# U.S. military expenditure and the dollar.

U.S.MILITARY EXPENDITURE AND THE DOLLAR

I. INTRODUCTION

Many recent contributions have tried to explain fluctuations in the real exchange rate of the dollar against major currencies, most of all the Japanese yen and the deutsche mark. Among these, Ayanian [1987] studies whether political risk is one fundamental variable to which the value of the dollar can be anchored. He argues that an increase in military expenditure in the United States should increase the foreign demand for dollar-denominated assets (based on a safe-haven argument) and appreciate the dollar. Ayanian claims that this kind of relationship exists between the Fed real exchange rate index and defense expenditure as a percentage of GNP for 1973-85.

This paper applies techniques recently developed in the nonstationary time series literature. We believe this to be the correct way to analyze problems related to the real exchange rate. The use of a longer time period and a (slightly) different specification of the real exchange rate equation shows that Ayanian's safe-haven argument can indeed be justified by the data.

The rest of this paper is organized as follows. Section II describes the essential features of the methodology used to analyze the relationship between the real exchange rate and expenditure on military defense. The third section discusses the choice of the data and the sample period. Section IV reports results, and section V concludes.

II. NONSTATIONARY TIME SERIES ECONOMETRICS

The work of Nelson and Plosser [1982] showed that a large number of economic time series can be described in terms of nonstationary stochastic processes of the form

[y.sub.t] = [mu] + [alpha] [y.sub.t-1] + [u.sub.t]

where [mu] is a constant drift, a=1, and u is an error term. If u is an identically and independently distributed series, then [y.sub.t] is a random walk. In general, such a representation is known as an integrated process of order one, or I(1).

Phillips [1986] gave a theoretical foundation to some of the findings of Granger and Newbold [1974], and showed that a spurious relation can emerge when an I(1) process is regressed against another I(1) process. Thus, two nonstationary series may not interact with each other even if the coefficients of the regression are significant according to the traditional t-test. In fact, in this case, the usual t-ratio does not have a limiting distribution, but actually diverges as the sample size increases (see Phillips [1986]). The correct econometric methodology for I(1) variables has recently been explored in Engle and Grager [1987], under the name of cointegration. Consequently, it is of considerable importance to decide whether a series is [I(0).sup.1] or I(1) before doing any empirical work.

Phillips [1987] and Phillips-Perron [1986] developed tests of nonstationarity that generalize the original test used in the Nelson-Plosser study, (the Dickey-Fuller or the Augmented Dickey-Fuller test), and other tests proposed in Dickey-Fuller [1981]. The new test is more general in that it allows for some degree of autocorrelation and heteroskedasticity in the evolution of the error term, u.

If the hypothesis of nonstationarity can be rejected, then standard econometric procedures can be applied. If not, the theory of cointegration may provide useful information about the relationship between the variables under study. Two variables (x and y) are cointegrated if they are individually of order I(1), but can be linearly combined in a way that the residuals from such linear combination are of order I(0) (that is, stationary). This means that each series, taken by itself, has a tendency to drift apart, but that there is some relationship between the two which link one to the other. This linear combination can be interpreted as a long-run equilibrium relationship. Moreover, Granger and Engle [1987] showed that if x and y are I(1) and are cointegrated, there will always exist an "error correction" representation of these variables of the following form:

[[Delta]x.sub.t] = [[Rho].sub.1]u.sub.t-1] + lagged([Delta]x.sub.t, [Delta]y.sub.t} + A(L)[epsilon].sub.1t (2a) [[Delta]y.sub.t] = --[[Rho].sub.2]u[sub.t-1 + lagged ([Delta]x[sub.t], [[Delta]y]sub.t]) + A(L)[epsilon]sub.2t (2b)

where [u.sub.t] = [y.sub.t] - [[tau]x.sub.t] is the residual from the cointegrated regression of y on x; A(L) is a finite polynomial in the lag operator L; [[epsilon].sub.1t', [[epsilon].sub.2t] are joint white noise; and ~[Rho].sub.1~ + ~[Rho].sub.2~ [is not equal to]0. The system (2) provides some indication about the short-run relation among the variables.

