DYNAMIC INCOME, PROGRESSIVE TAXES, AND 

THE TIMING OF CHARITABLE CONTRIBUTIONS' 

William C. Randolph 

Congressional Budget Office 

U.S. Congress 

OTA Paper 69 August 1994 

OTA Papers and Briefs are circulated so that the preliminary findings of tax research conducted 

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Office of Tax Analysis 

U.S.Treasury Department, Room 1064 

Washington, DC 20220 

Thanks to Gerald Auten, Leonard Burman, Eric Engen, William Gale, David Harris, 

David Johnson, James Nunns, Mark Wilhelm, and many other colleagues and seminar 

participants for comments and suggestions. Most research for this paper was conducted 

while the author worked for the Office of Tax Analysis, U.S. Treasury. All views are the 

author's, and do not represent official views or positions of the Congressional Budget Office 

or the U.S. Treasury. Address: Congressional Budget Office, 2nd and D Streets, S.W., 

Washington, DC, 20515; Tel: (202) 226-2859; INET: BILLR.TAD@CBO.GOV 
Abstract 

The permanent income hypothesis suggests that empirical studies have underestimated how much 

permanent income affects charitable giving if people smooth their giving when transitory income 

changes. But the studies may have also overestimatedthe effect of permanent changes in tax prices. 

This is because changes in transitory income also change the relative tax prices of current and future 

giving when marginal tax rates increase with income, which may cause people to substitutebetween 

current and future giving. I first examine these issues using a simple demand model. I then study 

the issues empiricallyusing a ten-yearpanel of tax-retum data (1979-1988) that spanstwo major taxlaw changes. The data allow me to separately estimate the effects of permanent income, transitory 

income, current tax prices, expected future tax prices, and other variables. Compared to price 

elasticities from previous studies, I find that giving is much less elastic with respect to permanent 

changes in tax prices, but more elastic with respect to transitoryprice changes. I also find that giving 

is much more elastic with respect to permanent income, but less elastic with respect to transitory 

income changes. The results imply that people smooth their giving when transitory income changes, 

but time their giving to exploit transitory price changes. 

I 

I ' 
1 

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1. Introduction 

Governments have historically supported philanthropic causes through a variety of direct 

spending and transfer programs, and by providing incentives designed to encourage private 

philanthropy through matching grants and special provisions of the tax system. Since its beginning, 

the U.S. income tax has provided incentives for private philanthropy by allowing people to deduct 

charitable gifts from taxable income. This deduction is widely thought to encourage giving because 

it decreases the amount of other consumptionpeople must forgo at the margin, the "tax price,'' for 

each additional dollar they give to charity. 

To measure the incentive effects, empirical studies have modelled giving by individuals as 

a commodity. The key results are summarized in terms of elasticities of demand for giving with 

respect to changes in after-tax income and tax prices. Clotfelter (1985) surveyed more than a dozen 

empirical studies of individual giving. The studies typically found that giving is income inelastic, 

but highly price elastic. Steinberg (1990) surveyed at least twenty more recent studies, and found 

that the results were not very robust to changes in data and model design. In a recent study, Auten, 

Cilke, and Randolph (1992) compared the predictions of a standard model of charitable giving to 

observed changes in giving by people in different income groups following two major tax changes 

in the 1980's. They found that the predictions were very different from the actual changes. For 

many income groups, predicted changes actually had the wrong sign. 

In this paper, I present evidence that the price and income elasticity estimates from previous 

studies were biased because they did not distinguish fully between direct and indirect effects of 

permanent and transitory income. Differencesbetween the direct effects are implied by Friedman's 

(1957) permanent income model. If people smooth their consumption, giving would be less 
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sensitive to transitory than permanent income. Some studies, including Schwartz (1970), Feldstein 

and Clotfelter (1976), Reece (1979), and Clotfelter (1980), have tried to separately measure the 

direct effects of permanent and transitory income, but the results have been weak. Previous studies 

have not, however, accounted for differences between the indirect price effects of permanent and 

transitory income. The effects are likely to differ because permanent and transitory income have 

different effects on the current and expected future tax prices of giving. Marginal taxrates increase 

with income, so a person with relatively high permanent income will tend to face a relatively low 

tax price both in current and future years. However, a person with a relatively high transitory 

income will tend to face a tax price that is currently low relative to future years, when transitory 

income is expected to be lower. 

Casual observation and some econometric evidence suggests that people are willing to 

substitute giving between current and future years to take advantage of changes in relative current 

and future taxprices. For example, in studies of the 1980's changes in tax laws, Clotfelter (1990) 

and Auten, Cilke, and Randolph (1992) observed one-time increasesin charitable giving during 1981 

and 1986. During those years, people appeared to accelerate future giving to avoid the pending 

statutory increases in tax prices. Broman's (1989) econometric analysis of behavior surroundingthe 

tax reductions passed in 1981 also suggests that people anticipated the changes by substituting 

current for future giving. As another example of substitution, charitable giving is sometimes used 

for end-of-year tax planning. In December, when people know whether taxable income for the past 

year is higher or lower than usual, they can either accelerate future giving to take advantage of a 

temporarily low tax price or defer giving to avoid paying a temporarily high taxprice. 
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As I show in the first part of this paper, if part of the tax-price variation in data used for past 

studies resulted from transitory income variation, and if people smooth their consumption, but are 

willing to substitutebetween current and future giving in response to changes in relative tax prices, 

the existing elasticity estimates will tend to understate the effects of changes in permanent income 

and overstate the effects of permanent price changes. Likewise, the elasticity estimates will tend to 

overstate the effects of changes in transitory income and understate the effects of transitory price 

changes. 

I first use a simple demand model to examine the basic empirical identification problem. 

I then estimate an empirical model of charitable giving based on a ten-year panel (1979-1988) of tax 

return data. The data allow me to separately estimate the direct income effects and indirect price 

effects of permanent and transitory income. I take advantage of the longitudinal aspect of the data 

and changes in the degree of marginal taxrate progressivity that followed the tax-law changes in 

1981 and 1986. In contrast to previous studies, rather than depending on cross-sectional variation 

of income along a given nonlinear tax-price schedule, the parameters are identified by statutory 

changes in the tax schedule.' The estimation method is similar to the method that Burman and 

Randolph (1993) used to estimate the effects on capital gains realizations of permanent and 

transitory changes in marginal tax rates. 

My results differ substantially from the results of previous studies. Giving appears to be 

much less sensitiveto permanent price changes and much more sensitiveto transitory price changes. 

Giving also appears to be much more sensitiveto permanent income and less sensitive to transitory 

Feenberg (1987) analyzed the potential problems caused by depending too heavily on 

nonlinearity of a particular tax schedule to identify charitable giving models. 
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income. These results suggest that previous studies have estimated the average effects of transitory 

and permanent price and income variations. The results also raise questions about the effectiveness 

of tax incentives in affectingthe level, rather than just the timing, of charitable giving by individuals. 

