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Defense spending and economic growth An alternative approach to the causality issue
Journal of Development Economics 35 (1991) 117-126. North-Holland
Defense spending and economic growth An alternative approach to the causality issue Charles J. LaCivita and Peter C. Frederiksen* Naval
Postgraduate
School,
Monterey,
CA 93943-5122
Received October 1987. final version received October 1989
Abstract: This paper re-examines the defense-growth causality issue. Using a 21-country sample and Granger causality methods developed by Hsiao, we find a feedback relationship exists for most countries. This implies that neither growth nor defense can be considered exogenous - a result suspected by Joerding in earlier work - but masked by his choice of an arbitrary lag structure.
1. Introduction In the last ten years, there has been a growing interest in the role of defense spending in developing countries.’ The area that has received the most attention has been whether defense spending helps or hinders economic growth. Much of the current work on this topic has stemmed from the work of Benoit (1978). Initially, he had expected to find a negative relationship between defense and growth. Instead, in his cross-sectional study of 44 countries, he found that ‘ . . . countries with a heavy defense burden generally had the most rapid rate of growth, and those with the lowest defense burden tended to show the lowest growth rates’ [Benoit (1978, p. 271)]. Since Benoit’s initial results, numerous additional studies have been undertaken; some have supported his results while others have found a statistically significant negative impact of defense on economic performance. In an excellent review of the literature, Chan (1985, p. 433) concluded that ‘ . . . there is no consensus about the actual existence and nature of such an impact’. He went on to conclude that ‘ . . . we have probably reached a point of diminishing returns in relying on aggregate cross-national studies to inform us about the economic impact of defense spending. . . . Future research will profit more from discriminating diachronic studies of individual countries’. *We would like to thank three anonymous referees for valuable comments. ‘See, for example, Deger (1986a). 0304-3878/91/$03.50
0 1991-Elsevier
Science Publishers B.V. (North-Holland)
118
C.J. LaCivita
and P.C. Frederiksen,
Defense
spending
and economic
growth
Two studies published since Chan’s review continue to illustrate the widely differing results which scholars in this area can obtain. For example, Biswas and Ram (1986, p. 370) developed an ‘augmented model’ and concluded that ‘. . . military expenditures neither help nor hurt economic growth in the LDCs to any significant extent’. On the other hand, in her study Deger (1986b, p. 193) concluded that ‘the empirical evidence goes against the findings of Benoit and others regarding the positive effects of defense on growth in LDCs . . . defense expenditure allocates scarce resources away from productive civilian investment and fails to mobilize or create any additional savings’. Many of the studies to date have failed to tackle the issue of causality and instead have chosen to accept Benoit’s original assumption that ‘ , . . the direct interaction between growth and defense burdens seems to run primarily from defense burdens to growth rather than vice versa. It seems clear that in the sample countries higher defense burdens stimulate growth.. .’ [Benoit (1978, p. 276)]. This assumption - that growth is the dependent instead of the independent variable - has recently been challenged by Joerding (1986). Employing Granger causality methods, he tested for the assumed exogeneity of defense budgets. Using a pooled sample containing 15 observations from each of 57 countries, Joerding employed a multivariate model which also included investment and government spending and concluded that defense expenditures are not strongly exogenous and that previous studies were thus flawed. Whether or not military spending promotes growth is an important policy consideration for developing countries searching for ways to improve economic performance. In this respect, we consider Joerding’s work to be a significant contribution to the literature and the understanding of the relationship between growth and defense.’ However, we believe there are three issues which merit further attention. First of all, Joerding lumps all countries into one sample. This suggests that any causal relationship which is uncovered is common to all countries .3 As was shown by Frederiksen and Looney (1983) in a review of Benoit’s work for example, splitting a pooled sample into separate groups (in their case by the level of resource constraints) can lead to quite different results. In other words we are suggesting that in some countries defense might lead to growth, in others growth to defense, and yet in others no significant relationship might exist. Second, by aggregating the sample, Joerding has assumed a common lag structure for all of the countries in the sample (in his study four years on the defense and growth variables). It seems to us quite reasonable to hypothesize that if a *However, one must use caution in using Granger causality to make conclusions about exogeneity. As a referee of this journal pointed out, Granger causality can be used to make statements about exogeneity only in linear models. It is possible that there exists a non-linear model in which defense spending is an exogenous variable. 3This is also the assumption underlying the cross-section studies.
