time-series nature of the data, a useful first diagnostic is to test for unit-roots in the variables included in (7) using both Dickey-Fuller and Phillips tests (allowing for drift and including four ‘augmenting’ lags of the difference). The evidence strongly indicates the presence of a single unit-root in virtually all variables at normal significance levels, a result consistent with the macroeconomic literature [e.g., Nelson and Plosser (1982)j. Treatment of this nonstationarity is thus essential for meaningful empirical results. Insofar as the individual variables in (7) are statistically integrated of order one, cointegration of the real trade balance, the real exchange rate, real output, and real foreign output is a necessary condition for the existence of any stationary relationship such as (7). Accordingly, tests for cointegration between B, q, Y, and Y* were computed using the methods of both Engle and Granger (1987) and Stock and Watson (1986). The results do not indicate the presence of cointegration at standard significance levels. Inclusion of oil or commodity prices does not change these results. The evidence from the cointegration test casts doubt on the existence of an underlying stationary steady-state relationship between the (levels of the) balance of trade and the variables most often considered to be its important determinants. These tests are not based on posited structural models and do not suffer from simultaneity problems. The results suffice to reject prima facie the belief that there is an easily quantifiable steady-state effect of the exchange rate on the balance of trade in any model which implies (7). A second implication is that first-differencing of all variables is not merely warranted, but also necessary for statistically reliable hypothesis tests. One may want to allow for MA errors in the event that the data has been overdifferenced. However, if one does not make allowance for the unit-root
60
A. K. Rose and J. L. Yellen. Is there u J-curw:’
nonstationarity manifest to traditional asymptotic variables in levels is also in the Granger-Newbold operation greatly reduces
4. Baseline
in the data by first-differencing the variables, appeals distribution theory are untenable. Analysis of the likely lead to regression results which are ‘spurious’ sense. A further advantage of differencing is that the multicollinearity.
results
This section presents baseline results concerning the determinants of U.S. bilateral trade patterns and examines the estimated exchange rate coefficients for evidence of the J-curve pattern. The evidence rejects the hypothesis of a statistically significant and stable J-curve. Eq. (7) models the trade balance as a linear function of GNP, foreign GNP, and the real exchange rate; the findings of the previous section lead one to transform all variables by taking first-differences of logarithms (except for B which is merely first-differenced). Accordingly, the empirical equation which is estimated is of the form
AB(t)=a+
5 [fi(i)AY(t-i)++)AY*(f-i)] /=0 + i 8(i)Aq(tI= 0
i) + u(t).
(9)
where A denotes the first-differencing operation and u(t) is modelled as both white noise and a MA(4) process. In the absence of any consensus view on the lag structures of the relevant explanatory variables. an agnostic approach is taken. The current and four lags of both foreign and domestic income are included in all the regressions. Four alternatives are considered for the real exchange rate: including only the current rate, the current and four lags of the rate, current plus eight lags, and current plus twelve lags. A constant is estimated to allow for potential deterministic drift [recently emphasized by Krugman and Baldwin (1987)]. Inclusion of the current values of income and the exchange rate immediately raises concerns about potential simultaneity bias. Measurement errors are an additional concern. Instrumental variables estimation is used in an attempt to correct both these problems. Unfortunately, it is not easy to find reliable instruments. For example, interest rates are a logical instrument for the exchange rate, since interest and exchange rates are theoretically related in a world with capital mobility; however, the interest rate may also be correlated with the errors of the trade balance equation if intertemporal substitution drives consumption and hence imports. Moreover. it is difficult [Meese and
A. K. Rose and J.L.
Yellen, Is there a J-curve?
61
Table 1 &i-squared
tests of the significance
of lags of the real exchange of trade equations (9).
rate in quarterly
Critical values xis
0.01
Chi-squared U.K.
Canada
France
post-war
balance
tests Germany
Italy
Japan
U.S. measure wrthout MA errors Current Current Current Current
y + + +
vs. no y’s 4 lags of y vs. no y’s 8 lags of 4 vs. no q’s 12 lags of 4 vs. no q’s
3.84 11.1 16.9 22.4
6.63 15.1 21.7 27.7
0.9 2.1 5.9 12.0
1.1 4.1 9.0 12.9
0.0 2.1 3.7 19.8
0.1 3.3 11.7 30.1h
4.3 5.0 12.4 27.Rh
0.7 6.8 10.2 9.7
- 0.4 6.1 5.8 15.3
0.0 2.9 11.3 31.4b
8.2h 15.P 14.6 35.1b
- 0.3 8.5 12.5 11.0
0.6 3.0 3.6 4.3
0.3 10.1 9.0 11.3
7.4 8.6 11.2 10.8
0.1 6.5 7.1 5.6
2.4 4.4 4.8 4.9
-1.6 5.8 7.3 10.1
9.5h 19.7h 16.3 19.0
0.0 7.0 11.3 7.8
U.S. meamre wrh 4 MA errors q VS. no q’s
Current Current Current Current
+ 4 lags of 4 vs. no q’s + 8 lags of q VS. no q’s + 12 lags of q VS. no q’s
Current Current Current Current
4 + + +
Current Current Current Current
q VS. no q’s
3.84 11.1 16.9 22.4
6.63 15.1 21.1 27.1
-0.1 1.9 4.x 8.5
5.8” 4.2 11.1 13.8
Foreign measure wrthour MA errou
vs. no q’s 4 lags of q vs. no q’s 8 lags of q VS. no q’s 12 lags of q VS. no q’s
3.84 11.1 16.9 22.4
6.63 15.1 21.7 21.7
1.2 39 8.8 10.7
2.2 3.3 9.8 10.9
Forergn measure wrrh 4 MA errors
+ 4 lags of q VS. no q’s + 8 lags of q VS. no q’s + 12 lags of q vs. no q’s
‘Significant bSignificant
3.84 11.1 16.9 22.4
6.63 15.1 21 7 21.7
0.0 2.3 9.1 11.8
1.9 1.8 11.1 13.0
at the 5% level. at the 18 level.
Rogoff (1988)] to identify any variable which exhibits a stable correlation with the exchange rate. Our baseline regressions use (real domestic and foreign) investment, government spending, and money as instrumental variables for the (contemporaneous values of the) income variables and the exchange rate. Table 1 contains statistical results for the baseline regressions. The Wald tests in table 1 test the hypothesis that the current and lagged values of the (first difference in the) real exchange rate are jointly insignificant in (9). Four null hypotheses are tested for each country, in particular, that (a) the current, (b) the current and four lags, (c) the current plus eight lags, and (d) the current plus twelve lags of the real exchange rate are jointly insignificant determinants of the trade balance [i.e., the null in each case is that S(i) = 0 for all i, against the alternative that S(i) # 0 for i = 0,. . . , p, p = 0,4,8,12]. For each of the six countries, sixteen chi-squared tests are tabulated: four for each of the four null hypotheses considered. The four permutations result from (a) two measures of the trade balance (a U.S. measure and a foreign
JMon
c
measure) and (b) two estimation methods (either with or without four MA error terms). Negative test statistics are possible because of the use of nonlinear instrumental variables (IV). The MA coefficients do not indicate overdifferencing; there are few signs of residual serial correlation.” The results are surprising in that there are few indications that the real exchange rate significantly affects the trade balance at all. regardless of the choice of lag length. This conclusion is relatively robust with respect to country, trade balance measure. inclusion of MA errors. and lag length. There is some evidence that lags of the real exchange rate are significant for trade with Germany and Italy. The sum of the coefficients is ‘correctly’ signed in that a depreciation improves the trade balance eventually, but there is no indication of the negative short-run response which characterizes the J-curve: the coefficients do not generally take on initially negative values and change sign as the lag order increases. The occasional findings of significant exchange rate impact are not robust across alternative specifications.5 To summarize, one alternative to the null hypothesis of a J-curve is that there is no significant exchange rate effect on the trade balance at all. for any lag length. Clearly, this alternative cannot be rejected on the basis of the test statistics tabulated in table 1.