2. The Direct and Indirect Effects of Income 

In this section, I use a simple demand model to show how permanent and transitory changes 

in income can affect individual charitable giving when marginal tax rates increase with income. 

Suppose that an individual chooses how much to consume personally and how much to give to 

charity in each of two periods. Income is exogenous and subject to tax, but giving is deductible. 

For simplicity, interest and discount rates are zero. The individual's decision problem is represented 

by equation (l), 

subject to: 

where g and x, are the levels of charitable giving and personal consumption in period t, 

respectively. Exogenous levels of pre-tax income are given by y, and y,. The tax function, T(.), is 

twice-differentiable, and marginal taxrates are assumed to be positive and non-decreasing, so that 

T(y), T'(y), and T"(y)rO for all Y.~ 

Differentiability simplifies the analysis considerably. Neither it nor the assumption of 

non-decreasing marginal tax rates is necessary for the results of this section. 
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The problem can be expressed in a more standard form by rearranging the budget constraint: 

where: 

Although the budget constraint is a nonlinear function of giving in each period, the individual's 

decision has a standard form in terms of marginal tax prices, P, and P,, and "modified"after-tax 

income, Y, and Y,. Modified after-tax income equals after-tax income when giving is zero plus an 

implicit premium that results from the fact that inframarginal amounts of giving are deducted at 

higher rates than the marginal tax rate. 

First ignoring nonlinearity of the budget constraint, demand exhibits Slutsky and other 

familiar properties in terms of P, and Y, for t = 1, 2. I use this fact along with the nonlinear 

dependence of the budget constraint on giving to derive the different effects of temporary and 

permanent changes in pre-tax income. The effects on giving can be decomposed into direct effects 

through changes in income and indirect effects through changes in tax prices. 

First, consider a permanent change in income. Pre-tax income can be decomposed into 

permanent, y', and temporal, y:, components, so that y, = yo+ y: for t = 1,2. The effect on g, of 

a change in the permanent component is given by equation (3). 

dy' (3) 
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where G1(PI,P,,Y*)and H1(PI,PZ,u*)are the ordinary and compensated demand functions for g,, 

respectively, and Y' is "permanent" modified after-tax income, i.e., (Y1+Yz)/2.3 

The first term in the numerator, PI- aG aY ,accounts for the direct effect of a permanent 

change in income. The second term in the numerator appears because marginal taxrates change with 

income. It shows that a permanent change in income will affect giving indirectly by changing the 

taxprices in both periods. This second term, including the minus sign, is non-negative because T"20 

and '/aP, + aH s 0 according to the Slutsky proper tie^.^ A permanent increase in income, for 

example, would increase giving by increasing resources and permanently decreasing the taxprice. 

For comparison, consider the effect of a temporary change in yITwithout a change in y;. 

The effect on giving in period 1 is now expressed by equation (4). 

Equation (3) and the expressions in the rest of this section were simplified by assuming 

that y1 equals y, initially, and preferences are weakly separable between giving and other 

consumption. Preferences are also symmetric in g, and g,, i.e., U(g,,g,,x,,x,) = U(g,,g,,x,,x,). 

The denominator in equation (3) is greater than or equal to 1 because marginal tax rates 

are increasing in income. It reduces all marginal effects in the numerator proportionally to 

account for curvature of the budget constraint. 
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Equation (4)differs from (3) in two significant ways. First, the direct effect in (3), 

P, 6G / aY * ,is reduced by half in (4)because the individual would choose to spread the change in 

ylTover two periods. Second, there is an additional term in (4)that accounts for the fact that a 

temporary change in income will have an additional indirect effect by changing the price of g, 

relative to g,. This term has the same sign as aH / aP2because T">O and aH '/aP,- i3-I'/aP,SO 

according to the Slutsky properties. Thus, if g, and g, are demand substitutes, so that i3-I / aP2is 

positive, the indirect price effect will be larger in absolute magnitude if the change in y1 is 

temporary, as in equation (4),than if the change is permanent, as in equation (3). 

Such behavior may be important for empirical analysis, especially for the analysis of crosssection data, from which we can't easily tell whether observed income differencesare permanent or 

transitory. To see this, first suppose we could observe giving in period 1 by two otherwise identical 

individualswho have a small differencebetween their levels of pre-tax permanent income. Based 

on the demand problem above, the difference between their levels of g, can be expressed as a 

function of differences in their period 1 levels of modified after-tax income and taxprices according 

to (5). 

when dy, = dy' and dylT= dy: = 0 
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According to (9,the marginal effect of the observed difference in Y, is Xi / I~Y,which is the same 

as the marginal effect of a change in modified after-tax permanent income. The marginal effect of 

the observed difference in P, is Xi l/aPl + Xi l/aP,, which is the same as the marginal effect of a 

proportional, "permanent", change in P, and P,. 

For comparison, suppose that the income difference is purely transitory, so that the two 

individualshave the same pre-tax lifetime wealth, i.e., dyIT= -dy,T and dy*=O. Now the observed 

difference in g, is given by equation (6). 

when dy, = dy,f = -dy: and dy' = 0 

Compared to equation (9,there will be no direct effect of the change in y, through its effect on Y, 

because the change in pre-tax income is purely transitory. The indirect effect of y, through its effect 

on PI will also differ from the corresponding effect in equation (5) because the intertemporal price 

effect, Xi / ap,, is subtracted instead of added. This is because a purely transitory change in income 

changes P, and P2 inverse proportionally, whereas a permanent change in income changes P, and 

P, in direct proportion. If g, and g, are substitutes and giving is a normal good, so that Xi l/ aPl is 

negative and Xi / ap, is positive, the marginal price effect in (6)will be larger in absolute value than 

the marginal price effect in (5). The observed effect of the price difference would therefore overstate 

the effect of a permanent change in tax prices. The observed effect of the income difference would 

understate the effect of a permanent change in income. 
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Suppose that we could observe a large number of such almost identical individuals in a crosssection sample, but the sample is a mixture of people who have differences in permanent and 

transitory income; we can't tell which. Based on such data, a linear regression of observationsof g, 

on Y, and P, would yield regression coefficient estimates that would be weighted averages of the 

marginal income and price effects shown in equations (5) and (6).5 The weights would be unknown, 

because they would be functions of the unknown extent to which cross-sectional income and price 

differencesare permanent or transitory. We could not use the estimated coefficients to identify the 

permanent and transitory marginal effects. Used as they are, the estimates would produce biased 

policy predictions. They would understate the effect of tax-policy induced permanent changes in 

after-tax income and overstate the effect of tax-policy induced permanent changes in tax prices. 