C.J. LaCivita
and P.C. Frederiksen,
Defense
spending
and economic growth
119
causal relationship does exist (either defense to growth or growth to defense) we could expect the time lag to differ from country to country. Third, Joerding’s method for choosing lag length was ad hoc. The purpose of this paper is to re-examine the defense-growth causality issue and at the same time to take into account the three issues noted above. We have done this by examining 21 countries individually over time and in a pooled sample. In the following section we present our empirical results and test two hypotheses. First, if a causal relationship between defense (D) and growth (G) does exist, we hypothesize that the relationship might differ from country to country. Second, we hypothesize that the lag structure between D and G or between G and D might also vary between countries. To test this hypothesis we employ a systematic approach to specify the lag structure. 2. Empirical results 2.1. Pooled versus individual studies
To test our hypotheses, we selected 61 developing countries.4 The data for the numerator of D, defense expenditures in current dollars, was taken from various annual issues of the United Nations Statistical Yearbook. The denominator of D, GDP in current dollars, and G, the growth rate of real GDP, were obtained from various annual issues of the International Monetary Fund’s International Financial Statistics Yearbook. Since we did not pool the data and we allowed for the possibility of lags longer than four years, we required a large number of annual observations for each country. We used all the data available for each country for the years 1952-1982. Since data for some countries was available for only a subset of this time period, the number of annual observations for each country in our sample ranged from 20 to 28. While this number is low, this is the only data currently available. In addition, some countries did not report defense spending while others did not report a sufficient number of observations to conduct the necessary statistical tests. We were able to obtain sufficient timeseries data for only 21 countries which formed the sample in this paper. To test the first hypothesis that the causal relationship might differ among countries (assuming a lag of four), we used the Granger causality procedure adopted by Joerding.’ The following equations were estimated to test for Granger causality: G=f(G-,
,..., G-,,D-,
,..., De4),
(1)
%ee Appendix I, p. 338, in Looney and Frederiksen (1986) for a list of the countries. ‘The Granger test for causality suggests that some variable X causes another variable Y if including the past values of X in the regression equation improves the predicted values of Y For an expanded discussion on the technique, see Jung (1986).
120
C.J. LaCivita
and P.C. Frederiksen,
Defense
spending
and economic
growth
Table 1 Causal relationships, 21 countries.” G to D Burma Ecuador Sri Lanka Syria Pooled sample
to G South Africa Thailand Venezuela
D
Feedback Colombia Iran
No relationship Argentina Chile Costa Rica Dominican Republic El Salvador Ghana Guatemala India Pakistan Philippines Spain Turkey
aResults of testing at the 10% level of significance.
D=f(G-,
,..., G-,,D-,
,..., D-J,
(2)
-4 represent values of D and G lagged from where the subscripts -l,..., one to four years, respectively, D is the ratio of defense spending to GDP, and G is the growth rate of real GDP. After eq. (1) was estimated, an F-test using a 10% level of significance was performed on the lagged values of D to determine if they belonged in the equation. If their inclusion significantly improved the prediction in G, then we conclude that defense Granger-causes growth. A similar procedure was performed on eq. (2) and the lagged values of G to determine if growth Granger-causes defense. As an initial step, we attempted to replicate Joerding’s results with our set of countries. Following Joerding, we pooled the data and assumed a lag length of four for growth and defense. Importantly, even with a different set of countries and excluding the investment and government variables and with data collected from different sources, we replicated Joerding’s results, finding that G Granger-causes D, but not vice versa. Furthermore, we also obtained approximately the same levels of statistical significance.‘j The results for each country and the pooled sample appear in table 1. As predicted, the causal relationship differed from country to country. In fact, four different forms of the relationship were found to exist: from G to D, feedback (G to D to G, etc.), and (for the majority of the sample) no statistical relationship between D and G. While the latter result could be an artifact of the small sample size for each country, in the next section we show that it is more probably due to the arbitrary choice of lag structure. % order to compare our results with those of Joerding, we chose our defense variable as military spending as a percent of Gross Domestic Product - the ‘defense burden’ - as have many studies in this area. We recognize that other proxy measures exist; see for example Biswas and Ram (1986).
C.J. LaCioitn and PC. Frederiksen, Defense spending and economic growth
121
Furthermore, we show that a more systematic method for choosing the lag structure drastically changes this result.
2.2. Choice of lag lengths
The results of Granger-causality tests depend critically on the choice of lag length. If the chosen lag length is less than the true lag length, the omission of relevant lags can cause bias. If the chosen lag length is greater than the true lag length, the inclusion of irrelevant lags causes the estimates to be inefficient. Most often, the choice of lag length is done in an ad hoc, arbitrary manner. Joerding (1986) chose his lag lengths based on preliminary autocorrelation estimates. While this is an improvement over arbitrary methods, it still does not account for the interaction among the variables and constrains all variables to the same lag length. As noted above, there is no a priori reason to assume that the lag lengths are equal for all the countries in a sample. For example, in an initial study of the Philippines, Frederiksen and LaCivita (1987) found no statistically significant relationship between economic growth and defense spending when both variables were entered with a lag of four. However, when the lag on both variables was set to two, we found that growth causes defense. Since both lag structures were chosen arbitrarily, we cannot say which is the correct specification. Hsiao (1981) has developed a systematic method for choosing lag lengths for each variable in an equation. Hsiao’s method combines Granger causality and Akaike’s final prediction error (FPE), defined as the (asymptotic) mean square prediction error, to determine both the optimum lag for each variable and causal relationships. In a paper examining the problems encountered in choosing lag lengths, Thornton and Batten (1985) found Hsiao’s method to be superior to both arbitrary lag length selection and several other systematic procedures for determining lag length.7 The first step in Hsiao’s procedure is to perform a series of autoregressive regressions on the dependent variable. In the first regression, the dependent variable is lagged once. In each succeeding regression, one more lag on the dependent variable is added. That is, we estimate M regressions of the form
G,=oz+ f bt-iGt-i+Ety i=l
‘They also show that the FPE criterion ‘gives relatively more importance to unbiasedness over effkiency, but is asymptotically inefficient in that, on average, it selects lags that are too long in large samples’ [Thornton and Batten (1985, p. 167)].
