1. Taxation

A useful first case to consider is lump-sum taxation, with all other aspects of government policy unchanged. In particular, the anticipated (and actual) path of government expenditure will be taken as invariant to the change in tax policy, permitting a focus on the pure income effects. The case is also a useful vehicle for presenting the range of alternative theoretical frameworks.

The framework suggested by Barro․associated with the concept of Ricardian equivalence․provides one important benchmark against which to evaluate the impact of lump-sum taxes (Barro, 1974). In addition to the assumption of rational expectations and the existence of well-developed capital markets, intergenerational altruism is assumed in the sense that the current generation is concerned about the welfare of future generations. ^2/ When some additional (though nontrivial) technical assumptions are made, an increase in lump-sum taxation will not influence consumption and savings plans. Alternatively, individuals will be indifferent between tax and debt finance since, for a given path of government expenditures, the timing of the flow of tax payments is irrelevant.

To the extent that (lump-sum) taxes are increased and the Government therefore reduces its borrowing, individuals would appreciate that this shift will imply a reduced level of taxation on a future generation and they would offset the implied intergenerational redistribution by altering planned bequests. The increase in government saving resulting from the increase in lump-sum taxation would be offset by a decline in private saving leaving national saving unchanged.

Critics of this theory have focussed on the assumptions needed for effective intergenerational altruism. For example, Buiter and Tobin (1979) note that some households are childless and others selfish, while others might be planning zero bequests, which could not then easily be reduced in response to a decline in public debt.

A related issue has been that large intergenerational transfers․the magnitude of which has been a subject of dispute ^3/․do not imply that intergenerational altruism is the motivating force, as they could be the unintended consequences of risk aversion in the context of uncertainty about length of life and incomplete annuities markets. ^4/ Alternatively, such transfers might reflect implicit contracts within families. ^5/

An additional criticism has focussed on the treatment of family behavior in Barro’s model. For example, Pollak (1988) notes that intergenerational transfers are frequently tied․that is, that the transfer is conditional on how it is used. Such behavior is only explicable if parents evaluate children’s behavior according to their own preferences, which may conflict with those of their children. In such circumstances, effective intergenerational linking of preferences․needed for the Ricardian equivalence result․breaks down.

Further, Bernheim and Bagwell (1988) develop a model with greater realism in the biological structure of families, resulting in a proliferation of linkages between related families. In such a model, not only does Ricardian equivalence hold, but also government transfers have no real effects and distortionary taxation and changes in relative prices play no role in resource allocation. The authors conclude that such extreme and implausible results indicate that the underlying assumptions may not be appropriate, in turn calling into question the Ricardian equivalence result. Finally, the neutrality results depend on a number of technical assumptions, including the requirement that public and private discount rates be identical. In effect this means that private discount rates should not reflect an adjustment for anticipated mortality.

The life-cycle model provides another important alternative. ^6/ In the pure version of the life-cycle model, in which there is no bequest motive, the relevant budget constraint can be expressed in terms of the present value of the individual’s lifetime earnings. The impact of an increase in lump sum taxation depends on how that increase is interpreted. If that increase is expected to be reversed in present value terms within its lifetime, then the current generation will not alter consumption behavior and a result analogous to the Barro result would emerge. If, however, the increase in taxation is to be reversed in the lifespan of some future generation, then the current generation’s lifetime or permanent income has been reduced and consumption will be reduced accordingly. Given the consumption-smoothing associated with the life-cycle model, the decline in consumption will only be some proportion of the increase in lump-sum taxation. The smaller this proportion, the smaller the increase in national saving. The crucial feature driving this result is the absence of bequests which implies that changes in lump-sum taxes can effect transfers across generations.

Keynesian models which incorporate liquidity constraints provide a further framework for analyzing the effects of tax/transfer policies. These models are exemplified by a recent paper by Hubbard and Judd (1986) in which the constraint is imposed that the net worth of individuals must always be non-negative․that is, that consumers be prohibited from borrowing against future income. This restriction is intended to capture the fact that capital, markets are not as complete as is implicitly assumed in both the life-cycle and the intergenerational frameworks. Instead, this model implies “liquidity constraints” since the non-negativity restriction requires consumption to be limited to current resources. Those consumers who cannot finance their desired level of consumption with current wealth will find their consumption levels responding even to anticipated changes in disposable income. In particular, consumers in such a situation would be forced to reduce their consumption in parallel with any increase in lump-sum taxation, implying a dollar-for-dollar increase in national saving, in contrast to the results derived in the life-cycle framework discussed above.

