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r f e e d f e r l ei bn rc ae r y e r r e a s l eb ra vn e k OF C H I C A G O A Series of Occasional Papers in Draft Form Prepared by Members of the Research Department for Review and Comment SM -87-10 N e t Private In ve stm e n t and Pub lic Ex p e n d itu re in th e U n ite d States 1953-1984 David Alan Aschauer SM-87-10 R FE E C L I B R A R Y E RNE F E D E R A L R E S E R V E O F C H IC A G O B A N K Net Private Investment and Public Expenditure in the United States 1953-1984 by David Alan Aschauer This paper has been presented at the Ministry of Finance, Toyko, Japan and The Board of Governors, Federal Reserve System. The views expressed are those of the author and do not necessarily reflect the opinions of the Federal Reserve System. Net Private Investment and Public Expenditure 1n the United States 1953-1984 David Alan Aschauer Abstract This paper 1s an empirical Investigation Into the effects of public expenditure— 1n particular, public Investment spending— on private capital accumulation. The empirical evidence 1s consistent with the major Implications of the neoclassical approach to fiscal policy. In particular, holding fixed the rate of return to private capital, public Investment spending 1s significantly more depressive to private Investment than 1s public consumption expenditure. Federal Reserve Bank of Chicago University of Michigan Northwestern University June 1987 Preliminary. Comments solicited. I. Introduction This paper 1s an empirical Investigation of the effects of various fiscal policy actions on private Investment. Conventional macroeconomic models suggest that the major Impact of fiscal policy on private Investment arises from changes 1n the overall level of taxation or the overall level of public sector expenditure. For Instance, 1t typically 1s argued that a decrease 1n taxes, holding fixed the level of government spending, will be associated with higher real Interest rates (as the government Issues debt securities to cover the deficit) and lower private Investment. Recently, theoretical models have been constructed, and empirical models have been estimated, which cast a dark shadow on the appropriateness of this traditional line of reasoning. Barro [1974] argues that given adequate concern about future generations, a fiscal policy as traced out above will have a negative Impact on private Investment as rational agents save the current tax cut 1n anticipation of the future taxes which will be necessary, under most circumstances, to service or amortize the public debt. There 1s a substantial amount of recent empirical evidence which 1s supportive of this theoretical equivalence between public debt and taxes 1n financing a given public expenditure stream. Kormendl [1983] studies consumption behavior and obtains the result that changes 1n the level of taxation have Insignificant effects on private consumption while Seater and Mariano [1985], also studying consumption behavior, find complete tax discounting as well after deriving an Improved permanent Income series. Aschauer [1985] derives an Euler equation for "effective" consumption— a weighted sum of private and public consumpt1on--and finds that public sector deficits are Important 1n explaining private consumption only to the extent 2 that the deficits aid in predicting future government spending. Plosser [1982] and Evans [1985] find insignificant effects of changes in the tax/debt mix on asset returns, while Evans [1986] provides evidence that public sector deficits are not responsible for movements in the exchange rate. A few studies also have argued that it is important to consider the differential impact of various forms of public expenditure on private sector variables. Barro [1981] splits public expenditure on goods and services into "transitory" and "permanent" components and gives evidence that output responds to a greater extent to temporary public purchases. Kormendi [1983] briefly considers the impact of public investment on private consumption and finds, empirically, little relationship. Although this result is consistent with the neoclassical approach, it is also consistent with a substantial crowding out of leisure and, consequently, an expansion of output. This paper also considers the impact of public investment spending, but on private investment, which allows for a tighter test of the appropriateness of the neoclassical approach to fiscal policy. In Section II the theoretical implications of various fiscal policies for private investment are traced out in a simple neoclassical set-up. Section III contains some empirical results on the influence of fiscal policies on the accumulation of private capital. Section IV concludes the paper by drawing together these results and by suggesting topics for future research. II. Theoretical Concerns The essential theoretical points may be illustrated in the context of a simple two period representative agent model. The agent has preferences given by (1) U = u(c*) yi< ! Hl P 3 where c*=c * ec9 1s a measure of current "effective" consumption, a linear combination of private consumption, c, and government consumption, c9, and