A variety of tests for cointegration recently have been proposed. Following the advice given by Engle and Granger [1987], the Augmented Dickey-fuller test (ADF) is employed here. The interested reader should see Engle and Granger [1987] and Phillips and Ouliaris [1987] for the description and derivation of this and other tests.

III. DESCRIPTION OF THE DATA

Ayanian studies the Fed real exchange rate index for the period 1973-85 (on an annual basis) as the independent variable of a simple ordinary least squares regression. Various dependent variables are considered among which are, crucially, the United States defense budget as a percent of GNP and the federal budget deficit as a percentage of GNP. He finds that the defense budget has a significant explanatory power for the real exchange rate, on the basis of the t-statistics.

This methodology, however, is unsatisfactory for two reasons. First of all the number of observations (thirteen) is very small and does not leave sufficient degrees of freedom to make a reliable statistical inference. Moreover, some of the variables included in the regressions may be nonstationary, so that statistical inference cannot be made on the basis of standard procedures. In the following, Ayanian's analysis is improved in two directions. First, the sample, which now consists of quarterly observations on the mark-dollar exchange rate for the period 1951.1-1986.3, is extended. This dramatically increases the power of the tests, a consequence of the extended length of the total sample more than of the increased periodicity of the data, as noted by Shiller and Perron [1985]. Also note that if Ayanian's regressions are run using the mark-dollar real exchange rate instead of the Fed index, the results are not significantly different. The mark-dollar exchange rate was chosen because of the importance of the European currency as a reserve unit in internationally diversified portfolios. If a safe-haven argument holds true, this exchange rate should be particularly sensitive to changes in investors' confidence. Second, we explicity test for nonstationarity of the variables and for cointegration when this is appropriate according to the unit-root test results.

It should be noted that the period 1951.2-1986.3 is characterized by different nominal exchange rate regimes. However, this is of no concern since the real exchange rate is used. One might think that this is going to affect the tests for nonstationary, since flexible exchange rate regimes are distinguished by a higher variability of the real exchange rate than fixed exchange rate regimes, as found by Mussa [1986]. But, as mentioned in the previous paragraph, Phillips and Perron [1986] and Phillips [1987] tests can handle a variety of processes for the error term, including the kind of heteroskedasticity which is likely to arise in this context.

The variables which are considered are the end-of-period deutsche mark real exchange rate (defined as (DM/$)[P.sub.US] / [P.sub.G]), U.S. military expenditure as a percentage of GNP, U.S. total expenditure as a percentage of GNP, U.S. real GNP, U.S. real military expenditure, and U.S. real total government expenditure.

IV. RESULTS

Table I summarizes the results of testing for nonstationarity of the series. The statistic [Zeta](t[alpha]) is a test of the hypothesis that in equation (1) [alpha] = 1, with a possible nonzero drift. The statistic [Zeta]([phi].sub.3) is a test of the joint hypothesis that [alpha] = 1 and that a time trend of the form (t - T/2) is absent. (2) The unit root hypothesis cannot be rejected for the real exchange rate, real military expenditure, real total expenditure or real GNP. Some doubts arise about the expenditure variables when considered as a percentage of GNP. According to [Zeta](t[alpha]) one can reject the unit root hypothesis at a level between 2.5 and 1 percent if the minimum and the median values of the statistics are considered. The null hypothesis cannot re rejected if the maximum value is considered. Analogous results come from [Zeta]([phi].sub.3); the only difference is that the joint hypothesis of unit root and no trend can be rejected more strongly.

Even if the hypothesis that the expenditure ratios are nonstationary cannot be rejected firmly, it could be argued that from a theoretical point of view, these ratios have to be stationary. Even if this were the case, however, it would make no sense to regress the real exchange rate (an I(1) variable) on the military expenditure to GNP ratio (an I(0) variable), since "dependent and independent variables have such vastly different temporal properties," according to Granger [1986, 216]. The residual from such a regression would be nonstationary, indicating that the I(0) variable doesn't have any power in reducing the uncertainty of the dependent variable. Note, also, that the distribution of the t-ratio will be different from its standard distribution, so that the usual critical values would not be the correct ones in this case.