122
C.J. LaCivita
and P.C. Frederiksen,
Defense
spending
and economic
growth
where the value of m ranges from 1 to M.8 For each regression we compute the FPE in the following manner: FPE(m) = 2,“’
: ESS(m)/lT:
where T is the sample size, and FPE(m) and ESS(m) are the final prediction error and the sum of squared errors, respectively. The optimal lag length, m*, is the lag length which produces the lowest FPE. Once m* has been determined, regressions are estimated with the lags on the other variable added sequentially in the same manner used to determine m*. Thus we estimate six regressions of the form:
G,=a+ z bt-iGr-i+ i Yr-iDr-i+Ety i=l
i=l
with n ranging from one to six. Computing regression equation as T+m*+n+ 1 FPE(m*, n) = T-m* _ n _ 1 EWm*,
the final prediction error for each
4/T
(6)
we choose the optimal lag length for D, n*, as the lag length which produces the lowest FPE. Using the final prediction error to determine lag length is equivalent to using a series of F tests with variable levels of significance. To test for causality, the FPE with D omitted from the model, FPE(m*), is compared to the FPE with D included in the model, FPE(m*,n*). If FPE(m*) < FPE(m*, n*), defense spending does not Granger-cause economic growth. If FPE(m*) > FPE(m*, n*), defense spending Granger-causes growth. Once the test has been performed with economic growth as the dependent variable, a similar test with the defense burden as the dependent variable is carried out. In addition, we used standard F tests to test for Granger causality on the models specified by the Hsiao procedure. These results are not part of the Hsiao procedure, which selects the model based on the FPE, and are ‘Although the choice of M (maximum lag length) is arbitrary, M should be as large as possible consistent with the sample size and the underlying economic process. In this respect, we have set M equal to six. In those few cases where the optimum m was found to be six, we tested with m equal to seven to determine if FPE(m= 7) <: FPE(m = 6). In all cases m equal to six was preferred.
C.J.
LaCioita and PC. Frederiksen,
Defense
spending and economic
123
growth
Table 2 Causal relationships using Hsiao’s method. Direction of causality D+G
Hsiao test result G-D
D+G
Feedback
No relationship
Country
Optimal lag (1)
Ecuador Sri Lanka Syria Turkey
f&l) I:*:; (1:1)
Colombia South Africa Venezuela Argentina Burma Chile El Salvador Ghana Iran Pakistan Philippines Spain Thailand Pooled sample Costa Rica Dominican Rep. Guatemala India
Ix; (1:1) (136)
(Ll) (193)
(176) (1,3) i::;
U:6)
(Ll) (Ll) (4,6)
(l>l) (17 1) (131)
(671)
G-D
Prob. level
Prob. level
Optimal
D+G
(4,4)
(2)
lag
(3)
(4)
0.76 0.52 0.38 0.65 0.01 0.15 0.03 0.12 0.07 0.05 0.08 0.07 0.03 0.04 0.10 0.00 0.01 0.02
0.92 0.80 0.87 0.96
(1,4) (2,4)
0.73 0.61 0.72 0.64
0.21 0.23
(2>1) (1,4) (191) i:* :; (4:3)
0.96
(136)
0.45 0.83
I? :; (5: 1) (1,4) (1,l)
0.31 0.73 0.02 0.99 0.97 0.92 -
(L2) I::; (619) (191)
Prob. level 9-0 (5) 0.01 0.00 0.08 0.11 0.40 0.94 0.17 0.06 0.01 0.03 0.07 0.17 0.17 0.02 0.09 0.00 0.13 0.00 0.65 0.97 0.38 0.57
Prob. level (4,4)
(6) 0.42 0.30 0.49 0.71 0.57 0.72 0.99 0.49 0.95 0.66 0.10 0.82 0.52 0.89 0.01 0.51 0.42 0.64
included only for reference. We also used F tests to compare the Hsiao specification against a common model with all lags set arbitrarily to four. The results using Hsiao’s method on both our pooled sample and each country appear in table 2. The numbers in column (1) indicate m* and n* when economic growth is the dependent variable. Column (2) is the probability level (based on an F-test) for rejecting the null hypothesis that defese does not Granger-cause economic growth, i.e. the probability of making a Type I error. For the individual countries, column (3) is the probability level (based on an F-test) for rejecting the null hypothesis that the Hsiao model is a better model than a common model which has all lags set arbitrarily to four. For the pooled sample, column (3) is the probability level for rejecting the null hypothesis that a four-lag model is preferred to the Hsiao model. Thus, a high probability for an individual country means that the Hsiao model could not be rejected in favor of the four-lag model whereas a low probability level for the pooled sample means that the four-lag model can be rejected in favor of the Hsiao model. A dash means that no F-test
I24
C.J. LaCivita
and P.C. Frederiksen,
Defense
spending
and economic
growth
was performed.’ Similarly, column (4) represents m* and IZ* when defense spending is the dependent variable, column (5) is the probability level for rejecting the null hypothesis that economic growth does not Granger-cause defense, and column (6) is the probability level for rejecting the Hsiao model in favor of the common model for individual countries or the common model in favor of the Hsiao model for the pooled sample. As noted above, the probability levels in columns (2) and (5) are included for reference only.” The Hsiao test results are based on the FPE (and not on F-tests) and are equivalent to using a series of F-tests with variable levels of significance. Even so, the results of the F-tests generally conform to the Hsiao results. These results are significantly different from those reported in table 1. First, both the pooled sample and the majority of countries now exhibit a feedback relationship between growth and defense. That is, we reject Granger non-causality in spite of our small sample sizes and the fact the FPE criterion leads to ine!Iicient estimates. Second, as we hypothesized, the estimated lag lengths differ among countries. Third, the lag lengths are also different between the defense and growth variables within each country. In all cases where an F-test could be performed, the Hsiao model could not be rejected in favor of the common model. The implications of our results are that the imposition of an arbitrary and common lag length hides the feedback relationship which we found for the majority of the countries and for the pooled sample. In particular, the results for the pooled data suggest that Joerding did not find feedback because of his choice of lag structure. Clearly, the appropriate relationship can be detected only by a proper specification of the model. 3. Summary and conclusions