where c* = c < ec9 Is future effective consumption. ■ preference, p, The utility rate of time 1s assumed to H e between zero and unity.1 Here e represents a constant marglnal/average rate of substitution between private and public consumption goods. The agent may transform current resources Into future consumption by making use of the private transformation technology: (2) y = f(k + 1, k9 + 19) where y 1s future private production, k and k9 are the current stocks of private and public capital, respectively, and 1 and 19 are private and public Investment levels. It Is assumed at this point that f| > 0, f2 > 0, and f n < - 0 while discussion of possible complementarities between private and public capital 1n the production process 1s postponed momentarily. The agent may borrow or lend 1n an economy-wide credit market at the Interest rate r and Is constrained 1n h1s choice of current and future consumption by the Intertemporal budget equation (3) c + 1 r r r where t and t are current and future levels of lump sum taxes.2 The government utilizes the revenues from lump sum taxation 1n order to engage 1n expenditure on public consumption goods or on public Investments.3 Allowing the government to have access to the credit market on the same terms as the representative agent, we have the public sector budget constraint4 (4) ^ r = t t i' r 4 The "Ricardian" view of fiscal policy Involves the representative agent taking Into account the public sector budget constraint (4) 1n making Intertemporal decisions. Accordingly, we consolidate the private and public budget equations to yield, 1 n terms of effective consumption, the economy-wide budget constraint (5) c* + 1 1 ^ + —* = y + r r _1. + (6 -i)(c^ + ££)■• r The agent chooses current and future effective consumption levels and the level of private Investment so as to maximize utility, expressed as 1 n equation (1 ), subject to the economy-wide Intertemporal constraint, equation (5) . First order necessary conditions for this problem are, 1n addition to equation (5), (6) itUL£-*l = r u'(c*) (7) p r = f-|(k + 1, k9 + 19). Equation (6 ) Indicates that the agent chooses effective consumption optimally when the utility gain from consuming an extra unit of goods 1 n the present, u'(c*), equals the present value of the utility gain from saving and obtaining r extra units of consumption 1n all future periods, ru'(c*)/p. Equation (7) Illustrates that the agent chooses future capital so as to equate the returns to physical capital and bonds. Equations (5), (6 ), and (7) may be employed to obtain solutions for c*, c*, and 1 as Implicit functions of the Interest rate, Initial capital stocks, and fiscal expenditure variables. However, as this paper focuses on the general equilibrium effects of fiscal actions, we assert goods market 5 equilibrium 1 n both periods, C* + 1 r- 19 t ( 1- G ) c 9 = y (8) c* + ( l - e ) c 9 ■ (9) = f ( k + 1, k9 f 19) which, upon substitution 1n (6 ) along with (7), yields u'(v-(l-9)c9-1-19) (10) _ f (kr-1 ,k94-19) p u'(f(k+i,k9+ig)-(i-e)c9) Equation (10) now will be used to consider the effect of alternative fiscal policies on private capital accumulation. are: The specific policies looked at a change 1 n the temporal pattern of taxation; a rise 1 n public consumption (current account) expenditure; and an Increase In public Investment (capital account) expenditure. A . A Change 1n the Temporal Pattern of Taxation Consider, to begin, the substitution of future for present taxation, while holding the time profile of public expenditure on goods and services fixed. The simple neoclassical model as sketched out here Implies an equivalence between taxation and public debt Issuance to finance the current level of public expenditure on consumption or capital goods. Specifically, for a particular path of public expenditure, the decision by the government to lower current taxes, sell public debt, and raise future taxes to service the debt has no effect on the agent's Intertemporal opportunities as Indicated by equation (5). In this model, as long as the public sector bonds pay the same rate of return as private sector bonds, an attempt by the government to 6 manipulate aggregate demand in such a fashion will be frustrated. In particular, as current and future consumption levels are undisturbed, it follows that there is no "crowding out" of private investment through this channel. B. An Increase in Public Consumption Next consider an increase in the level of public expenditures on nondurable goods and services such as paper for the bureaucracy, police services, military uniforms, and the like. The effect of such a change in public policy on private investment will depend on three factors, namely: the extent to which the public sector consumption goods substitute for their private sector counterparts; the persistence of the expenditure change; and the time profile of the agent's marginal propensity to consume out of wealth. Let a change in current public consumption expenditure be followd by a change in future public consumption purchases equal to a times the current change. Hence if the current shock is transitory, a=0 while if permanent, a=l . Differentiation of equation (10) results in5 = e d-e) (3c* _ a 3c*) di (cg j r & aw aw where a = fii - £ (rac*/aw + ac*/aw)> r Clearly, if e=l there is no effect of a change in the level of public consumption expenditure on the agent's effective intertemporal consumption opportunities and private investment is left unaltered. The higher public expenditure crowds out an equivalent amount of private consumption expenditure, leaving effective consumption levels unchanged. 