The next step was testing for cointegration by running the cointegrating regression of the real exchange rate on a constant and the potentially cointegrated variables, and calculating the ADF test. Because of space limits, the results for the ADF test are reported first (see Table II), and the results of the cointegrating regression are reported only for those combinations of variables which are of interest on the basis of the ADF. (The ratios of military and total expenditure to GNP were considered but did not give any sign of cointegration with the real exchange rate, and for this reason the results are not reported.)

The real exchange rate appears to be cointegrated with real military expenditure and real GNP when the two are considered together, and with real military and total expenditure and GNP, when the three are considered together. there is no sign of cointegration if one drops real military expenditure or real GNP, suggesting that cointegration for the set of three variables might be due mostly to these two variables.

The cointegrating regression for the exchange rate against real military expenditure and real GNP is reported in Table III. The signs of the variables are consistent with those found by Ayanian. An increase in U.S. military expenditure is associated with a real appreciation of the dollar. The third table also reports an estimate of the error correction mechanism, relating the change in the real exchange rate to the disequilibrium component prevailing in the previous year (the estimated error from the cointegrating regression) and to the changes in the other variables involved in the cointegrating regression. According to the error correction equation, the particularly significant variables are the level of past disequilibrium (u.sub.t-1), the change in military expenditure lagged three and four quarters, and the one-lagged change in the real exchange rate.

V. CONCLUSIONS

This paper finds a significant relationship between the mark-dollar real exchange rate and the levels of U.S. real GNP and real military expenditure for the period 1951.1-1986.3. Ayanian [1987] reached a similar conclusion. However, the evidence he presented was weak, given the extremely small number of observations, and it was derived ignoring the stationarity properties of the series under consideration.

Finally, one should be warned against a theoretical interpretation of this relationship. The "military safe-haven" argument may be a politically tempting and certainly controversial way of reading the evidence. However, the results reported here connot be interpreted as a test of this (or any other) theory. They just provide an additional stylized fact that should be taken into account when theoretical models of the real exchange rate are developed.

(1) A variable is integrated of order zero, I(0), when it is stationary in its levels.

(2) T is the number of observations.

REFERENCES

Ayanian, R. "Political Risk, National Defense and the Dollar." Economic Inquiry, April 1988, 345-51.

Dickey, D. A. and W. A. Fuller. "Likelihood Ratio Statistics for autoregressive Time Series with a Unit Root." Econometrica, July 1981, 1057-78.

Engle, R. F. and C. W. J. Granger. "Co-Integration and Error Correction: Representation, Estimation and Testing." Econometrica, March 1987, 251-76.

Fuller, W. A. Introduction to Statistical Time Series. New York: Wiley 1976.

Granger, C. W. J. "Development in the Study of Cointegrated Economic Variables." Oxford Bulletin of Economics and Statistics, August 1986, 213-28.

Granger, C. W. J. and P. Newbold. "Spurious Regressions in Econometrics." Journal of Econometrics, July 1974, 111-20.

Mussa, M. "Nominal Exchange Rate Regimes and the Behavior of Real Exchange Rates: Evidence and Implications." Carnegie-Rochester Conference Series on Public Policy, 1986, 117-214.

Nelson, C. R. and C. I. Plosser. "Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications." Journal of Monetary Economics, September 1982, 139-62.

Phillips, P. C. B. "Understanding Spurious Regressions in Econometrics." Journal of Econometrics, December 1986, 311-40.

Phillips, P. C. B. "Time Series Regression with a Unit Root." Econometrica, March 1987, 277-301.

Phillips, P. C. B. and S. Ouliaris. "Asymptotic Properties of Residual Based Tests for Cointegration." Cowles Foundation Discussion Paper No. 847, Yale University, 1987.

Phillips, P. C. B. and P. Perron. "Testing for a Unit Root in Time Series Regression." Cowles Foundation Discussion Paper No. 795, Yale University, 1986.

Shiller, R. J. And P. Perron. "Testing the Random Walk Hypothesis: Power versus Frequency of Observation." Economic Letters, 18(4), 1985, 381-86.