In this paper we have re-examined the defense-growth causality issue. For the most part, previous studies have assumed that defense causes growth. gin models where the optimal lag on both variables is four or less, the F-test is straightforward because the Hsiao model is nested in the four-lag model. For example, if the optimal lag is (2,2), the null hypothesis is that ps =p4= y3= ys=O. If the computed F-value is greater than the critical value, we reject the Hsiao specification in favor of the common model. However, if the optimal lag is greater than four for one variable but less than four for the other, the null hypothesis is composite and is difficult to test. For example, if the optimal lag is (2,6), the null hypothesis is &=/Cd = 0, ys, y4 #O. This is a composite hypothesis which is not nested and cannot be tested in a straightforward manner. If the optimal lags are greater than four for both variables, the test is again straightforward because the four-lag model is nested in the Hsiao model. lOIndeed, the interpretation of these F-tests must be done with caution. Since the FPE is used to determine the optimal lag length before the F-tests are performed, the F-tests are probably biased. To determine the direction of this bias, the joint distribution of the two tests must be derived.
C.J. L&i&a
and PC. Frederiksen, Defense spending and economic growth
125
These studies relied on cross-sectional data and assumed that correlation implied causation. A recent study by Joerding addressed the causality issue directly using Granger causality tests. He concluded that for his sample of countries growth Granger-causes defense, implying that defense spending is not an exogenous variable. Although Joerding’s contribution to the literature is significant, we felt that his results may have been an artifact of pooling time-series data, on the one hand, and his choice of an arbitrary lag length on the other hand. As a first step, we replicated Joerding’s results by pooling our sample of countries and assuming an arbitrary lag structure of four years. However, when we examined each country individually using this lag structure, we found no relationship between defense and economic growth for the majority of our sample. As noted above, this might imply that the growth of defense relationship found by Joerding was a result of his pooling methodology. Next, we used Granger causality methods developed by Hsiao on each country in our sample and on a pooled sample. We tested two hypotheses: (a) the relationship between growth and defense might differ among countries; and (b) the lag structure might also differ among variables within a country. Our results confirmed these two hypotheses. Most importantly, our results show a feedback relationship exists between growth and defense spending for both the majority of the countries in our sample and the pooled sample. This feedback relationship implies that neither economic growth nor defense can be considered exogenous. This was. Joerding’s intuition, but the result was hidden by his choice of an arbitrary lag structure. Our results using Hsiao’s method show that in fact Joerding’s intuition was correct. These findings have important implications for ongoing research into the relationship between defense spending and economic growth in developing countries. First, for most countries, it appears than neither defense nor economic growth can be considered as exogenously determined variables. As suggested by Joerding, this means that researchers should use a simultaneous equation model to investigate any further relationship between the two variables. Second, researchers should not expect to find that one model tits every country. For example, the lag lengths are likely to differ between countries as is the observed relationship between economic growth and the military burden.
References Benoit, E., 1978, Growth and defense in developing countries, Economic Development and Cultural Change 26,271-280. Biswas, B. and R. Ram, 1986, Military expenditures and economic growth in less developed countries: An augmented model and further evidence, Economic Development and Cultural Change 34,361-372.
I.D.E.-E
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C.J. LaCivita
and P.C. Frederiksen,
Defense
spending
and economic
growth
Chan, S., 1985, The impact of defense spending on economic performance: A survey of evidence and problems, Orbis 29,403-434. Deger, S., 1986a, Military expenditure in Third World countries (Routledge and Kegan Paul, London). Deger, S., 1986b, Economic development and defense expenditures, Economic Development and Cultural Change 35, 179-196. Frederiksen, PC. and C.J. LaCivita, 1987, Defense spending and economic growth: Time series evidence on causality for the Philippines, 1956-1982, Journal of Philippine Development 14, 354-360. Frederiksen, PC. and ‘R.E. Looney, 1983, Defense expenditures and economic growth in developing countries, Armed Forces and Society 9, 633-645. Hsiao, C., 1981, Autoregressive modeling and money-income causality detection, Journal of Monetary Economics 7, 85-106. International Monetary Fund, various years, International financial statistics yearbook, various issues (International Monetary Fund, Washington, DC). Joerding, W., 1986, Economic growth and defense spending Granger causality, Journal of Development Economics 21, 35-40. Jung, W.S., Financial development and economic growth: International evidence, Economic Development and Cultural Change 34, 333-346. Looney, R.E. and PC. Frederiksen, 1986, Defense expenditures, external public debt and growth in developing countries, Journal of Peace Research 23, 329-338. Thornton, ‘D.L. and D.S. Batten, 1985, Lag-length selection and tests of Granger causality between money and income, Journal of Money, Credit, and Banking 17, 164-178. United Nations, various years, UN statistical yearbook, various issues (United Nations, New York).