A range of models exist, therefore, where the implications of changes in lump-sum taxation for consumption behavior run the gamut from no change (in the Barro framework) to a potentially fully offsetting change (in the liquidity-constrained framework). Which framework is the most appropriate representation of consumer behavior is essentially an empirical question. ^7/

2. Transfer payments

The analysis of changes in transfers in many respects is similar to that of changes in taxation. When analyzing the case of changes in (lump-sum) taxation, a given path of expenditures was assumed․as a result, changes in (lump sum) taxation could be associated with changes in government debt of an equal but opposite magnitude. Changes in transfers, however, can be financed by changes in taxation or bond finance. It is assumed here that changes in transfer payments would be associated with offsetting changes in borrowing and, therefore, in future tax liabilities. ^8/ Thus, much of the analysis that was used in evaluating the impact of (lump-sum) taxation also applies to the case of transfers.

Some transfer programs are established with the explicit intent of effecting income transfers within generations. In contrast, the analysis of (lump-sum) taxation above abstracted from the possibility of intragenerational income transfers by implicitly assuming identical individuals. When it is recognized that some transfer programs are tilted toward the lower income segments of society, then the income-constrained framework discussed above might well be relevant․the marginal propensity to consume out of transfer income could be high, even approaching unity. As a result, reductions in expenditures of this type might be expected, everything else being equal, to have a relatively significant depressing impact on consumption.

Other transfer programs are notable for their intertemporal implications. For example, in the case of social security, a reduction in benefits in the form of an “adverse” change in the rules determining social security payments could affect the savings behavior of all individuals through the impact of that change on expectations, since, in a life-cycle framework, such a reduction would create an incentive for the current working generation to increase its savings. Therefore, in such circumstances, a change in transfer payments could be expected to have an appreciable positive impact on private savings. ^9/ In particular, the tendency for a reduction in social security benefits to induce an increase in national saving might well be greater than the corresponding tendency of an increase in taxation to do so, everything else being held equal. ^10/

As with taxation, transfer payments are generally the source of distortions. This is most obviously the case with price subsidies and price supports where the explicit intent is to interfere with market behavior. However, these distortions, while they may have a significant impact in the markets for the commodities involved, are unlikely qualitatively to alter conclusions concerning the impact of changes in the relevant transfer programs on aggregate consumption and saving.

The last two subsections have considered the case of tax/transfer changes with a view both to evaluating a range of alternative frameworks for analyzing the impact of fiscal changes and to assessing the potential impact of that type of fiscal change on national saving. Some tentative observations can be made at this stage. First the assumptions needed in order for the Barro framework to be valid are stringent and, at least in some respects, seem implausible. Second, the choice of which model is most appropriate may well depend on the circumstances. For example, the income constrained framework may be most relevant when analyzing the impact of changes in income maintenance programs whereas the life-cycle model might be most appropriate when evaluating changes in social security.

3. Expenditure on goods and services

To analyze the impact of changes in expenditures on goods and services, it is assumed that any reduction in government expenditures on goods and services is associated with a corresponding decrease in borrowing. Thus, the impact of such a decrease in borrowing on consumption and saving will be a function of how the path of future tax payments is anticipated to change. This aspect of the analysis parallels that presented immediately above in the case of changes in lump-sum taxation.

However, changes in government expenditures influence economic activity through a number of additional channels. First, in providing goods and services, the Government lays claim to a proportion of the productive resources of the economy. One could assume that these resources would otherwise have been unemployed. However, given the relatively high level of resource utilization currently in the United States, it is instead assumed that the resources used in the process of producing the goods and services supplied by the government would have been otherwise productively employed. ^11/

The issue is how changes in the supply of these goods and services affect the balance between consumption and saving. The impact will depend on the degree of substitutability or complementarity between those expenditures and aggregate private expenditures. The determining factors include both the nature of individual preferences and the technology for organizing the distribution of goods production. The latter is important since the ease with which private producers can substitute their production of a given good for government provision of that good will often depend primarily on the way the market is organized.