5. Robustness
checks
Both theoretically and from the viewpoint of the existing literature, it is surprising that the real exchange rate does not appear to have a statistically significant impact on the trade balance. In this section we attempt to account for this negative finding by exploring the robustness of the baseline results to both economic and econometric perturbations. The issues which are investigated include (a) choice of IV estimator rather than OLS, (b) choice of unconstrained exchange rate lags rather than a more complicated distributed lag technique, (c) focus on net exports of goods rather than exports and imports separately, (d) choice of sample, (e) choice of single-equation technique and a purely bilateral model of trade flows, (f) imposition of homogeneity of degree zero with respect to changes in P, P*, and E, (g) dynamic specification issues, (h) biases due to omitted variables, and (i) the first-differencing transformation. These results are described more extensively in the working paper version of this paper.
4Comparable conclusions can be obtained the relevant quarterly data is available.
for Korea,
the only less developed
country
for which
5The intercept terms, while often estimated to be negative, are usually statistically insignificant. Of the 120 estimates, one (for Japan) was nonzero at the 0.05 level. In contrast, Krugman and Baldwin have suggested that U.S. trade in the aggregate exhibits a significant negative trend.
A. K. Rose and J. L. Yellen. Is there a J-curve?
63
The key findings described above - an insignificant effect of exchange rates on trade and no systematic evidence of an initial perverse effect of real exchange rates on trade - are found to be robust with one exception. When the baseline regressions are run with data in levels rather than first-differences, evidence of significant effects of exchange rates on trade is found. However, as was argued above, this methodology is inappropriate in view of the nonstationarity of the underlying time series. To check the sensitivity of the results with respect to estimation technique, the baseline equations were reestimated with alternative sets of instruments, OLS, and polynomial distributed lags. With occasional exceptions, the finding of no significant effects of exchange rates on trade persists.6 The initially negative response of trade to exchange rate movements which characterizes the J-curve is hypothesized to stem from the movement of the value of imports rather than exports. To determine whether this import behavior might be masked by our focus on the net trade balance, the baseline equations were reestimated using (changes in) the logs of real exports and imports as separate regressands. There is weak evidence of an initially perverse response in imports from Germany and the U.K., but, overall, the data do not indicate that aggregation of import and export values is responsible for the findings. To investigate the sensitivity of the results to the choice of sample period, the baseline equations were estimated both through 1979 and for the regime of floating rates starting in the second quarter of 1973. However, the negative results do not result from the sample chosen. The theoretical model excludes the possibility of ‘third-country’ effects. For instance, eq. (9) models bilateral trade with Canada as being dependent only on the Canada/US. real exchange rate and not on, say, the Japan/U.S. real exchange rate as well. Therefore (changes in) the real effective exchange rate (and its lags) were included as conditioning variables in (9); the results do not change. The set of bilateral equations (9) was also estimated jointly with three-stage least squares, to account for the possible correlations of the residuals across countries. However, this does not enable us to isolate significant exchange rate effects, even allowing for common responses of B to 4 and Y* fluctuations across countries. The baseline regressions impcse the assumption of zero degree homogeneity of the real trade balance with respect to the components of the real exchange rate - the nominal exchange rate, foreign and domestic prices - in both the short and long run. Warner and Kreinin (1983) have argued that this restriction is empirically questionable. To investigate the sensitivity of the results to this assumption, the equations were reestimated allowing for both short- and ‘Using evidence countries.
OLS, there is some evidence of long exchange rate lags in the German equation, strong of significant exchange rate lags for Italy and insignificant lags for the other four
long-run nonhomogeneity of the real exchange rate. However. the data are quite consistent with the joint hypothesis that the current and lagged values of both price differentials and the nominal exchange rate (both in logged differences) are jointly insignificant in the trade balance equations. In order to check the sensitivity of the results to possible alternative dynamic specifications of (9), the equations were also reestimated with four lags of the dependent variable. as might be appropriate if the trade balance is characterized by a partial adjustment mechanism. The addition of these lags of the dependent variables does not materially change the findings. As noted above, investigators who have estimated structural models of the trade balance typically include a handful of variables in eqs. (1) and (2) in addition to output and relative prices. It is clearly of interest to evaluate whether the exchange rate coefticients are seriously biased because such variables have been omitted from (9). While variables such as commodity and energy prices can be added to (9) without changing the results. the work of Meese and Rogoff (1988) is extremely relevant in this context. Meese and Rogoff showed that exchange rates do not generally display stable correlations with a wide variety of relevant economic variables. The omission of a variable does not ordinarily bias the estimated coefficients if it is orthogonal to the included variables. This finding supports the contention that the estimated exchange rate coefficients are consistent despite the omission of potentially relevant variables in the trade equation. Most previous studies of the relationship between trade and exchange rates have used logs of levels rather than first-differenced data. As argued above, this methodology is inappropriate and results in misleading test statistics in the presence of nonstationary variables. The baseline equations were reestimated using data in levels, with and without polynomial distributed lags. simply to determine whether the differencing transformation accounts for the divergence between our results with those predicted by the J-curve. The differencing transformation does affect the results; there are strong signs that the exchange rate significantly affects net trade in the German, Italian, British, and Japanese equations. Moreover, the cumulative effect of exchange rates on trade for these countries is positive, which is consistent with the existence of a J-curve. However, even in this situation. there are few signs of the perverse short-run effects predicted by the J-curve. An initially negative response of the trade balance to a depreciation is apparent only for trade with Germany and France. Although this last exercise provides a partial reconciliation of our results with conventional wisdom, the equations estimated using data in (logarithms of) levels are likely to be ‘spurious’ in the Granger-Newbold sense. Specifically, residual serial correlation has likely understated the relevant standard errors, thus biasing inference tests towards the conclusion that relationships exist where they in fact do not: further, conventional statistical theory has been applied to nonstationary variables.