3. Empirical Model 

I address these intertemporal issues empirically by using a ten-year panel of individual taxreturn data that spans a period in which there were significant statutory changes in income tax rates 

and longitudinal variations in income for individuals in the sample. As an empirical strategy, I 

generalize the standard model of charitable giving, in which giving depends only on current income 

and prices, to include expected future income and prices. This allows me to examine whether there 

are differences between the effects of transitory and permanent changes in income and prices. 

Rather than extending the Cobb-Douglas type demand function typically used in previous 

studies by simply adding regression terms for expected future income and prices, I extend the model 

This assumes that the estimation method would account for the fact that Y,and PI are 

endogenous functions of g,. 
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by using a more flexible demand specification based on the expenditure-share form of the flexible 

"almost ideal" demand (AID) model of Deaton and Muellbauer (1980).6 

- pit gd - 6& + 6& + x,p + 6,Log(-) ut--- pit + b,Log(P,') 

yit P,' 

where Y, = yit - T, - (l-Pit)~ 

According to (7), individual i in year t decides how much to "spend" on charity. The dependent 

variable, oit,is the share of current income spent on charity. It equals the current tax price of 

giving, Pit,times the amount of giving, g, ,divided by current modified after-tax income, Y, . As 

in Section 2, though expressed differently,modified after-tax income equals after-tax income before 

giving is deducted plus the implicit premium realized by givers when inframarginal giving is 

deductible at higher tax rates than the marginal tax rate. 

The giving decision is affected by current income, Y, ,expected-fhre income, Yit*,the 

current tax price, Pit,and the expected-future tax price, Pit*.The model thus allows people to base 

giving decisions on current income and tax prices, and whether current income and tax prices are 

high or low relative to future years. 

Because other consumer expenditures are not observed in tax-return data, to derive (7) 

from an expenditure share equation, I substituted current income, Y, for total expenditure and 

added expected future income, Y*, to the right side in a way similar to Y. This implicitly 

assumes that total expenditure and giving may depend on both current and expected future income. 
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Following the analysis in Section 2, I expect a proportional change in Y and Y* to affect 

giving more than a change in Y only, and a proportional change in P and P* to affect giving less than 

a change in P only. The functional form, however, also allows the opposite. This flexibility is 

important because giving may be more, rather than less, sensitive to transitory income changes. For 

example, people may smooth their other consumption by adjusting charitable giving instead of 

borrowing or saving. Likewise, people may be less rather than more sensitive to temporary price 

changes because it takes them time to adjust to price changes, as suggested by Clotfelter (1980). 

Other potentially important terms are also included in the model. Observed individual 

characteristics are included in the vector X, . These include a person's age and age-squared, which 

allows for a life-cycle pattern of giving behavior unaccounted for by the other variables. A life-cycle 

pattern of giving might exist if people's discount rates differ from market interest rates, if people 

schedule consumption around raising children, or if there is a precautionary motive behind the 

schedule of life-cycle consumption or giving decisions. Xi, also includes a dummy variable for 

marital status. An additional variable, the count of total tax exemptions, is also included to allow 

the size of a consumer unit to affect the level of giving. 

To allow for unobserved individual characteristicsthat may affect giving, the model includes 

an individual-specific intercept, bOi.The intercept is also allowed to vary over time by including am, 

which is controlled for by including time dummy variables. This allows for the effects of aggregate 

changes in interest rates, other macroeconomic conditions, or government social policies that may 

affect individual charitable giving. For example, during a recession, the need for charity may 
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increase, and those still doing well may respond by giving more. Giving may also change because 

people substitute privately for aggregate changes in government social programs (Kingma, 1989). 

4. TheData 

The data were selected from a ten-year panel of U.S. federal tax return data, from 1979 

through 1988 (U.S. Department of the Treasury, 1979-1988). This panel follows the tax returns 

of more than 12,000 people who were listed as the primary tax-return filers in each year. The 

originalpanel sample was stratified to over-sample tax returns of people who reported relatively high 

incomes in 1981. This ensures that the sample includes a relatively large number of high-income 

taxpayers, who account for a substantial fraction of total giving by individuals. For example, about 

a third of all deductible contributions in 1990 were made by people with incomes exceeding 

$lOO,OOO in 1991 dollars (Auten, Cilke, and Randolph, 1992). 

One advantage of tax-return data is that it provides detailed information about many 

components of income. The detail provides a means for studying charitable giving, and allows 

precise measurement of marginal tax rates, total federal taxes, and tax prices of charitable giving. 

Another important advantage is that the panel is ten years long, and spans two major tax-law changes 

in 1981 and 1986. Ten years of annual income for each taxpayer allow me to estimate the effects 

of permanent and transitory income on giving. Combined with the tax law changes, the longitudinal 

income data also allow me to estimate the effects of current and future tax prices. 

The sample for estimation includes only panel members who filed tax returns in all ten years. 

As in previous charity studies based on tax return data, the sample excludes people who did not 
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report amounts of giving because they did not itemize deduction^.^ Observations for the years 1981, 

1982, 1986,and 1987 were also excluded for estimation. They were the years the major tax changes 

were passed and the years immediately following. By excluding those years, I focus the estimation 

on measuring the degree to which the direct income effects and indirect price effects of permanent 

and transitory income differ during "normal" years like those covered by many past studies of 

charitable giving. This allows me to examine whether the previous results are biased.8 

All dollar amounts were converted to constant 1991 dollars. Pre-tax income was measured 

by starting with each taxpayer's Adjusted Gross Income (AGI) for each year. AGI was then 

modified to adjust for changes in its legal definition over the years. The most important 

modification was to add the portion of net long term capital gains excluded from AGI before 1987.9 

One critical variable is the ten-year (real) average of pre-tax income, which is used to create 

instruments for estimation. 

Total taxes and marginal tax rates were computed based on federal tax rates and taxable 

income in each year. The tax price is defined, as in Section 2, as the value of other consumption 

forgone at the margin per dollar of charitable giving. However, the price measure is complicated 

This may cause selection bias if, for example, people who are more likely to itemize 

deductions are also likely to give more thanothers, conditional on all other variables in the model. 

However, this potential problem is probably not serious because other unrelated decisions, 

especially whether to own and mortgage a home, are the main determinants of whether people 

itemize tax deductions. 

* As a sensitivity test, discussed in Section 8, the model was re-estimated using all ten 

years, but it made little difference in the results. 