7 However, available empirical evidence suggests that public consumption goods substitute poorly for their private sector counterparts. Kormendl [1983] and Aschauer [1985] obtain estimates of e 1n the range (.20, .35). Accordingly, a rise 1n the level of government consumption would be expected to reduce the agent's effective consumption possibilities and result 1 n a possible effect on private Investment as the agent reallocates the "burden" of the public sector expansion Intertemporally. Assuming 0 < e < 1, consider the case where the rise 1n public consumption 1s permanent, a=l. Equation (11) Indicates that private Investment will be unaltered given a flat time profile of the marginal propensity to consume since the agent then would bear the burden equally over time. On the other hand, 1 f the agent's marginal propensity to consume profile has an upward (downward) 1 1 1 1 , private Investment will fall (rise) as the agent chooses to bear the majority of the negative wealth effect 1 n the future (present). Finally,assuming that 0 < e < 1 and that thetime profile propensity to consume 1 s flat, but of the marginal the change1 n public consumptionspending 1 s to some extent transitory, we have dl__ = £ n-e)(l-a) ac * dc9r a aw which may be rewritten as d1 = -n-eHl-g) dc9 nr(l-fn/p(ac/aw)) so that we have -I<d1/dc9<0. Thus, on net, a rise 1n public consumption expenditure 1s likely to have a negative Impact on private Investment expenditure, the effect being stronger (a) the more transitory Is the rise 1 n public purchases and/or (b) the less the publlcally provided goods substitute for private goods on the margin. 8 C. A Rise In Public Investment We now turn our consideration to the Impact of various forms of public 1nvestment-~Veterans' Administration hospitals, dams, highways, etc.--on private capital formation. Public capital 1s assumed to enhance private production, holding fixed the private capital stock, according to equation (2 ), rewritten here y = f(k + 1, k9 * 19). Utilizing equation (10) we find that the Impact of a rise 1n public Investment on private capital accumulation 1 s given by the expression (f -f )ac*/aw (12) di_ = -l dl9 £ __2__] _______ r a As a reference case, suppose that private and public capital are perfect substitutes 1 n the private production process, so that future output 1 s dependent only on the national capital stock, k, + k9, where k = k + 1 and k9 = k9 + 1 9; specifically, we write y = f(k + k9) with f' > 0, f" < 0. In this case, only the first term on the right hand side of equation (1 2 ) remains, Indicating a complete crowding out of private by public capital accumulation. For the most part, public Investment policy would be Irrelevant to private sector outcomes, with the only exception being that private capital would become a smaller fraction of the national capital stock. In general, however, public capital 1s likely to bear some complementary relationship to private capital, so f-|2 > 0 * In this Instance, a rise 1 n public Investment and direct substitution for private Investment will have 9 additional effects. First, the reduction in the private capital stock will boost the marginal product of private capital and, given the interest rate, will provide a mitigating effect on private investment expenditure; this is captured by the second term in equation (12). Second, the rise in public capital, given f-|2 > 0 * raises the marginal product of capital directly and provides an additional offset to the direct effect on private investment as is evidenced by the third term. Finally, the public capital stock may be too low, in which case f2 > f1 , or too high, so f2 < f-|. If the public sector has overaccumulated capital, then an addition to the public capital stock and an equal crowding out of private capital will lower future output, creating a negative future income effect. The attempt by the agent to bear some of this future burden in the present results in a final possible partial offset to the direct effect of higher public capital accumulation on private investment expenditure as in the last term in equation (1 2 ). Thus, holding fixed the rate of return to the private capital stock (thereby putting aside the second and third terms in equation (1 2 )), higher public investment would be expected to crowd out a nearly equal amount of private investment, somewhat less if the public sector has accumulated too much capital, but somewhat more in the alternative case. To summarize the analysis of this section, an empirical study of the effects of fiscal policy on private investment should, according to the neoclassical model, produce results consistent with the following hypotheses. First, an increase in public