A. K. Rose und J. L. Yellen, Is thereo J-curve?
65
6. Aggregate results The results obtained with bilateral country level data provide little or no support for a J-curve in the American trade balance. Because most of the existing literature uses highly aggregated data, it is clearly of interest to determine if the use of bilateral data is responsible for our negative results. When (9) is estimated with aggregate data, the choice of estimation techniques significantly affects the results obtained. OLS estimates provide weak support for the existence of a J-curve; IV estimation, in contrast, confirms the negative results established with bilateral data. To evaluate the J-curve hypothesis at the aggregate level, the model was estimated with the quarterly aggregate data used in two recent papers [Helkie and Hooper (1987), Krugman and Baldwin (1987)]. A variety of alternative measures were used for almost all of the relevant variables.7 In an effort to make our estimates as comparable as possible with those of the literature, sample data from 1968 through 1986 was employed for most of the analysis which follows. All of the variables seem to have unit-roots; again, one cannot reject the hypothesis of no cointegration between the real value of the trade balance, the logs of real output (both foreign and domestic), and the log of the real exchange rate. Curiously, while exports do not seem to be cointegrated with the real exchange rate and foreign output, imports are cointegrated with domestic output and the real exchange rate. This could indicate the presence of nonstationary measurement errors in the foreign output variables, reinforcing our belief that an instrumental variables technique is appropriate. Initially, (9) is estimated with OLS. The strongest signs of significant exchange rate effects are seen when the current exchange rate and twelve of its lags are included in (9). In this case, the F-test of the joint hypothesis that all the exchange rate coefficients are zero is rejected at around the 5% level (the exact significance level is somewhat sensitive with respect to the variables which proxy q, Y*, and B). The sum of the exchange rate coefficients is positive. This finding of ‘significant exchange rate effects’ can be made considerably stronger by judicious use of PDLs. A short J-curve can also be detected. The current and first two lags of the exchange rate appear to have negative effects. However, these coefficients are estimated very imprecisely; the alternative hypothesis that the current and first two lags of the exchange rate are zero cannot be rejected at the 50% significance level. The estimated coefficients also do not smoothly progress from negative to positive values and back to zero again. Rather, there are ‘incorrectly’ signed coefficients at lag lengths of about three years which are larger in economic magnitude than the initial ‘J-curve’ effect. However, if PDLs with endpoint constraints are used, ‘We use four measures of the trade balance. three real exchange proxies; see the working paper version for details.
rates, and four foreign
output
66
A. K. Rose und J. L. Yelletl. Is there (I J-curue.“
this feature of the data can be eliminated. It thus seems that we are able to reproduce what appears to be the folk wisdom of a short J-curve. However, given our fears about potential errors in variables and simultaneity problems, it seems critical to corroborate these estimates with an instrumental variables technique. Accordingly, eq. (9) was estimated with IV; a number of different sets of instrumental variables were employed. These include combinations of domestic and foreign capital stocks, domestic and foreign potential GNP, commodity prices, the short American interest rate, and admissible lags of output, foreign output, and the real exchange rate. When the equations are estimated with a variety of sets of instruments gleaned from these variables, there are very few indications that the real exchange rate and its lags are significant determinants of the balance of trade. The hypothesis that the coefficients on the current and up to twelve lags of the real exchange rate are zero in the trade balance equation is never rejected at even the 0.10 significance level. This result is robust with respect to choice of variables, instruments, sample period, lag order, and so forth. Moreover, the coefficients on the real exchange rate do not follow any discernible pattern. In particular, the coefficient for the current value is typically estimated to be (insignificantly) positive. the first lag coefficient negative, and the second positive.’ The method of estimation does alter the results obtained with aggregate data: a J-curve is apparent with OLS estimates, but not with IV. Given our doubts about the validity of the instrumental variables, it seems wise to test for the appropriateness of the IV estimator: we therefore computed Hausman specification tests. While the exact significance level depends on the precise choice of variables (for regressand, regressors, and instruments), the specihcation tests generally indicate that OLS is an inappropriate estimator at significance levels which are marginally significant (ranging up to the 0.05 significance level). Given the poor power characteristics of the Hausman tests
“A typical
set of estimates
/ +
1.2 &/-lo) (2.7)
0.12 J_L.( -2) (5.0 1 + 1.3 JP-2) (4.8) T= 71(1969.2-1986.4).
(standard
errorb in parcnthcaes)
L&Q-11)
looks like:
0.2 AC/( ~ 12) ~ 1.3 J I (6.3) (5.2) + 1.2 A.!,(- 3)0.5 Jv(-4)-0.‘) -\i,*(3.0) (9.4) (2.9) + 1.0 A.,,*( - 3) - 1.3 A,,*(- 4). (4.8) (4.3) .s.e. =O.ll. D.W. = 2.13.
1.1 JL,( (5.7)
-1)
1.6 J1.*(-I) (5.7)
Four MA coefficients are not reported, The tirst live instrumental variables mentloned in the text (domestic and foreign potential output and capital, and commodity prices) and three of their lagh. together with the first four lags of output and foreign output. are used as instrumental variables.
A. K. Rose und J. L. Yellen. Is there a J-curue?
61
and the consistency between the Hausman test results and the lack of cointegration, the results indicate the need for some sort of IV estimator. It seems reasonable to conclude that the aggregate data does not provide reliable evidence of either the negative short-run effect or the positive long-run effect, which jointly constitute the J-curve.
7. Conclusions In this paper the hypothesis of the J-curve has been examined with both bilateral and aggregate American data. No statistically reliable evidence of the J-curve was found. Indeed, the hypothesis that there is no response of the trade balance to the real exchange rate, in either the short run or long run, is just as consistent with the data as the J-curve hypothesis. The divergence between our negative results on the trade balance-exchange rate nexus, and more conventional findings, can be attributed primarily to two factors. First, the theoretical structure of the model and the data indicate that potential simultaneity of the trade balance, exchange rates, and output is an issue that cannot be ignored. Second, there is strong empirical evidence that the variables considered have unit-roots, implying that some transformation (e.g., first-differencing) is necessary to induce stationarity. Few existing studies have taken these features into account. When these matters are accounted for, there is little evidence of a J-curve, or indeed of any reliable link between the balance of trade and the real exchange rate. Many of the hypotheses underlying the empirical model have been relaxed, but there does not appear to be a key assumption delivering this negative result. We conclude that there is little empirical support for the J-curve. The existence of a J-curve depends on a number of assumptions: a short-run inelastic response of import volume to import prices, a short-run elastic response of import prices to the exchange rate, and a sluggish response of export value to the exchange rate. The individual hypotheses which collectively constitute the J-curve have not been separately tested and rejected. Close examination of the various premises underlying the J-curve may provide more detail as to why the hypothesis is not supported by the data. References Artus, J.R., 1975, The 1967 devaluation of the pound sterling, I.M.F. Staff Papers 22, 595-640. Dornbusch, R., 1975, Exchange rates and fiscal policy in a popular model of international trade. American Economic Review 65, 859-871. Dombusch. R. and P. Krugman, 1976, Flexible exchange rates in the short run. Brookings Papers on Economic Activity, 537-575. Engle. R.F. and C.W.J. Granger, 1987, Co-integration and error correction: Representation, estimation and testing, Econometrica 55, 1251-1276. Helkie, W.L. and P. Hooper, 1987, The U.S. external deficit in the 1980s International finance discussion paper no. 304 (Board of Governors, Federal Reserve System, Washington. DC),
68
A.K. Rose und J. L. Yellen, Is there u J-curcv:~
Krugman. P.R. and R.E. Baldwin, 1987. The persistence of the U.S. trade d&it. Brooking\ Papers on Economic Activity 1. l-43. Lindert, P.H., 1986, International economics (Irwin. Homewood. IL). Mann, C.L.. 19X6, Prices, profit margins. and exchange rates. Federal Rescue Bulletin. 3666379. Meese, R.A. and K. Rogoff, 1988, Was it real?, Journal of Finance 43. 933-94X. Nelson, C. and C. Plosser. 1982. Trends and random walks in macroeconomic time series. Journal of Monetary Economics 10, 139-162. Spitaller. E., 19X0, Short-run effects of exchange rate changes on terms of trade and trade balance. I.M.F. Stat?’ Papers 27, 320-34X. Stock, J.H. and M.W. Watson. 1986, Testing for common trends. Workmg paper (Harvard University, Cambridge. MA). Warner, D. and M.E. Kreinin. 19X3, Determinants of international trade Ilowa. Review of Economics and Statistics 65. 96-104. Wilson. J.F. and W.E. Takacs. 1980. Expectations and the adjustment of trade flows under floating exchange-rates: Leads, lags and the J-tune, International finance discussion paperna. 160 (Board of Governors, Federal Reseme System. Washington. DC).
of Monetary
Economics
24 (1989) 53-68.