Many other modifications were made to AGI to measure pre-tax income. The 

modifications are the same as those described in detail in Auten, Cilke, and Randolph (1992). 
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by the fact that cash and non-cash gifts have different prices, and the panel data do not report 

separate amounts for cash and non-cash gifts. For cash gifts, the price equals 1 minus the marginal 

tax rate for ordinary income. For gifts of appreciated assets such as corporate shares, the tax price 

is reduced further to account for taxes not paid on the unrealized appreciation. To account for these 

price differences,following Feldstein (1975) and other studies, I calculate the tax price as follows. 

where T,'is the marginal tax rate on ordinary income, 1, is the fraction of net long term capital gains 

included in AGI, 4, is the fraction of total giving made up of appreciated assets, and "a" is the gainto-value ratio for gifts of appreciated assets, multiplied by the expected present value of capital gains 

tax payments that would have been made in the fbture had the donated assets been sold instead. The 

constant, a, was set equal to 0.5, which was estimated by Feldstein (1975) and Feldstein and 

Clotfelter (1976), and has been used in several studies since (Clotfelter, 1985). I estimated the 

appreciated assets fraction, fit, for six different income classes in each year based on analysis in 

Auten, Cilke, and Randolph (1992). For years included in the panel, its value ranged from 0.05 in 

1980 for incomes below $20,000 to 0.48 in 1980 for incomes exceeding $1 million (1991 dollars). 

Means of selected variables are shown in Table 1. The total of 53,703 observations 

represents six years of data (1979, 1980, 1983, 1984, 1985, and 1988) for the 75 percent of the 

original sample of 12,000 taxpayers who itemize tax deductions. Differences between unweighted 

and sample-weighted means result from the original sample stratification. As shown, the sample 
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over-representspeople with high incomes, who also tend to be older and give more than others on 

average.lo 

5. Estimation 

The main challenges for estimation are that Y and P are endogenous functions of giving and 

Y* and P* are unobserved. I use an instrumental variables method, similar to that used by Burman 

and Randolph (1994), to decompose the observed variation in Y and P into exogenous transitory 

and permanent components. To simplify the discussion, equation (7) is rewritten as (9). 

0, = 6,[Log(P,) - Logpi)] + 6,Log(Pi) 

(9) 

+ 6,[Log(YJ - Log(Yi)] + a,log(Y;) + 

I call Log(P,,*) and Log(Yit*)the "permanent" components of prices and income as a 

convenient shorthand, but they are really not permanent. They are expectationsthat can change over 

time when tax laws change or other information is acquired. Similarly, I call the differences of 

current levels from expected future levels of incomes and prices the "transitory" components. 

To estimate the model, I need at least four exogenous instruments: at least two that are 

correlated with the permanent components, but not with the transitory components, and at least two 

that are correlated with the transitory components, but not with the permanent components." As 

lo An extensive descriptive data analysis of essentially the same data can be found in 

Auten, Cilke, and Randolph (1992). 

l1 When the individual-specific effect, tjOi,is treated as a random effect for estimation, 

i.e., part of the error structure, the instruments must not be correlated with it. When tjOiis treated 

as a fixed effect, the requirement is weaker, but the instruments for the permanent components 
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instruments that should satisfy these requirements, I use the logarithm of current pre-tax income, 

the logarithm of its ten-year average, and the products of these two variables with two dummy 

variables that indicate major statutory changes in tax rates. The first dummy variable indicates 

whether the year of an observation is between the tax-law changes in 1981 and 1986. The second 

dummy variable indicates whether the year is after the tax reform in 1986. These dummy-variable 

interactions allow future expectations of after-tax income and tax prices to be different under 

different tax laws for particular levels of current and average pre-tax income. 

Conditional on other variables in the model, I expect the ten-year average of pre-tax income 

to be correlated with expectationsbecause it is correlated with individual characieristicsthat would 

cause persistent differences between incomes and, therefore, after-tax incomes and tax prices. 

Further, I expect interactions of the tax-period dummy variables with average pre-tax income to be 

correlated with expected future after-tax incomes and tax prices because the changes in tax laws 

should change how the expectations depend on average pre-tax income. Likewise, the differences 

between current and average pre-tax income, and its interactions with the tax-period dummy 

variables, should be correlated with the transitory components of after-tax incomes and tax prices. 

These instruments might not separate perfectly the permanent and transitory components. 

For example, the instrument based on differences between current and average pre-tax incomes may 

be correlated over time for each individual, conditional on the other variables. In that case, the 

instruments for the transitory componentswould have persistent components that are correlated with 

expected future incomes and tax prices. If so, results in Burman and Randolph (1994) imply that 

must have some variation independent of the fixed effect over the sample period. 
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the estimates of transitory income and price effects would be biased toward the corresponding 

permanent effects. My tests would therefore be conservative because they would be biased (if at all) 

against rejecting the hypothesis maintained in previous studies that the permanent and transitory 

effects are equal.12 

Details of the estimation method are in the Appendix. I use a two-stage least squares 

algorithm in which there are four first-stage regressions: one for each of the permanent and 

transitory components of income and prices. Current values of income and prices are used as 

dependent variables in first stage regressions for permanent and transitory components, but the 

regressions for the permanent income and permanent price components are estimated by excluding 

any instruments that depend on the difference between current and average pre-tax income. This 

decomposes the observed variations in after-tax incomes and prices into two parts. One part is 

determined by variation in the instruments that results from variation in average pre-tax income and 

its interactionswith changes in tax laws. The other part is determined by variation in the instruments 

that results fiom longitudinal variation of individuals' differences between current and average 

income and its interactions with changes in tax laws. 

6. Estimated Effects of Income and Prices 

The estimated parameters for equation (7) are shown in Table 2. These estimates are based 

on the random-effects model, in which the individual-specific effect, boi ,is assumed to be random 

l2 Under the null hypothesis that the permanent and transitory effects are equal, there 

would be no bias even if the instruments do not fully separate permanent from transitory 

components. 
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and uncorrelated with the other regressors. According to the results, the hypothesis that permanent 

and transitory income have equal effects on giving can be confidently rejected. Permanent and 

transitory income would have equal effects if the coefficients of Log(Y*) and Log(Y/Y*) were 

equal. However, the coefficients differ by 0.049, which is about ten times the standard error of the 

difference (0.0048, not shown). Likewise, the coefficients of all price terms are significantly 

different from zero. This implies that the effects of current and expected future tax prices are 

significantly different. The importance of these differences can be measured by comparing 

elasticities. 

The elasticities of giving with respect to permanent and transitory income are given by 

equation (10). 

The permanent income elasticity, eg,yl,is the elasticity of giving with respect to a change in income 

when Y and Y* are changed proportionally. The transitory income elasticity, eg,y,is the elasticity 

of giving with respect to a change in current modified after-tax income, Y, holding permanent 

modified after-tax income, Y*, constant. 

The elasticities of giving with respect to permanent and transitory changes in tax prices are 

expressed as follows, evaluated at P =P*. 
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The permanent price elasticity, eg,p*,is the elasticity of giving with respect to a proportional change 

in current and expected future tax prices. The transitory price elasticity, eg,p,is the elasticity with 

respect to a change in the current tax price, holding the expected future tax price constant.I3 The 

permanent price elasticity and permanent income elasticities could be used, for example, to make 

long term predictions about the effects of statutory taxpolicy changes that permanently affect tax 

prices and modified after-tax income. 

