The dollar and U.S. inflation: Some evidence from a VECM process (+).

Darrat, Ali F. ; Chopin, Marc C. ; Dickens, Ross N. 等

Ali F. Darrat (*)

Marc C. Chopin (**)

Ross N. Dickens (***)

1. Introduction

Since the advent of floating exchange rates in early 1973, the values of world currencies have endured large fluctuations. Several countries which experienced currency depreciation suffered domestic inflationary pressures apparently due, at least in part, to the consequent rise in import and import-related prices. When the value of home currency falls relative to foreign currencies, domestic prices of imported goods rise. If these imports represent a major component of domestic consumption, prices of overall consumer goods rise, thus increasing domestic inflation. Another channel by which movements in the exchange rate may lead to changes in domestic inflation can be found in the "currency substitution" hypothesis [see Cuddington (1983) and Batten and Hafer (1986)] which contends that rational money holders maximize their returns from holding domestic and foreign currencies. Thus, an expected devaluation of currency could reduce the demand for domestic currency, leading in turn to an excess supply of domestic money and to subsequent inflationary pressures. (1)

Under floating exchange rates and with large fluctuations in the dollar exchange rate, especially since 1985, it seems important to investigate whether a reliable relationship exists between the dollar exchange rate and U.S. prices. Indeed, if movements in the dollar exchange rate substantially influence domestic inflation, achieving the goal of price stability would become increasingly difficult with a volatile currency value.

While a few studies, like Woo (1984) and Glossman (1985), find little or no impact of the dollar exchange rate on U.S. prices, the body of available evidence surveyed in Hafer (1989) overwhelmingly supports a significant negative correlation between changes in the dollar exchange rate and U.S. prices. Hafer reports short-run (long-run) estimates of domestic price increases of about 2% (5%) for every 10% fall in the dollar exchange rate. Data over 1974-1994, for example, reveal that the correlation coefficient between changes in U.S. prices and the dollar exchange rate is indeed negative and statistically significant (= -0.40, t = -6.80). Such negative associations stoke fears in the financial press that failing to maintain a strong dollar could ignite U.s. inflation [see, for example, Boyd (1989) and Phillips (1998)].

Although the apparent correlation between changes in the dollar exchange rate and U.S. prices cannot be denied, this relationship is neither sufficiently tight nor persistently negative. For example, from March 1985 to February 1989, the correlation coefficient was significantly positive (= +0.32, t = +2.29). In addition, the often-cited negative correlation between changes in prices and the dollar exchange rate may be the outcome of prices influencing the exchange rate. Some researchers, like Dornbusch and Fischer (1987), interpret the Purchasing Power Parity (PPP) theory as implying that higher domestic inflation "causes" higher rates of currency depreciation in order to maintain the terms of trade constant. (2) Therefore, the observed negative correlation between changes in the dollar exchange rate and domestic prices may be the result of the latter causing the former, opposite to what is commonly believed.

Instead of focusing on the direction of causality, most previous studies confine their attention to the correlation between the dollar exchange rate and prices [see, for example, Woo (1984), Glassman (1985), Hakkio and Whittaker (1985), and Solomon (1985)]. Clearly, statistical correlations between two variables, by themselves, are insufficient to establish the direction of causality. (3) Therefore, these studies are unable to distinguish between cause and effect. In fact, the observed correlation between the dollar exchange rate and domestic prices is consistent with four alternative causal hypotheses, each with quite different policy implications. These hypotheses are: (a) changes in the exchange rate cause the inflation rate (the conventional hypothesis), (b) inflation causes changes in exchange rates (the relative PPP proposition), (c) the two variables are mutually causal, and (d) the two variables are not causally related at all. If hypotheses (a) and (b) are jointly valid, then the correct inference i s hypothesis (c). Under this scenario, correlationbased analysis is potentially misleading. Hypothesis (d) suggests that changes in exchange rates and inflation lack any causal relationship and are instead influenced by other macroeconomic variables. (4) Established theory [see Obstfeld and Rogoff (1996)] suggests a number of factors that could influence both exchange rates and inflation. In particular, these theories indicate the potential importance of macroeconomic policies, interest rates, and real income for determining inflation and exchange rates [see, for example, Modigliani and Papademos (1980), Feldstein (1995), Darrat (1985a, 1985b, 1988), and Krugman (1995)].