North-Holland
IS THERE A J-CURVE?* Andrew K. ROSE and Janet L. YELLEN University of California, Berkeley, CA 94720, USA Received June 1987, final version received April 1988
If the response of the value of the trade balance to movements in the real exchange rate is described by a J-curve, then a real depreciation initially worsens a balance of trade deficit, only improving it over time. This paper investigates whether a J-curve can be detected in the last twenty-five years of American data. No statistically reliable evidence of a stable J-curve is detected. The model is checked extensively to support this finding.
1. Introduction
It is commonly believed that the response of a country’s trade balance to movements in its real exchange rate follows a J-curve. According to this view, a currency depreciation improves the balance of trade in the long run, but worsens the trade balance in the short run. The ‘perverse’ initial response occurs if the immediate effect of a depreciation is to raise spending on imports, measured in local currency, by more than any initial increase in export revenues. The trade balance is likely to decline subsequent to a depreciation if export and import volumes adjust slowly to movements in relative prices, but import prices respond quickly to exchange rate changes. This paper examines the question of whether the American trade balance has habitually displayed a J-curve. The major finding is a negative one; the hypothesis of a J-curve can be rejected robustly with American data. We find no convincing evidence that the short-run response of net merchandise trade to real exchange rate movements is perverse, either in bilateral U.S. trade or in *We would like to thank: Pier Ardeni and Matt Lynde for research assistance; William Helkie of the Federal Reserve Board for providing data; and Jeff Frankel, William Helkie, Peter Hooper, Ellen Meade, Dick Meese, Jurg Niehans, Jim Wilcox, a referee, and seminar narticinants at Berkeley and Stanford for comments. The research for this paper was supported by the buggenheim Foundation, the National Science Foundation under arant SES 86-005023. and the Institute for Business and Economic Research of the Universit; of California, Berkeley. This is a condensed version of a working paper with the same title. That paper, as well as our data and programs, are available upon request.
0304-3932/89/$3.5001989,
Elsevier Science Publishers
B.V. (North-Holland)
54
A. K. Rose and J. L Yellen, Is there a J-curve?
aggregate U.S. data. In addition, there is little evidence of a reliable long-run relationship between the U.S. trade balance and the real exchange rate. In section 2 the theory relevant for the empirical work is presented. Section 3 contains a discussion of the modelling approach and some data diagnostics. The econometric technique involves the estimation of a ‘partial’ reduced form equation for the net merchandise trade balance. Tests for unit-roots reveal nonstationarity in the data. Cointegration tests cast doubt on the existence of any underlying stationary relationship between the levels of the real trade balance and its theoretically most important determinants: the real exchange rate, domestic and foreign real income. Section 4 describes the main tests for the existence of the J-curve. Baseline equations are estimated with instrumental variables on bilateral data. No evidence of a J-curve is found. A negative short-run reaction of the trade balance to the real exchange rate is not detected; neither is a long-run positive response. The sensitivity of these results is systematically checked in section 5. A variety of auxiliary assumptions are relaxed, but the statistical rejection of the J-curve is found to be robust. Section 6 uses aggregate data to test for the J-curve. The choice of estimation method is found to influence the results. If OLS is used, weak evidence of a J-curve is detected. However, instrumental variables techniques are shown to be appropriate and reveal no signs of a J-curve. A final section contains a few conclusions.
2. Theory Standard ‘two-country’ models of trade [see, for example, Lindert (1986)] assume that the volume of imported goods demanded by domestic (foreign) residents depends positively on real domestic (foreign) income and negatively on the relative price of imported goods:
D,,,=D,(Y,p,)
and
D,*=D,*(Y*,P,*),
where D, (02) is the quantity of goods imported by the home (foreign) country; Y (Y*) is the level of real income measured in domestic (foreign) output; p, is the relative price of imported goods to domestically produced goods, both measured in home currency; and p,* is the analogous relative price of imports abroad. These equations represent Marshallian demand functions, with relative price and income elasticities expected to be negative and positive in sign, respectively. A number of different approaches have been adopted to analyze the determinants of supply. One simple model postulates a world of perfect competition, where the supply of exportables in each country depends posi-
A. K. Rose and J. L Yellen, Is there
55
a J-curve?
tively on the relative price of exportables:’
(2) where S, and S,* are the supplies of home (foreign) exportables, respectively; p, is the home country relative price of exportables, defined as the ratio of the domestic currency price of exportables, P,, to the domestic price level, P; p,* is analogously defined as the foreign currency price of exportables, P,*, divided by P*, the foreign price level.
The domestic relative price of imports can be expressed as p,=E.P,*/P=(E.P*/P).(P,*/P*)=q.pp,*,
(3)
where E is the nominal exchange rate, defined as the domestic currency price of foreign exchange; and q is the real exchange rate, defined as q = E. P*/P. Analogously to (3), the relative price of imports abroad is Pt = PJ4.
(4)
In equilibrium, quantities transacted and the relative prices of exported goods in each country are determined by the two equilibrium conditions: D,,, = S,*
and
D*=S m
(5)
X’
The value of the home country’s balance of trade in real (domestic output) terms, B, is the value of net exports in domestic currency divided by P: B=p;D,*--q.p,*.D,,,.
(6)
In the presence of capital flows, B need not equal zero. Eqs. (l)-(5) can be solved for the levels of domestic imports and exports and the relative price ratios, p, and p,*, as functions of q, Y, and Y*. Accordingly, B can be written as a ‘partial reduced form’ (i.e., an equation derivable from a set of partially solved structural equations): B = B(q,
Y, Y*).
(7)
In this paper, eq. (7) is treated as the equation of interest. The estimated empirical equations are essentially log-linear approximations to (7) augmented by a ‘suitable’ number of lags, a constant, and a ‘well-behaved’, ‘small disturbance term to represent ‘unimportant’ omitted factors. ‘Many models of imperfectly competitive similar to (7) below; see Mann (1986).
import
supply lead to a ‘reduced
form’ equation
for B
56
A.K. Rose and J. L. Y&n,
Is there n J-curve?
