Crowding out: A test of some direct substitutability hypotheses

STEPHEN M. MlLlER University

Crowding Out: A Tit Direct Substitutabiky Hypotheses*

of

Connecticut

of Some

The crowding-out effect has received considerable attention in recent years. Models of crowding out can be categorized into ex-ante and ex-post theories. Within the category of ex-ante theories are those models that rely upon direct substitution effects [e.g., Bailey (1972), David and Scadding (1974)j. This paper presents a theoretical model that includes different theories of direct substitution effects as special cases. Once parameter restrictions are associated with the various forms of direct substitutability, the paper performs tests of the alternative hypotheses.

1. Introduction In recent years, the efficacy of fiscal policy has been seriously questioned. The crowding-out controversy raises the question of whether or not increased government demand displaces private demand. Simulation results on econometric models of the U.S. economy lend some support to the crowding-out hypothesis.’ In general, the results indicate that fiscal stimulus does give rise to positive impact multipliers measured in nominal terms. In real terms, however, crowding out does occur but with a rather long lag. The exception to these results is provided by the Federal Reserve Bank of St. Louis model that produces crowding out both in real and in nominal terms. Moreover, the crowding-out effect is nearly complete within four quarters as compared to several years for the other models. Alternative theoretical explanations of the crowding-out phenomena have been given in the literature.’ These models can be *During the development of this paper, the comments of W.F. Lott, W.A. McEachern, A.A. Romeo, I. Wexler, and an anonymous referee were extremely helpful. My thanks also are extended to my research assistant F.X. Hackett. The University of Connecticut Computer Center provided the necessary computer time. ‘Fromm and Klein (1973) present a comparison of eleven econometric models of the United States. ‘A review of some alternative models that exhibit crowding out is given by Carlson and Spencer (1975). More recently, Buiter (1977) developed a full-employment model to examine the effect of “direct” crowding out on fiscal policy. journd Copyright

of Macroeconomics, 0 1983 by Wayne

Fall 1982, Vol. State University

4, No. 4, pp. Press.

419-432

419

Stephen M. Miller categorized into ex-ante and ex-post theories. If changes in fiscal policy first cause adjustments in other system variables that then affect private demand, then the theory is ex post. For ex-ante theories, changes in fiscal policy cause behavioral adjustments that crowd out private demand before other system variables are affected. An example of ex-post crowding out is the financial-market feedback effect on aggregate demand. An example of ex-ante crowding out is the possibility of direct substitution effects between personal and corporate saving. This paper addresses the latter possibility of direct substitution effects. Direct substitution effects were discussed by Bailey (1962, 1971, 1972). His concept of “perfect foreknowledge” [(1972), p. 6511 implies that the household sector determines its saving decision in conjunction with the corporate and government sectors’ savings plans. Perfect, direct substitutability requires that the household sector offset any change in the corporate or government sectors’ decision on a one-to-one basis. Consequently, the saving decision is at the national rather than the household level. Bailey [(1962), p. 72; (1971), p. 1551 a 1so considered the effect of assuming that households view government consumption expenditure as perfectly substitutable for household consumption expenditure. Hence, the consumption function would be aggregated to include both household and government consumption expenditure. David and Scadding (1974) introduced the concept of “ultrarationality” as an alternative to perfect foreknowledge. Their modification was based on the observation that the private saving rate is more stable than either the personal or national saving rates. Ultrarationality views the household sector’s saving decision as responding only to the corporate sector’s saving plan. The household sector offsets the corporate sector’s decision on a one-to-one basis. The appropriate level of aggregation under this specification is at the private level. Two additional implications of ultrarationality are that tax-financed government expenditure and consumption expenditure trade off one to one and that bond-financed government expenditure substitutes on a one-to-one basis with investment expenditure. The former result is consistent with Bailey’s assumption of direct substitutability between household and government consumption if one assumes that tax-financed government expenditure is equivalent to government consumption expenditure [see David and Scadding (1974), p. 2411. The objective of this paper is to specify a model that allows for any degree of substitutability between household decisions and 420