investment expenditure, given the return to the private capital stock, should have in significant negative impact on the level of private capital formation. Given that public and private capital are perfect substitutes in private production, the crowding out of private capital should be complete, while in more general cases the crowding out will be more or less depending on the extent to which the public sector has accumulated the 10 appropriate level of capital. Second, given that public consumption expenditure 1 s sufficiently transitory, an Increase 1 n such spending should depress private Investment as agents attempt to reallocate the burden of the expenditure over their economic lifetimes. However, this avenue of crowding out 1 s likely to be less Important than that of public Investment, particularly 1 n a period of limited variability 1 n public consumption goods purchases. III. Empirical Analysis The empirical analysis focuses on the effect of public expenditure on private Investment. The private Investment series 1s net fixed Investment 1n nonresldentlal equipment and structures and 1 s obtained from various Issues of the Survey of Current Business. 6 This annual series 1s computed along "perpetual Inventory" lines by subtracting cumulative depredation from the gross capital stock (cumulative gross Investment minus discards) 1 n order to obtain the net capital stock. This net capital stock 1s valued In current, as opposed to historical, prices and thus 1 s a close measure of the replacement value of the private nonresldentlal capital stock. The accuracy of this procedure, however, depends crucially upon (a) the chosen depreciation methodology- stra1 ght-Hne, double-declining balance, etc.--and (b) the useful service lives employed for depreciation purposes. The particular series used 1n this paper 1s computed using stra1ght-11ne depreciation over 85% of the service lives published 1n Bulletin F of the Treasury Department. Future research 1 s Intended to make use of somewhat broader notions of the capital stock (e.g., Inclusive of residential capital) and alternative methods of depredation . 7 The specific series utilized 1n the current study- equipment and structures- was chosen because 1 t seemed a priori to be most comparable to n available public investment series. The straight-line, 85% service life methodology is that lying behind most of the net investment series published in the "National Income and Product Accounts" and elsewhere in the Survey of Current Business. A rate of return to private capital variable is taken from a study by Feldstein and Jun [1986] on the effects of distortional tax changes on private investment expenditure. This rate of return is computed as the ratio of net (of depreciation) corporate profits plus net interest expenses plus state and local property taxes to the total value of the net capital stock (net stock of equipment and structures plus inventories plus land) times one minus the total effective tax rate on capital (corporate profits taxes, state and local property taxes, taxes on dividends, interest, and capital gains). Under conditions of perfect competition and constant returns of scale, this variable would be a measure of the after tax marginal product of private capital. As computed, this variable measures the rate of return on nonfinancial corporate capital since the net of depreciation corporate profits series published in the Survey of Current Business presently is restricted to that legal category. The public investment series consists of federal, state, and local net expenditures on equipment and structures, inclusive of military expenditures on these items. A priori, one might expect that while these latter expenditures substitute somewhat poorly for private capital in the production process-thereby leading to less than complete crowding out-they nonetheless will have a significant positive effect on the private rate of return to fixed capital by reducing the probability of future expropriation or the limitation of overseas markets. Depreciation of this form of capital to derive a net capital stock series is based on comparisons with similar private capital, data form governmental agencies on actual service lives, and on the assumptions made by Goldsmith in a background study on corporate stock ownership by institutional investors. 8 12 Two other variables will enter the empirical analysis as well. Current account expenditures by the public sector are measured by subtracting the net public Investment series from total purchases of goods and services by the government. It thus 1s Inclusive of replacement Investment expenditures as well as of government purchases of consumption goods and services. An output deviation variable is computed as the deviation of the actual growth rate of gross national product from the constant, average growth rate of gross national product over the sample period, 1953-84, of 3.1 percent per year. Sample statistics for these variables, all of which (with the exception of the rate of return to capital) are measured relative to gross national product, are presented 1n Table I. Thus 1 = private net investment as a ratio to gross national product, r = net rate of return to private nonflnanclal corporate capital, 19 = public net Investment as a ratio to gross national product, c9 = public current account expenditures relative to gross national product, and t = total tax revenues as a percentage of gross national product. Note, in particular, that public investment was, on average, more than 50 percent as large as private investment during the sample period (1 . 