Division of Research School of Business Administration March 1988 THE EFFECTS OF GOVERNMENT SPENDING ON PRIVATE CONSUMPTION: THEORY AND EVIDENCE Working Paper #562 Roger C. Kormendi Philip Meguire The University of Michigan Laura LaHaye University of Illinois, Chicago We wish to thank David Aschauer, Robert Barro, Douglas Bernheim and the participants in the Macro workshop at The University of Michigan for their comments. An earlier version of this paper was presented at the Conference on Budget Deficits and Government Spending at the University of Rochester on October 24-25, 1986. FOR DISCUSSION PURPOSES ONLY None of this material is to be quoted or reproduced without the expressed permission of the Division of Research Copyright 1988 University of Michigan School of Business Administration Ann Arbor Michigan 48109

The Effects of Government Spending on Private Consumption: Theory and Evidence by Roger C. Kormendi* Laura LaHaye** Philip Meguire* I. INTRODUCTION Consistent with the recent course of much of macroeconomics, the analysis of fiscal policy has undergone significant changes during the past decade or so. The Ricardian Equivalence Proposition (REP), for example, has become a benchmark for analysis of government debt, even for those who are skeptical of its empirical validity. Similarly, although perhaps less dramatically, a neoclassical benchmark has also been emerging in the analysis of the determinants and effects of government purchases. Like the REP, this new benchmark has its roots in the equilibrium approach to macroeconomics. The seminal effort is due to Bailey (1962, 1971). Among other contributors to the theory and its empirical basis have been Buiter (1977), Hall (1980), Barro (1981, 1984), Plosser (1982), Kormendi (1983), Benjamin and Kochin (1984), Aschauer (1985), Judd (1985), Ahmed (1986), and Aschauer and Greenwood (1986). Borrowing from the title of Aschauer's (1986) excellent survey, we call this new theoretical benchmark the "Equilibrium Approach" to the analysis of government spending. The Equilibrium Approach combines several distinct elements. It 1) assumes that government purchases are exogeneous to consumption and output; 2) incorporates the direct substitutability of government purchases for private consumption and investment into the framework of the Permanent Income Hypothesis; and 3) allows government purchases to affect real output through the labor supply response to the wealth and intertemporal substitution effects of -1 -

-2 - government purchases, as well as through the provision of public inputs into private production processes. Although details of these elements can be altered without doing fundamental violence to the approach —in particular the exogeneity of government purchases —these three elements form the basis of the Equilibrium Approach benchmark in its current state. This paper contains two main parts. First, we develop the theory of incorporating the consumption effects of government purchases into a three equation system for government purchases, output and consumption suitable for estimation. In doing so, we derive the cross-equation restrictions implied by the theory under standard but restrictive assumptions, such as constant real interest rates and ideal data. We will argue, however, that reasonable extensions of the theory would result in underidentification of certain key parameters, thus precluding standard tests of the theory using overidentifying restrictions. For this reason, we do not focus here on single country tests of the cross-equation restrictions. Instead, in the second part of the paper, we use 29 years of post-War time series data from a panel of 30 countries, and ask whether the estimated parameters for each country obey certain relations across the countries in the panel, relations predicted by the Equilibrium Approach. In this regard, we follow Lucas (1973), Kormendi and Meguire (1984), and Kormendi and LaHaye (1987). The paper proceeds as follows. In Section II, we first review the consumption-income model of Kormendi and LaHaye, and then modify it to obtain the three-equation system mentioned previously. We present our estimates of this system and our examination of the cross-country relations in the parameters estimated from the time series for each country in Section III. We discuss our results and directions for further research in Section IV.

-3 - II. THE EQUILIBRIUM APPROACH TO GOVERNMENT SPENDING II. 1. Preliminaries We begin by restating the two-equation model presented in Kormendi and LaHaye (1987), which draws on the work of Hall (1978) and Flavin (1981). We then introduce a series of modifications which results in the three-equation specification to be estimated in Section III. The economy's oneperiod budget constraint is given by (1) w = (l+r)wt_ + t - ct - gt ' where wt is the end-of-period capital stock (non-human wealth), r the constant real rate of interest, x labor income, c consumption expenditures, and g is 2 government purchases. Various concepts of permanent income can be obtained from the period t infinite horizon budget constraint (2) rwt_1 + (l-a)S aE a Ext - (l-a)S JE = (1-a)z aJE c t+j j-l j t+j j where the summations range from 0 to infinity, a = 1/(l+r), and Et is the expectations operator conditional on information available in period t. We assume full current information, i.e., Et = Vt, -V. t tt We use the following definitions: (3) xP = (l-a)S aEt t+j xP - E = (1-a)Sa (E -E )x t = Xt t t-l t t-t-1 t+j gtt =- (l-ca)S acE gtt+j e = g E - t j t gt t t-l t p + P = yP -E1yp =8P Y = t-1 + yt t-lyt zP YP ey ~ = O -0 O t t t z x g t t t