Defense spending and economic growth An alternative approach to the causality issue Charles J. LaCivita and Peter C. Frederiksen* Naval
Postgraduate
School,
Monterey,
CA 93943-5122
Received October 1987. final version received October 1989
Abstract: This paper re-examines the defense-growth causality issue. Using a 21-country sample and Granger causality methods developed by Hsiao, we find a feedback relationship exists for most countries. This implies that neither growth nor defense can be considered exogenous - a result suspected by Joerding in earlier work - but masked by his choice of an arbitrary lag structure.
1. Introduction In the last ten years, there has been a growing interest in the role of defense spending in developing countries.’ The area that has received the most attention has been whether defense spending helps or hinders economic growth. Much of the current work on this topic has stemmed from the work of Benoit (1978). Initially, he had expected to find a negative relationship between defense and growth. Instead, in his cross-sectional study of 44 countries, he found that ‘ . . . countries with a heavy defense burden generally had the most rapid rate of growth, and those with the lowest defense burden tended to show the lowest growth rates’ [Benoit (1978, p. 271)]. Since Benoit’s initial results, numerous additional studies have been undertaken; some have supported his results while others have found a statistically significant negative impact of defense on economic performance. In an excellent review of the literature, Chan (1985, p. 433) concluded that ‘ . . . there is no consensus about the actual existence and nature of such an impact’. He went on to conclude that ‘ . . . we have probably reached a point of diminishing returns in relying on aggregate cross-national studies to inform us about the economic impact of defense spending. . . . Future research will profit more from discriminating diachronic studies of individual countries’. *We would like to thank three anonymous referees for valuable comments. ‘See, for example, Deger (1986a). 0304-3878/91/$03.50
0 1991-Elsevier
Science Publishers B.V. (North-Holland)
118
C.J. LaCivita
and P.C. Frederiksen,
Defense
spending
and economic
growth
Two studies published since Chan’s review continue to illustrate the widely differing results which scholars in this area can obtain. For example, Biswas and Ram (1986, p. 370) developed an ‘augmented model’ and concluded that ‘. . . military expenditures neither help nor hurt economic growth in the LDCs to any significant extent’. On the other hand, in her study Deger (1986b, p. 193) concluded that ‘the empirical evidence goes against the findings of Benoit and others regarding the positive effects of defense on growth in LDCs . . . defense expenditure allocates scarce resources away from productive civilian investment and fails to mobilize or create any additional savings’. Many of the studies to date have failed to tackle the issue of causality and instead have chosen to accept Benoit’s original assumption that ‘ , . . the direct interaction between growth and defense burdens seems to run primarily from defense burdens to growth rather than vice versa. It seems clear that in the sample countries higher defense burdens stimulate growth.. .’ [Benoit (1978, p. 276)]. This assumption - that growth is the dependent instead of the independent variable - has recently been challenged by Joerding (1986). Employing Granger causality methods, he tested for the assumed exogeneity of defense budgets. Using a pooled sample containing 15 observations from each of 57 countries, Joerding employed a multivariate model which also included investment and government spending and concluded that defense expenditures are not strongly exogenous and that previous studies were thus flawed. Whether or not military spending promotes growth is an important policy consideration for developing countries searching for ways to improve economic performance. In this respect, we consider Joerding’s work to be a significant contribution to the literature and the understanding of the relationship between growth and defense.’ However, we believe there are three issues which merit further attention. First of all, Joerding lumps all countries into one sample. This suggests that any causal relationship which is uncovered is common to all countries .3 As was shown by Frederiksen and Looney (1983) in a review of Benoit’s work for example, splitting a pooled sample into separate groups (in their case by the level of resource constraints) can lead to quite different results. In other words we are suggesting that in some countries defense might lead to growth, in others growth to defense, and yet in others no significant relationship might exist. Second, by aggregating the sample, Joerding has assumed a common lag structure for all of the countries in the sample (in his study four years on the defense and growth variables). It seems to us quite reasonable to hypothesize that if a *However, one must use caution in using Granger causality to make conclusions about exogeneity. As a referee of this journal pointed out, Granger causality can be used to make statements about exogeneity only in linear models. It is possible that there exists a non-linear model in which defense spending is an exogenous variable. 3This is also the assumption underlying the cross-section studies.