I. INTRODUCTION

Many recent contributions have tried to explain fluctuations in the real exchange rate of the dollar against major currencies, most of all the Japanese yen and the deutsche mark. Among these, Ayanian [1987] studies whether political risk is one fundamental variable to which the value of the dollar can be anchored. He argues that an increase in military expenditure in the United States should increase the foreign demand for dollar-denominated assets (based on a safe-haven argument) and appreciate the dollar. Ayanian claims that this kind of relationship exists between the Fed real exchange rate index and defense expenditure as a percentage of GNP for 1973-85.

This paper applies techniques recently developed in the nonstationary time series literature. We believe this to be the correct way to analyze problems related to the real exchange rate. The use of a longer time period and a (slightly) different specification of the real exchange rate equation shows that Ayanian's safe-haven argument can indeed be justified by the data.

The rest of this paper is organized as follows. Section II describes the essential features of the methodology used to analyze the relationship between the real exchange rate and expenditure on military defense. The third section discusses the choice of the data and the sample period. Section IV reports results, and section V concludes.

II. NONSTATIONARY TIME SERIES ECONOMETRICS

The work of Nelson and Plosser [1982] showed that a large number of economic time series can be described in terms of nonstationary stochastic processes of the form

[y.sub.t] = [mu] + [alpha] [y.sub.t-1] + [u.sub.t]

where [mu] is a constant drift, a=1, and u is an error term. If u is an identically and independently distributed series, then [y.sub.t] is a random walk. In general, such a representation is known as an integrated process of order one, or I(1).

Phillips [1986] gave a theoretical foundation to some of the findings of Granger and Newbold [1974], and showed that a spurious relation can emerge when an I(1) process is regressed against another I(1) process. Thus, two nonstationary series may not interact with each other even if the coefficients of the regression are significant according to the traditional t-test. In fact, in this case, the usual t-ratio does not have a limiting distribution, but actually diverges as the sample size increases (see Phillips [1986]). The correct econometric methodology for I(1) variables has recently been explored in Engle and Grager [1987], under the name of cointegration. Consequently, it is of considerable importance to decide whether a series is [I(0).sup.1] or I(1) before doing any empirical work.

Phillips [1987] and Phillips-Perron [1986] developed tests of nonstationarity that generalize the original test used in the Nelson-Plosser study, (the Dickey-Fuller or the Augmented Dickey-Fuller test), and other tests proposed in Dickey-Fuller [1981]. The new test is more general in that it allows for some degree of autocorrelation and heteroskedasticity in the evolution of the error term, u.

If the hypothesis of nonstationarity can be rejected, then standard econometric procedures can be applied. If not, the theory of cointegration may provide useful information about the relationship between the variables under study. Two variables (x and y) are cointegrated if they are individually of order I(1), but can be linearly combined in a way that the residuals from such linear combination are of order I(0) (that is, stationary). This means that each series, taken by itself, has a tendency to drift apart, but that there is some relationship between the two which link one to the other. This linear combination can be interpreted as a long-run equilibrium relationship. Moreover, Granger and Engle [1987] showed that if x and y are I(1) and are cointegrated, there will always exist an "error correction" representation of these variables of the following form:

[[Delta]x.sub.t] = [[Rho].sub.1]u.sub.t-1] + lagged([Delta]x.sub.t, [Delta]y.sub.t} + A(L)[epsilon].sub.1t (2a) [[Delta]y.sub.t] = --[[Rho].sub.2]u[sub.t-1 + lagged ([Delta]x[sub.t], [[Delta]y]sub.t]) + A(L)[epsilon]sub.2t (2b)

where [u.sub.t] = [y.sub.t] - [[tau]x.sub.t] is the residual from the cointegrated regression of y on x; A(L) is a finite polynomial in the lag operator L; [[epsilon].sub.1t', [[epsilon].sub.2t] are joint white noise; and ~[Rho].sub.1~ + ~[Rho].sub.2~ [is not equal to]0. The system (2) provides some indication about the short-run relation among the variables.

A variety of tests for cointegration recently have been proposed. Following the advice given by Engle and Granger [1987], the Augmented Dickey-fuller test (ADF) is employed here. The interested reader should see Engle and Granger [1987] and Phillips and Ouliaris [1987] for the description and derivation of this and other tests.