-4 - 'P, permanent total income, is a scalar measure of the economy's current and Ytp expected future resource constraints. zP, permanent "disposable" income, is a a similar measure of the constraints on households, which by (2) equals the 3 present discounted value of expected (infinite) lifetime consumption. The O's are innovations to permanent labor income (x), permanent government purchases (g) and permanent disposable income (z). Let the expected lifetime utility of households be an additively separable function of consumption, having the form W = 6 E [U(cj ) + V(lt,+ )] t t+j j t+j where 6 = l/(l+p) and p is the constant utility rate of time preference, U and V are time invariant functions, and 1 is leisure. Then the usual Euler equation linking the expected marginal utility of consumption across periods applies (Hall [1978]). The exact form of the consumption function and the time series behavior of ct will naturally depend on the form of U. For the case of quadratic utility (4) c = k + kz t o t0 4 where k0 and k are related to p, r and the bliss level of consumption. More generally, however, (4) can be interpreted as a linear approximation to the "true" relation between current consumption and the scalar measure of the economy's intertemporal budget constraint as embodied in zp. Using (1) and (3), it can be shown that Et zP = (l+r)z - rctl t- tl - rt-1 so that if consumption is given by (4), the expected component of current consumption is

-5 - (5) E t = (I+r(1-k))ct_ - rko, t-1ct 2t- 0 The unexpected component, resulting from new information on permanent labor income and government purchases, is (6) ct - Et t kO z Combining (5) and (6), and adding a disturbance term ect which is assumed orthogonal to the other rhs variables, we obtain (7) Ac = -rk0 + r(l-k)ct + k O et Ac~t 0 b-1 z ct Dividing by ct_1 to correct for heteroskedasticity yields (8), the consumption function estimated in Kormendi and LaHaye: Ac -rk (8) - = + r(l-k) + k O' + ec ct-1 -zt ct' where the primes indicate innovations obtained from appropriately weighted regressions. In order to complete the model we must relate the permanent income innovation, o', to observed data. With labor income and government purchases data Zt we could simply estimate a disposable labor income process, using the same weighting as in the consumption equation, A(x-g) r A(x-g)t-l --- = Z h. x) + E, t-l i1i=1 Ct —1 to obtain = = ( r ii ) S1~g), (x-g)t. Z aI h. (x-g)t z (x-g)t ii i i=1

-6 - Because we do not have labor income data for our panel of 30 countries, we estimate the time series process for "disposable total income" (y - g) where y is GNP (y = rw + x): (9) A (y-g)= Ef A (y-g)+ e' (9) E f. ct-l i=1 1 t-l t and define O' Ve' where V -. The term V, derived from the t t r 1 - Z a f. i=l 1 time series properties of disposable income, can be interpreted on the "persistence" of disposable income innovations. Now, all that remains is to make some assumption about the relation between the observable 0' and the unobservable O'. At this point assume that t Zt disposable labor income x-g is a constant fraction * of disposable total income y-g. In this case, Ot = QOt, and (8) becomes zt Ac -rk0 (10) c = c_ + r(1-k) + (kqV)e + e' C-0 Ct-1 t ct An unrestricted form of (10) suitable for estimation is Act (11) c t- = O [ c -] + B t+ ct Even given some interest rate r (and hence a), the parameters V, k0, k and * are just identified within the context of the system (9) and (10), so that it is not possible to test 0 = kjV directly. Moreover, if interest rates are endogeneous, in which case $ > kqV (as per Michener [1984]), or if variables have been excluded from (9) that are useful for predicting y, in which case, < kPV is likely (see Kormendi and LaHaye [1986]) then tests of the relation between 3 = kqV computed over a single country or regime are difficult to interpret.

-7 - For these reasons, Kormendi and LaHaye estimated (9) jointly with (11), and then asked whether there was evidence of a positive relation between the estimated values of 0 and V from each country. As long as observed parameters such as * are not correlated with V across countries, variation in such parameters will reduce the measured correlation between B and V, biasing results away from the PIH. This cross-sectional procedure admits a positive relation more general than simple proportionality between the measured 0 and "true" e. It is also robust to any "excess sensitivity" of consumption to income innovations induced by endogeneous interest rate movements. II.2. Effects of Government Purchases on Consumption Kormendi and LaHaye define private disposable income as GNP net of government purchases. This definition implicitly assumes that the persistence of innovations in GNP and government purchases are equal. It also assumes that such purchases do not substitute for, or interact in any other way with, private spending on consumption and investment. For these reasons, we now modify the preceding model by allowing the processes governing total income and government purchases to be estimated separately. This allows us to 1) estimate separate persistence parameters, V and V, for the two processes; 2) distiny g guish between the effects on consumption, 8y and g, of innovations in income (ey) and government purchases ( g); and 3) incorporate the substitutability of government purchases for private spending. The basic three equation model is Agt Agt t-i (12) = S a. - + b.. i+ Et ctI i t1 ctl i 1 Ct gt AYt Agt-i, t-i = c. + S d - +. c_ i I1 ct_1 i 1 c1 yt