The first two columns in Table 3 show the income and price elasticitiesthat are implied by 

estimates from Table 2. Column 1 shows the estimated elasticities evaluated at the unweighted 

sample means of the dependent variable (0.04) and tax price (0.56) over all years of the sample. 

Column 2 shows the estimated elasticities evaluated at means weighted by population weights and 

(real) dollars of giving by each taxpayer.14 Elasticities evaluated at the weighted means are more 

appropriate than those at the unweighted means for making predictions about changes in aggregate 

giving following changes in incomes or prices. 

l3 The 2 appears before 6,for the permanent price elasticity because both P and P*are 

changed proportionally, whereas only P changes for the transitory price elasticity. 

l4 The weighted means over all years were 0.089 for the dependent variable and 0.66 for the 

tax price. 
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The estimated permanent income elasticities are 1.27, unweighted, and 1.12, weighted. In 

comparison, the estimated transitory income elasticities are only 0.05, unweighted, and 0.57, 

weighted. Whether weighted or unweighted, the hypothesis that the permanent income elasticity 

equals the transitory income elasticity can be rejected at less than the 1 percent level. Unweighted, 

the difference between permanent and transitory income elasticities is 1.22 with a standard error of 

0.12. Weighted, the difference is 0.55 with a standard error of 0.05. The fact that the permanent 

income elasticity is larger than the transitory income elasticity suggests that people smooth their 

giving relative to transitory changes in income. 

These income elasticity estimates are much different from the results typical of previous 

studies. For example, Clotfelter (1990) reports that an income elasticity of 0.78 is representative of 

previous results. The fact that 0.78 falls between the estimated permanent and transitory income 

elasticities is consistent with the hypothesis that previous studies have estimated an average of the 

permanent and transitory income elasticities because observed income variation results fiom a 

mixture of permanent and transitory variation. 

The differences between permanent and transitory price elasticity estimates in Table 3 are 

just as striking. At the unweighted sample means, the estimated permanent price elasticity is -0.06, 

and is not significantly different from zero. At weighted means, the permanent price elasticity is 

-0.49 with a standard error of 0.06. This estimate is substantially smaller in absolute value than the 

price elasticity of -1.27 reported by Clotfelter (1 990) as being representative of previous studies. 

The transitory price elasticity estimate, which equals -2.35, unweighted, and -1.57, 

weighted, is substantially larger in absolute value than the permanent price elasticity. The 

hypothesis that the transitory price elasticity equals the permanent price elasticity can be rejected at 
-21 -

less than the 1 percent level. Unweighted, the difference between permanent and transitory price 

elasticities is 2.29 with a standard error of 0.17. Weighted, the difference is 1.07 with a standard 

error of 0.08. This provides strong evidence against the assumption made in past studies that 

transitory and permanent price effects are equal. People are apparently willing to substitute their 

giving between current and future years to take advantage of changes in relative current and future 

tax prices that occur when transitory changes in income temporarily move them up or down the 

.marginal tax-rate schedule. 

To measure how these results can affect policy predictions compared to previous results, 

consider the effects of a proportional change in all marginal tax rates. According to my estimates 

and those from previous studies, a decrease in marginal tax rates would tend to decrease giving 

because tax prices would increase, and the price elasticity is negative. However, after-tax income 

would also increase, which would tend to increase giving because income elasticities are positive. 

The net effect would depend on the relative permanent price and permanent income elasticities,the 

marginal tax rates, and the degree of progressivity of marginal tax-rates. The importance of these 

factors is summarized by the following expression for the elasticity of giving with respect to a 

permanent proportional change in all marginal taxrates, the "surtax" elasticity. 

where: 
- 22 -

where and ?are the marginal and average tax rates, respectively, and A is the proportional 

change in tax rates. 

Under different assumptionsabout marginal and average tax rates, Table 4 compares surtax 

elasticities based on price and income elasticity estimates typical of previous studies with surtax 

elasticities based on parameter estimates from Table In the first panel, which is based on price 

and income elasticities typical of previous studies, for all values of marginal and average tax rates, 

a proportional decrease in marginal tax rates is predicted to decrease giving. For example, a 1.0 

percent decrease in marginal tax rates would decrease giving by 0.54 percent when the marginal tax 

rate is 40 percent and the average tax rate is 20 percent. Note that the surtax elasticity increases as 

marginal tax rates increase and as marginal tax rates become more progressive. 

The second panel shows surtax elasticities based on my estimation results. For many values 

of the marginal and average tax rates, the sign of the surtax elasticity actually changes relative to the 

top panel. At higher marginal tax rates and degrees of progressivity, the tax elasticities have the 

same sign, but are substantially smaller than the corresponding elasticities in the top panel. These 

large differences in policy predictions relative to the top panel are the combined results of a larger 

permanent income elasticity and smaller permanent price elasticities implied by the parameter 

estimates in Table 2. They demonstratethat failure to distinguish between transitory and permanent 

income and price effects can lead to substantially biased policy predictions. 

l5 For the simulations, o was held constant at its giving-weighted mean of 0.089. 
- 23 -

7. Estimated Effects of Other Variables 

The estimated coefficients for other variables are shown in Table 2. The estimated 

coefficientsof age and age-squared imply that people increase their giving expenditure as they grow 

older, and at an increasing rate, other things constant. Evaluated at the unweighted sample mean of 

the dependent variable, the relationship between giving and age is not statistically different fkom zero 

before age 50. After that, an extra year adds about 1 percent to the amount of giving at age 50,3 

percent at age 60,4 percent at age 70, and 6 percent by age 90.16 Figure 1 illustratesthe age pattern. 

The thickest solid line shows the implied pattern for a hypothetical person for which the dependent 

variable equals 0.04 at age 50, other variables constant.” 

Giving may increase with age because age may proxy for life-cycle wealth accumulation. 

However, the simplest life-cycle hypothesis implies a wealth profile that increases and then 

decreases, whereas the life-cycle pattern of giving increasesmonotonically, and at an increasing rate. 

Such an age pattern of giving is consistent with the precautionary savings behavior that would occur 

if people are risk averse and uncertain about future income or how long they will live. If people are 

uncertain about their own ability to consume in the future and they can’t perfectly insure by 

purchasing annuities, for example, it may be prudent to defer charitable contributionstoward the end 

of the life cycle. Charitable giving, in contrast to food, housing, children, and transportation, might 

l6 These estimated percentages are all significantly different from zero at less than the 1 

percent level. 

l7 The step function in Figure 1 is the pattern implied by alternative estimates for a model 

that was specified in terms of ten-year age brackets instead of age and age-squared. The result 

suggests that the estimated age pattern is not the forced result of using a quadratic function to 

summarize the profile. All other estimation results were essentially unaffected by this experiment. 
- 24 -

be relatively easy to defer. Another possible explanation of the age pattern is that there is a vintage 

effect that occurs because the age variable has both longitudinal and cohort-based sources of 

variation. For example, older cohorts may be more generous than younger cohorts. It is not 

possible, however, to separate the life-cycle pattern from cohort differences from these data. 