The effect of a depreciation of the real exchange rate on the real balance of trade depends on the sign of the partial derivative of B with respect to q in (7). This effect is positive if the ‘Bickerdike-Robinson-Metzler (BRM) condition’ is satisfied [Dornbusch (1975)]; in the case of initially balanced trade and infinite supply elasticities, this reduces to the well-known Marshall-Lerner condition. Using the notation of our model, the Bickerdike-RobinsonMetzler condition is
-q.D,;p.~[(1-1).&*/(~+&*)1
‘0.
where q(v*) and E (E*) denote the absolute values of the price elasticities of demand and supply respectively at home (abroad). Estimating this partial derivative in both the long and short run is the primary objective of this paper. A J-curve is defined as the combination of a negative short-run derivative with a positive long-run derivative. The question posed - under what circumstances does a real depreciation improve the real trade balance in the long run but worsen it in the short run? - is distinctly partial equilibrium in nature.’ A typical J-curve scenario runs as follows: the initial effect of a depreciation is to raise the domestic prices of imported goods, because prices of export goods are sticky in sellers’ currencies. Thus q rises while p, and p_,? remain fixed in (6). There is only a small immediate impact on the volume of trade flows [i.e., D,,, and D,* in (6) change little]. Therefore, the value of exports ( P,~. D,*) rises only slightly, while the value of imports (q .p: . D,* ) rises substantially due to the increased cost of an unchanged quantity of imports. Consequently, the balance of trade in real terms deteriorates in the short run. Naturally, this argument is predicated on the assumption of a large export supply elasticity and a low short-run import demand elasticity. As time passes, the increased price of imports eventually diminishes import volume; export volume and value also increase over time because the price elasticity of foreign import demand is larger in the long run than in the short run. Thus, although the depreciation has an initially negative impact on the real trade balance. the effect is reversed over time, leading to a cumulatively positive effect; thus the short-run response is ‘perverse’. The graph of the response of the trade balance over time to a once-and-for-all real depreciation, resembles a ‘J’ tilted to the right. The prevailing view appears to be that a J-curve exists; the perverse effect is thought to have a duration of about a year [e.g., Dornbusch and Krugman (1976) and Krugman and Baldwin (1987)]. ‘The theoretical model consisting of (l)-(6) is not complete; in a full general equilibrium. y. Y. and Y* are also endogenous. If the exchange rates are endogenous. it is not apparent that the BRM condition provides the answer to any interesting question [Dombusch (1975)].
A. K. Rose and J. L. Yellen, Is there a J-curve?
57
No theoretical argument leads one to the presumption that the response of the trade balance to an exchange rate perturbation is initially perverse. A set of sufficient conditions consists in two logically separate empirical conditions: low short-run price elasticities of demand for imports both at home and abroad, and a swift response of U.S. import prices to the exchange rate (due, in the theoretical model presented above, to a relatively large foreign export supply elasticity). There is also no theoretical reason why the long-run response of the balance of trade to a real depreciation must necessarily be positive; this occurs only if the BRM condition is satisfied. While the conditions which lead to a J-curve may strike some as realistic, the complement to this set of hypotheses seems equally plausible. In particular, there is evidence [see Mann (1986)] that import prices actually adjust slowly to exchange rate changes, which would undermine the initial negative effect embodied in the J-curve. On balance, the existing empirical literature does not point strongly to either view. Indeed, the paucity of evidence in the academic literature is striking. 3. Methodology and data preliminaries In this section, the methods used in this paper are briefly contrasted with those of other investigators, the data is described, and diagnostic tests for unit-root nonstationarity and cointegration are presented. 3. I. Methodology The vast majority of the existing empirical literature derives the impact of exchange rates on trade by estimating and solving a set of structural supply and demand equations for exports and imports. These equations represent variants of (1) and (2); see, e.g., Hooper and Helkie (1987), Krugman and Baldwin (1987), and Warner and Kreinin (1983).3 The majority of the literature estimates ‘pass-through’ equations as empirical specifications of (2); these typically take the form
Pm= P,(R P*, E, Z,> and
P,* = P,*(P,
P*, E, Z,),
(8)
where Z, is a vector of relevant exogenous variables. These markup equations summarize pricing behavior by firms. The effect of a depreciation can then be 3Many discussions of the J-curve are based on estimates of only a subset of the structural equations. For instance, Spitaller (1980) discusses the short-run effects of a depreciation based on pass-through equations alone, explicitly abstracting from volume effects, while Wilson and Tahacs (1980) assume that export prices in local currencies remain unchanged following a depreciation. For counterevidence concerning the validity of both of these extreme assumptions see Hooper and Helkie (1987) or Krugman and Baldwin (1987).
58
A.K. Rose and J. L. Yellen, Is there a J-cume?
determined by solving the empirical ‘structural’ (volume and pass-through) equations [(l) and (8)] for the ‘reduced form’ corresponding to (7). Using this approach, Krugman and Baldwin’s estimates yield a J-curve with a perverse effect with a cumulative duration of four quarters; the estimates of Artus (1975) and Hooper and Helkie (1987) imply J-curves lasting only one quarter. The analysis in this paper does not distinguish between the price and volume effects of a real depreciation. Rather than solving estimated versions of (1) and (2) eq. (7) is-instead estimated directly. There is only one theoretical restriction that this approach imposes on the estimation process: homogeneity of degree zero in P, P*, and E. This restriction is appropriate in most models; the assumption is later relaxed and tested. To determine the nature of the J-curve, direct estimation of (7) is preferable to the more detailed structural approach prevalent in the literature. The question of interest concerns the dynamic response of the net trade balance, measured in real (domestic output) terms, to movements in the real exchange rate. The answer to this question is directly obtainable from (7) and does not require knowledge of the structural parameters in (l)-(2). We have little confidence that existing volume and pass-through (really demand and supply) equations provide a good approximation to the data generation process.
3.2. Data Most previous studies of the trade balance use extremely aggregated data; this is potentially troublesome for several reasons. If one considers the domestic country to be the U.S. and the foreign country to be the rest of the world (ROW), then to estimate (7) one needs to construct proxies for both ROW income and the American real exchange rate vis-a-vis ROW. In an effort to minimize measurement problems, bilateral data with the other members of the Group of Seven (Japan, Canada, U.K., France, Germany, and Italy) are used for much of the analysis. Trade with the other members of the Group of Seven has played an important role for America throughout the postwar period. Further, if the response of the trade balance to the real exchange rate varies by country with the nature of the trade, there is another benefit from disaggregation. Bilateral data also largely avoids prob!ems associated with petroleum imports and agricultural exports. To compare our methodology with those of previous papers, widely used aggregate data are also exploited. The basic source for the balance of trade data is the IMF’s monthly bilateral merchandise export and import series. These series give the value of U.S. merchandise imports and exports in nominal dollar terms. The dependent variable in our analysis - B, the ‘real’ net merchandise trade balance - is defined as the difference between merchandise exports and imports, measured in current U.S. dollars, deflated by the American GNP deflator. Conceptually, B measures the net merchandise trade balance in units of ‘U.S. output’.