-8 - Act Iy yt + 8g ' + -' Ctl Eat - by y t lggt + ~ct Due to the presence of lagged income in government purchases equation, income innovations will result in revisions of expected permanent purchases, and vice versa. In the discussion that follows, it will be convenient to refer to (weighted) innovations in the present discounted value of future total income as 0e' = (-a) * E yt keeping in mind that income, either total The innovations aJ (E - E )t+jI t 1) Ct-1 these are not the same as innovations in permanent labor (0 ) or disposable O' xt zt are given by (13) 0' gt = V e' + V e' gg gt gy yt = V e' + V e' yg gt yy yt where V gg V gy 1 - Sa d. 1 A ESab. A A V YY V yg i 1 - Ea a. 1 A i Ac c. 1 A i (1i i A = -a a.(1 - aa ) - (Ealbi)(aici) Assuming now that x y, yields Assuming now that x = *y, yields = ~Oyt which implies G' = 0y t - 0' ~ Zt Yt gt Hence, the theory which results in the consumption equation (8) yields the following restrictions on the model (12):

-9 - (14) B = k[+V - V ] y yy gy = -k[V - <V ] g gg yg In the analysis so far, government purchases are simply acting as a direct drain on the intertemporal budget constraint facing households, "as if" they were waste. This could be due either to their separability from private consumption in utility functions, or to their having no inherent value. Now consider the possibility that government purchases substitute directly for private consumption or investment. Following the framework set out by Kormendi (1983), Barro (1984) and Aschauer (1985), we may think of households as choosing a level of effective consumption c* that maximizes expected utility, where c* = c + Acg and xc is the measure of consumption substitutability. Under this c c concept of effective consumption, household expected utility functions take the form W = 6Et [U(cb + cgt ) +V( +j'gt+ ) Rearranging the budget constraint (1) (1') w = (+r)wt + x - ct - (-c)gt and repeating the development of the model through (4) yields the effective consumption function. (4') ca = k + kyP* t 0 t where y = YP - (1- )gP. Following the development through (8) and substit = y t tuting Ac + e 'Ag for Ac* yields the following modified version of our our basic consumption equation.

-10 - Act rko0 gt (8') l = r(l-k) - c - c + k[Oc - (1-O ] + c ct-I ct- c ct xt c gt ct If we consider the possibility that 1 unit of government purchases substitutes directly for o. units of private investment expenditures, the wealth effect (l-w)O' in (8') is replaced by (1- -wi))', and the remainder of the c gt c -c i gt analysis remains unchanged. Substituting for Ot and 0' and combining terms xt gt yields Ac 81 B Et1 Ag (15) +lsBo + + E ' + ec C(15 c Ct'o l c1 2 ct* y yt g gt ct t-1 t-1 t-1 where 82 -= and 2 c (16) By = k[qV - (i1- -ti)Vy] yy c gy Bg = -o -k[(1-c-tio)V - +V y g c - K c 1 99gg yg The main difference between the consumption relation in (12) and (15) is that the latter contains lags of government purchases and income through the appearance of EtlAgt, subject to the relevant cross-equation restrictions. In comparing (16) and (14), the V term in B and the V in g are now multigy y gg g plied by 1-t -ai to reflect the fact that wealth effects are mitigated to the extent that government purchases are substitutable for consumption and investment. Although the presence of tc and l-o -.i alters somewhat the interpretac c 1 tion of the B -V and 3 -V cross-country relations, the basic strategy Y gy g gg of investigating such relations is unaffected. In particular, both B and V Y YY and B and V should be positively related; and, conditional upon t + o. < 1, g yg c i both B and V and 8 and V should be negatively related. Note that y gy g gg c + o. 1 is the condition for government spending to have a negative wealth c 1