In summary, then, appropriate tests of the causal relationship between changes in exchange rates and inflation should take into account the potential impact of monetary policy, fiscal policy, interest rates and real income. Otherwise, causal inferences obtained from bivariate (exchange rate/inflation) models are suspect due to the omission-of-variables' bias [see Lutkepohl (1982)]. (5)

This paper examines the causal linkage between the dollar exchange rate and U.S. prices in a multivariate context. To avoid possible misspecification from ignoring long-run relationships among the variables, we also incorporate the underlying cointegratedness among the variables and estimate a vector error-correction model (VECM). These models place only minimum prior restrictions on the estimated parameters. Such a feature of the VECM is particularly important since, as Dornbusch and Fischer (1987) point out, there is a great deal of uncertainty about the nature of the link between exchange rates and prices, as well as about the dynamics of the exchange rate itself.

The remainder of the paper is structured as follows. Section 2 outlines the data and methodology. We discuss the empirical results and policy implications in Section 3. Section 4 concludes the paper.

2. Data and Methodology

We use U.S. monthly data spanning the period April 1973 through December 1997 to estimate a six-variable VECM model. The start of the sample period coincides with the implementation of the floating exchange rate regime. Adding data from the earlier Bretton Woods' (fixed exchange-rate) era contaminates the sample with two distinct regimes, perhaps reducing the reliability of the estimates. The variables are the inflation rate (I), where prices are measured by the U.S. consumer price index (CPI); the bilateral exchange rate (E) between the U.S. dollar and the Japanese yen; the U.S. threemonth Treasury bill rate (R); the monetary base (B) to represent monetary policy moves; the par value of publicly held federal debt securities (F) to represent fiscal policy actions; (6) and the Industrial Production Index (X) to measure the real side of the economy. All data series come from the Citibase Data Tape.

Some remarks regarding our definitions of the variables seem in order. Our inflation measure is based on the CPI, since it generally displays the highest (negative) correlation with exchange rates perhaps due to the fact that import prices directly enter the CPI [see Hafer (1989)]. By contrast, import prices are reflected only indirectly in other price measures (like the GNP deflator) through their impact upon the prices of domestically produced goods. Consequently, most previous studies that report a significant relationship between prices and exchange rates use the CPI. Nevertheless, using the GNP deflator instead of the CPI altered none of our main conclusions.

Following Hafer (1989), we employ the bilateral U.S. dollar/Japanese Yen exchange rate to represent the exchange rate variable in our model. We choose the $/[yen] exchange rate since Japan claims a significant share of the U.S. overall foreign trade. Indeed, Japan has become the largest trading partner for the U.S. in recent years according to data from the U.S. Census Bureau. In addition, and particularly since September 1985, major OECD countries use the $/[yen] exchange rate as a prime tool to analyze the overall dollar behavior in international financial markets. Numerous U.S. official statements reveal that the $/[yen] exchange rate represents a major factor underlying U.S. foreign and domestic economic developments. In light of these and other arguments [see Hafer (1989)], we choose to report our results for the $/[yen] exchange rate. It should be noted that our results do not seem sensitive to the particular exchange rate used in the paper. In fact, qualitatively similar conclusions emerged with the t rade-weighted exchange rate which reflects the value of the dollar against a basket of several foreign currencies, including the Yen (these alternative results are available upon request). However, as a referee insightfully pointed out, growing US trade with Canada and Mexico in the aftermath of NAFTA may require examination of the case using the US dollar exchange rate against the Canadian dollar and/or the Mexican peso. This is undoubtedly an interesting topic for future research.

The VECM model is a linear representation of the joint stochastic process that generates the variables. Each of the variables in the model is considered endogenous, comprising of two components: a linear function of the past realization of all variables in the system (including a variable's own lagged values), as well as an unpredictable innovation component. Several econometricians [e.g., Sims (1982), and Todd (1990)] recommend the use of these models as a useful alternative to "structural" modeling. (7) Note that lags in VECM models need not be equal across all equations and variables, as Ahking and Miller (1985) point out. To avoid possible lag misspecifications, we use Akaike's final prediction error (FPE) criterion to determine the lag structure. (8) Thornton and Batten (1985) recommend this criterion over alternative lag-selection procedures. Generally, the FPE procedure chooses relatively long lags as it emphasizes unbiasedness over efficiency. There is, of course, no assurance that the lag profile ch osen by the FPE criterion in any given case is the only appropriate profile in the lag space, and it is also possible that the lag-length chosen may be data-specific [see Thornton and Batten (1985)]. Therefore, we subject the FPE-lag structures to further (over- and under-fitting) testing to ensure robustness.