Crowding

Out

the decisions of the corporate and government sectors. Perfect foreknowledge, ultrarationality, and other specifications emerge as special cases of the more general model. In Section 2, we construct this general model of household choice. This leads to the derivation of reduced-form equations that are employed to test alternative hypotheses. Section 3 presents the empirical results. Conclusions are contained in Section 4. 2. A Model of Household Choice We specify a household utility function that permits different degrees of substitutability between household decisions and corporate and/or government decisions. The utility function is U = U [C, SW); s(B), S(G), W)l,

(1)

where C and S(H) are household consumption and saving respectively, S(B) is business (corporate) saving, S(G) is government saving, and G(C) is government consumption expenditure.3 In the neo-Keynesian framework, the household decision is independent of corporate and government decisions. Thus, all first- and higherorder partial derivatives of U involving S(B), S(G), and G(C) are zero. Under direct substitutability, these variables influence the household consumption-saving decision. There remains, however, the question of whether these variables are exogenous or endogenous to the household decision process. It can be argued that stockholders determine corporate decisions (i.e., corporate saving) and that voters determine government decisions (i.e., government saving and government consumption expenditure). We postulate the other extreme; the household sector does not control, but only responds to, the decisions of the corporate and government sectors.4 3We are abstracting from the well-known problems of constructing an aggregate preference ordering. One might prefer to use an inter-temporal maximization with current and next-period consumption as arguments of the utility function. This intertemporaf problem, however, reduces to the one in the text if the market interest rate and the next-periods (anticipated) income are constant. Additionally, the formulation in the text is in the spirit of the substitutability arguments. For example, Bailey (1972) states: “If prior to such a change the household had found its optimal suoing plan and its optimal portfolio, its best reaction to a change in borrowing by business or government would be precisely to offset the impact of that change on its own portfolio” (p. 651). [Emphasis added.] The household sector is viewed as adjusting its own saving in response to changes in business and government saving. ‘This assumption appears to capture the reaction process described by Bailey and cited in the previous footnote. 421

Stephen M. Miller The household sector maximizes the utility function subject to its budget constraint. National-income accounting gives us the budget constraint. GNP=Y=C+S(H)+S(B)+T,

(2)

where GNP is gross national product and T is net taxes (i.e., tax receipts minus transfers). The household chooses C and S(H) so as to maximize utility. The Lagrangian function is L = U + h[Y - T - C - S(H) - S(B)]. The first-order

conditions

for a maximum

(3)

are5

U,-h=O,U,-h=O, and Y - T - C - S(H) - S(B) = 0.

(4)

Comparative-static results are developed by taking the total differentials of the first-order conditions. In matrix form, we have - UlldS(G)

- U,,dG(C)

- U,,&(G)

- U&G(C)

. I (5)

Under neo-Keynesian assumptions, S(B), S(G), and G(C) are not substitutable for S(H) and/or C. This yields the following set of restrictions:

u13= u, = uu = u,, =

u,,

= u, = 0 .

(6)

On the other hand, perfect substitutability between S(H) and S(B) or S(G) and between C and G(C) implies that the respective mar“The 422

U, are the

partial

derivatives

of U with

respect

to the

ith

argument.

Crowding

ginal rates of substitution MR&

= U&J,

Out

(MRS) equal one. Thus, we have

= MRS,

= U&J,

= MRS,, = U,/U, = 1 .

Partially differentiating these MRS conditions S(H) yields the following restrictions:

(7)

with respect to C and

u12= u,,,u?., = G.3, u,,= u,,, U, = U,, U,, = U,,, and U,, = U,, .

(8)

The information contained in (6) and (8) can be employed to obtain comparative-static results under the alternative assumptions of no substitutability and perfect substitutability. For example, suppose we assume perfect substitutability between S(H) and S(B). This results in the following restrictions: U,, = U13 and U,, = U, . Given these restrictions, dC/dS(B)

it can be demonstrated = 0; x3(H)/dS(B)

from (5) that

= -1 .