-11 - effect. In section III we will develop the cross-country hypotheses in more detail in conjunction with the empirical results. III. EMPIRICAL RESULTS III.1. The Data. Data by country for the period 1951 to 1979 were taken from the International Financial Statistics (IFS) computer tape. We used national accounts data on private consumption expenditures (IFS series 96f) to measure consumption, on government purchases (91f) to measure government consumption, and on GDP (99b) to measure aggregate output. Each of these series was divided by the CPI (series 64; 1975=1.0) and population (99z) in order to restate it in real per capita terms. Thirty countries were found with continuous data over the designated sample period. IFS data do not treat purchases of durable goods by the government and private sectors identically. With the exception of the U.S., government purchases do not include government expenditures on structures and non-military durable equipment; instead these are included in gross fixed capital formation (93e). On the other hand, private consumption does include expenditures on 9 consumer durables. Government consumption excludes the purchases of government enterprises, which are either treated as intermediate inputs or are included in gross fixed capital formation. The output of nonfinancial government enterprises is treated identically to that of private enterprises (IMF [1986]). Therefore our analysis cannot address any substitution in consumption between the output of public and private enterprises. III.2. The Relation Between Consumption and Disposable Income. As a point of reference, we first present some results similar to those found in Kormendi and LaHaye (1986). The estimates of Bj and V., j=1,...,30, *J c3

-12 - underlying Table 1 were derived from estimates of equations (9) and (11) for each of the 30 countries. We used the sample average propensity to consume as a measure of k.. The notation P(zl, z21z3) denotes the partial correlation across countries between zl and z2, controlling for z3. Of special interest is the strong positive value of p(Q, Vlk), which accords with the implication of the PIH that the propensity to consume out of innovations in disposable income (a) should be greater when the effect of such innovations on permanent disposable income is greater. The partial correlation between a and k is 12 likewise large. 12 III.3. The Effects of Income and Government Spending on Consumption: Descriptive Results. We now turn to estimates of (12) for our panel of 30 countries. The parameters of interest are the four persistence measures V, Vgg Vyg Vgy YY gg Yg gy and the propensities to consume out of innovations By and Bg These are shown in Table 2 along with their (approximate) standard errors. An examination of these estimates reveals some interesting regularities. By is positive, usually several standard errors from zero, and varies significantly from country to country. Moreover the By and Vy in Table 2 and the 8 and V underlying Table 1 are roughly similar across countries. Thus the ay and V do not appear highly y YY sensitive to the choice of specification. The values for Bg and Vgg, on the other hand, reveal that the restrictions implied by the 2 equation model of Kormendi-LaHaye are not robust. In particular, the relations 0g = -By and V = Vy do not appear to hold, although there does seem to be an apparent gg yy negative correlation between y and Bg. We will return to this observation 14 shortly.14 Unlike ay, g has a mean that is essentially zero, but takes on both positive and negative values, often more than two standard errors from zero,

-13 - suggesting that the dispersion about the zero mean is not simply the result of 15 estimation error. This may be important for the interpretation of the effects of government purchases. To see why, refer to (14) where Bg is expressed in terms of V and V. There we see that Bg > 0 would require gg yg g V > V. That is, the negative direct effect of an innovation in government Yg gg purchases (V ) would have to be more than offset by a positive indirect wealth gg effect of such innovations on expected future income through the coefficients of lagged g (c.) in the income equation. Examination of the relative magnitudes of V and V, however, suggests that this is improbable for all but a gg Yg very few countries. A positive g could also be the result of "super-efficient" substitutag bility of government purchases for private spending. As shown in (16), if government spending substitutes for both private consumption and investment, then V is multiplied by (1-o -o.). If W. > 1, then f > 0 could obtain, gg c i g i.e., government spending could have a positive direct wealth effect which exceeds the negative direct substitution effect. If such a positive wealth effect were a significant characteristic of the bulk of the countries in our panel, it would betray itself through a positive relation across countries between g and Vgg, even absent direct measures of Wc and wi. If, on the other hand, this direct wealth effect were positive for some countries and negative for others, the observed pattern of the g's could be explained thereby, but the relation between Bg and V across countries would be difficult to interpret g gg unless direct measures of ec and o. were obtainable. III.4. The Effects of Government Spending and Income on Consumption: CrossCountry Results. We now turn to Table 3 which contains our findings on the relations across countries among the estimated parameters. The number of hypothesized relations