We begin our empirical analysis by inspecting each of the six variables for nonstationarity using the Augmented Dickey-Fuller (ADF) test. Again, we employ the FPE criterion to choose the proper lag specification in the ADF test. The results suggest that the variables appear stationary in logarithmic first-differences. (9) As mentioned earlier, we determine the lag structure for each of the six equations in the VECM model by the FPE criterion, in conjunction with the "specific gravity" criterion of Caines et al. (1981). These methods are well-known in applied econometrics and we therefore do not explain them here [see Darrat and Barnhart (1989) for details].

Importantly, Engle and Granger (1987) also suggest the need to test for cointegration prior to estimating the models. They argue that inferences from standard VARs are incorrect if the variables are cointegrated and no allowance is made for the cointegrating relationships. We use the Johansen (1988) efficient procedure to test for cointegration in a multivariate setting. The Johansen test is based on the well-accepted likelihood ratio principle, and evidence by Gonzalo (1994) shows that the Johansen approach performs better than several alternative multivariate testing procedures.

The VECM model is normalized so that only lagged values of the variables are used as explanatory variables. Note that contemporaneous relationships among the endogenous variables in the VECM model are reflected in the innovations. We pool the six equations and estimate them as a system using the Zellner Seemingly Unrelated Regression (SUR) technique. Compared to a single-equation (OLS) procedure, Zellner's SUR yields estimates that are both consistent and asymptotically more efficient, provided that the errors across equations are correlated (but errors within each equation are themselves uncorrelated). The estimated VECM model is viewed as a maintained hypothesis regarding the causal relationships under investigation. We perform likelihood ratio (LR) tests within system estimations to test the joint significance of lagged coefficients. A significant LR statistic supports the presence of a Granger-causal ordering of the strong form.

3. Empirical Results and The Implied Causality Inferences

As we discussed earlier, a necessary prelude to investigating causal relationships is to test for possible cointegratedness among the variables of the model. Table 1 has the results from the Johansen test of cointegration. As recommended by Johansen (1995), we test the joint hypothesis of both the cointegrating rank and the deterministic components based on the Pantula principle to choose the model most consistent with the data under investigation.

According to the trace statistics of the Johansen test, we can easily reject the null hypothesis of no cointegration among the variables, in favor of the alternative presumption that there is at least one cointegrating vector. The maximal eigenvalue test concurs with that verdict and specifically suggests that there is one nonzero cointegrating vector in the system. (10) Consequently, each equation in the model should include the corresponding error-correction term and we extract those terms from the Johansen approach. Using the procedure described above, we obtain the following VECM system for the U.S. over the monthly sample from April 1973 through December 1997:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where L is the lag operator; D[I.sub.t] = (1 - L)log [I.sub.t], I is the inflation rate; D[E.sub.t] = (1 - L)log [E.sub.t], E is the $/[yen] bilateral exchange rate; D[R.sub.t] = (1-L)log [R.sub.t], R is the three-month Treasury bill rate; D[B.sub.t] = (1 - L)log [B.sub.t], B is the monetary base; D[F.sub.t] = (1-L)log [F.sub.t], F is the par value of publicly held federal debt securities; D[X.sub.t] = (1 - L)log [X.sub.t], X is the Industrial Production Index; [[beta].sup.k.sub.ii](L) is the kth lag coefficient on variable j in equation i; the [alpha]'s are constants; the [lambda]'s are the coefficients on the associated lagged EC terms; (11) and the e's are white-noise error terms. To conserve space, we relegate the individual parameter estimates from the above system to an appendix (available upon request). However, one must exercise some caution when discussing these individual estimates due to the reduced-form nature of the model [see Sims (1980)].