8 percent compared to 3.3 percent of gross national product) while being characterized by nearly the same amount of volatility, with a standard deviation of 0.8 percent as opposed to 0.9 percent of gross national product. Further, the maximum value of public net investment, 3.4 percent of output (attained in 1953), 1s roughly two thirds as large as the maximum value for private net investment, 5.4 percent of gross production (achieved in 1966). Finally, on average public net investment amounted to roughly 7.4 percent of total government expenditures on goods and services. Public consumption expenditures accounted, on average, for a significantly larger share of output, 21.2 percent, and varied from a low of 18.3 percent in 1979 to a high of 26 percent in 1953. The share of gross product devoted to 13 these uses during the period 1981-1984 averaged 19 percent. The output (growth rate) deviation variable ranged between -5.7 percent and 3.2 percent. The potential Importance of the public expenditure variables for private Investment 1 n an Intertemporal setting seems clear from these statistics. We now focus on the relationship between private Investment and public expenditure. We begin by Investigating the Impact of public Investment on private capital accumulation, given the rate of return to private capital. Although the theoretical exposition Involved no costs of adjusting the private capital stock, most Investment studies have found various lags 1 n response of Investment to be Important. Accordingly, we regress private Investment on the contemporaneous and two lagged values of both the rate of return to capital and public Investment. (a) of Table II. The result 1s to be found 1n column We find that private Investment responds strongly to the rate of return variable, lagged one year, 1 n the positive manner suggested by theory. Further, private Investment 1s significantly adversely affected by contemporaneous movements 1n the public Investment variable. The point estimate of -1.34 suggests that the crowding out through this channel 1s greater than one-to-one, although the null benchmark hypothesis of 100 percent crowding out cannot be rejected at usual significance levels. Note that the low value of the Durbln-Watson statistic Indicates the possibility of serial correlation 1 n the residuals of the estimated equation. Reest1mat1ng this equation allowing for a first order autocorrelation correction yields the estimates contained 1n column (b) of Table II. As before, private Investment reacts positively to a one year lag of the rate of return to capital but also, at the 10 percent level of significance, to the two year lagged return variable. Again, only the contemporaneous value of the public Investment variable 1 s of significant Importance 1 n explaining private Investment expenditure. 14 Columns (c) and (d) of Table II Indicate that the exclusion of the time trend from the regression does not have a substantial Impact on the results, though It reduces the absolute value of the coefficient on the current public Investment variable (and lowers Its standard error). Columns (e) through (h) Investigate the effect of eliminating first the two year and then the one year lagged value of the public Investment variable from the equation. The net effect Is to alter to only a minor degree the coefficient estimates of the rate of return variable while lowering, In absolute value, the estimated parameter value of the public Investment variable. Columns (1) and (j), obtained by eliminating the contemporaneous value of the rate of return, appear to offer the best parsimonious description of the relationship between private Investment, the marglnal/average product of capital, and public Investment. All Included variables are significant at the 5 percent level, Including a minor negative trend In private Investment as a ratio to gross national product. The computed value for the F-statlstlc relevant for testing the appropriateness of restricting to equal zero the coefficients on the contemporaneous rate of return variable and the lagged public Investment variable Is 1 .02 , substantially below the five percent critical value for the F(3,23) distribution of 3.03. Private Investment reacts positively to movements In the marglnal/average productivity of capital, with the cumulative effect of a one percentage point rise In capital's marginal product lifting Investment by roughly nine tenths of a percentage point. A two standard deviation rise In the contemporaneous level of public Investment of 0.016 depresses private Investment by 0 .0 2 1 , or roughly 2.3 times Its own standard deviation. Given the rate of return variable, the point estimate In columns (1 ) and (j) suggest more than complete crowding out, although the 95 percent confidence Interval Is wide, stretching from -.46 to -2.10. 