-14 - increases considerably when we pass from a two-equation to a three-equation system. As in Table 1, we summarize these hypotheses in column 4 in the form of expected signs of partial correlation coefficients. We focus on the partial correlation of By or Bg with the parameter in column 3, holding constant the Y g parameters in the appropriate list at the foot of the Table. A brief keyword summary of the theoretical motivation for each hypothesis is included in column 5. Two of the hypotheses merit additional discussion. First, the correlation between 1y and 3g should be negative (HI). This emerges from a theory of cony g sumption based on private disposable income (y-g), in which case By = -Bg obtains. Even if factors not modelled, such as joint endogeneity of consumption and government purchases, break this mirror-equality, a general negative relation between By and 1g could still obtain. Second, the wealth effect of government purchases on consumption (g ) would be negatively related to the g mean "size" of the government sector relative to income (H9), given diminishing marginal substitution of public for private spending. To this end we introduce the parameter k, the share of government purchases in income, a quantity analogous in construction to k, the average propensity to consume. Column 6 of Table 3 presents the sample partial correlations conditioned on a fuller set of parameters described at the foot of the Table. Column 7 gives the partial correlations conditioned on a reduced set of parameters (also detailed at the foot of the Table) from which were excluded those parameters whose partial correlations with By and 0B were small and insignificant. All correlations were computed with the omission of Canada, because both its its 16 V and standard error were clear outliers. gg The correlation between By and 1g is indeed large and negative, as hypothesized. 17The correlations of with k and V are large, positive and esized. The correlations of 13 with k and V are large, positive and y c yy

-15 - significant, which is consistent with Kormendi and LaHaye's findings. The S -Vg correlation (H4) sheds light on the wealth (resource constraint) effects of government purchases. V is the effect of an innovation in current income gY on the permanent flow of government spending. If such purchases absorb future resources on net so that Ac + oi < 1, this correlation should be negative, which we observe. The theory is mute on the signs of the B -V and a -V Y gg Y gg correlations, and these turn out to be effectively zero. The results for Hi through H6 are in accord with the predictions of our simple version of the Equilibrium Approach to government spending, once we make the ancillary assumption that permanent government purchases have negative wealth effects. However, if these negative wealth effects were the major part of the story, the many positive and significant estimates of ag in Table 2 would be difficult to explain, as discussed earlier. This should be kept in mind as we turn to the correlations involving 5g in H7 through H12. Note immediately that the correlation between g and k is large and posig c tive (especially when conditioned on the reduced parameter set of column 7), which is at odds with the assumption that government purchases have negative wealth effects. This correlation suggests that [(l-c -w.)V - V ] < 0 holds. c 1 gg yg This, in combination with the strength of the correlation and the magnitudes of V and V, implies that xt + o. may indeed exceed 1. The B -V corregg Y c i g gg lation, while not very significant, is still positive, again suggesting that X + a. > 1. There is little evidence that B reflects sizeable cross-effects c 1 g of shocks to government purchases on permanent income, as H9 would suggest. The correlation between B and V is small. The theory does not address yg either the -V correlation (H10), or the correlation (H11). While g yy g gy the latter is small, the former is positive and rather significant. We offer no explanation for this unexpected result.

-16 - The last hypothesis (H12) involves the effect of k, our measure of the "size" of government, on g. If the substitutability of public for private spending declines as public spending increases, then ag should be negatively correlated with k, which seems to be the case, especially for the correlations in column 7 computed with a reduced set of control parameters. The results for By are virtually all consistent with the theoretical predictions, and strongly so at that. On the other hand, the results for Bg are mixed and do not fully square with those for y. The difficulty seems to be that Bg is often large and positive, which is consistent with a large substitutability of government purchases for private spending inducing a positive wealth effect. However, such a large substitution effect is not consistent with the observed negative Sy - V correlation. A possible explanation could y gy be that xc + xi is distributed across countries symmetrically about 1. We suspect, however, that the explanation is more likely to lie in the joint endogeneity of consumption and government purchases to resource shocks. IV. Conclusion This paper has presented some results from an empirical investigation of the effects of government spending on consumption and real output. The focus has been on the effects of innovations in spending and income. The theoretical framework underlying this investigation is the newly emerging equilibrium Approach to the analysis of government spending. Our strategy has been as follows. First, we specify a three-equation system for consumption, output and government spending derived from a simple stylized version of the Equilibrium Approach. Second, we estimate this system using post-war time series data from a panel of the 30 countries. Third, we focus on parameters associated with the effects of spending and income shocks and investigate whether these

-17 - parameters conform cross-sectionally to the predictions of the Equilibrium Approach. We find that estimates of the parameters pertaining to income innovations conform fairly well as a whole to the predictions of the theory. The analogous parameters for innovations in government spending, on the other hand, although interpretable under the theory, yield mixed results. In particular, some of our findings are consistent with a positive wealth effect of government spending, while others suggest the contrary. Two directions for further research bear some discussion at this point. First, some of our findings might more easilv be explained if government spending were endogeneous to income, or jointly endogeneous with private consumption (e.g., in response to latent shocks such as to future productivity). Although such shocks are difficult to identify using time series data from a single country, it may be possible to test for the presence of such shocks using extensions of the cross-country methodology set out here. Second, we have not attempted here to estimate directly the substitutability parameter for government spending, as Aschauer (1985) has shown to be possible. Preliminary results using data on tax revenues to help identify this parameter have shown some promise. Unfortunately such data are as yet available only for a subset of the countries in our panel. We are currently attempting to augment our data base in order to pursue these inquiries.