Before discussing the causality implications of the empirical results, it should be pointed out that we conducted a series of over- and under-fitting diagnostic tests within system estimations. These tests suggested the need to introduce some minor modifications in the lag structure of the model. This finding should not be entirely surprising since the model was initially specified on the basis of individual (single) equation estimations. Thus, differences may (or perhaps should) be found between the specifications of single equations and that of a pooled system. We incorporate the implied system modifications and perform another round of diagnostic tests on the resultant model. The diagnostic tests clearly favor the adjusted model as given above. (12) In particular, various structural instability tests (Cusum and Cusum-Square procedures) do not reveal any evidence of a significant structural break, particularly in the exchange-rate equation. This is important since our estimation period covers the floating exchange-rate regime (1973-1997) which contains several instances (e.g., the Plaza Accord of September 1985) whereby Central Banks in the G-7 attempted to "manage" the float Absence of significant structural shifts imply that possible biases due to the managed floating episodes, if they existed, are likely to be minimal.

We now discuss the causality inferences implied by the VECM system. Table 2 displays the LR statistics to test the joint significance of the non-zero (off-diagonal) elements of the maintained model. In the presence of cointegration, these LR statistics gauge short-run Granger-causality, while the significance of the coefficients on the error-correction terms in the various equations may be taken as evidence of long-run Granger causality. (13)

The central finding from our estimations is that there exists a substantive short-run relationship such that the dollar exchange rate exerts a significant and unidirectional causal impact upon U.S. prices. Specifically, we can easily reject at the 5% level the null hypothesis that changes in the dollar exchange rate do not Granger-cause short-run changes in U.S. inflation (see test 1 in Table 2). At the same time, we fail to reject the reverse notion that changes in the U.S. inflation do not Grangercause short-run movements in the dollar exchange rate. Two specification tests support this latter inference. The FPE criterion suggests the need to drop the price variable from the exchange rate equation, implying the absence of even weak shortrun causal effects from prices to exchange rates. Furthermore, this evidence from single-equation estimations is corroborated by system estimations since we relax the zero restriction on the price variable within the model system, but fail to find it significant. (14)

The empirical results also suggest that the sensitivity of U.S. inflation to movements in the dollar exchange rate is not only statistically significant, but it is also rapid and completed within only two months. (15) We find similar results from the associated variance decompositions (VDCs) that show the percentage of the forecast error variance for each variable attributable to its own innovations and to shocks to the other variables in the model. Using the Choleski decomposition method over several monthly horizons (one to twenty months), and with alternate sequencing of the variables, the results reveal large effects of changes in the dollar exchange rate on inflation, which quickly reach their peak by the fifth or sixth month. In contrast, VDCs suggest that the effects of inflation on the exchange rate are small and almost non-existent until the eighth month when inflation begins to show some noticeable impact. (16) Such a high speed with which the exchange rate impinges on U.S. inflation may in part ref lect the agility of foreign exchange markets in processing new information. Observe further that our estimation period witnessed a dramatic increase in the volume of international trade and foreign exchange transactions, along with growing foreign currency futures markets. These developments may invigorate the response of macroeconomic variables, like the inflation rate, to developments in foreign exchange markets.

Our results further suggest that, besides changes in the dollar exchange rate, two other factors also Granger-caused short-run changes in U.S. inflation; namely, the growth rates of the monetary base and of the industrial production index (see, respectively, tests 2 and 3 in Table 2). Thus, and in accordance with the familiar monetarist thesis, monetary policy is an important tool for achieving price stability. This inference is further supported by the results from VDCs which reveal large and persistent effects of money on prices.

As to the factors behind short-run movements in the dollar exchange rate, the empirical results suggest that only changes in the stance of monetary policy exert a significant (and quick) impact upon the dollar exchange rate. None of the other potential determinants of the exchange rate (inflation, interest rates, federal debt, or industrial production) appears capable of exerting significant short-run movements in the dollar's value. Interestingly, these results are supportive of the Ricardian hypothesis and Evans' (1986) conclusion in regards to the irrelevance of the federal government budget to the determination of the dollar exchange rate.

