Liquidity constraints and the substitutability between private and government consumption: the role of military and non-military spending.

Evans, Paul ; Karras, Georgios

I. INTRODUCTION

Using data for a number of economies, we investigate (i) the relationship between private consumption and two types of government spending (military and non-military), and (ii) the severity of liquidity constraints. Because of their importance for macroeconomic modeling in theory and practice,(1) both issues have been the subjects of considerable theoretical and empirical investigation. On the issue of liquidity constraints, the most influential research has relied on Hall's [1978] Euler-equation approach to the Permanent Income Hypothesis. In an attempt to reconcile Hall's and Flavin's [1981] methodologies, Hayashi [1982] modified Hall's martingale result to allow for the possibility that a subset of consumers are liquidity constrained, and showed that liquidity constraints can result in consumption's "excess sensitivity" to current income. Campbell and Mankiw [1989; 1990; 1991] and Jappelli and Pagano [1989] have applied Hayashi's methodology using data from the U.S. and several other OECD countries.

On the substitutability issue, Aschauer [1985] has modified Hall's Euler equation to allow for substitutability between government spending and private consumption, and found that the two are substitutes for the U.S. Karras [1994], however, using a similar approach and data for 30 countries concludes that private and government consumption are better described as complementary or unrelated. Liquidity constraints and substitutability have been combined in studies by Graham and Himarios [1991], Cushing [1992], and Graham [1993], using U.S data, and by Evans and Karras [1996] for a number of countries.

A crucial limitation of most of these studies is the use of aggregate government consumption data, which counterintuitively imposes a common substitutability parameter on all components of government spending.(2) Using recently available time-series data for a large number of countries, the present paper relaxes this restriction by decomposing government consumption into military and non-military components, enabling us to separately identify their relationship to private consumption.

The allocation of government consumption between military and non-military functions has varied greatly across countries. The Appendix reports the average size of military and non-military government shares in GDP, as well as the military/non-military ratio by country over the 1970-1989 period. Average military expenditure as a fraction of GDP, for example, has ranged in our sample from 0.11% in Mexico to 12.30% in Jordan. Similarly, the fraction of government consumption absorbed by military expenditure has ranged from 1.09% in Mauritius to 66.82% in Poland. This sizable variability is promising in terms of cross-sectional identification power, but it also suggests that the estimated parameters must not be assumed to be common across countries.

The estimated model is derived in Section II, which combines liquidity constraints and substitutability by nesting the approaches of Hayashi [1982] and Aschauer [1985]. In the same section we discuss data sources and the estimation strategy, which permits the estimated parameters to vary by country in a way that helps determine how they are influenced by country-specific factors. Section III estimates the model for a panel of the 66 countries for which annual data on all series are available for the 1970-1989 period. The paper's main conclusions are given in Section IV.

II. METHODOLOGY AND DATA

We assume that consumers in economy i at time t derive utility from effective consumption, [c.sup.*], which we define as

(1) [Mathematical Expression Omitted],

where c is private consumption, [g.sup.m] and [g.sup.nm] are the military and non-military components of government consumption. The parameters [[Theta].sup.m] and [[Theta].sup.nm] measure the degree of substitutability between c and [g.sup.m], and c and [g.sup.nm], respectively.(3) The representative consumer then attempts to maximize

(2) [Mathematical Expression Omitted],

where E denotes mathematical expectation, [Beta] is the subjective discount factor, u[prime] [greater than] 0, and u[double prime] [less than] 0. A positive [[Theta].sup.n] or [[Theta].sup.nm] means that the corresponding component of government services and private consumption are substitutes in the sense that an increase in [g.sup.m] or [g.sup.nm] diminishes the marginal utility of c. In fact, the higher [[Theta].sup.m] or [[Theta].sup.nm] is, the better [g.sup.m] or [g.sup.nm] substitutes for private consumption. If, on the other hand, [[Theta].sup.m] or [[Theta].sup.nm] is negative, the corresponding type of government services and private consumption are complementary in the sense that an increase in [g.sup.m] or [g.sup.nm] raises the marginal utility of c.(4) A priori, we expect military government spending on defense to be a poorer substitute or a better complement for c than other components of government services such as those on education and health (i.e., [[Theta].sup.m] [less than] [[Theta].sup.nm]).

Under plausible assumptions, the first-order conditions for the maximization of equation (2) imply that [c.sup.*] follows a random walk.(5) However, following Hayashi [1982] and Campbell and Mankiw [1989], we assume that only a subset of the population is able to maximize equation (2). Specifically, suppose that there are two types of consumers, type 1 and type 2. Type 1 consumers behave as described above and thus their effective consumption follows a random walk:

(3) [Mathematical Expression Omitted],

where [Mathematical Expression Omitted], and the [u.sub.i,t]s are white noise. Using the definition of effective consumption we get

(4) [Mathematical Expression Omitted],

where [Delta] is the difference operator.