15 As a further check on the robustness of the relationship between private and public investment, the basic specification was reestimated in first differenced form. These results are in columns (a) and (b) of Table III. Here the intercept indicates an insignificant downward trend in private investment during the sample period. The estimates, when compared to the relevant columns in Table II, are basically unaffected, although the parameter value associated with the public investment variable is further reduced. It is comforting that the data thus support the theory not only on average but also from year to year as well. It might be argued that estimation by ordinary least squares (with or without correction for serial correlation) is inappropriate since the public investment variable is measured relative to the contemporaneous value of gross national product and is likely to be determined simultaneously with the private investment variable. Using the lagged value of the public investment variable and public investment relative to trend gross national product as instruments, the equation was estimated by two stage least squares to yield 1^- = 4 . 8 1 a ( 2 ) - 4.32a(4) (1.98a(2)) (2.43a(4)) time + .5 3 r^ _i (.16) + .33rj-_2 (.13) - 1. 0 5 1 gj -- + e^ (.37) DW = 1.06 R2 = .65 SER = 5.91a(3) which exhibits a substantial reduction, in absolute value, of the coefficient on public investment from that obtained 1n most previous cases. After taking account of the possible serial correlation by quasi-differencing the data, we obtain 16 it = 2.46a(2) - 2.26a(4) time + .57rt_i + .33 rt_2 - 1.08igt + et (1.57a(2)) (1.91a(4)) (.14) (.13) (.42) DW = 1.62 R2 = .59 SER = 5.27a(3) The point estimate on the public investment variable now is much closer to indicating 100 percent crowding out and an appropriate level of public capital accumulation, although this statement must be made with caution due to the size of the associated standard error. A more conventional explanation of the crowding out of private investment might also be given. Specifically, the rise in public investment creates an excess demand in the capital goods producing sector and raises the relative price of capital which, in turn, lowers private investment. Thus, the public investment variable acts as a proxy for the cost of capital. After defining the relative price of capital, pk^, as the ratio of the implicit deflator for gross private nonresidential investment to the deflator for gross national product, we get if = - 6.90a(3) - 4.70a(4) time + .62rf_n + .31rf_o - 1.16igt + .06pkf + et -(.07) (3.19a(4)) (.14) (.13) (.41) (.06) P = .38(.19) R2 = .74 SER = 4.80a(3) Here the estimation made use of a first order autocorrelation correction, with estimated coefficient given by P. The relative price of new capital goods enters with a sign opposite to that which would be expected on theoretical grounds, although it is statistically insignificant from zero at usual levels. Further, the addition of this variable is incapable of substantially lowering (in absolute value) the estimated coefficient on public investment, 17 thereby casting doubt on the appropriateness of the more conventional explanation for the crowding out of private Investment discussed above. It might also be thought that the public Investment variable is proxylng for cyclical effects. As a check on this possibility, the basic specification was augmented by a variable measuring the deviation of the growth rate of output from trend, with the result below: 1t = .07 - 6.71a(4) time + .55r^_i + .36r^_2 - l.371g^ + .07ydev^ + e^ (.02) (3.02a(4)) (.13) (.12) (.39) (.04) P = .48(.18) R2 = .77 SER = 4.50a(3) Addition of the output growth deviation variable does not 1n any way reduce the Importance of public Investment 1 n the regression; the point estimate of the public Investment coefficient remains substantially greater than unity 1 n absolute value. The output variable enters with the logical sign but 1s only of marginal Importance 1 n helping to explain private Investment. Next, consider the Introduction of current account expenditures by the public sector— defined above as all purchases of goods and services minus net public Investment— Into the regression equation. The result of ordinary least squares estimation 1s given 1n column(a) of Table IV. particular Interest. Two results are of First, the estimated coefficient on the public consumption variable 1 s negative and highly statistically significant. Second, the estimated coefficient on the public Investment variable 1s lowered, 1 n absolute value, to a level consistent with nearly complete crowding out of private capital accumulation. Inspection of column (b) of Table IV Indicates that these results are not sensitive to correction for first order autocorrelation. 