While it is easy to visualize a range of aggregate substitutability/complementarity possibilities, it would be difficult to assign a given good definitively to a point within that range and thus it would not be possible to determine a priori the impact of a reduction in government expenditures on private consumption expenditures. On this last point, consider the polar case which occurs when the relevant government expenditures are perfect substitutes for private expenditures. That case parallels the lump sum taxation case considered earlier. The crucial feature is the reduction in borrowing consequent upon a reduction in government expenditures; how that reduction influences consumer behavior depends both on how individuals perceive the time path of future tax payments to be altered and on the type of budget constraint which is relevant.

In the Barro world discussed earlier, the reduction in government spending will be associated with an equal reduction (in present value terms) in taxation at some point in the future and individuals will therefore react by substituting privately provided goods precisely to offset the reduced public provision. By so doing, they will reduce bequests by an amount equal in present value terms to the increase in income the future generation will experience as a result of reduced taxation. National saving would be unaffected. In contrast, in the pure life-cycle model, to the extent that the associated tax reduction will benefit a future generation, the current generation will experience a correspondingly smaller increase in life-cycle income and will adjust consumption accordingly. National saving will increase by some proportion of the increase in government saving.

Alternatively, consider what would happen if the expenditure reductions involved goods which are complementary to private consumption. Then, as well as the effects outlined in the perfect substitutes case, there will be an additional positive impact on private saving, the precise magnitude of which it would be difficult to quantify.

In sum, it would be difficult on a priori grounds to determine the differential impact of tax increases and expenditure reductions on national saving. The outcome depends on the interaction of a number of factors, including the nature of the relevant budget constraints, the distributional impact of the measures under consideration, the effect of changes in fiscal policies on expectations, and the degree of substitutability/complementarity with private consumption. Subsequent sections will consider the empirical evidence.

1. General review

Empirical studies relating to Ricardian equivalence have focussed on several features of household behavior. First, if households face binding liquidity constraints preventing them from smoothing income over the life cycle, then intergenerational smoothing seems implausible. While the debate continues, the broad conclusion from this research appears to be that a significant proportion of consumers is in fact income constrained. For example, Hall and Mishkin (1982) found that roughly 20 percent of consumers appeared to be income-constrained and Hayashi (1982) developed similar results. In a related vein, Flavin (1981) found strong sensitivity of consumption to current income, beyond that predicted by her version of the life cycle model, indicating the existence of binding liquidity constraints. Mariger (1986) estimated structural consumption functions on cross-section data from Federal Reserve surveys, and found substantial evidence for the existence of liquidity constraints.

A second area of research examines the implications of the social security system for household saving and capital formation. Ricardian equivalence predicts that the existence of an unfunded social security system would have no implications for capital formation, because private intergenerational transfers would offset the intergenerational transfers resulting from the social security system.

Most of the articles in the empirical literature on this issue tested the significance of social security by adding a “social security wealth” variable to a conventional consumption function. In a series of articles, Feldstein (1974, 1977, 1982a) argued that empirical results using this approach supported the view that social security reduced household saving and capital formation․even after discovery of a major computational error in his early results (Leimer and Lesnoy, 1982). Barro (1978), among others, argued the opposite. Evans (1983b) suggested that the significance of social security could be tested more simply by examining whether the marginal propensity to consume was higher for transfer income․including social security payments․than other forms of disposable income; he found tentative evidence that social security did depress household saving and capital formation, arguing against Ricardian equivalence. Auerbach and Kotlikoff (1983), using an overlapping generations life cycle model with assumed parameters, constructed pseudo time series data, for which it was known in advance․by construction․that social security depressed household saving. When conventional time series regression tests were run on the pseudo-data, however, the hypothesis that social security depressed saving was sometimes accepted and sometimes rejected depending in particular on the precise specification and the length of the sample. On this basis, they concluded that time series tests of the significance of social security were inherently biased against finding a significant effect of social security on saving. Mariger (1986) on the basis of econometric analysis of cross-section data․an analysis largely free of the problems, outlined above, that have plagued empirical analyses on time series data in this area․found evidence for a significant and substantial depressing effect of the social security system on saving and capital formation.