Type 2 consumers are assumed to be subject to a binding liquidity constraint so that they consume their entire disposable income according to the following "role-of-thumb" behavior:

(5) [c.sub.2,i,t] = [[Lambda].sub.i] [y.sub.i,t],

where [Lambda], the ratio of disposable income of type 2 consumers to national disposable income, is assumed to be constant over time for each country. Combining equations (4) and (5) gives

(6) [Mathematical Expression Omitted],

which will be estimated by pooling annual data for a sample of 66 countries over the 1970-4989 period.(6) In order to allow the parameters [Lambda], [[Theta].sup.m], and [[Theta].sup.nm] in (6) to vary by country, we specify

(7) [[Lambda].sub.i] = [[Beta].sub.0] + [Beta][prime][X.sub.i],

(8) [Mathematical Expression Omitted],

and

(9) [Mathematical Expression Omitted],

where [[Beta].sub.0], [[Gamma].sub.0], and [[Delta].sub.0] are parameters; [Beta], [Gamma], and [Delta] are parameter vectors; and X, Z, and W are vectors of country characteristics. Substituting in equation (6), we can write the regression to be estimated as

(10) [Mathematical Expression Omitted].

We assume that the [u.sub.i,t]s are uncorrelated across countries and estimate the [[Alpha].sub.i]s as country fixed effects.(7)

Theoretically, the error term [u.sub.i,t] is orthogonal to all variables dated t - 1 and earlier and this provides us with a list of instrumental variables for the potentially endogenous variables [Delta][y.sub.t], [Mathematical Expression Omitted], and [Mathematical Expression Omitted]. In practice, however, the time aggregation imposed on equation (10) by the use of annual averages, and the inclusion of expenditure on consumer durables in our measure of consumption, introduce an MA(1) component in [[Epsilon].sub.i,t].(8) For this reason, instrumental variables dated t - 1 must be excluded in order to estimate the parameters in equation (10) consistently.

The data are obtained from the Penn World Table, Mark 5.6 of Robert Summers and Alan Heston [1991] as updated in 1994. We confine ourselves to the 66 countries for which "Standard of Living" (STLIV) data exist for each of the years from 1970 to 1989. STLIV is calculated as the sum of private consumption plus government consumption net of military expenditure, so we compute military expenditure simply by subtracting STLIV from the sum of private and government consumption (all in percentages of GDP). The Table in the Appendix gives a list of these countries. All series are per capita and measured in terms of an international basket of goods. Average saving rates, government sizes, and the variance of the transitory component of GDP are also constructed using the Summers-Heston data.

III. EMPIRICAL RESULTS

Table I reports four estimated specifications of equation (10). The first two specifications are based on standard cross-section/time-series regressions that assume all slope parameters to be common across countries (that is, [Beta] = [Gamma] = [Delta] = 0). The last two specifications of the Table make use of equations (7), (8), and (9), to relax this constraint.

The first column of Table I estimates equation (10) subject to the additional constraint [[Theta].sup.m] = [[Theta].sup.nm]. We impose this condition not because we believe that it holds in practice, but in order to better contrast our findings with the literature. The point estimates of the two coefficients are plausible, suggesting that liquidity-constrained consumers account for 25% of income, and that private and government consumption are substitutes ([Theta] = 1.71). However, none of the two estimated parameters is statistically different from zero.

In the second column of Table I the military and non-military components of government consumption are allowed to enter separately (but all slope parameters are still assumed to be equal across countries). With respect to liquidity constraints, the estimated [Lambda] of .27 is slightly higher than in the previous regression, and is now statistically significant. Regarding the government variables, the estimated [[Theta].sup.m] is -0.75, while [[Theta].sup.nm] is 2.20. The implication is that military services complement private consumption, whereas non-military services substitute for it. Note, however, that only [[Theta].sup.nm] is statistically significant.

Next we want to allow [Lambda], [[Theta].sup.m], and [[Theta].sup.nm] to vary across countries, and examine how they may be affected by country characteristics. The simplest way to do this is to follow the two-step procedure of Evans and Karras (1996), the first step of which requires estimating equation (6) separately for each country using time-series observations only, while in the second step, the estimated parameters are regressed cross sectionally on country-specific variables. Because of the limited availability of the STLIV variable (1970-1989, which means that the first-step regressions have to rely on fewer than twenty degrees of freedom), and in order to exploit efficiency gains from joint estimation, we prefer to combine the two steps as in equation (10).(9) This requires that we identify variables to include in X, Z, and W.