-18 -Table 1 Partial Correlations Relevant to the PIH Hypothesized Value Sign (Standard Error) p(B,kVy) +.72 ~~~~~~y ~(.14) p(y.,V Jk) +.59 '~y~~ ~~y ~(.16)

-19 - Table 2A Estimates and Approximate andard Errors for the Consumption Equation Coefficients of the Innovations in Income and Government Purchases Country By Soy g Australia Austria Bolivia Canada Colombia Costa Rica Denmark Dominican Republic Fed. Rep. of Germany Finland France Greece Guatemala Iceland Ireland Israel Netherlands New Zealand Norway Panama Paraguay Peru Philippines South Africa Sri Lanka Sweden Switzerland United Kingdom United States Venezuela MEAN STD. DEV. 0.44 0.38 0.70 0.34 0.22 0.81 0.53 0.73 0.16 0.62 0.67 0.40 0.62 0.43 0.54 0.41 0.16 0.68 0.14 0.99 0.92 0.55 0.37 0.40 0.56 0.39 0.35 0.59 0.43 0.30 0.04 0.08 0.03 0.05 0.11 0.11 0.07 0.11 0.04 0.09 0.07 0.09 0.11 0.09 0.08 0.07 0.07 0.13 0.09 0.32 0.13 0.06 0.10 0.05 0.17 0.06 0.03 0.11 0.02 0.07 0.09 0.06 0.62 - 0.86 0.52 - 0.52 2.77 - 1.43 - 0.03 - 0.39 1.08 - 0.90 - 1.39 1.36 0.12 1.80 - 2.00 0.00 1.64 0.51 - 0.03 - 0.96 - 0.45 - 0.73 1.29 0.70 0.68 0.58 0.20 - 0.88 0.13 - 1.13 0.29 0.52 0.39 0.21 0.76 0.72 0.08 0.33 0.43 0.75 0.48 0.34 0.58 1.05 0.72 0.07 0.43 0.91 0.54 1.22 0.62 0.30 0.47 0.42 1.01 0.42 0.20 0.45 0.12 0.82 0.49 0.21 0.08 1.08 0.52 0.29 Note: SBx is the asymptotic standard error of Bx x

-20 - Table 2B Persistence Measures and Their Approximate Standard Errors Country V YY SV YY V gg SV V gg gy SV V gy yg SV yg Australia Austria Bolivia Canada Colombia Costa Rica Denmark Dominican Republic Fed. Rep. of Germany Finland France Greece Guatemala Iceland Ireland Israel Netherlands New Zealand Norway Panama Paraguay Peru Philippines South Africa Sri Lanka Sweden Switzerland United Kingdom United States Venezuela 0.87 0.90 1.30 0.80 0.69 0.76 1.07 1.01 0.84 0.86 0.78 0.86 0.42 0.67 0.75 1.21 0.91 1.00 0.69 1.11 1.26 0.37 0.67 0.89 0.97 1.07 1.09 0.73 1.06 0.66 0.17 0.20 0.04 0.20 0.15 0.14 0.21 0.19 0.20 0.11 0.15 0.12 0.05 0.11 0.13 0.23 0.22 0.17 0.16 0.27 0.33 0.05 0.14 0.15 0.29 0.25 0.08 0.20 0.08 0.13 1.02 1.03 0.89 2.68 0.76 0.75 0.57 0.54 1.56 0.70 0.46 0.77 0.70 0.88 0.47 0.96 1.20 0.41 0.64 0.64 0.81 0.56 0.39 0.76 0.75 0.83 0.79 0.76 1.13 0.37 0.30 0.37 0.21 2.13 0.15 0.16 0.14 0.12 0.52 0.22 0.04 0.22 0.17 0.20 0.09 0.33 0.29 0.06 0.17 0.17 0.18 0.24 0.08 0.13 0.24 0.17 0.16 0.15 0.24 0.14 0.12 0.08 0.01 0.32 0.01 -0.03 -0.05 0.06 0.02 0.04 -0.03 -0.02 0.02 0.01 0.04 0.62 0.09 -0.01 0.02 0.11 -0.13 0.09 0.04 0.07 0.07 0.09 0.05 0.09 0.16 0.05 0.05 0.05 0.01 0.26 0.02 0.03 0.15 0.05 0.04 0.02 0.02 0.02 0.02 0.01 0.02 0.29 0.05 0.01 0.02 0.06 0.08 0.03 0.02 0.03 0.05 0.04 0.02 0.08 0.06 0.02 -1.92 0.35 -1.16 0.04 0.49 -0.17 0.22 -0.20 1.03 -1.97 0.85 0.34 -0.46 1.48 0.37 0.17 1.33 1.13 0.98 0.79 0.39 -1.00 -0.12 0.42 0.50 -0.99 0.74 0.27 -0.11 -0.69 1.11 1.39 0.80 1.59 1.05 0.64 0.20 0.43 2.38 1.08 0.35 1.08 0.36 1.47 0.71 0.26 1.29 0.73 1.10 0.80 0.76 0.37 0.56 0.67 1.33 1.02 0.61 0.40 0.31 1.06 MEAN STD. DEV. 0.87 0.16 0.83 0.26 0.07 0.05 0.10 0.86 0.21 0.07 0.43 0.37 0.13 0.07 0.87 0.48 Note: SV is the asymptotic xy standard error of V xy