00)

From the first-order conditions for a maximum, one derives the demand equations for household consumption and saving as functions of the exogenous variables S(B), S(G), G(C), Y and T. Since Y and T have the same effect in absolute value on C and S(H), the reduced-form regression equations are as follows: C = a, + a,S(B) + a,S(G) + a,G(C) + a, (Y - T) + e, and S(H) = b, + b,S(B) + b,S(G) + b,G(C)

+ b, (Y - T) + e, ,

(11)

where u’s and b’s are parameters to be estimated and e, and e, are random errors. David and Scadding (1974) attempted to rationalize their view of substitutability with Bailey’s concept by assuming that “. . . the private sector regards tax-financed government expenditures as belonging to the category of consumption, and bond-financed public 423

Stephen M. Miller outlays as investment . . . ” (p. 241). Under this specification, T is used as a proxy for G(C). Therefore, the other set of regression equations is as follows:

C = a1 + a2 S(B) + a3 S(G) + cx4T + a5 Y + E,

and

S(H)= PI + PzS(B)+ PaS(G)+ P4 T + P5 Y + E,,

(12)

where a’s and /3’s are parameters to be estimated and E, and E, are random errors. We can derive from these general specifications restricted models based on either no-substitutability or perfect-substitutability assumptions between S(H) and S(B), S(H) and S(G), or C and G(C) (or T). Using (5), th ese various substitutability assumptions lead to the parameter restrictions contained in Table 1.

3. Estimates of the Model In this section, we present regression estimates of Equations (11) and (12) using annual data for 1948-78. The data are as follows? C E personal consumption expeqditure in millions of dollars; CD = personal consumption expenditure on durables in millions of dollars; S(H) = personal saving in millions of dollars; S(B) = gross private savings minus personal savings in millions of dollars; G = federal, state and local government purchases of goods and services in millions of dollars; G(C) = federal, state and local purchases of goods and services minus federal, state and local purchases of structures and durables in millions of dollars; 6Data for the years 1948-72 were obtained from a recent revision in national income accounts in the Suruey of Current Business (1976). The years 1973-78 have been subsequently revised and were obtained in the Suruey of Current Business (1976, 1979). Additional variables used in deflating the data were the personal-consumption-expenditure implicit price deflator and the population in thousands. The population figures were obtained from the Economic Report of the President (1980). 424

1.

Substitutability,

*Tests

Perfect

of these

are

reported

Equation

(12)

Equation

Equation

hypotheses

Substitutability,

No Substitutability,

Perfect

Equation

(11)

Restrictions

Equations

Parameter

No Substitutability,

TABLE

in Tables

(12)

(11)

5.

a2 + a5 = 0 Pz + P5 = 0

a2 + a5 = 0 b, + b, = 0

S(H) and S(B)

Substitutability

2, 3, 4, and

under Different S(H) and S(G)

Assumptions” 0

a4 + a5 = 0 P4 + P5 = 0

a: < 0 b, > 0

?I0

C and G(C)

Stephen M. Miller T = federal,

state and local receipts minus the difference between federal, state and local government expenditures and purchases of goods and services in millions of dollars; Y = gross national product in millions of dollars;

S(G) = T -

G.

In estimating Equations (11) and (12), we have employed the information contained in the budget constraint. That is, we estimated the models imposing the theoretically implied cross-equation constraints on the parameters. These restrictions are as follows: a,+b,=O,a,+b,=-l,a,+b,=O,a,+b,=O,a,+bs

=I; 03)

(14) for Equations (11) and (12), respectively. Two additional points require discussion before we examine the econometric results. First, David and Scadding (1974) demonstrated gross-private-saving-rate (GPSA) stability through the absence of a long-run trend as well as small year-to-year variability. We examine both of these results by employing both a measuredincome and a permanent-income formulation of the consumption and saving functions. The measured-income formulations are given in Equations (11) and (12). Th e p ermanent-income formulations are developed by assuming that permanent consumption (saving) depends upon permanent values of the independent variables. Moreover, all permanent values are weighted averages of past values where the weights decline at a constant percentage rate and are identical across variables. This Koyck transformation of permanent variables leads to the following set of estimating equations: C = (1 - e) [a, + a,!!@) t u,S(G) t u,G(C)

t u,(Y - T)]

t HZ-, t n, ;

S(H) = (1 - 4) [b, + &S(B) + &S(G) t b,G(C) 426

t b&Y --T)]

Crowding + CS(H)-, + 12,.