For the selection of variables to include in X we are guided by the cross-country empirical findings of Evans and Karras [1996] who show that [Lambda], the fraction of national income accruing to liquidity constrained consumers, is statistically significantly related to the saving rate (negatively) and transitory output variability (positively). Theoretically, the justification is as follows. A priori, we expect that the ratio of national income accruing to liquidity-constrained consumers is a negative function of accumulated wealth: consumers with assets that can be used as collateral are less likely to be liquidity constrained than [TABULAR DATA FOR TABLE I OMITTED] consumers with few such assets. One determinant of asset accumulation for which data exist is the saving rate. A high saving rate over a period of time should be associated with a low value for [Lambda]. Theoretically, the variability of transitory income should also affect [Lambda]. If unconstrained households save (dissave) all positive (negative) transitory income, the likelihood that individuals will exhaust their assets and become liquidity constrained should increase with the variance of transitory income. We use the technique proposed by Robert Hodrick and Edward Prescott [1980] to decompose the logarithm of output for each country into permanent and transitory components, and we measure variability by the standard deviation of the transitory component.(10)

Evans and Karras [1996] also found that the substitutability between private consumption and total government services is negatively related to the fraction of government spending that goes to national defense. Obvious candidates to include in Z and W, therefore, are the average shares of each type of government services in GDP.(11)

The third column in Table I reports the full specification. The signs of the estimated coefficients are generally as expected, and five of the seven parameters are statistically significant at the 10% level or less. As suggested by theory, the fraction of liquidity-constrained consumers is related negatively to the country's average saving rate, and positively to the standard deviation of the country's transitory component of GDP (and both of these relationships are statistically significant). The implied [Lambda]s by country are given in ascending order at the top panel of Figure 1: almost all are between zero and one, and quite precisely estimated.

The next two panels of Figure 1 report the implied [[Theta].sup.m]s and [[Theta].sup.nm]s by country using the estimates of column (3) in Table I. While less precisely estimated than the [Lambda]s, the point estimates of virtually all [[Theta].sup.m]s are negative, whereas the [[Theta].sup.nm]s are positive. This is consistent with complementarity between c and [g.sup.m], and substitutability between c and [g.sup.nm].(12) Finally, note that the statistically significantly negative coefficient of [Mathematical Expression Omitted] implies that [[Theta].sup.m] is a positive function of military government expenditure as a fraction of GDP.(13)

As the country fixed effects in specification (3) are not jointly statistically significant (F-statistic = 0.64; significance level = 0.99), we also estimate the equation without them and report the results in column (4) of Table I. While the signs and statistical significance of most of the estimated parameters are unaffected, there are two changes when the fixed effects are omitted: the coefficient of [Delta]y*[[Sigma].sup.HP] becomes insignificant, whereas that of [Delta][g.sup.nm]* [Mathematical Expression Omitted] becomes significantly negative, implying again a positive relationship between [[Theta].sup.nm] and non-military government expenditure as a fraction of GDP. Figure 2 plots the implied [Lambda]s, [[Theta].sup.M]s, and [[Theta].sup.nm]s by country using the estimates of column (4) in Table I.(14) While it is apparent that the parameters are more precisely [TABULAR DATA FOR TABLE II OMITTED] estimated when the fixed effects are excluded, the qualitative results are little changed. Once again, most of the [Lambda]s are between zero and one (as expected), and the [[Theta].sup.nm]s are negative. One difference is with respect to the estimated [[Theta].sup.nm]s: about one third of them are now negative. Note, however, that only for the positive ones does the band of two standard deviations fail to include zero.

We tried a number of additional specifications, including estimating equation (10) for several subsets of countries, such as the OECD countries, or the countries that have participated in the International Comparison Programme (ICP) benchmark study. We found that the point estimates and significance of the [Lambda]s are very robust to these changes in sample, whereas the estimated [[Theta].sup.m]s and [[Theta].sup.nm]s are more fragile and often do not differ statistically from zero. These disappointing results suggest that any higher quality in the OECD or ICP data is more than offset by their homogeneity and the reduction in sample size which diminish the cross-sectional variation needed for precise identification of the estimates.

The fragility of the [Theta]s indicated by these tests motivated us to estimate versions of equation (10) which exclude military consumption, non-military government consumption, or both. The results of these regressions, three of which are reported in Table II, are consistent with our earlier findings for the full sample. The estimated [Lambda] is in the neighborhood of 25%, [[Theta].sup.m] is -2.44 and [[Theta].sup.nm] is 2.82, suggesting complementarity between c and [g.sup.m], and substitutability between c and [g.sup.nm]. In addition, liquidity constraints are alleviated by increases in savings rates, and aggravated by increases in output variability. Figure 3 compares the [Lambda]s implied by column (3) of Table II to those implied by column (3) of Table I. It is evident that the [Lambda]s implied by the model of Table II have a wider range and greater standard errors than those of Table I, so that a benefit of including the government variables is greater precision in the estimation of the severity of liquidity constraints.