A. K. Rose and J. L. Yellen, Is there a J-curve?
59
Because export and import data is collected both at domestic and foreign borders, there are two measures of trade flows. Both are used below. Logarithms of American and foreign real GNP/GDP are used as demand proxies. The real exchange rate is the log of the product of the nominal bilateral exchange rate, the foreign GNP deflator, and the inverse of the U.S. GNP deflator. As the nominal exchange rate accounts for most movements of the real exchange rate, the results are insensitive to the exact choice of price deflators. Our desire to use GNP measures as both income proxies and as the appropriate price deflators constrained the empirical work to the quarterly frequency. However, the use of monthly data only strengthens the conclusions that are found below. Most of the data spans the first quarter of 1960 through the last quarter of 1985; the Italian data is presently unavailable for the last three quarters of 1985, while the French data spans 1965 through the third quarter of 1985. 3.3. Tests for unit-roots and cointegration Given the time-series nature of the data, a useful first diagnostic is to test for unit-roots in the variables included in (7) using both Dickey-Fuller and Phillips tests (allowing for drift and including four ‘augmenting’ lags of the difference). The evidence strongly indicates the presence of a single unit-root in virtually all variables at normal significance levels, a result consistent with the macroeconomic literature [e.g., Nelson and Plosser (1982)j. Treatment of this nonstationarity is thus essential for meaningful empirical results. Insofar as the individual variables in (7) are statistically integrated of order one, cointegration of the real trade balance, the real exchange rate, real output, and real foreign output is a necessary condition for the existence of any stationary relationship such as (7). Accordingly, tests for cointegration between B, q, Y, and Y* were computed using the methods of both Engle and Granger (1987) and Stock and Watson (1986). The results do not indicate the presence of cointegration at standard significance levels. Inclusion of oil or commodity prices does not change these results. The evidence from the cointegration test casts doubt on the existence of an underlying stationary steady-state relationship between the (levels of the) balance of trade and the variables most often considered to be its important determinants. These tests are not based on posited structural models and do not suffer from simultaneity problems. The results suffice to reject prima facie the belief that there is an easily quantifiable steady-state effect of the exchange rate on the balance of trade in any model which implies (7). A second implication is that first-differencing of all variables is not merely warranted, but also necessary for statistically reliable hypothesis tests. One may want to allow for MA errors in the event that the data has been overdifferenced. However, if one does not make allowance for the unit-root
60
A. K. Rose and J. L. Yellen. Is there u J-curw:’
nonstationarity manifest to traditional asymptotic variables in levels is also in the Granger-Newbold operation greatly reduces
4. Baseline
in the data by first-differencing the variables, appeals distribution theory are untenable. Analysis of the likely lead to regression results which are ‘spurious’ sense. A further advantage of differencing is that the multicollinearity.
results
This section presents baseline results concerning the determinants of U.S. bilateral trade patterns and examines the estimated exchange rate coefficients for evidence of the J-curve pattern. The evidence rejects the hypothesis of a statistically significant and stable J-curve. Eq. (7) models the trade balance as a linear function of GNP, foreign GNP, and the real exchange rate; the findings of the previous section lead one to transform all variables by taking first-differences of logarithms (except for B which is merely first-differenced). Accordingly, the empirical equation which is estimated is of the form
AB(t)=a+
5 [fi(i)AY(t-i)++)AY*(f-i)] /=0 + i 8(i)Aq(tI= 0
i) + u(t).
(9)
where A denotes the first-differencing operation and u(t) is modelled as both white noise and a MA(4) process. In the absence of any consensus view on the lag structures of the relevant explanatory variables. an agnostic approach is taken. The current and four lags of both foreign and domestic income are included in all the regressions. Four alternatives are considered for the real exchange rate: including only the current rate, the current and four lags of the rate, current plus eight lags, and current plus twelve lags. A constant is estimated to allow for potential deterministic drift [recently emphasized by Krugman and Baldwin (1987)]. Inclusion of the current values of income and the exchange rate immediately raises concerns about potential simultaneity bias. Measurement errors are an additional concern. Instrumental variables estimation is used in an attempt to correct both these problems. Unfortunately, it is not easy to find reliable instruments. For example, interest rates are a logical instrument for the exchange rate, since interest and exchange rates are theoretically related in a world with capital mobility; however, the interest rate may also be correlated with the errors of the trade balance equation if intertemporal substitution drives consumption and hence imports. Moreover. it is difficult [Meese and
A. K. Rose and J.L.
Yellen, Is there a J-curve?
61
Table 1 &i-squared
tests of the significance
of lags of the real exchange of trade equations (9).
rate in quarterly
Critical values xis
0.01
Chi-squared U.K.
Canada
France
post-war
balance
tests Germany
Italy
Japan
U.S. measure wrthout MA errors Current Current Current Current
y + + +
vs. no y’s 4 lags of y vs. no y’s 8 lags of 4 vs. no q’s 12 lags of 4 vs. no q’s
3.84 11.1 16.9 22.4
6.63 15.1 21.7 27.7
0.9 2.1 5.9 12.0
1.1 4.1 9.0 12.9
0.0 2.1 3.7 19.8
0.1 3.3 11.7 30.1h
4.3 5.0 12.4 27.Rh
0.7 6.8 10.2 9.7
- 0.4 6.1 5.8 15.3
0.0 2.9 11.3 31.4b
8.2h 15.P 14.6 35.1b
- 0.3 8.5 12.5 11.0
0.6 3.0 3.6 4.3
0.3 10.1 9.0 11.3
7.4 8.6 11.2 10.8
0.1 6.5 7.1 5.6
2.4 4.4 4.8 4.9
-1.6 5.8 7.3 10.1
9.5h 19.7h 16.3 19.0
0.0 7.0 11.3 7.8
U.S. meamre wrh 4 MA errors q VS. no q’s
Current Current Current Current
+ 4 lags of 4 vs. no q’s + 8 lags of q VS. no q’s + 12 lags of q VS. no q’s
Current Current Current Current
4 + + +
Current Current Current Current
q VS. no q’s
3.84 11.1 16.9 22.4
6.63 15.1 21.1 27.1
-0.1 1.9 4.x 8.5
5.8” 4.2 11.1 13.8
Foreign measure wrthour MA errou
vs. no q’s 4 lags of q vs. no q’s 8 lags of q VS. no q’s 12 lags of q VS. no q’s
3.84 11.1 16.9 22.4
6.63 15.1 21.7 21.7
1.2 39 8.8 10.7
2.2 3.3 9.8 10.9
Forergn measure wrrh 4 MA errors
+ 4 lags of q VS. no q’s + 8 lags of q VS. no q’s + 12 lags of q vs. no q’s
‘Significant bSignificant
3.84 11.1 16.9 22.4
6.63 15.1 21 7 21.7
0.0 2.3 9.1 11.8
1.9 1.8 11.1 13.0
at the 5% level. at the 18 level.
Rogoff (1988)] to identify any variable which exhibits a stable correlation with the exchange rate. Our baseline regressions use (real domestic and foreign) investment, government spending, and money as instrumental variables for the (contemporaneous values of the) income variables and the exchange rate. Table 1 contains statistical results for the baseline regressions. The Wald tests in table 1 test the hypothesis that the current and lagged values of the (first difference in the) real exchange rate are jointly insignificant in (9). Four null hypotheses are tested for each country, in particular, that (a) the current, (b) the current and four lags, (c) the current plus eight lags, and (d) the current plus twelve lags of the real exchange rate are jointly insignificant determinants of the trade balance [i.e., the null in each case is that S(i) = 0 for all i, against the alternative that S(i) # 0 for i = 0,. . . , p, p = 0,4,8,12]. For each of the six countries, sixteen chi-squared tests are tabulated: four for each of the four null hypotheses considered. The four permutations result from (a) two measures of the trade balance (a U.S. measure and a foreign
JMon
c
measure) and (b) two estimation methods (either with or without four MA error terms). Negative test statistics are possible because of the use of nonlinear instrumental variables (IV). The MA coefficients do not indicate overdifferencing; there are few signs of residual serial correlation.” The results are surprising in that there are few indications that the real exchange rate significantly affects the trade balance at all. regardless of the choice of lag length. This conclusion is relatively robust with respect to country, trade balance measure. inclusion of MA errors. and lag length. There is some evidence that lags of the real exchange rate are significant for trade with Germany and Italy. The sum of the coefficients is ‘correctly’ signed in that a depreciation improves the trade balance eventually, but there is no indication of the negative short-run response which characterizes the J-curve: the coefficients do not generally take on initially negative values and change sign as the lag order increases. The occasional findings of significant exchange rate impact are not robust across alternative specifications.5 To summarize, one alternative to the null hypothesis of a J-curve is that there is no significant exchange rate effect on the trade balance at all. for any lag length. Clearly, this alternative cannot be rejected on the basis of the test statistics tabulated in table 1.