III. DESCRIPTION OF THE DATA

Ayanian studies the Fed real exchange rate index for the period 1973-85 (on an annual basis) as the independent variable of a simple ordinary least squares regression. Various dependent variables are considered among which are, crucially, the United States defense budget as a percent of GNP and the federal budget deficit as a percentage of GNP. He finds that the defense budget has a significant explanatory power for the real exchange rate, on the basis of the t-statistics.

This methodology, however, is unsatisfactory for two reasons. First of all the number of observations (thirteen) is very small and does not leave sufficient degrees of freedom to make a reliable statistical inference. Moreover, some of the variables included in the regressions may be nonstationary, so that statistical inference cannot be made on the basis of standard procedures. In the following, Ayanian's analysis is improved in two directions. First, the sample, which now consists of quarterly observations on the mark-dollar exchange rate for the period 1951.1-1986.3, is extended. This dramatically increases the power of the tests, a consequence of the extended length of the total sample more than of the increased periodicity of the data, as noted by Shiller and Perron [1985]. Also note that if Ayanian's regressions are run using the mark-dollar real exchange rate instead of the Fed index, the results are not significantly different. The mark-dollar exchange rate was chosen because of the importance of the European currency as a reserve unit in internationally diversified portfolios. If a safe-haven argument holds true, this exchange rate should be particularly sensitive to changes in investors' confidence. Second, we explicity test for nonstationarity of the variables and for cointegration when this is appropriate according to the unit-root test results.

It should be noted that the period 1951.2-1986.3 is characterized by different nominal exchange rate regimes. However, this is of no concern since the real exchange rate is used. One might think that this is going to affect the tests for nonstationary, since flexible exchange rate regimes are distinguished by a higher variability of the real exchange rate than fixed exchange rate regimes, as found by Mussa [1986]. But, as mentioned in the previous paragraph, Phillips and Perron [1986] and Phillips [1987] tests can handle a variety of processes for the error term, including the kind of heteroskedasticity which is likely to arise in this context.

The variables which are considered are the end-of-period deutsche mark real exchange rate (defined as (DM/$)[P.sub.US] / [P.sub.G]), U.S. military expenditure as a percentage of GNP, U.S. total expenditure as a percentage of GNP, U.S. real GNP, U.S. real military expenditure, and U.S. real total government expenditure.

IV. RESULTS

Table I summarizes the results of testing for nonstationarity of the series. The statistic [Zeta](t[alpha]) is a test of the hypothesis that in equation (1) [alpha] = 1, with a possible nonzero drift. The statistic [Zeta]([phi].sub.3) is a test of the joint hypothesis that [alpha] = 1 and that a time trend of the form (t - T/2) is absent. (2) The unit root hypothesis cannot be rejected for the real exchange rate, real military expenditure, real total expenditure or real GNP. Some doubts arise about the expenditure variables when considered as a percentage of GNP. According to [Zeta](t[alpha]) one can reject the unit root hypothesis at a level between 2.5 and 1 percent if the minimum and the median values of the statistics are considered. The null hypothesis cannot re rejected if the maximum value is considered. Analogous results come from [Zeta]([phi].sub.3); the only difference is that the joint hypothesis of unit root and no trend can be rejected more strongly.

Even if the hypothesis that the expenditure ratios are nonstationary cannot be rejected firmly, it could be argued that from a theoretical point of view, these ratios have to be stationary. Even if this were the case, however, it would make no sense to regress the real exchange rate (an I(1) variable) on the military expenditure to GNP ratio (an I(0) variable), since "dependent and independent variables have such vastly different temporal properties," according to Granger [1986, 216]. The residual from such a regression would be nonstationary, indicating that the I(0) variable doesn't have any power in reducing the uncertainty of the dependent variable. Note, also, that the distribution of the t-ratio will be different from its standard distribution, so that the usual critical values would not be the correct ones in this case.

The next step was testing for cointegration by running the cointegrating regression of the real exchange rate on a constant and the potentially cointegrated variables, and calculating the ADF test. Because of space limits, the results for the ADF test are reported first (see Table II), and the results of the cointegrating regression are reported only for those combinations of variables which are of interest on the basis of the ADF. (The ratios of military and total expenditure to GNP were considered but did not give any sign of cointegration with the real exchange rate, and for this reason the results are not reported.)