A fourth element of the empirical literature relating to Ricardian equivalence focuses on testing the impact of the age distribution of income and wealth on consumption. Under Ricardian equivalence, consumption by particular members of an extended family or dynasty depends on the resources of other family members, which implies that consumption should be invariant to shifts in the age distribution of income and wealth. After conducting careful tests, Boskin and Kotlikoff (1985) found that in fact the age distribution made a significant contribution to the explanation of consumption.

Another relevant area of research relates to the significance of intergenerational transfers for capital accumulation. If these transfers are relatively small, it would seem unlikely that the bulk of households are acting in the way proposed by Barro. The empirical evidence on the significance of bequests is unclear. Kotlikoff and Summers (1981) initially argued that bequests accounted for roughly 80 percent of capital accumulation in the United States, but Modigliani (1984 and 1988) after finding an error in their computations, suggested that the fraction was much lower. If the latter were correct, this would be further indirect evidence against Ricardian equivalence. Moreover, even if intergenerational transfers were established as accounting for the bulk of U.S. capital formation, several plausible behavioral formulations exist․as noted earlier․which would be consistent with this outcome and yet would not entail Ricardian equivalence.

The most substantial strand of empirical work dealing with Ricardian equivalence has related a measure of private consumption to government spending, taxation, transfer and government debt variables, as well as income and wealth. The basic equation is typically a variation on that outlined below:

where

C	=	private consumption 12/
Y	=	a measure of income (typically national income or net national product)
W	=	household wealth, excluding government debt
G	=	government purchases of goods and services
T	=	tax revenue
TR	=	government transfers to persons
D	=	government debt,

View Table

C	=	private consumption 12/
Y	=	a measure of income (typically national income or net national product)
W	=	household wealth, excluding government debt
G	=	government purchases of goods and services
T	=	tax revenue
TR	=	government transfers to persons
D	=	government debt,

and all variables are measured in real terms. ^13/

Under Ricardian equivalence, changes in taxation do not affect consumption when government spending is constant (a₄ = 0); changes in transfer payments do not influence consumer spending, for a given level of income (a₅ = 0); and the private sector does not view government debt as net wealth (a₆ = 0). The appropriate sign and magnitude of the coefficient on government spending on goods and services is ambiguous, depending on the degree of substitutability/complementarity of such spending with private consumption.

There have been many studies involving variations on this theme, the bulk of which conclude that deficits do affect consumer spending, and that Ricardian equivalence does not hold. ^14/ Interpretation of these studies is complicated by a variety of difficulties including simultaneous equations bias; spurious correlations induced by cyclical comovements between variables that are unrelated on a cyclically adjusted basis; flaws in methods used to deflate nominal variables; multicollinearity; difficulties in disentangling the contemporaneous effects of changes in fiscal variables from signalling effects that may be taking place with regard to their own future values; ^15/ and disagreements as to appropriate sample period․including in particular whether data covering war years should be included. ^16/

The more interesting․albeit less frequently addressed․issue concerns magnitudes. If the polar proposition of Ricardian equivalence does not hold, to what extent are changes in taxation offset by private behavioral responses? Bernheim (1987) addresses this issue, concluding that most studies indicate that reducing taxes with government spending held constant is likely to raise consumption by 40-50 percent of the magnitude of the tax cut. Boskin (1988) suggests a consensus of a net deficit for tax substitution effect on consumption of between 20 and 40 cents per dollar. Another paper directly discussing the magnitude of deviations from Ricardian equivalence is that of Darby, Gillingham and Greenlees discussed in detail in the next subsection.

2. The Darby, Gillingham, Greenlees paper

The work of Darby on the consumer expenditure function, which has been recently updated and extended by Darby, Gillingham, and Greenlees (DGG) in a U.S. Treasury research paper ^17/ is examined in some detail here, because it attempts a quantitative assessment of the extent of deviations from Ricardian equivalence. Although the DGG paper does not attempt to present an official view, it may nevertheless have been influential in policy discussions.