18 It 1s of Interest to determine 1f public consumption or public Investment 1s more depressive to private Investment spending. The statistic relevant for testing the null hypothesis of equal effects versus a larger effect of public Investment 1s distributed as a t variable; computation yields values of -1.36 and -1.52 for the ordinary least squares and first order autocorrelation correction estimations, respectively. Accordingly, 1t 1s not possible to claim at this stage that public Investment 1 s significantly more potent 1 n 1 t 's Impact on private capital spending. The equation was reestimated treating the expenditure variables as endogenous, using the expenditure variables relative to trend output and lagged expenditure variables as Instruments. estimates 1n column (c) of Table IV. In raw form, the data yield the Importantly, the public consumption variable becomes much less Important 1 n explaining movements In private Investment, with a point estimate of -.27, and which 1 s statistically Insignificant at the 5 percent level. The coefficient on public Investment still Indicates nearly complete crowding out, while the rate of return variables remain at nearly the same values and levels of significance. Quas1 -d1 fferenclng the data and reestimating yields the same Interpretation. Now, the relevant t-stat1st1cs take on the values of -2.18 and -2.07, which allow rejection of the hypothesis of equal effects on private Investment 1 n favor of that of public Investment having more Importance. IV. Conclusion This paper Investigates the relationship between private net Investment 1n nonresldentlal structures and equipment and public spending. The empirical results suggest that, consistent with neoclassical theory, higher public expenditure 1 s associated with lower private Investment, given the rate of 19 return to private capital. The extent of the ex ante crowding out of private investment appears greater for public net investment than for public consumption and replacement investment expenditure. Specifically, the point estimates suggest that an increase in the ratio of public capital accumulation to output of one percentage point reduces private capital spending by one to one and one half percentage points, while an equal sized rise in public consumption would depress private investment by roughly 0.20 of a percentage point. This last result is consistent with increases in public consumption expenditure which are largely permanent, a result which is reflective of the sample period chosen for this study. Interesting topics for future research appear to be: consideration of different series on private and public net capital accumulation, utilizing differing depreciation methodologies; analysis of the impact of changes in various types of public investment; and the detailed investigation of possible complementarities in production operating through impacts on the marginal product of private capital. The neoclassical approach to the effects of public sector deficits on private investment expenditure emphasizes real, as opposed to purely financial, considerations. This paper has provided some evidence consistent with that approach and shows that while pure deficits may not matter, public spending— especially public investment--is of crucial importance in determining the overall rate of capital accumulation in the economy. 20 Table I Summary Statistics of Variables (1953-84) Mean Standard deviation Maximum Minimum 1 0.030 0.009 0.051 0.013 r 0.038 0.013 0.068 0.012 19 0.018 0.008 0.034 0.006 c9 0.212 0.019 0.260 0.183 ydev 0.000 0.025 0.032 -0.568 21 Table II Dependent Variable ~ i ^ time rt .03 -1.59a ( ) 4 -.22 () c .02* (3.94a ( ) 3 1) ( d .01* (5.00a (3 ) ) (.16) .25 (.15) .14 (.14) () b () a constant (.03) (3.44a (4)) (.16) .04 -3.04a ( ) 4 -.04 (.03) (4.00a (4)) rt-l .65* (.19) .58* (-16) .63* (.18) .54* (.15) rt-2 .1 2 (.16) .26** (.14) .18 (.14) .22 (.14) ’ 9t -1.34* (.52) (.48) -1.23* (.45) -1.26* (-42) '9t-l .82 (.78) .66 (.66) .86 (.76) .79 (.64) i9t2 -.01 (.51) .02 (.48) .08 (.46) .14 (.44) .34 (.21) .32 (.20) P ~ DW - 1. 7 - .2 R2 = .70 . SER = 5 ,20a( ) : 3 -1.43* R2 = .7 .5 SER r 4 70a ( ) . 3 DW r 1.31 , R2 = .70 . SER 5.20a ( ) 3 R2 = .74 : SER = 4.80a ( ) 3 Note: Standard errors in parentheses. An * denotes statistical significance of the 5 percent level; ** at the 10 percent level. a(x) E 10~x. 22 Table II (coni'd) () e constant time rt .03 -1.56a( ) 4 -.22 () f (.02) (3.10a(4)) (.16) .04 -3.04a ( ) (3.70a (4)) 4 -.04 () h (9) (.03) (.15) .05* (.02) .06* -4.16a ( ) (2.16a (4)) -5.912(4)** 4 -.13 (.02) (3.08a(4)) (.15) -1.40a ( ) 3 (.13) rt-i .65* (.18) .58* (.15) .64* (.19) .59* (.15) rt-2 .1 2 (.15) .26** (.14) .30* (.14) .33* (.13) -1.34* (.46) -1.43* (.46) -1.01* (.41) -1.25* (.44) ’9t-l .1 8 (.55) .67 (.54) - ’9t-2 - - - P - - .34** V DU = 1.27 R2 = .70 SER = 5.20a ( ) 3 (.20) R2 = .75 SER = 4.70a( ) 3 - D ^ 1.21 U R2 = .67 SER = 5.40a ( ) 3 - .36** (.19) R2 = .73 SER = 4.90a ( ) : 3 23 Table II (Cont'd) () i constant time .05* - 5 . 08a (4]1* () j (.02 ) (2 .4 l a (4)) .0 6* (-03) - 6 . 22a ( 4 ) * ( 3 .0 7 a ( 4 ) ) - rt rt-i .56* (-16) .59* (.14 ) r t~2 .34* (.13 ) .33* (.13 ) (-36) -1 .2 8 * (.4 1) - 1 .1 9 * ’ 9t_l - '* t - 2 P .44* D W = 1.02 R2 , .66 5ER r 5 . 50a (3) R2 SER (.18) , v .74 4 . 80a (3) 24 Table III Dependent Variable = Ait constant -8.06a ( ) 4 (1.24a(3)) -1.06a(3) 1.13a ( ) 3 Art .09 (.15) - Art-1 .60* (.14) .62* (.13) Art-2 .29* (.14) .32* (.13) -1.54* (.50) -1.40* (.48) Aigt - &i9t-1 .44 (.55) - - A’9t-2 .08 (.48) - - DW - 1.93 6 R2 s . 