Out 01’)

and C = (1 - A) [a, + a2S(B) + a.$(G)

+ a,T + a,Y] + XC-, + qc ;

S(H)= (1 - A)[PI + P,S@)+ Pas(G)+ P4T+ &D’l + AS(H)-, + qs .

(12’)

The tests presented in Table 1 as well as the constraints contained in Equations (13) and (14) are also applicable to Equations (11’) and (12’).

Second, the specification of the consumption variable to include durable expenditure might be questioned. That is, cannot durable expenditure be treated as saving rather than consumption? As a response to such a question, we reran Equations (ll), (ll’), (12), and (12’) with consumption defined as consumption expenditure excluding durables plus an adjustment for the imputed services received by the household sector from holding the stock of consumer durables (C - CD + SCD), saving defined as [S(H) + CD], and income defined as (Y + SCD).’ Th e results of all the regression analysis are reported in Tables 2, 3, 4, and 5.’ Examining the results for direct substitutability between S(H) and S(B), we ,find strong support for at least partial substitutability. For consumption and saving Equations I and II, the tests for no substitutability (i.e., a2 + a5 = 0 or c+ + a5 = 0) are rejected at the one-percent level in every case. Moreover, in two of the four ‘The SCD data were obtained from the Federal Reserve Boards Quarterly Econometric Model. A simple average was employed to convert the quarterly observations into an annual series. SCD includes the depreciation on, and the imputed income from, consumer durables. The use of this data restricted the regression results to a 1959 through 1978 sample period. The Federal Reserve Boards model adjusts income to include SCD. A similar procedure is followed in this paper (i.e., the income measure becomes Y + SCD). Consequently, saving is not symmetrically adjusted by SCD. ‘The regression results were derived using the Time Series Processor Version 2.8B (October 1977). Results reported in this paper are all derived from the seeming-unrelated-regression technique with the cross-equation parameter constraints imposed. We also employ ordinary least squares and obtained similar results. In an attempt to control for potential simultaneous-equation bias, the two-stage leastsquares technique was also utilized, but the results obtained were not significantly different from the ordinary least squares. 427

is co

S(H) + CD

III.

Estimates:

(-1.09)

-0.0002 (-0.92) 0.0002 (0.92)

(-1.68)

0.0005** (2.12) -0.0005** (-2.12) 0.0004*** Cl.@3 -0.0004***

0.2688* (4.10) -0.2688* (-4.10) 0.0443 (0.W -0.0433 (-0.56) 0.0262 (0.32) -0.0262 (-0.32)

(-1.06)

0.0813 (1.W -0.0813

b3

bl

0.0005 0.w -0.0005

a3

Equations

a1

-0.3339*** (-1.92) -0.6661* (-3.82) -0.1460 (-0.79) -0.8540* (-4.64) -0.5682* (-2.71) -0.4318** (-2.06) -0.8559* (-3.84) -0.1441 (-0.65)

and Saving Function

0.0206 (0.18) -0.0206 (-0.18) 0.3159** (2.51) -0.3159** (-2.51) 0.3586** (2.41) -0.3586** (-2.41) 0.2139 (1.20) -0.2139 (-1.20)

b4

a4

(11) and (11’)’

0.8258* (17.12) 0.1742* (3.61) 0.7225* (13.98) 0.2775* (5.37) 0.6940* (14.25) 0.3060* (6.28) 0.8088* (15.85) 0.1912* (6.07)

b5

a5

0.0248 (0.79) 0.0248 (0.79)

-0.0062 (-0.18) -0.0062 (-0.18)

e

e

‘All regressions were obtained using the Time Series Processor Version 2.8B (October 1977). The seemingly unrelated regression routine was used to estimate the consumption and saving equations simultaneously with the cross-equation constraints imposed. Regressions were run adjusting and not adjusting for autocorrelation. A likelihood-ratio test was employed to test for the presence of autocorrelation. All the equations reported have been adjusted for autocorrelation. The numbers in parentheses are Z scores. All tests are two tailed except for us and bs which are one tailed. *Means the coefficient is significantly different from zero at the one-percent level; **at the five-percent level; and ***at the tenpercent level.