The specification adopted by DDG was as follows: ^18/

where all nominal quantities are deflated by the deflator for consumer spending.

The time series data for permanent income, with income defined alternatively in “traditional” and Ricardian terms, are calculated based on a procedure outlined in DGG. ^19/ This procedure (based on the so-called Holt-Winters forecasting model ^20/) calculated the logarithm of permanent income as a weighted average of the logarithms of actual income and permanent income the previous period, together with a growth rate term. The growth rate term in turn is defined as a weighted average of the growth rate in the previous period and the change in the logarithm of permanent income. The parameters in these two equations for the derivation of permanent income are generated so as to maximize the goodness of fit in the estimated equations for consumer expenditure. The parameter values which result imply very slow adjustment of perceived permanent income to changes in actual income. Thus the estimated equations are able to “explain”․in a statistical sense․the rapid growth of consumer spending (and the associated decline in the household savings rate) in the last few years as stemming from the “fact” that permanent income is judged to be substantially above actual income. ^21/ The idea that consumers may believe actual income to be substantially below permanent income has intuitive appeal for times of cyclical downturn, but it is not clear why this should be the case in the fourth year of an economic expansion, as was the case in 1986 in the United States. ^22/

Moreover, the behavior of consumers in this model when the Ricardian income measure is adopted is particularly puzzling. On the one hand, these consumers are highly rational and forward looking; they foresee and offset the increased future tax burden stemming from a higher government deficit in the present. On the other hand, these consumers are highly myopic in the sense that they initially perceive all shocks as temporary, and adjust their estimate of permanent income only very slowly to changes in actual data.

Other features of the specification include the use of the real money supply (M1) as an indicator of wealth instead of a broader measure; the use of a relative price term (durables versus the remainder), even while both durable and other consumer goods are included in the dependent variable; the inclusion of a nominal rather than a real interest rate, and the imposition of a lag structure on the government deficit variable which is distributed over four periods for both the annual and the quarterly equations․that is, for four years in the annual equation and for four quarters in the quarterly equations.

According to DGG, the interpretation of their results is relatively straightforward. ^23/ By their interpretation, the empirical results suggest that, under the traditional model, a dollar increase in taxation would lower consumer spending by 83 cents and household saving by 17 cents in the long run; thus national saving would rise by 83 cents. A dollar cut in government purchases would raise consumer spending and lower household saving by 15 cents in the long run; national saving would rise by 85 cents.

Under the Ricardian model, a dollar increase in taxes would reduce consumer spending by 24 cents and household saving by 76 cents in the long run; thus national saving would increase by only 24 cents. However, a dollar cut in government purchases would increase consumer spending by 67 cents in the long run and thus reduce household saving by 33 cents; national saving would increase by 67 cents.

The results under the Ricardian specification have been cited in support of the proposition that spending cuts are a more effective way to raise national saving than tax increases. However, the results under the traditional specification indicate that spending cuts and tax increases would essentially be equally effective in terms of raising national saving. Since DGG note that the data seem unable to discriminate between the two specifications, the more circumspect interpretation may be that․even abstracting from a number of reservations about the estimated equations discussed above․it is not clear whether cuts in government spending are or are not more effective instruments for raising long-run national saving than increases in taxation.

In order to pursue the line of research advocated by DGG somewhat further, additional empirical work was performed in a similar vein. Equations were estimated for consumer expenditure with income, wealth, and government deficit terms as explanatory variables. The results are presented in Table 1. The main changes from the original specification are the exclusion of the permanent income variable; the use of broader measures of household wealth․rather than the money supply․disaggregated between government debt and the remainder to permit a test of the significance of the former; and the exclusion of the interest rate and relative price terms.

Table 1.