1 SER = 5.20a(3) DW = 2.00 R2 = .57 3 SER = 5.50a ( ) 25 Table IV (a) constant time .22* (b) (c) OIS FOAC 2SLS (.04) -1.26a(3)* (2.31a(4)) .22* (.04) -1.27a(3)* (2.58a (4)) .13* (d) 2SLS (FOAC) (-06) -8.04a(4)* (3.26a( ) 4 .05 (.04) -3.68a( ) (2.61a(4)) 4 rt-i .40* (.12) .47* (.11) .47* (.14) .55* (.13) rt-2 .62* (.11) .54* (.11) ,47* (.14) .37* (.13) -.95* (.26) -1.03* (-29) -.99* (.30) -1.05* (.38) -.59* (.12) -.55* (.13) -.27 (.19) -.16 (.21) .23 (.20) c9t P - - DW = 1.49 R2 = .83 SER = 3.90a ( ) 3 R2 = .84 SER = 3.50a ( ) 3 - - DM = 1.19 R2 = .74 SER = 4.84a(3) - DW = 1.68 R2 = .65 SER = 4.78a( ) 3 26 References Aschauer, David Alan, "A Theory of Crowding Out," Ph.D. thesis, University of Rochester, 1984. ____________________, “The Equilibrium Approach of Fiscal Policy." Staff Memoranda, Federal Reserve Bank of Chicago, 1986. ____________________, "Fiscal Policy and Aggregate Demand," American Economic Review. LXXV (1985), 117-27. Barro, Robert J., "Are Government Bonds Net Wealth?" Economy. IIIVXC (1974), 1095-1117. Journal of Political __________________ , "Output Effects of Government Purchases," Journal of Political Economy. IXC (1981), 1086-1117. Boskln, Michael J., Robinson, Marc S., and Roberts, John S, "New Estimates of Federal Government Tangible Capital and Net Investment," NBER Working Paper 1774, 1985. Bulletin F — Income Tax. Depredation and Obsolescence. Estimated Useful Lives and Depredation Rates. U.S. Department of Treasury (Washington, D.C.: U.S, Government Printing Office, 1942). Evans, Paul, "Do Large Deficits Produce High Interest Rates?" Economic Review. LXXV (1985), 68-87. American ____________________, "Is the Dollar High Because of Large Budget Deficits?" Journal of Monetary Economics. XVIII (1986), 227-50. Feldsteln, Martin. "Government Deficits and Aggregate Demand," Journal of Monetary Economics. IX (1982), 1-20. ___________________, Capital Taxation. (Cambridge MA, Harvard University Press, 1983). ___________________, and Jun, Joosung, "The Effects of Tax Rules on Nonresldent1al Fixed Investment," NBER Working Paper 1857, 1986. Fixed Reproducible Tangible Wealth of the United States. 1925-79. U.S. Department of Commerce, Bureau of Economic Analysis (Washington, D.C., U.S. Government Printing Office, 1982). Kormendl, Roger C-, "Government Debt, Government Spending, and Private Sector Behavior," American Economic Review, LXX1II (1983), 994-1010. "National Income and Product Accounts" In Survey of Current Business. U.S. Department of Commerce, Bureau of the Economic Analysis (Washington, D.C.: U.S. Government Printing Office, various years). 27 Plosser, Charles, "Government Financing Decisions and Asset Returns," Journal of Monetary Economics. IX (1982), 325-52. Seater, John 0., "Does Government Debt Matter?" XVI (1986), 121-32. Journal of Monetary Economics. ___________________, and Mariano, Roberto, "New Tests of the Life-Cycle and Tax Discounting Hypotheses," Journal of Monetary Economics. XV (1985), 195-215. 28 Footnotes ^To focus on the "present" and the "future" we take all future periods (of equal length) to be Identical so lifetime utility is given by U = u(c*) + ~L_ u(c*) + Up (Up) u(c*) + - - Q J ML*. p 2As in footnote 1 , all future periods are assumed identical so that the present value of consumption, etc., is given by PV(c) = c + 1 +r + 2 (Ur) r Also, in obtaining an intertemporal constraint as in (3), a solvency condition has been imposed such that as time nears infinity the present value of the agent's stock of debt approaches zero; this rules out the possibility of perpetual debt finance. 3The theoretical section deals only with changes in lump sum taxes. Changes in distortional tax rates, investment tax credits, and depreciation schedules generally will affect private investment (see, for example, Feldstein [1983]). Empirically, the rate of return variable employed below takes into account these effects so that given the net (of tax) rate of return to capital we may isolate the first order effects of changes in taxes. ^Similar arguments to those in footnote (2) apply here. 5Here, we define 3c*/aw = ru'(c*)u"(c*)/[u'(c* ) ] 2 ac*/aw = - ru'(c*)u"(c*)/[u'(c* ) ] 2 as the present and future marginal propensities to consume out of wealth, respectively. 29 Footnote (cont'd) 6A complete listing of the data used In this study Is available from the author on request. 7 Boskln, Robinson, and Roberts [1985] derive estimates of public fixed Investment by making use of an alternative depreciation methodology based on used asset price data. However, this series Is Inclusive only of federal expenditures on capital goods. 8For details, see Fixed Reproducible Tangible Wealth of the United States, 1925-79. 9 Feldste1n [1983] also employs the lagged rate of return In his study of private Investment and notes that this "lag In response has been found In all previous Investment studies . . . " and that It reflects possible delays In the making of capital acquisition plans and delays 1 n the production of capital goods.
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