In addition to the above short-run causality findings, the results from the VECM further imply interesting long-run causality inferences. In particular, while the EC term is statistically significant in the inflation equation ([[lambda].sub.1] [not equal to] 0), the corresponding EC term fails to achieve statistical significance in the exchange rate equation ([[lambda].sub.2] [approximately equal to] 0).Therefore, the potent unidirectional causal impact of the dollar exchange rate on U.S. inflation discussed earlier is not limited to the short-run, but it apparently extends to the long-run as well. (17)

Besides the relationship between the dollar exchange rate and U.S. inflation, the estimated VECM process yields other interesting results. For example, we find that fiscal policy directly influences real output (see test 22 in Table 2). By contrast, monetary policy appears neutral for real output as reflected in a zero cell for the base money in the real output equation (an over-fitting test also yields an insignificant statistic). Consequently, the VECM results are consistent with the dominance of fiscal policy over monetary policy for stabilizing real economic activity, whereas the reverse is true for stabilizing inflation [see Darrat (1986) for a similar conclusion drawn from a different model]. However, observe that while monetary policy does not directly influence real output, it nevertheless exerts some real indirect effects through interactions with interest rates (see tests 10 and 21 in Table 2). Moreover, the Federal Reserve appears to react primarily to developments in the financial market since on ly interest rates significantly influence the base money (test 14 in Table 2). By contrast, the reaction function of fiscal policy is a little more involved, with fiscal policymakers reacting to movements both in the exchange rate and in real output.

4. Concluding Remarks

This paper uses monthly U.S. data over the period April 1973 through December 1997 to investigate the interrelationship between the dollar exchange rate and U.S. inflation. The results, obtained from a cointegration and error-correction multivariate model, consistently indicate the presence of a unidirectional and significant causal effect flowing from changes in the dollar exchange rate to U.S. inflation both in the short- and in the long-run. Indeed, recent statements in the popular press are consistent with our conclusion regarding the presence of a potent impact of changes in the dollar's value on U.S. inflation. (18)

Econometrically, these findings support the use of exchange rates as an exogenous variable in modeling U.S. inflation. From the perspective of policymaking, our empirical results suggest that movements in the dollar exchange rate should be taken into account when forming anti-inflation policy. Analysis of recent policy actions of the Federal Reserve suggests that some weight has indeed been given to exchange-rate movements in pursuing domestic inflation goals. In particular, the Federal Reserve has raised its interest-rate target at least six times since June 1999 in an attempt to restrict growth in money stock and stave off potential inflation pressures. Apparently, these restrictive policy actions were induced, at least in part, by faster than expected economic growth and by an exceedingly strong dollar relative to most world currencies.

Besides the dollar exchange rate, the results further show that monetary policy significantly influences U.S. inflation. We may infer that it is primarily these potent monetary policy effects that have insulated U.S. prices from recent pronounced changes in the dollar value. Indeed, in light of our finding of a significant and a rapid impact of money growth on U.S. inflation, it seems that the Federal Reserve has shouldered much of the responsibility with respect to promoting price stability in recent years.

(*.) Professor of Economics, College of Administration and Business, Louisiana Tech University

(**.) Associate Professor of Economics, College of Administration and Business, Louisiana Tech University

(***.) Associate Professor of Finance, Mitchell College of Business, University of South Alabama

(+.) We wish to thank an anonymous reviewer for helpful comments. The usual disclaimer applies. Corresponding author: Ali F. Darrat, Department of Economics and Finance, Louisiana Tech University, P.O. Box 10318 T.S., Ruston, Louisiana 71272. Tel.: 318-257-3874; Fax: 318-257-4253, e-mail: Darrat@cab.Latech.edu.

Notes

(1.) Hafer (1989) provides a lucid theoretical discussion of several other channels (both direct and indirect) through which the dollar exchange rate can impinge on domestic inflation.

(2.) As Dornbusch and Fischer (p. 757) put it "exchange rate changes are caused by divergences in inflation rates between countries, with the exchange rate changing in a way that maintains the terms of trade [(exchange rate x foreign prices)/domestic prices] constant" (emphasis added). Similar statements can be found in popular textbooks like Obstfeld and Rogoff (1996). However, other researchers [e.g., Yarbrough and Yarbrough (1997)] reject the above argument and contend instead the PPP has no bearing on the direction of causality between exchange rates and prices.