IV. S(H) + CD

IV. c - CD + SCD

c - CD + SCD

Eq.

Consumption

III.

II. S(H)

II. c

I. S(H)

I. c

Consumption Saving Eq.

TABLE 2.

S(H) + CD

III.

‘See Table 2.

IV. S(H) + CD

IV. c - CD + SCD

c - CD + SCD

E9.

Consumption

III.

II. S(H)

II. c

I. S(H)

I. c

Consumption Saving Eq.

TABLE 3.

(-4.60)

-0.8324* (-3.71) -0.1676 (-0.75)

(-0.71)

-0.0003 (-1.21) 0.0003 (1.21)

(1.19)

(-3.88)

-0.1551

(-1.19)

0.0002

-0.5052* (-2.72) -0.4948* (-2.66) -0.8449*

-0.0003 (-1.57) 0.0003 (1.57) -0.0002

-0.0003***

(1.74)

(-1.74)

a2 Pz

Estimates:

-0.1655 (-0.91) -0.8345*

Function

0.0003***

ffl Pr

and Saving

I34

(0.73)

(-4.21)

(-3.99)

-0.3700** (-2.26)

(1.01)

(-3.85)

(-1.01)

0.1218

-0.6300*

(-2.38)

-0.3739**

(4.18)

0.1933*

(17.45)

0.8067*

(4.16)

0.1900*

(17.74)

0.0734** (1.W O.BlOO*

(23.75)

(-10.06)

0.0843 (0.78) -0.6261*

0.9276*

(5.79)

0.2509*

(17.29)

0.7491*

P5

a5

- 1.0843*

(-3.49)

-0.4500*

-0.1218

0.w

0.1603

(-1.38)

0.3688* (4.41) -0.3688* (-4.41) -0.1603

(-0.73)

-0.0667

-0.5500*

P3

0.0667

(Yq

(12) and (12’)”

a3

Equations

(1.26)

0.0409

(1.26)

0.0409

0.0968** (2.40)

(2.40)

0.0968**

A A

Stephen M. Miller

TABLE 4.

Additional

Parameter

Tests: Equations

(11) and (11’)” (a3 - 4

=

lb, - b, + 1) I. C and S(H)

0.4920”

II. C and S(H)

(3.41) 0.5765" (3.85)

III.

c and IV. c and

CD S(H) CD S(H)

+ + + +

SCD CD SCD CD

-0.7445* (-7.45) -0.4536* (-4.73) -0.6507* (-6.19) -0.7826* (-7.08)

0.1259 (0.70)

-0.0471 (-0.25)

‘See Table 2. bSince the cross-equation parameter expressed in terms of a’s are identical

restrictions have been with the tests expressed

imposed, in terms

the tests of b’s

consumption functions, the coefficient of S(B) is not significantly different from zero at the ten-percent level. These latter results are consistent with perfect substitutability between S(H) and S(B). The results for direct substitutability between [S(H) + CD] and S(B) are reversed from the discussion in the previous paragraph. That is, we find strong support for no substitutability. The tests for no substitutability cannot be rejected at the ten-percent level in every case. Moreover, in three of the four saving functions,

TABLE 5.