United States: Equations for Consumer Spending ^1/

^1/All variables were deflated by the implicit deflator for consumer spending, and population, with lags as appropriate. The dependent variable was real per capita consumer spending. Notation as follows: YD - disposable income; Y1 = net national product, plus general government spending (excluding that on goods and services) less general government revenue; Y2 = net national product less general government spending on goods and services; W = household net worth; D = household holdings of government securities (federal, state and local); CE = household holdings of corporate equities; DEF = the general government deficit (that is, federal plus state and local). Data were annual from 1958 to 1987, with estimation by OLS, using version 1.11 of the AREMOS package supplied by Wharton Econometrics. The data were the most up-to-date U.S. national accounts and wealth data available, as of September 1988. A data appendix is available from the authors on request. Constants are not reported.

Table 1.

United States: Equations for Consumer Spending ^1/

Equation Number	YD	YD-1	Y1	Y1-1	Y2	Y2-1	Y1-YD	Y1-1-YD-1	Y2-YD	Y2-1-YD-1	${\mathrm{W}}_{\mathrm{-}{\mathrm{1}}_{\mathrm{-}{\mathrm{CE}}_{\mathrm{-}\mathrm{1}}}}\mathrm{-}{\mathrm{D}}_{\mathrm{-}\mathrm{1}}$	D-1	CE-1	DEF	DEF-1	DEF-2	R-2	SEE	DW
1.	0.76	0.04	․	․	․	․	․	․	․	․	0.021	0.180	0.001	-0.12	0.24	0.19	0.999	0.052	1.88
	(9.0)	(0.4)									(2.5)	(3.4)	(0.1)	(1.3)	(2.9)	(2.2)
2.	․	․	0.49	0.23	․	․	․	․	․	․	0.038	0.090	0.019	0.11	0.24	0.29	0.999	0.055	1.64
			(8.4)	(3.3)							(4.8)	(2.0)	(2.0)	(1.2)	(2.7)	(3.9)
3.	0.63	0.14	․	․	․	․	0.25	0.06	․	․	0.026	0.143	0.008	-0.03	0.23	0.25	0.999	0.048	1.99
	(6.7)	(1.4)					(1.5)	(0.4)			(3.3)	(3.4)	(0.8)	(0.3)	(3.0)	(3.0)
4.	․	․	․	․	0.49	0.23	․	․	․	․	0.038	0.090	0.019	0.60	0.46	0.29	0.999	0.055	1.64
					(8.4)	(3.3)					(4.8)	(2.0)	(2.0)	(5.8)	(3.6)	(3.9)
5.	0.63	0.14	․	․	․	․	․	․	0.25	0.06	0.026	0.143	0.008	0.22	0.29	0.25	0.999	0.048	1.99
	(6.7)	(1.4)							(1.5)	(0.4)	(3.3)	(3.4)	(0.8)	(1.1)	(1.5)	(3.0)

^1/All variables were deflated by the implicit deflator for consumer spending, and population, with lags as appropriate. The dependent variable was real per capita consumer spending. Notation as follows: YD - disposable income; Y1 = net national product, plus general government spending (excluding that on goods and services) less general government revenue; Y2 = net national product less general government spending on goods and services; W = household net worth; D = household holdings of government securities (federal, state and local); CE = household holdings of corporate equities; DEF = the general government deficit (that is, federal plus state and local). Data were annual from 1958 to 1987, with estimation by OLS, using version 1.11 of the AREMOS package supplied by Wharton Econometrics. The data were the most up-to-date U.S. national accounts and wealth data available, as of September 1988. A data appendix is available from the authors on request. Constants are not reported.

View Table

Table 1.