(3.) Two recent studies employ a causality approach to examine the relationship between changes in exchange rates and prices; namely Whitt, Koch and Rosenweig (1986) for the U.S., and Kholdy and Sohrabian (1990) for Canada, Germany, and Japan. However, both studies use the restrictive bivariate causality framework and, as such, their results may suffer from an omission of variables' bias as we discuss below.

(4.) As Granger (1980) and Lutkepohl (1982) demonstrate, it is possible for variables to be highly correlated, yet causally independent. Lutkepohl (1982, p. 367) writes, "this conclusion is a consequence of the well-known problem that a low dimensional subprocess contains little information about the structure of a higher dimensional system," p. 367.

(5.) We, of course, do not imply that the variables we consider here exhaust all potentially important factors. Nevertheless, we believe that the proposed variables are well grounded in theory and the resultant multivariate model does represent a clear improvement over bivariate-based studies.

(6.) Since issues of new U.S. Treasury securities generally sell at prices close to par value, changes in the par value of outstanding Treasury securities can provisionally represent fiscal policy (federal budget deficit) moves.

(7.) Clearly, this procedure lacks universal acceptance and many researchers, including Cooley and LeRoy (1985), remain skeptical.

(8.) We search for proper lags within a lag space of sixteen months. If we find the lag length for any variable to be sixteen months, we extend the lag profile for that variable by at least two more lags to check whether the sixteen-month lag is indeed appropriate.

(9.) The results from the ADF test (available upon request) are robust to Schwert's (1987) criticism, as well as to the inclusion or exclusion of a time trend. Note that logarithmic first-differences of the variables approximate their percentage changes (growth rates). Taking prices as an example, the logarithmic first-difference yields the inflation rate.

(10.) Following Gonzalo (1994), we use lag specifications in the Johansen test that jointly minimize the Akaike Information Criterion (MG) as well as whiten the residuals. A lag of seven months achieves both goals in our case. The results, however, are not significantly different with other reasonable lag specifications.

(11.) We lag the EC terms only once since additional terms are already reflected in the distributed lags of the first-differences of the variables. See Miller (1991).

(12.) The final model receives further support from a battery of tests that generally show no evidence of autocorrelation, omission of variables, or structural instability. Details of these tests are available upon request.

(13.) Granger (1988) supports this interpretation of short-run versus long-run causality, and Jones and Joulfaian (1991) use it.

(14.) It appears that such pronounced effects of the dollar exchange rate on U.S. prices are transmitted primarily through price importation rather than via currency substitution. We state this since currency substitution between the dollar and the yen appears weak, at least during the estimation period. In separate estimations of U.S. money demand (using, alternatively, M1 and M2), currency substitution as measured by the differential between inflation rates in U.S. and Japan proves statistically insignificant (details are available upon request). Several recent empirical studies also draw similar conclusions regarding the minimal role of currency substitution in a variety of contexts. See, for example, Mizen and Pentecost (1996) and Arnold (1996). Of course, our results are confined to the U.S. dollar/Japanese yen case and do not necessarily preclude the presence of significant currency substitutions involving the dollar against other non-yen currencies.

(15.) In contrast, Whitt, Koch, and Rosenweig (1986) report a rather long lag of more than twenty-four months for the effect of changes in exchange rates on U.S. inflation. A number of factors may contribute to this apparent disparity in the lag lengths. Note first that our model is multivariate compared to their admittedly biased bivariate model. Their long lag may also be reflecting the complex, yet overlooked, process by which omitted variables impinge on inflation. Furthermore, we determine our lag structure using the FPE criterion and unconstrained OLS estimations, while they determine their lag structure by means of a combined Almon/Koyck scheme. Recent applied literature criticizes both Almon and Koyck procedures on the ground that they suffer from potentially serious drawbacks.

(16.) We derive similar conclusions from estimating the associated impulse response functions (IRFs) that measure how the dependent variables respond over time to a one-standard deviation change in each shock. To conserve space, we do not report results from VDCs and IRFs, but they are available upon request. Note that Runkle (1987) and Spencer (1989) raise serious doubts on the usefulness of the VDCs and IRFs.

(17.) The VECM results render a similar conclusion for the effect of the base money on prices. That is, growth in monetary base exerts a significant and a unidirectional effect on inflation both in the short- and in the long-run.