C.J. LaCivita
and P.C. Frederiksen,
Defense
spending
and economic growth
119
causal relationship does exist (either defense to growth or growth to defense) we could expect the time lag to differ from country to country. Third, Joerding’s method for choosing lag length was ad hoc. The purpose of this paper is to re-examine the defense-growth causality issue and at the same time to take into account the three issues noted above. We have done this by examining 21 countries individually over time and in a pooled sample. In the following section we present our empirical results and test two hypotheses. First, if a causal relationship between defense (D) and growth (G) does exist, we hypothesize that the relationship might differ from country to country. Second, we hypothesize that the lag structure between D and G or between G and D might also vary between countries. To test this hypothesis we employ a systematic approach to specify the lag structure. 2. Empirical results 2.1. Pooled versus individual studies
To test our hypotheses, we selected 61 developing countries.4 The data for the numerator of D, defense expenditures in current dollars, was taken from various annual issues of the United Nations Statistical Yearbook. The denominator of D, GDP in current dollars, and G, the growth rate of real GDP, were obtained from various annual issues of the International Monetary Fund’s International Financial Statistics Yearbook. Since we did not pool the data and we allowed for the possibility of lags longer than four years, we required a large number of annual observations for each country. We used all the data available for each country for the years 1952-1982. Since data for some countries was available for only a subset of this time period, the number of annual observations for each country in our sample ranged from 20 to 28. While this number is low, this is the only data currently available. In addition, some countries did not report defense spending while others did not report a sufficient number of observations to conduct the necessary statistical tests. We were able to obtain sufficient timeseries data for only 21 countries which formed the sample in this paper. To test the first hypothesis that the causal relationship might differ among countries (assuming a lag of four), we used the Granger causality procedure adopted by Joerding.’ The following equations were estimated to test for Granger causality: G=f(G-,
,..., G-,,D-,
,..., De4),
(1)
%ee Appendix I, p. 338, in Looney and Frederiksen (1986) for a list of the countries. ‘The Granger test for causality suggests that some variable X causes another variable Y if including the past values of X in the regression equation improves the predicted values of Y For an expanded discussion on the technique, see Jung (1986).
120
C.J. LaCivita
and P.C. Frederiksen,
Defense
spending
and economic
growth
Table 1 Causal relationships, 21 countries.” G to D Burma Ecuador Sri Lanka Syria Pooled sample
to G South Africa Thailand Venezuela
D
Feedback Colombia Iran
No relationship Argentina Chile Costa Rica Dominican Republic El Salvador Ghana Guatemala India Pakistan Philippines Spain Turkey
aResults of testing at the 10% level of significance.
D=f(G-,
,..., G-,,D-,
,..., D-J,
(2)
-4 represent values of D and G lagged from where the subscripts -l,..., one to four years, respectively, D is the ratio of defense spending to GDP, and G is the growth rate of real GDP. After eq. (1) was estimated, an F-test using a 10% level of significance was performed on the lagged values of D to determine if they belonged in the equation. If their inclusion significantly improved the prediction in G, then we conclude that defense Granger-causes growth. A similar procedure was performed on eq. (2) and the lagged values of G to determine if growth Granger-causes defense. As an initial step, we attempted to replicate Joerding’s results with our set of countries. Following Joerding, we pooled the data and assumed a lag length of four for growth and defense. Importantly, even with a different set of countries and excluding the investment and government variables and with data collected from different sources, we replicated Joerding’s results, finding that G Granger-causes D, but not vice versa. Furthermore, we also obtained approximately the same levels of statistical significance.‘j The results for each country and the pooled sample appear in table 1. As predicted, the causal relationship differed from country to country. In fact, four different forms of the relationship were found to exist: from G to D, feedback (G to D to G, etc.), and (for the majority of the sample) no statistical relationship between D and G. While the latter result could be an artifact of the small sample size for each country, in the next section we show that it is more probably due to the arbitrary choice of lag structure. % order to compare our results with those of Joerding, we chose our defense variable as military spending as a percent of Gross Domestic Product - the ‘defense burden’ - as have many studies in this area. We recognize that other proxy measures exist; see for example Biswas and Ram (1986).
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Furthermore, we show that a more systematic method for choosing the lag structure drastically changes this result.
2.2. Choice of lag lengths
The results of Granger-causality tests depend critically on the choice of lag length. If the chosen lag length is less than the true lag length, the omission of relevant lags can cause bias. If the chosen lag length is greater than the true lag length, the inclusion of irrelevant lags causes the estimates to be inefficient. Most often, the choice of lag length is done in an ad hoc, arbitrary manner. Joerding (1986) chose his lag lengths based on preliminary autocorrelation estimates. While this is an improvement over arbitrary methods, it still does not account for the interaction among the variables and constrains all variables to the same lag length. As noted above, there is no a priori reason to assume that the lag lengths are equal for all the countries in a sample. For example, in an initial study of the Philippines, Frederiksen and LaCivita (1987) found no statistically significant relationship between economic growth and defense spending when both variables were entered with a lag of four. However, when the lag on both variables was set to two, we found that growth causes defense. Since both lag structures were chosen arbitrarily, we cannot say which is the correct specification. Hsiao (1981) has developed a systematic method for choosing lag lengths for each variable in an equation. Hsiao’s method combines Granger causality and Akaike’s final prediction error (FPE), defined as the (asymptotic) mean square prediction error, to determine both the optimum lag for each variable and causal relationships. In a paper examining the problems encountered in choosing lag lengths, Thornton and Batten (1985) found Hsiao’s method to be superior to both arbitrary lag length selection and several other systematic procedures for determining lag length.7 The first step in Hsiao’s procedure is to perform a series of autoregressive regressions on the dependent variable. In the first regression, the dependent variable is lagged once. In each succeeding regression, one more lag on the dependent variable is added. That is, we estimate M regressions of the form
G,=oz+ f bt-iGt-i+Ety i=l
‘They also show that the FPE criterion ‘gives relatively more importance to unbiasedness over effkiency, but is asymptotically inefficient in that, on average, it selects lags that are too long in large samples’ [Thornton and Batten (1985, p. 167)].