-21 - Table 3 Partial Correlations Relevant to the Equilibrium Approach to Government Spending Hypothesis (1) Correlation Between Hypothesized Sign (4) Theoretical Basis (5) Partial Correlation (Standard Error) (6) (7) (2) (3) H1 l y g H2 8 k y c H3 V y yy H4 8 V y gy H5 V y gg H6 0 V Y yg H7 8 k g c + + 0 0 + Information on private disposable income y. Propensity to consume out of permanent income. Role of "persistence" of income shocks. Cross-effect of current income shock on future government purchases. < 0 if such purchases have negative wealth effects, i.e., if wc + wi < 1, and vice versa. None None Propensity to consume out of the permanent resource effect of government spending shocks. < 0 if [(l-wc-)i)Vgg - Vyg] > 0. -.68 (.15).75 (.14).62 (.17) -.39 (.19) -.75 (.14).78 (.13).61 (.17) -.40 (.19) -.09 (.18) -.06 (.20).40 (.21).47 (.18) H8 V g gg H9 a V g yg H10 B V g YY H11 B v g gy + 0 0 Wealth effect of government purchases. < 0 if we + wi < 1. Cross-effect of government spending shocks on future income. None None.23 (.21).14 (.23).42 (.20).02 (.19) -.29 (.22).21 (.19).44 (.19) H12 B k g g Effect of size of government on wealth effect of government spending shocks. -.42 (.19) Note: The partial correlations are computed between y or 8 (column 2) and the parameter given in column (3), controlling for other parameters as described below. Value Column #t of Col. (2) Parameters Controlled for in Computing Partial Correlations. 6 6 ag g} kc, Vyy Vgg Vgy y c,yy gg, gy a8, k, V,V I k g Vyy gy 8, k, V,V, k. y c yy gg g 7 7 8 0

-22 - Table 4 Estimated Contemporaneous Effects of Government Purchases on Output (yg and Vice Versa (gy ), with Approximate Standard Errors gy1 Country Byg Soyg yg 8gy SBgy Australia Austria Bolivia Canada Colombia Costa Rica Denmark Dominican Republic Fed. Rep. of Germany Finland France Greece Guatemala Iceland Ireland Israel Netherlands New Zealand Norway Panama Paraguay Peru Philippines South Africa Sri Lanka Sweden Switzerland United Kingdom United States Venezuela 2.84 1.17 3.21 -0.35 2.39 1.45 0.70 -0.82 2.33 3.99 2.55 1.46 1.30 10.29 6.10 -0.10 3.95 0.59 0.27 1.34 -0.24 0.64 1.76 3.97 2.31 1.23 3.32 1.34 2.43 6.19 1.32 1.28 3.00 1.05 1.30 1.33 0.27 0.67 1.81 1.72 1.67 1.89 1.11 1.43 1.65 0.21 0.90 1.53 1.23 0.73 1.00 1.18 0.96 1.48 1.13 1.56 1.60 0.84 1.13 2.08 1.30 0.54 0.06 0.03 0.01 -0.01 0.05 0.03 0.30 -0.07 0.03 0.04 0.03 0.02 0.04 0.07 0.06 -0.09 0.12 0.01 0.01 0.09 -0.01 0.02 0.08 0.06 0.06 0.02 0.04 0.07 0.06 0.04 0.04 0.06 0.03 0.03 0.01 0.03 0.03 0.03 0.12 0.06 0.02 0.02 0.02 0.03 0.03 0.01 0.02 0.19 0.03 0.03 0.05 0.05 0.04 0.04 0.04 0.02 0.03 0.03 0.02 0.04 0.03 0.01 0.04 0.03 MEAN STD. DEV. 2.25 2.29 Note: SBxy is the asymptotic standard error of Bxy P g was estimated by addadding to the income (second) equation of system (12) the term Bygect, and reestimating the system subject to the additional nonlinear cross-equation restrictions. 0 was estimated as the least squares projection coefficient of the residuals fr~8 the government purchases (first) equation in (12) on those from the income equation (without fygsgt)* Shgy was computed from the formula (Bgy + Byg)Syg, derived from the fact that the t-statistics for Bgy and Byg are equal.