(18.) See, for example, Phillips (1948). In a recent episode aired on May 11, 1999, commentators on the CNN program, Moneyline Focus, also argued that the strong dollar in the late 1 990s is primarily credited for stifling U.S. inflation.

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TABLE 1

Cointegration result from the Johansen approach

 [lambda]-
 Trace
Null Alternative Test
Hypothesis Hypothesis Statistic

r=0 r[greater than or equal to]1 115.17 (*)
r[less than or equal to]1 r[greater than or equal to]2 63.50
r[less than or equal to]2 r[greater than or equal to]3 33.49
r[less than or equal to]3 r[greater than or equal to]4 13.67
r[less than or equal to]4 r[greater than or equal to]5 2.92
r[less than or equal to]5 r=6 0.02

 [lambda]- [lambda]-
 Trace Max
Null Alternative Test
Hypothesis C.V.(95%) Hypothesis Statistic

r=0 94.15 r=1 51.67 (*)
r[less than or equal to]1 68.52 r=2 30.01
r[less than or equal to]2 47.21 r=3 19.82
r[less than or equal to]3 29.68 r=4 10.75
r[less than or equal to]4 15.41 r=5 2.91
r[less than or equal to]5 3.76 r=6 0.02

 [lambda]-
 Max
Null
Hypothesis C.V.(95%)

r=0 39.37
r[less than or equal to]1 33.46
r[less than or equal to]2 27.07
r[less than or equal to]3 20.97
r[less than or equal to]4 14.07
r[less than or equal to]5 5.76

Note: Maximum lag in the Johansen test is 12, and the appropriate
AIC-based lag is lag is 7. The critical values come from Osterwald-Lenum
(1992, Table 1). The deterministic components are chosen by the Pantula
Principal which dictated the exclusion of the linear trend from both the
cointegrating relationship and the short-run model with an intercept
only in the short-run model. Nevertheless, the results are robust with
different lags and deterministic components. An (*)indicates rejection
of the null hypothesis (in favor of the corresponding alternative) at
the 5 percent significance level.
TABLE 2

Log-likelihood ration test statistics of implied Granger-causality
hypotheses (Derived from the off-diagonal elements of the VECM
maintained model)

 LR Test Degrees of
Null Hypothesis Statistics Freedom

 DI Equation

(1) [[beta].sub.12](L) = 0 8.88 (**) 2
(2) [[beta].sub.14](L) = 0 9.59 (**) 4
(3) [[beta].sub.16](L) = 0 13.83 (**) 3
(4) [[lambda].sub.1] = 0 9.33 (**) 1

 DE Equation

(5) [[beta].sub.23](L) = 0 6.55 4
(6) [[beta].sub.24](L) = 0 13.95 (**) 5
(7) [[lambda].sub.2]2 = 0 0.32 1

 DR Equation

(8) [[beta].sub.31](L) = 0 30.46 (**) 6
(9) [[beta].sub.32](L) = 0 3.04 (*) 1
(10) [[beta].sub.34](L) = 0 10.18 (**) 3
(11) [[beta].sub.35](L) = 0 3.15 (*) 1
(12) [[beta].sub.36](L) = 0 52.77 (**) 13
(13) [[lambda].sub.3] =0 6.22 (**) 1

 DB Equation

(14) [[beta].sub.43](L) = 0 23.56 (**) 3
(15) [[lambda].sub.4] =0 0.03 1

 DE Equation

(16) [[beta].sub.52](L) = 0 8.55 (**) 3
(17) [[beta].sub.54](L) 0 2.58 1
(18) [[beta].sub.56](L) = 0 17.01 (**) 8
(19) [[lambda].sub.5] =0 23.38 (**) 1

 DX Equation

(20) [[beta].sub.61](L) = 0 2.63 1
(21) [[beta].sub.63](L) = 0 22.77 (**) 5
(22) [[beta].sub.65](L) = 0 22.82 (**) 7
(23) [lambda] = 0 9.34 (**) 1

Notes: See notes to Table 1. The superscripts in the log polynomials
(equal to the degrees of freedom) are omitted for clarity. An
(*) indicates rejection of the null hypothesis of noncausality at the
five percent level of significance, while (**) indicates rejection at
the one percent level.