The real exchange rate appears to be cointegrated with real military expenditure and real GNP when the two are considered together, and with real military and total expenditure and GNP, when the three are considered together. there is no sign of cointegration if one drops real military expenditure or real GNP, suggesting that cointegration for the set of three variables might be due mostly to these two variables.

The cointegrating regression for the exchange rate against real military expenditure and real GNP is reported in Table III. The signs of the variables are consistent with those found by Ayanian. An increase in U.S. military expenditure is associated with a real appreciation of the dollar. The third table also reports an estimate of the error correction mechanism, relating the change in the real exchange rate to the disequilibrium component prevailing in the previous year (the estimated error from the cointegrating regression) and to the changes in the other variables involved in the cointegrating regression. According to the error correction equation, the particularly significant variables are the level of past disequilibrium (u.sub.t-1), the change in military expenditure lagged three and four quarters, and the one-lagged change in the real exchange rate.

V. CONCLUSIONS

This paper finds a significant relationship between the mark-dollar real exchange rate and the levels of U.S. real GNP and real military expenditure for the period 1951.1-1986.3. Ayanian [1987] reached a similar conclusion. However, the evidence he presented was weak, given the extremely small number of observations, and it was derived ignoring the stationarity properties of the series under consideration.

Finally, one should be warned against a theoretical interpretation of this relationship. The "military safe-haven" argument may be a politically tempting and certainly controversial way of reading the evidence. However, the results reported here connot be interpreted as a test of this (or any other) theory. They just provide an additional stylized fact that should be taken into account when theoretical models of the real exchange rate are developed.

(1) A variable is integrated of order zero, I(0), when it is stationary in its levels.

(2) T is the number of observations.

REFERENCES

Ayanian, R. "Political Risk, National Defense and the Dollar." Economic Inquiry, April 1988, 345-51.

Dickey, D. A. and W. A. Fuller. "Likelihood Ratio Statistics for autoregressive Time Series with a Unit Root." Econometrica, July 1981, 1057-78.

Engle, R. F. and C. W. J. Granger. "Co-Integration and Error Correction: Representation, Estimation and Testing." Econometrica, March 1987, 251-76.

Fuller, W. A. Introduction to Statistical Time Series. New York: Wiley 1976.

Granger, C. W. J. "Development in the Study of Cointegrated Economic Variables." Oxford Bulletin of Economics and Statistics, August 1986, 213-28.

Granger, C. W. J. and P. Newbold. "Spurious Regressions in Econometrics." Journal of Econometrics, July 1974, 111-20.

Mussa, M. "Nominal Exchange Rate Regimes and the Behavior of Real Exchange Rates: Evidence and Implications." Carnegie-Rochester Conference Series on Public Policy, 1986, 117-214.

Nelson, C. R. and C. I. Plosser. "Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications." Journal of Monetary Economics, September 1982, 139-62.

Phillips, P. C. B. "Understanding Spurious Regressions in Econometrics." Journal of Econometrics, December 1986, 311-40.

Phillips, P. C. B. "Time Series Regression with a Unit Root." Econometrica, March 1987, 277-301.

Phillips, P. C. B. and S. Ouliaris. "Asymptotic Properties of Residual Based Tests for Cointegration." Cowles Foundation Discussion Paper No. 847, Yale University, 1987.

Phillips, P. C. B. and P. Perron. "Testing for a Unit Root in Time Series Regression." Cowles Foundation Discussion Paper No. 795, Yale University, 1986.

Shiller, R. J. And P. Perron. "Testing the Random Walk Hypothesis: Power versus Frequency of Observation." Economic Letters, 18(4), 1985, 381-86.

Printer friendly Cite/link Email Feedback | |

Author: | Grilli, Vittorio; Beltratti, Andrea |
---|---|

Publication: | Economic Inquiry |

Date: | Oct 1, 1989 |

Words: | 2310 |

Previous Article: | Investment in sister's children as behavior towards risk. |

Next Article: | Karl Brunner, 1916-1989. |

Topics: |