Marital status apparently makes no difference, regardless of whether the person is married 

filing separately with no other dependents (Married=l, Exemptions=l) or married filingjointly with 

no other dependents (Married=l, Exemptions=2). Giving apparently increases with the addition of 

exemptions, but at a rate substantially less than proportional to the increase in exemptions. For 

example, following an increase in exemptions, the estimated percentage increase in giving is only 

about 5 percent of the percentage increase in exemptions when there are 2 exemptions. The 

corresponding increase is still only about 10 percent when there are 4 exemptions.18 This less than 

proportional increase would result, for example, if giving is a quasi-public good within a 

hou~ehold.'~ 

The coefficients of the year dummy variables show that there was a significant increase in 

giving during the middle years of the panel (1983 through 1985) followed by a decline, holding all 

other variables constant. For the middle years, the average increase in the dependent variable was 

l8 These are evaluated at the sample mean of 0.04 for the dependent variable. The 

estimated percentage change equals the coefficients of Exemptions, multiplied by the number of 

exemptions, divided by 0.04. 

l9 Economic inferences should be made cautiously because the information on a tax return 

does not necessarily represent the finances of a household. Further, extra exemptions are not 

necessarily children. Throughout the first part of the sample period, people could claim an extra 

exemption if they were over age 65 or blind. I conducted a sensitivity test using an alternative 

variable that excluded the blind and over-65 exemptions. The results were unchanged. 
- 25 -

about 0.012, which is a 30 percent increase relative to the unweighted sample mean of the dependent 

variable over all years. Although the exact cause of this increase can not be identified, it may have 

resulted from a behavioral response to the recession of the early 1980s, or aggregate reductions in 

certain government social programs during the middle years. An increase in private giving to offset 

reductions in social programs would, for example, be consistent with the crowding-out behavior 

studied by Kingma (1989) and others. 

The variances of the individual-specific intercept and the regression error imply that the 

unobserved individual-specific differences account for a substantial portion of the observed variation 

in giving. The total variance of the dependent variable is 0.0071. Almost 50 percent (0.0035) of this 

variance is explained by the unobserved individual-specific differences. In contrast, all other 

regressors together account for only about 10 percent of the total variance of the dependent variable. 

This demonstratesthat the unobserved differences are important. It is not possible, however, to infer 

fiom these results whether the unmeasured differences result fiom innate taste differences or some 

other variables not included in the regression, such as education, unmeasured wealth, or family 

background.20 

8. Sensitivity Experiments. 

Columns 3 and 4 in Table 3 show the results of two sensitivity experiments designed to 

examine, further, how my price and income elasticity estimates differ from previous studies. The 

. experiments allow me to determine how much of the difference from previous results is caused by 

2o Section 9, which presents fixed-effects estimates for reduced models, addresses the 

possibility that the unobserved differences are correlated with other regressors. 
-26-

the distinction I make between permanent and transitory incomes and prices, and how much of the 

change is caused by differences in data, functional form, and estimation methods. 

In the first experiment, shown in column 3, the expected future price, Log(P*), was omitted 

from the estimated model. The only tax price variables included were Log(P) and Log(P)-squared. 

Otherwise, the estimation method was the same as for the full model. As shown, the income 

elasticity estimates are about the same as those for the full model in column 2, but the current price 

elasticity estimate is between the permanent and transitory price elasticity estimates from the full 

model and close to the results from previous studies. This results because variation in the current 

tax price is a mixture of permanent and transitory price variation. 

For the experiment shown in column 4, all expected future tax price and permanent income 

terms were excluded from the model. This restricted model is closest to the standard model fiom 

previous studies. The restricted estimates are very close to the income elasticity of 0.78 and price 

elasticity of -1.27 that Clotfelter (1 990) characterized as representative of estimates from previous 

studies. Such closeness is remarkable, partly because the source of tax price variation for my study 

is almost entirely different from the source of tax price variation in previous studies. In the past, the 

main source of taxprice variation in microdata studies has been cross-sectional variations along the 

nonlinear marginal tax rate schedule caused by cross-section variations in taxable income. Here, by 

construction of my estimation method, the tax price instruments only exhibit variation independent 

of income variation because there were statutory tax changes after 1981 and 1986. Without the taxperiod dummy variable interactionsas instruments, the income and tax-price parameters would not 

be separately identified. 
- 27 -

The results of these experiments strongly suggest that the full-model estimates differ from 

the results of previous studies because the full model distinguishesbetween permanent and transitory 

income and taxprice variations. The differences in estimates do not appear to have resulted from 

other differences in the empirical model, data, or estimation method. 

The results from additional sensitivity experiments are shown in Table 5. For each 

experiment, the top panel shows the implied elasticities evaluated at the giving-weighted means. 

To diagnose whether any sensitivity or robustness carries over to values away from the mean, the 

bottom panel also shows elasticities evaluated at a tax price of 0.4.The first row of each panel 

shows the estimates based on the full-model parameter estimates from Table 2 for comparison. 

Experiment 1 shows the estimates based on two-stage least squares when the unobserved 

individual-specific effects are ignored.*]Experiment 2 also ignores the unobserved individualspecific effects, but uses a Tobit method to account for the 4percent of observationsthat had zero 

amounts of charitable giving. Note that use of the Tobit method makes little difference. In both 

experiments, however, the sign of the permanent price elasticity changes relative to the full model 

when evaluated at the giving-weighted means, although the elasticity changes very little when 

evaluated at the lower tax price, as in the bottom panel. The sensitivity at the mean, but not at a 

lower tax price, suggests that the functional form might not be flexible enough. Any potential 

problem, however, appears to be of second-order importance. The results at the mean are still 

21 These estimates are actually from an intermediate stage of estimation for the generalized 

two-stage least squares estimation method used for the full-model results in Table 2. The parameter 

estimates are shown in Appendix Table A.2. 
- 28 -

consistent with my central results that giving by individuals is most responsive to transitory rather 

than permanent variation in tax prices. 

Experiment 3 replaces the quadratic function in age with a step function that changes at tenyear intervals. The estimated step function is shown in Figure 1. Experiment 4 uses an altemative 

exemptions variable that excludes exemptionsthat could be taken by taxpayers for being blind or 

over age 65 in the first part of the sample period. Neither of these experiments affects the key 

estimation results. 