5. Robustness
checks
Both theoretically and from the viewpoint of the existing literature, it is surprising that the real exchange rate does not appear to have a statistically significant impact on the trade balance. In this section we attempt to account for this negative finding by exploring the robustness of the baseline results to both economic and econometric perturbations. The issues which are investigated include (a) choice of IV estimator rather than OLS, (b) choice of unconstrained exchange rate lags rather than a more complicated distributed lag technique, (c) focus on net exports of goods rather than exports and imports separately, (d) choice of sample, (e) choice of single-equation technique and a purely bilateral model of trade flows, (f) imposition of homogeneity of degree zero with respect to changes in P, P*, and E, (g) dynamic specification issues, (h) biases due to omitted variables, and (i) the first-differencing transformation. These results are described more extensively in the working paper version of this paper.
4Comparable conclusions can be obtained the relevant quarterly data is available.
for Korea,
the only less developed
country
for which
5The intercept terms, while often estimated to be negative, are usually statistically insignificant. Of the 120 estimates, one (for Japan) was nonzero at the 0.05 level. In contrast, Krugman and Baldwin have suggested that U.S. trade in the aggregate exhibits a significant negative trend.
A. K. Rose and J. L. Yellen. Is there a J-curve?
63
The key findings described above - an insignificant effect of exchange rates on trade and no systematic evidence of an initial perverse effect of real exchange rates on trade - are found to be robust with one exception. When the baseline regressions are run with data in levels rather than first-differences, evidence of significant effects of exchange rates on trade is found. However, as was argued above, this methodology is inappropriate in view of the nonstationarity of the underlying time series. To check the sensitivity of the results with respect to estimation technique, the baseline equations were reestimated with alternative sets of instruments, OLS, and polynomial distributed lags. With occasional exceptions, the finding of no significant effects of exchange rates on trade persists.6 The initially negative response of trade to exchange rate movements which characterizes the J-curve is hypothesized to stem from the movement of the value of imports rather than exports. To determine whether this import behavior might be masked by our focus on the net trade balance, the baseline equations were reestimated using (changes in) the logs of real exports and imports as separate regressands. There is weak evidence of an initially perverse response in imports from Germany and the U.K., but, overall, the data do not indicate that aggregation of import and export values is responsible for the findings. To investigate the sensitivity of the results to the choice of sample period, the baseline equations were estimated both through 1979 and for the regime of floating rates starting in the second quarter of 1973. However, the negative results do not result from the sample chosen. The theoretical model excludes the possibility of ‘third-country’ effects. For instance, eq. (9) models bilateral trade with Canada as being dependent only on the Canada/US. real exchange rate and not on, say, the Japan/U.S. real exchange rate as well. Therefore (changes in) the real effective exchange rate (and its lags) were included as conditioning variables in (9); the results do not change. The set of bilateral equations (9) was also estimated jointly with three-stage least squares, to account for the possible correlations of the residuals across countries. However, this does not enable us to isolate significant exchange rate effects, even allowing for common responses of B to 4 and Y* fluctuations across countries. The baseline regressions impcse the assumption of zero degree homogeneity of the real trade balance with respect to the components of the real exchange rate - the nominal exchange rate, foreign and domestic prices - in both the short and long run. Warner and Kreinin (1983) have argued that this restriction is empirically questionable. To investigate the sensitivity of the results to this assumption, the equations were reestimated allowing for both short- and ‘Using evidence countries.
OLS, there is some evidence of long exchange rate lags in the German equation, strong of significant exchange rate lags for Italy and insignificant lags for the other four
long-run nonhomogeneity of the real exchange rate. However. the data are quite consistent with the joint hypothesis that the current and lagged values of both price differentials and the nominal exchange rate (both in logged differences) are jointly insignificant in the trade balance equations. In order to check the sensitivity of the results to possible alternative dynamic specifications of (9), the equations were also reestimated with four lags of the dependent variable. as might be appropriate if the trade balance is characterized by a partial adjustment mechanism. The addition of these lags of the dependent variables does not materially change the findings. As noted above, investigators who have estimated structural models of the trade balance typically include a handful of variables in eqs. (1) and (2) in addition to output and relative prices. It is clearly of interest to evaluate whether the exchange rate coefticients are seriously biased because such variables have been omitted from (9). While variables such as commodity and energy prices can be added to (9) without changing the results. the work of Meese and Rogoff (1988) is extremely relevant in this context. Meese and Rogoff showed that exchange rates do not generally display stable correlations with a wide variety of relevant economic variables. The omission of a variable does not ordinarily bias the estimated coefficients if it is orthogonal to the included variables. This finding supports the contention that the estimated exchange rate coefficients are consistent despite the omission of potentially relevant variables in the trade equation. Most previous studies of the relationship between trade and exchange rates have used logs of levels rather than first-differenced data. As argued above, this methodology is inappropriate and results in misleading test statistics in the presence of nonstationary variables. The baseline equations were reestimated using data in levels, with and without polynomial distributed lags. simply to determine whether the differencing transformation accounts for the divergence between our results with those predicted by the J-curve. The differencing transformation does affect the results; there are strong signs that the exchange rate significantly affects net trade in the German, Italian, British, and Japanese equations. Moreover, the cumulative effect of exchange rates on trade for these countries is positive, which is consistent with the existence of a J-curve. However, even in this situation. there are few signs of the perverse short-run effects predicted by the J-curve. An initially negative response of the trade balance to a depreciation is apparent only for trade with Germany and France. Although this last exercise provides a partial reconciliation of our results with conventional wisdom, the equations estimated using data in (logarithms of) levels are likely to be ‘spurious’ in the Granger-Newbold sense. Specifically, residual serial correlation has likely understated the relevant standard errors, thus biasing inference tests towards the conclusion that relationships exist where they in fact do not: further, conventional statistical theory has been applied to nonstationary variables.
A. K. Rose und J. L. Yellen, Is thereo J-curve?
65
6. Aggregate results The results obtained with bilateral country level data provide little or no support for a J-curve in the American trade balance. Because most of the existing literature uses highly aggregated data, it is clearly of interest to determine if the use of bilateral data is responsible for our negative results. When (9) is estimated with aggregate data, the choice of estimation techniques significantly affects the results obtained. OLS estimates provide weak support for the existence of a J-curve; IV estimation, in contrast, confirms the negative results established with bilateral data. To evaluate the J-curve hypothesis at the aggregate level, the model was estimated with the quarterly aggregate data used in two recent papers [Helkie and Hooper (1987), Krugman and Baldwin (1987)]. A variety of alternative measures were used for almost all of the relevant variables.7 In an effort to make our estimates as comparable as possible with those of the literature, sample data from 1968 through 1986 was employed for most of the analysis which follows. All of the variables seem to have unit-roots; again, one cannot reject the hypothesis of no cointegration between the real value of the trade balance, the logs of real output (both foreign and domestic), and the log of the real exchange rate. Curiously, while exports do not seem to be cointegrated with the real exchange rate and foreign output, imports are cointegrated with domestic output and the real exchange rate. This could indicate the presence of nonstationary measurement errors in the foreign output variables, reinforcing our belief that an instrumental variables technique is appropriate. Initially, (9) is estimated with OLS. The strongest signs of significant exchange rate effects are seen when the current exchange rate and twelve of its lags are included in (9). In this case, the F-test of the joint hypothesis that all the exchange rate coefficients are zero is rejected at around the 5% level (the exact significance level is somewhat sensitive with respect to the variables which proxy q, Y*, and B). The sum of the exchange rate coefficients is positive. This finding of ‘significant exchange rate effects’ can be made considerably stronger by judicious use of PDLs. A short J-curve can also be detected. The current and first two lags of the exchange rate appear to have negative effects. However, these coefficients are estimated very imprecisely; the alternative hypothesis that the current and first two lags of the exchange rate are zero cannot be rejected at the 50% significance level. The estimated coefficients also do not smoothly progress from negative to positive values and back to zero again. Rather, there are ‘incorrectly’ signed coefficients at lag lengths of about three years which are larger in economic magnitude than the initial ‘J-curve’ effect. However, if PDLs with endpoint constraints are used, ‘We use four measures of the trade balance. three real exchange proxies; see the working paper version for details.