-23 - FOOTNOTES 1. The relation between a firm's earnings and the rational valuation of its stock is similar to the relation between income and consumption under the PIH. Kormendi and Lipe (1986) examine the relation between the effect of an earnings innovation on stock returns and the persistence of the earnings process across a panel of 145 firms, and find evidence that these are positively related across firms as predicted by classical models of firm valuation. 2. In the context of a small open economy for which an exogeneous interest rate may be a tenable assumption, the capital stock wt includes net foreign assets. 3. This definition of disposable income implicitly assumes the "Ricardian Equivalence" of tax and debt finance. 4. The exclusion of additional influences, including current leisure (or equivalently work effort) and government purchases reflects the separability of U and V, not the form of U. 5. Mankiw and Shapiro (1985) have shown that the excess sensitivity of consumption to income can be spurious when income and consumption are detrended rather than differenced. This, among other reasons, is why the dependent variables in (7) (and ultimately (17)) and (9) are in differenced form. 6. The more "persistent" the y process, the smaller will be the extent of "excess sensitivity" and hence measured 3. This would also bias results away from the PIH. 7. Each equation in (12) also includes a constant term and the variable 1/ctl, which have been omitted for simplicity.

-24 - 8. Alternatively, assuming that x - g = |(y-g) yields 0 = kd[V - V ] y YY gy g = kd[V - V ] g *yg gg 9. Since private consumption expenditures include consumer durables, modifying our model along the lines of Mankiw (1982) and Bernanke (1985) would be of interest. 10. kj is the mean of cjt(y-g)., t=1954,...,1979. 11. As discussed in Kormendi and LaHaye (1986), measurement error in y may bias estimates of B towards 0. Likewise, if the measurement error were more transitory than the true (y-g), V may also be biased towards 0. Thus the measured correlation between 8 and V is potentially biased upwards. If this were the case, any positive correlation between 8 and V observed over the entire sample would be attenuated when computed over subsamples stratified by an ordinal measure of data quality. Summers and Heston (1984) group countries into four categories based on the quality of their national accounts data. We repeated the cross-sectional estimates reported in Tables 1 and 3, controlling for data quality using the taxonomy of Summers and Heston, and found the correlations to be unaffected. Also, if the results in Table 1 were due to measurement error varying systematically across countries, one would expect the correlations to decline upon controlling for the standard error of the income equation. Again, this did not occur. 12. These partial correlations can be computed over ranks instead of the raw data. The resulting non-parametric rank partial correlations are only slightly smaller than those in Table 1.

-25 - 13. We estimated the 3 equations in (12) over the time series for each country by nonlinear multivariate regression, subject to the cross-equation restrictions implied by the presence of innovations in g and y in the consumption equation. We included 3 lags of (changes in) consumption and income in the consumption and income equations, so that i=l to 3 for each of ai, bi, ci and di. The system (12) was estimated using two passes of TSP's LSQ command, with the reported results taken from the second pass. The first pass estimated the system with an unrestricted cross equation residual covariance matrix but with y and g constrained. The coefficients to be estimated were assigned starting values of zero (0.1 when assigning a 0 would result in a degenerate model) and the identity matrix was used to initialize the residual covariance matrix. The estimated covariance matrix from the first pass was then diagonalized and held fixed during the second pass. Starting values of coefficients for the second pass were the estimated values from the first pass. 14. Although our main concern is not Hall-Flavin tests of the consumption equation, the outcomes of such tests are quite similar to those reported in Kormendi and LaHaye. Slightly more than the expected number of counries reject the Hall-Flavin restrictions at low marginal significance levels. Relaxing these restrictions for those countries does not materially affect any of the crosscountry results below. 15. For 15 out of the 30 countries, the implied t statistic for Bg exceeds 1.65 in absolute value, when under a null of g = 0, only about 3 countries would be expected to do so. 16. The deletion of Canada does not materially affect any of the correlations that do not involve V gg

-26 -17. The mean across countries of the estimation error correlation between y and fg is -.30. This contributes to, but does not dominate, the total measured correlation of -.69, leaving room for theoretical determinants. No other pairs of parameters exhibited an estimation error correlation that could contribute materially to the total correlations in Table 3. 18. The sample mean of V is.83, that of V is.11; see Table 2. gg yg

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