IV. CONCLUSIONS

In this paper, using annual data from the 1970-1989 period for a sample of 66 countries, we investigated (i) the relationship between private consumption and two types of government spending (military and non-military), and (ii) the severity of liquidity constraints. Our main findings can be summarized as follows.

There is evidence that private consumption and non-military government spending are generally substitutes ([[Theta].sup.nm] [greater than or equal to] 0), whereas private consumption and military spending are better described as complements ([[Theta].sup.m] [less than or equal to] 0). In addition, the degrees of substitutability for both types of government services appear to be increasing functions of the share of each type in GDP. We find, however, that the estimated [Theta]s are sensitive to the number of countries included in the sample and often fail to differ significantly from zero.

The fraction of income that accrues to liquidity constrained households is typically positive ([Lambda] [greater than or equal to] 0), and the severity of liquidity constraints is negatively related to saving rates, and positively related to the variability of transitory income. In addition, the estimated [Lambda]s are very robust and quite precisely estimated.

[TABULAR DATA FOR APPENDIX OMITTED]

We wish to thank two anonymous referees for helpful comments and suggestions.

1. Barro's [1981] neoclassical model, for example, the effects of government purchases on output and interest rates depend inversely on the degree of substitutability between private and government consumption. Similar consideration would apply in the general equilibrium model of Baxter and King [1993]. Liquidity constraints are also important in determining the extent to which the Ricardian Equivalence proposition is expected to hold.

2. An exception is Graham [1993] who decomposes government spending in defense and nondefense components. Using U.S. data, he finds that private consumption and the nondefense component appear to be substitutes, whereas the defense component has no apparent relation to private consumption.

3. This generalizes Martin Bailey's [1971] original definition of effective consumption as [Mathematical Expression Omitted], where [Mathematical Expression Omitted] is total government consumption. This of course is a special case of equation (1) with [[Theta].sup.m] = [[Theta].sup.nm] = [Theta].

4. A negative [[Theta].sup.m] or [[Theta].sup.nm] does not imply that [g.sup.m] or [g.sup.nm] must have a negative marginal utility, since the utility function can be modified to

[Mathematical Expression Omitted],

with [[Phi].sub.1] [greater than] 0, [[Phi].sub.2] [greater than] 0. See Barro [1989]. Since [Phi] enters separably it has no effect on the consumer's choice. Similarly, [[Theta].sup.m] [less than] 1 or [[Theta].sup.nm] [less than] 1 does not imply that government military or nonmilitary spending must have lower marginal utility than private consumption.

5. One such set of assumptions is that the utility function displays constant absolute risk aversion and that the distribution of [Mathematical Expression Omitted] conditional on all information known in period t - 1 possesses a moment generating function and constant moments of order two or higher [Lam, 1987]. Mankiw [1981] derives a random walk using a Taylor approximation of the first-order condition.

6. Equation (6) nests several of the models used in previous studies. Aschauer [1985] and Karras [1994] estimate equation (6) subject to [Lambda] = 0; Campbell and Mankiw [1989, 1991], Jappelli and Pagano [.1989], and Jin [1993] estimate equation (6) subject to [[Theta].sup.M] = [[Theta].sup.nm] = 0; Campbell and Mankiw [1990] and Evans and Karras [1996] estimate equation (6) subject to [[Theta].sup.m] = [[Theta].sup.nm].

7. We also allowed for the possibility of nonzero symmetrical correlation of the [u.sub.i,t]s across the countries by estimating with time fixed effects: [u.sub.i,t] = [v.sub.t] + [[Epsilon].sub.i,t]. As the estimated [v.sub.t]s are not jointly statistically significant, such specifications are not reported in the empirical section.

8. Working [1960] demonstrates this result for time aggregation, and Mankiw [1982] for consumer durables.

9. We did carry out the country-by-country exercise for the 66 economies in the sample and the results were as follows: (i) all but nine of the estimated [Lambda]s are between zero and one, and only seven of the estimated [Lambda]s are not statistically significant; (ii) 24 of the estimated [[Theta].sup.m]s are statistically significant (11 positive and 13 negative); (iii) 34 of the estimated [[Theta].sup.nm]s are statistically significant (25 positive and nine negative).

10. Evans and Karras [1996] try a number of other variables that might affect the extent of liquidity constraints according to theory, but none of them turns out to be statistically significantly related to [Lambda].

11. We also included in Z and W the variable CRISES which measures the number of government crises by country per year from 1960 to 1985, from Barro and Wolf [1989], and which was found in Evans and Karras [1996] to be negatively related to the degree of substitutability between c and g. The variable failed to be significant both for the military and non-military components.

12. It is also consistent with the findings of Graham [1993] for the U.S.

13. This is consistent with the finding in Karras [1994] for overall government spending.

14. For the individual country-by-country estimates, see the last three columns of the Appendix.

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