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spending
and economic
growth
where the value of m ranges from 1 to M.8 For each regression we compute the FPE in the following manner: FPE(m) = 2,“’
: ESS(m)/lT:
where T is the sample size, and FPE(m) and ESS(m) are the final prediction error and the sum of squared errors, respectively. The optimal lag length, m*, is the lag length which produces the lowest FPE. Once m* has been determined, regressions are estimated with the lags on the other variable added sequentially in the same manner used to determine m*. Thus we estimate six regressions of the form:
G,=a+ z bt-iGr-i+ i Yr-iDr-i+Ety i=l
i=l
with n ranging from one to six. Computing regression equation as T+m*+n+ 1 FPE(m*, n) = T-m* _ n _ 1 EWm*,
the final prediction error for each
4/T
(6)
we choose the optimal lag length for D, n*, as the lag length which produces the lowest FPE. Using the final prediction error to determine lag length is equivalent to using a series of F tests with variable levels of significance. To test for causality, the FPE with D omitted from the model, FPE(m*), is compared to the FPE with D included in the model, FPE(m*,n*). If FPE(m*) < FPE(m*, n*), defense spending does not Granger-cause economic growth. If FPE(m*) > FPE(m*, n*), defense spending Granger-causes growth. Once the test has been performed with economic growth as the dependent variable, a similar test with the defense burden as the dependent variable is carried out. In addition, we used standard F tests to test for Granger causality on the models specified by the Hsiao procedure. These results are not part of the Hsiao procedure, which selects the model based on the FPE, and are ‘Although the choice of M (maximum lag length) is arbitrary, M should be as large as possible consistent with the sample size and the underlying economic process. In this respect, we have set M equal to six. In those few cases where the optimum m was found to be six, we tested with m equal to seven to determine if FPE(m= 7) <: FPE(m = 6). In all cases m equal to six was preferred.
C.J.
LaCioita and PC. Frederiksen,
Defense
spending and economic
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growth
Table 2 Causal relationships using Hsiao’s method. Direction of causality D+G
Hsiao test result G-D
D+G
Feedback
No relationship
Country
Optimal lag (1)
Ecuador Sri Lanka Syria Turkey
f&l) I:*:; (1:1)
Colombia South Africa Venezuela Argentina Burma Chile El Salvador Ghana Iran Pakistan Philippines Spain Thailand Pooled sample Costa Rica Dominican Rep. Guatemala India
Ix; (1:1) (136)
(Ll) (193)
(176) (1,3) i::;
U:6)
(Ll) (Ll) (4,6)
(l>l) (17 1) (131)
(671)
G-D
Prob. level
Prob. level
Optimal
D+G
(4,4)
(2)
lag
(3)
(4)
0.76 0.52 0.38 0.65 0.01 0.15 0.03 0.12 0.07 0.05 0.08 0.07 0.03 0.04 0.10 0.00 0.01 0.02
0.92 0.80 0.87 0.96
(1,4) (2,4)
0.73 0.61 0.72 0.64
0.21 0.23
(2>1) (1,4) (191) i:* :; (4:3)
0.96
(136)
0.45 0.83
I? :; (5: 1) (1,4) (1,l)
0.31 0.73 0.02 0.99 0.97 0.92 -
(L2) I::; (619) (191)
Prob. level 9-0 (5) 0.01 0.00 0.08 0.11 0.40 0.94 0.17 0.06 0.01 0.03 0.07 0.17 0.17 0.02 0.09 0.00 0.13 0.00 0.65 0.97 0.38 0.57
Prob. level (4,4)
(6) 0.42 0.30 0.49 0.71 0.57 0.72 0.99 0.49 0.95 0.66 0.10 0.82 0.52 0.89 0.01 0.51 0.42 0.64
included only for reference. We also used F tests to compare the Hsiao specification against a common model with all lags set arbitrarily to four. The results using Hsiao’s method on both our pooled sample and each country appear in table 2. The numbers in column (1) indicate m* and n* when economic growth is the dependent variable. Column (2) is the probability level (based on an F-test) for rejecting the null hypothesis that defese does not Granger-cause economic growth, i.e. the probability of making a Type I error. For the individual countries, column (3) is the probability level (based on an F-test) for rejecting the null hypothesis that the Hsiao model is a better model than a common model which has all lags set arbitrarily to four. For the pooled sample, column (3) is the probability level for rejecting the null hypothesis that a four-lag model is preferred to the Hsiao model. Thus, a high probability for an individual country means that the Hsiao model could not be rejected in favor of the four-lag model whereas a low probability level for the pooled sample means that the four-lag model can be rejected in favor of the Hsiao model. A dash means that no F-test
I24
C.J. LaCivita
and P.C. Frederiksen,
Defense
spending
and economic
growth
was performed.’ Similarly, column (4) represents m* and IZ* when defense spending is the dependent variable, column (5) is the probability level for rejecting the null hypothesis that economic growth does not Granger-cause defense, and column (6) is the probability level for rejecting the Hsiao model in favor of the common model for individual countries or the common model in favor of the Hsiao model for the pooled sample. As noted above, the probability levels in columns (2) and (5) are included for reference only.” The Hsiao test results are based on the FPE (and not on F-tests) and are equivalent to using a series of F-tests with variable levels of significance. Even so, the results of the F-tests generally conform to the Hsiao results. These results are significantly different from those reported in table 1. First, both the pooled sample and the majority of countries now exhibit a feedback relationship between growth and defense. That is, we reject Granger non-causality in spite of our small sample sizes and the fact the FPE criterion leads to ine!Iicient estimates. Second, as we hypothesized, the estimated lag lengths differ among countries. Third, the lag lengths are also different between the defense and growth variables within each country. In all cases where an F-test could be performed, the Hsiao model could not be rejected in favor of the common model. The implications of our results are that the imposition of an arbitrary and common lag length hides the feedback relationship which we found for the majority of the countries and for the pooled sample. In particular, the results for the pooled data suggest that Joerding did not find feedback because of his choice of lag structure. Clearly, the appropriate relationship can be detected only by a proper specification of the model. 3. Summary and conclusions