The fifth experiment included all years in the sample for estimation. For this experiment, 

I made no attempt to properly model expectations of future statutory tax changes that were known 

by people at the ends of 1981 and 1986. Surprisingly, the elasticity estimates change very little 

relative to the estimates based on fewer years, in spite of the fact that future expectations are 

measured incorrectly in 1981 and 1986. This robustness probably results from the fact that the 

model includes annualtime-dummy variables, which would partly control for the effects of one-time 

shifts in expectations. Consistent with this explanation, the dummy variable coefficient for 1986 

(not shown) indicates there was a 14 percent increase in giving during 1986 relative to 1985, other 

things constant. This suggests that people accelerated giving during 1986 in anticipation of the 

pending increases in the tax prices of giving. 

For all estimates reported so far, the instruments based on pre-tax income include capital 

gains. If capital gains and charitable giving are simultaneouslydetermined, conditional on the other 

variables, there may be an endogeneity bias in the parameter estimates. To test for this possibility, 

in experiment 6, capital gains were excluded from the instrument based on current pre-tax income. 

As shown, when evaluated at the giving-weighted mean, only the permanent price elasticity estimate 
-29-

is changed. However, at the lower taxprice in the bottom panel, there is virtually no difference from 

the full model results. The results of experiment 6 suggest that if capital-gains endogeneity is a 

problem for the estimates, it is only of second-order importance,influencing only the shape of the 

permanent price elasticity as a function of tax prices. 

9. Random-Effects Versus Fixed-Effects Estimates 

The estimates presented so far were produced under an assumption that the unobserved 

individual-specific effect in (7) is random and not correlated with the other right-hand variables and 

instruments. In principle, this assumptioncan be tested by comparingthe random-effectsestimates 

with fixed-effectsestimates. To do this, fixed effects can be removed by first-differencing the data 

over time, or by subtractingindividual-specificmeans from all variables before estimation. For the 

full model in (7), unfortunately,this estimation strategy also eliminates important variation in the 

instrumentsfor Y' and P'. The instrumentsfor Y' and P' are nearly collinear over the sample period 

after the individual-specificmeans are removed. As a result, I can not estimate or control separately 

the effects of Y' and P' using a fixed-effectsmethod. 

Nevertheless, it is important to examine the fixed- versus random-effects issue because 

studies by Clotfelter (1980) and Broman (1989) used panel data to show that current-year price 

elasticity estimate becomes substantiallysmaller when the panel data are first-differenced.,which 

would remove fixed effects from the model. Clotfelter's (1980) analysis suggestedthat the elasticity 

estimate is smaller because people adjust to price changes slowly. Broman (1989), however, 

provided evidencethat people actually adjust to price changes quickly. Her study implies that the 

price elasticity estimates for the first-differenced model are smaller because first-differencing 
1 

- 30 -

eliminates a bias caused by unobserved fixed effects. According to Broman's results, not only did 

the unobserved fixed effects bias previous price elasticity estimates, but they also biased the 

estimated adjustment parameter in Clotfelter's (1980) model. 

Table 6 shows random-effects and fixed-effects estimates for two reduced models. The first 

model, shown in columns 1 and 2, excludes Y' and P' ,similar to previous panel studies.22 The 

second model, shown in columns 3 and 4,includes Y' but excludes P'. Consistent with results of 

the previous panel studies, the price elasticity estimate changes from -1.29 for the random-effects 

model in column 1 to -0.76 for the fixed-effects model in column 2. This result suggests that there 

is an omitted-variables bias in the reduced model. The bias is caused by correlation of the 

unobserved individual-specific effect with other variables in the model. According to the full model 

in (7), the random effects estimates in column 1 are biased because the individual-specific means 

of Y' and P' are part of the unobserved individual-specific effect in the reduced regressions. The 

individual-specific means of Y' and P' are correlated with the instruments used to estimate the 

effects of Y and P. 

The fixed-effects method used for column 2, however, does not eliminate all omittedvariables bias because Y' and P' also change over time in a way that is positively correlated with 

changes in Y and P. Evidence of the bias can be seen by comparing columns 2 and 3. Column 3 

shows that when changes in Y' are added to the reduced fixed-effects model from column 2, the 

current-year price elasticity increases in absolute value from -0.76 to -1.39. Further, the income 

Broman (1989) included an expected future price term, but only to capture the effect 

of expected statutory changes after 1981. Otherwise, current values of Y and P were assumed to 

equal expected future values. 
- 31 -

elasticity estimate changes from 0.70 for current income to 1.66 for permanent income and 0.56 for 

transitory income. 

The fixed-effects estimates are biased in these reduced models because there were statutory 

changes in tax rates during the sample period. In the absence of statutory changes, Y' and P' tend 

to be negatively correlated because marginal tax rates increase with income. During the sample 

period, however, both Y' and P' increased because marginal tax rates were reduced. Once the 

individual-specific means are removed from the data for fixed-effects estimates in columns 2 and 

3, the positive correlationbetween changes in Y' and P' remains. Because the changes in Y' and P' 

are also positively correlated with changes in P, the price elasticity estimate in column 2 has a 

positive bias. For these same reasons, the permanent income elasticity estimate in column 3 is 

biased upward because P' is excluded from the model. For the random-effects method in column 

4,which also excludes P', most of the positive bias in the permanent income elasticity estimate in 

column 3 disappears because Y' and P' are not positively correlated when there are no statutory 

changes, and individual-specific means are not removed before estimation. 

10. Conclusions: 

My results imply that intertemporal income variations combine with progressive marginal 

taxrates to affect the way people plan their charitable contributions. Consistent with the permanent 

income hypothesis about consumption in general, people appear to smooth their annual giving 

relative to transitory changes in income. For price variation, however, the effect is just the opposite. 

Because marginal taxrates increase with income, transitory income variations change the relative 

current and future tax prices of giving. People appear to respond by substituting between current 
-32-

and future giving. In other words, they time their contributionsto take advantage of transitory price 

changes, treating current and future giving as substitutes. 

The results imply that by ignoring the separate effects of permanent and transitory income, 

previous studies have typically underestimated the effect of changes in permanent income and 

overestimated the effect of permanent changes in taxprices. Compared to the previous studies, I 

find that giving is a substantially less price elastic and more income elastic in terms of permanent 

.changesin prices and income. Giving also appears to be more price elastic and less income elastic 

than past studies in terms of transitory changes in prices and income. 

For tax policy predictions, it is often the permanent behavioral effects that matter most. 

Except during a transition period, the effects of a permanent change in taxpolicy are determined by 

the behavioral effects of permanent changes in incomes and taxprices. As I have shown, the policy 

predictions can differ substantiallywhen based on estimates of the permanent elasticities rather than 

the elasticities from previous studies, which only predict the effects of changes in current income 

and prices. 
- 33 -

REFERENCES 

Amemiya,Takeshi, Advanced Econometrics, Cambridge,Massachusetts: Harvard University Press, 

1985. 