United States: Equations for Consumer Spending ^1/

Equation Number	YD	YD-1	Y1	Y1-1	Y2	Y2-1	Y1-YD	Y1-1-YD-1	Y2-YD	Y2-1-YD-1	${\mathrm{W}}_{\mathrm{-}{\mathrm{1}}_{\mathrm{-}{\mathrm{CE}}_{\mathrm{-}\mathrm{1}}}}\mathrm{-}{\mathrm{D}}_{\mathrm{-}\mathrm{1}}$	D-1	CE-1	DEF	DEF-1	DEF-2	R-2	SEE	DW
1.	0.76	0.04	․	․	․	․	․	․	․	․	0.021	0.180	0.001	-0.12	0.24	0.19	0.999	0.052	1.88
	(9.0)	(0.4)									(2.5)	(3.4)	(0.1)	(1.3)	(2.9)	(2.2)
2.	․	․	0.49	0.23	․	․	․	․	․	․	0.038	0.090	0.019	0.11	0.24	0.29	0.999	0.055	1.64
			(8.4)	(3.3)							(4.8)	(2.0)	(2.0)	(1.2)	(2.7)	(3.9)
3.	0.63	0.14	․	․	․	․	0.25	0.06	․	․	0.026	0.143	0.008	-0.03	0.23	0.25	0.999	0.048	1.99
	(6.7)	(1.4)					(1.5)	(0.4)			(3.3)	(3.4)	(0.8)	(0.3)	(3.0)	(3.0)
4.	․	․	․	․	0.49	0.23	․	․	․	․	0.038	0.090	0.019	0.60	0.46	0.29	0.999	0.055	1.64
					(8.4)	(3.3)					(4.8)	(2.0)	(2.0)	(5.8)	(3.6)	(3.9)
5.	0.63	0.14	․	․	․	․	․	․	0.25	0.06	0.026	0.143	0.008	0.22	0.29	0.25	0.999	0.048	1.99
	(6.7)	(1.4)							(1.5)	(0.4)	(3.3)	(3.4)	(0.8)	(1.1)	(1.5)	(3.0)

^1/All variables were deflated by the implicit deflator for consumer spending, and population, with lags as appropriate. The dependent variable was real per capita consumer spending. Notation as follows: YD - disposable income; Y1 = net national product, plus general government spending (excluding that on goods and services) less general government revenue; Y2 = net national product less general government spending on goods and services; W = household net worth; D = household holdings of government securities (federal, state and local); CE = household holdings of corporate equities; DEF = the general government deficit (that is, federal plus state and local). Data were annual from 1958 to 1987, with estimation by OLS, using version 1.11 of the AREMOS package supplied by Wharton Econometrics. The data were the most up-to-date U.S. national accounts and wealth data available, as of September 1988. A data appendix is available from the authors on request. Constants are not reported.

Equations (1) - (3) in Table 1 follow the traditional specification, differing only in the precise definition of the income terms. ^24/ According to equation (2)․and using the method of interpretation proposed by DGG (outlined in the footnote on the previous page)․an increase in personal taxation would reduce consumer spending by 136 percent of the increase in taxes so that household saving would be raised by 36 percent, and national saving by 136 percent of the tax change. By contrast, a cut in government spending on goods and services would redude consumer spending by 64 percent of the spending cut, augmenting national saving by 164 percent of the cut. Equation (3) also indicates more pronounced effects on national savings from cutting spending than from raising taxes, though the differences are quite small.

Equations (4) and (5) in Table 1 adopt a Ricardian specification with the income variable taken as net national product less government spending on goods and services. Reflecting the constraints of the specification, cuts in government spending are estimated to be roughly twice as effective as tax increases in augmenting national savings. Thus, as was the case with the DGG results, a traditional specification generated results consistent with that specification while a Ricardian specification generated results closer to the Ricardian end of the spectrum.

Another observation to be made on all the estimated equations presented in Table 1․including those with a Ricardian specification․is that in every case, the coefficient on government debt was statistically significant and exceeded that on the remainder of household net worth by a wide margin, providing evidence against the belief that government debt is not viewed as wealth by households.

A more detailed look, at the results presented in Table 1 indicates a basic pitfall in the overall approach adopted by DGG. Equations (2) and (A) purport to be fundamentally different specifications․the first traditional and the second Ricardian․leading to different results and interpretations. However, closer inspection reveals that equation (4) is in fact a linear transformation of equation (2) and similarly that equation (5) is a linear transformation of equation (3). ^25/ Thus the statistical information contained in equations (2) and (4) is identical and one cannot therefore draw distinct inferences from them.

Returning to the equations presented in the DGG paper, the equations estimated with the alternative income variables․traditional and Ricardian․are not exact linear transformations of each other, because the parameters used to generate the data for permanent income differ somewhat. However, the two equations are close to being precise linear transforms of each other, which makes the drawing of very different inferences about the effects of alternative fiscal measures on national saving suspect at best․since the equations contain essentially the same information.