In this paper we have re-examined the defense-growth causality issue. For the most part, previous studies have assumed that defense causes growth. gin models where the optimal lag on both variables is four or less, the F-test is straightforward because the Hsiao model is nested in the four-lag model. For example, if the optimal lag is (2,2), the null hypothesis is that ps =p4= y3= ys=O. If the computed F-value is greater than the critical value, we reject the Hsiao specification in favor of the common model. However, if the optimal lag is greater than four for one variable but less than four for the other, the null hypothesis is composite and is difficult to test. For example, if the optimal lag is (2,6), the null hypothesis is &=/Cd = 0, ys, y4 #O. This is a composite hypothesis which is not nested and cannot be tested in a straightforward manner. If the optimal lags are greater than four for both variables, the test is again straightforward because the four-lag model is nested in the Hsiao model. lOIndeed, the interpretation of these F-tests must be done with caution. Since the FPE is used to determine the optimal lag length before the F-tests are performed, the F-tests are probably biased. To determine the direction of this bias, the joint distribution of the two tests must be derived.
C.J. L&i&a
and PC. Frederiksen, Defense spending and economic growth
125
These studies relied on cross-sectional data and assumed that correlation implied causation. A recent study by Joerding addressed the causality issue directly using Granger causality tests. He concluded that for his sample of countries growth Granger-causes defense, implying that defense spending is not an exogenous variable. Although Joerding’s contribution to the literature is significant, we felt that his results may have been an artifact of pooling time-series data, on the one hand, and his choice of an arbitrary lag length on the other hand. As a first step, we replicated Joerding’s results by pooling our sample of countries and assuming an arbitrary lag structure of four years. However, when we examined each country individually using this lag structure, we found no relationship between defense and economic growth for the majority of our sample. As noted above, this might imply that the growth of defense relationship found by Joerding was a result of his pooling methodology. Next, we used Granger causality methods developed by Hsiao on each country in our sample and on a pooled sample. We tested two hypotheses: (a) the relationship between growth and defense might differ among countries; and (b) the lag structure might also differ among variables within a country. Our results confirmed these two hypotheses. Most importantly, our results show a feedback relationship exists between growth and defense spending for both the majority of the countries in our sample and the pooled sample. This feedback relationship implies that neither economic growth nor defense can be considered exogenous. This was. Joerding’s intuition, but the result was hidden by his choice of an arbitrary lag structure. Our results using Hsiao’s method show that in fact Joerding’s intuition was correct. These findings have important implications for ongoing research into the relationship between defense spending and economic growth in developing countries. First, for most countries, it appears than neither defense nor economic growth can be considered as exogenously determined variables. As suggested by Joerding, this means that researchers should use a simultaneous equation model to investigate any further relationship between the two variables. Second, researchers should not expect to find that one model tits every country. For example, the lag lengths are likely to differ between countries as is the observed relationship between economic growth and the military burden.
References Benoit, E., 1978, Growth and defense in developing countries, Economic Development and Cultural Change 26,271-280. Biswas, B. and R. Ram, 1986, Military expenditures and economic growth in less developed countries: An augmented model and further evidence, Economic Development and Cultural Change 34,361-372.
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spending
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growth
Chan, S., 1985, The impact of defense spending on economic performance: A survey of evidence and problems, Orbis 29,403-434. Deger, S., 1986a, Military expenditure in Third World countries (Routledge and Kegan Paul, London). Deger, S., 1986b, Economic development and defense expenditures, Economic Development and Cultural Change 35, 179-196. Frederiksen, PC. and C.J. LaCivita, 1987, Defense spending and economic growth: Time series evidence on causality for the Philippines, 1956-1982, Journal of Philippine Development 14, 354-360. Frederiksen, PC. and ‘R.E. Looney, 1983, Defense expenditures and economic growth in developing countries, Armed Forces and Society 9, 633-645. Hsiao, C., 1981, Autoregressive modeling and money-income causality detection, Journal of Monetary Economics 7, 85-106. International Monetary Fund, various years, International financial statistics yearbook, various issues (International Monetary Fund, Washington, DC). Joerding, W., 1986, Economic growth and defense spending Granger causality, Journal of Development Economics 21, 35-40. Jung, W.S., Financial development and economic growth: International evidence, Economic Development and Cultural Change 34, 333-346. Looney, R.E. and PC. Frederiksen, 1986, Defense expenditures, external public debt and growth in developing countries, Journal of Peace Research 23, 329-338. Thornton, ‘D.L. and D.S. Batten, 1985, Lag-length selection and tests of Granger causality between money and income, Journal of Money, Credit, and Banking 17, 164-178. United Nations, various years, UN statistical yearbook, various issues (United Nations, New York).