Additional

I. C and S(H) II. C and S(H) III.

c - CD + SCD and S(H) + CD

IV. c - CD + SCD

and S(H) + CD

Parameter

0.5836* (3.86) 0.4224* (2.71)

-0.0349 (-0.11) -0.0257 (-0.13)

‘See Table 2. bSince the cross-equation parameter expressed in terms of Q’S are identical 430

Tests: Equations

restrictions with tests

-0.6824* (-8.77) -0.5588* (-7.10) -0.9703* (-9.14) -0.9285* (-8.54)

(12) and (12')"

0.1991** (2.15)

-0.1567** (-2.03) 0.1839 (1.46) 0.1767 (1.36)

have been imposed, expressed in terms of

the $s.

tests

Crowding

Out

the coefficient of S(B) is not significantly different from zero at the ten-percent level. Examining the results for direct substitutability between S(H) [or S(H) + CD] and S(G), we find little support for any substitutability. In only two cases is the coefficient of S(G) in the saving equation significantly negative at even the ten-percent level. Moreover, we reject, in all cases, the hypothesis that (b, - b, + 1) or (& - p5 + 1) is zero at the one-percent level. Examining the results for direct substitutability between C [or C - CD + SCD] and G(C), we can find no support. In two of the four cases examined, the coefficient of G(C) was significantly different from zero at the five-percent level in the consumption and saving functions. The coefficients, however, had the wrong sign. An increase in G(C) caused an increase in C. Examining the results for direct substitutability between C [or C - CD + SCD] and T [i.e., David and Scadding’s (1974) hypothesis], we find little, but some, support for direct substitutability. In three of the four cases examined, the coefficient of T is less in absolute value than the coefficient of Y although only significantly less at the five-percent level in one case. The fourth case, C and S(H) re g ressions on permanent income, does have the coefficient of T significantly greater in absolute value than the coefficient of Y at the five-percent level. Moreover, the coefficient of T is not significantly different from minus one at the ten-percent level. This latter result is consistent with perfect substitutability between C and T.

4. Conclusion Direct-substitutability hypotheses bear directly on the efficacy of fiscal policy. This paper has attempted to formulate tests of various direct-substitutability hypotheses. Our results fall into two distinct categories. First, when consumption is defined to be total consumption expenditure, we find strong support for substitutability between the household saving decision and the corporate saving decision. We do not find much evidence of direct substitutability between household decisions and government decisions. Thus, the results seem closest in spirit to the ultrarationality model than to the perfect-foreknowledge or the no-substitutability models. Second, when consumption is defined to be consumption of nondurables and services plus an imputed service flow from the stock of consumer durables, we find strong support for no substi431

Stephen M. Miller

tutability. We do not find any evidence of substitutability between household saving and business or government saving. Moreover, the no-substitutability hypothesis for consumption and government consumption expenditure or taxes cannot be rejected except in one case. Here, the results seem closest in spirit to the no-substitutability model than to the ultrarationality or the perfect-foreknowledge models. Received: Nouember, 1980 Final version received: june,

1982

References Bailey, Martin J. National Income and the Price Level. New York: McGraw-Hill, 1962. -. National Income and the Price Level. 2nd ed. New York: McGraw-Hill, 1971. -. “The Optimal Full Employment Surplus. ” Journal of Political Economy 80 (July/August 1972): 649-61. Buiter, Willem H. “‘Crowding Out’ and the Effectiveness of Fiscal Policy. ” Journal of Public Economics 7 (1977): 309-28. Carlson, Keith M. and Roger W. Spencer. “Crowding Out and Its Critics. ” Federal Reserve Bank of St. Louis Review 57 (December 1975): 2-17. Council of Economic Advisers. Economic Report of the President. Washington: U.S. Government Printing Office, 1980. David, Paul A. and John L. Scadding. “Private Savings: Ultrarationality, Aggregation and ‘Dennison’s Law’. ” Journal of Political Economy 82 (March/April 1974): 225-49. Fromm, Gary and Lawrence R. Klein. “A Comparison of Eleven Econometric Models of the United States. ” American Economic Review 63 (May 1973): 385-93. U.S. Department of Commerce. Bureau of Economic Analysis. Survey of Current Business. 56 (January 1976): Parts I and II, 56 (July 1976) and 59 (July 1979).

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