rates, and four foreign
output
66
A. K. Rose und J. L. Yelletl. Is there (I J-curue.“
this feature of the data can be eliminated. It thus seems that we are able to reproduce what appears to be the folk wisdom of a short J-curve. However, given our fears about potential errors in variables and simultaneity problems, it seems critical to corroborate these estimates with an instrumental variables technique. Accordingly, eq. (9) was estimated with IV; a number of different sets of instrumental variables were employed. These include combinations of domestic and foreign capital stocks, domestic and foreign potential GNP, commodity prices, the short American interest rate, and admissible lags of output, foreign output, and the real exchange rate. When the equations are estimated with a variety of sets of instruments gleaned from these variables, there are very few indications that the real exchange rate and its lags are significant determinants of the balance of trade. The hypothesis that the coefficients on the current and up to twelve lags of the real exchange rate are zero in the trade balance equation is never rejected at even the 0.10 significance level. This result is robust with respect to choice of variables, instruments, sample period, lag order, and so forth. Moreover, the coefficients on the real exchange rate do not follow any discernible pattern. In particular, the coefficient for the current value is typically estimated to be (insignificantly) positive. the first lag coefficient negative, and the second positive.’ The method of estimation does alter the results obtained with aggregate data: a J-curve is apparent with OLS estimates, but not with IV. Given our doubts about the validity of the instrumental variables, it seems wise to test for the appropriateness of the IV estimator: we therefore computed Hausman specification tests. While the exact significance level depends on the precise choice of variables (for regressand, regressors, and instruments), the specihcation tests generally indicate that OLS is an inappropriate estimator at significance levels which are marginally significant (ranging up to the 0.05 significance level). Given the poor power characteristics of the Hausman tests
“A typical
set of estimates
/ +
1.2 &/-lo) (2.7)
0.12 J_L.( -2) (5.0 1 + 1.3 JP-2) (4.8) T= 71(1969.2-1986.4).
(standard
errorb in parcnthcaes)
L&Q-11)
looks like:
0.2 AC/( ~ 12) ~ 1.3 J I (6.3) (5.2) + 1.2 A.!,(- 3)0.5 Jv(-4)-0.‘) -\i,*(3.0) (9.4) (2.9) + 1.0 A.,,*( - 3) - 1.3 A,,*(- 4). (4.8) (4.3) .s.e. =O.ll. D.W. = 2.13.
1.1 JL,( (5.7)
-1)
1.6 J1.*(-I) (5.7)
Four MA coefficients are not reported, The tirst live instrumental variables mentloned in the text (domestic and foreign potential output and capital, and commodity prices) and three of their lagh. together with the first four lags of output and foreign output. are used as instrumental variables.
A. K. Rose und J. L. Yellen. Is there a J-curue?
61
and the consistency between the Hausman test results and the lack of cointegration, the results indicate the need for some sort of IV estimator. It seems reasonable to conclude that the aggregate data does not provide reliable evidence of either the negative short-run effect or the positive long-run effect, which jointly constitute the J-curve.
7. Conclusions In this paper the hypothesis of the J-curve has been examined with both bilateral and aggregate American data. No statistically reliable evidence of the J-curve was found. Indeed, the hypothesis that there is no response of the trade balance to the real exchange rate, in either the short run or long run, is just as consistent with the data as the J-curve hypothesis. The divergence between our negative results on the trade balance-exchange rate nexus, and more conventional findings, can be attributed primarily to two factors. First, the theoretical structure of the model and the data indicate that potential simultaneity of the trade balance, exchange rates, and output is an issue that cannot be ignored. Second, there is strong empirical evidence that the variables considered have unit-roots, implying that some transformation (e.g., first-differencing) is necessary to induce stationarity. Few existing studies have taken these features into account. When these matters are accounted for, there is little evidence of a J-curve, or indeed of any reliable link between the balance of trade and the real exchange rate. Many of the hypotheses underlying the empirical model have been relaxed, but there does not appear to be a key assumption delivering this negative result. We conclude that there is little empirical support for the J-curve. The existence of a J-curve depends on a number of assumptions: a short-run inelastic response of import volume to import prices, a short-run elastic response of import prices to the exchange rate, and a sluggish response of export value to the exchange rate. The individual hypotheses which collectively constitute the J-curve have not been separately tested and rejected. Close examination of the various premises underlying the J-curve may provide more detail as to why the hypothesis is not supported by the data. References Artus, J.R., 1975, The 1967 devaluation of the pound sterling, I.M.F. Staff Papers 22, 595-640. Dornbusch, R., 1975, Exchange rates and fiscal policy in a popular model of international trade. American Economic Review 65, 859-871. Dombusch. R. and P. Krugman, 1976, Flexible exchange rates in the short run. Brookings Papers on Economic Activity, 537-575. Engle. R.F. and C.W.J. Granger, 1987, Co-integration and error correction: Representation, estimation and testing, Econometrica 55, 1251-1276. Helkie, W.L. and P. Hooper, 1987, The U.S. external deficit in the 1980s International finance discussion paper no. 304 (Board of Governors, Federal Reserve System, Washington. DC),
68
A.K. Rose und J. L. Yellen, Is there u J-curcv:~
Krugman. P.R. and R.E. Baldwin, 1987. The persistence of the U.S. trade d&it. Brooking\ Papers on Economic Activity 1. l-43. Lindert, P.H., 1986, International economics (Irwin. Homewood. IL). Mann, C.L.. 19X6, Prices, profit margins. and exchange rates. Federal Rescue Bulletin. 3666379. Meese, R.A. and K. Rogoff, 1988, Was it real?, Journal of Finance 43. 933-94X. Nelson, C. and C. Plosser. 1982. Trends and random walks in macroeconomic time series. Journal of Monetary Economics 10, 139-162. Spitaller. E., 19X0, Short-run effects of exchange rate changes on terms of trade and trade balance. I.M.F. Stat?’ Papers 27, 320-34X. Stock, J.H. and M.W. Watson. 1986, Testing for common trends. Workmg paper (Harvard University, Cambridge. MA). Warner, D. and M.E. Kreinin. 19X3, Determinants of international trade Ilowa. Review of Economics and Statistics 65. 96-104. Wilson. J.F. and W.E. Takacs. 1980. Expectations and the adjustment of trade flows under floating exchange-rates: Leads, lags and the J-tune, International finance discussion paperna. 160 (Board of Governors, Federal Reseme System. Washington. DC).