Auten, Gerald A., Cilke, James and Randolph, William C., "The Effects of Tax Reform on 

Charitable Contributions,"National Tax Journal, September 1992,Q, 267-290. 

Broman, Amy, "Statutory Tax Rate Reform and Charitable Contributions: Evidence from a Recent 

Period of Reform," Journal of the American Taxation Association,Fall 1989,u, 7-20. 

Burman, Leonard E. and Randolph, William C., "MeasuringPermanent Responsesto Capital Gains 

Tax Changes in Panel Data," mimeo, U.S. Congressional Budget Office, 1993 and 

forthcoming,American Economic Review. 

Clotfelter, Charles T., "Tax Incentives and Charitable Giving: Evidence from a Panel of 

Taxpayers,"Joumal of Public Economics, 13, June 1980,u, 319-340. 

Clotfelter, Charles T., Federal Tax Policv and Charitable Giving, Chicago and London: The 

University of Chicago Press, 1985. 

Clotfelter, Charles T., The Impact of Tax Reform on Charitable Giving, a 1989 Perspective," in 

Joel Slemrod, ed., Do Taxes Matter? The Impact of the Tax Reform Act of 1986, 

Cambridge,Massachusetts,and London: The MIT Press, 1990,203-235. 

Deaton, Angus S., and John Muellbauer, "An Almost Ideal Demand System," American Economic 

Review, June 1980,n, 312-326. 

Feenberg, Daniel, "Are Tax Price Models Really Identified: the Case of Charitable Giving," 

National Tax Joumal, December 1987,a,629-633. 

Feldstein, Martin, "The Income Tax and Charitable Contributions: Part I-Aggregate and 

DistributionalEffects," National Tax Journal, 1975,2, 8 1-100. 

Feldstein, Martin and Clotfelter, Charles T., "Tax Incentives and Charitable Contributions in the 

United States: A MicroeconometricAnalysis," Journal of Public Economics, 1976,5, 1-26. 

Friedman, Milton, A Theorv of the ConsumFtion Function, Princeton: Princeton University Press, 

1957. 

Fuller, Wayne A. and Battese, G. E., "Transformations for Estimation of Linear Models with 

Nested-error Structure,"Journal of the American StatisticalAssociation, 1973,@, 626-632. 
-34-

Kingma, Bruce R., "An Accurate Measurement of the Crowd-out Effect, Income Effect, and Price 

Effect for Charitable Contributions,"Journal of Political Economy, 1989,z, 1 197-1205. 

Reece, William S., "CharitableContributions: New Evidence on Household Behavior," American 

Economic Review, 1979,@, 142-1 5 1. 

Schwartz, Robert A., "Personal PhilanthropicContributions,"Journal of Political Economy, 1970, 

2,1264-1291. 

Steinberg,Richard, "Taxes and Giving: New Findings," Voluntas, 1990,1,61-79. 

U.S. Department of the Treasury, Internal Revenue Service, Statistics of Income Division, Special 

Panel of Tax Returns, 1979-1988. 
- 35 -

Appendix 

Estimation steps for the full model are described as follows, where Z = (Log(y>,d2Log(y),4Log(y)) 

and Z = (Log@,d&og@),c&Log@). Current pre-tax income is y, and 7 is its ten-year average for 

each individual. The tax-law period dummy variables, d, and d,, indicate whether the year is 

between 1982 and 1986 (inclusive) or after 1986, respectively. 

First step: First, regress Log(Y) and Log(P) on X, the dummy variables for years, and Z*. Use this 

regression to create fitted values to be used in place of Log(Y*) and Log(P*). Second, regress 

Log(Y) and Log(P) on X, the dummy variables for years, Z*, and Z - Z*. Use this regression to 

create fitted values to be used in place of Log(Y) and Log(P). Estimates from the first step appear 

in Table A.1. 

Second step (2SLS): Use 2SLS to estimate the share equation parameters. The endogenousright 

hand variables are Log(P/P*), Log(Y/Y*), [Lo~(P/P*)]~, and Log(P) Log(P*), which are constructed 

by substituting fitted values of Log(Y*) and Log(P*) from the first step, above. The excluded 

exogenousvariables are constructedby substitutingthe fitted values of Log(Y), Log(P), Log(Y*), 

and Log(P*) from the first step into Log(P/P*), Log(Y/Y*), [Lo~(P/P*)]~, and Log(P) Log(P*). 

Estimates from the second step appear in Table A.2. 

Third step (G2SLS): Estimated share equation residuals from the second step are used to estimate 

the variances of the noise error term, eit,and the individual-specificrandom effect, &,. For this 
- 36 -

step, each variable that was used in the second step is first transformed by subtracting a fraction of 

each panel member's mean across years. The transformed variables are then used to repeat the 2SLS 

step and obtain operational G2SLS estimates.23 

23 The estimates are "operational" because they use consistent estimates of the variance 

terms in place of actual values. The data transformation was originally derived by Fuller and 

Battese (1973) for the two-way variance components regression model. 
Table 1: Means of Selected Variables 

Sample-population 

Variable Unweightedmeans weighted means

Marital status 0.86 0.82 

Exemptions 3.3 3.2 

Total observations 53,703 53,703 
Table 2: Charity Share Equation Parameter Estimates 

(standard errors in parentheses) /a 

Variable 

Intercept 

Age 

Age squared 

Married 

Exemptions 

Dummy, 1980 

Dummy, 1983 

Dummy, 1984 

Dummy, 1985 

Dummy, 1988 

Notes: 

Coefficient 

-0.075 

(0.01) 

-0.0011 

(0.0003) 

2.0E-05 

(2.3E-06) 

-0.0019 

(0.0014) 

0.00097 

(0.0003) 

0.0067 

(0.001) 

0.013 

(0.001) 

0.012 

(0.001) 

0.012 

(0.001) 

-0.0012 

(0.0019) 

Variable 

Log(Y*) 

Log(YN*) 

Log(PIP*) 

Log(P/P*) A2 

Var(delta) /b 

Var(epsi1on) 

Coefficient 

0.011 

(0.0007) 

-0.038 

(0.001) 

0.066 

(0.009) 

-0.040 

(0.006) 

0.087 

(0.008) 

0.0035 

0.0029 

0.0064 

0.0071 

53,703 

Total error variance 

Var(dependent variable) 

Observations 

/a Estimatesfrom generalized two-stage least squares 

/b Variance of individual-specificrandom effect 
Table 3: Estimated Income and Tax Price Elasticities 

(based on parameterestimates from Table 2; standard errors in parentheses) 

Unweightedmeans /a I Giving-weightedmeans /b

I I ExcludingP* I ExcludingP*, Y* 

Income (point elasticities) 

Permanent,d(Y/Y*) = 0 

Current 

Transitory, dY* = 0 

Tax price (point elasticities) 

Permanent,d(P/P*) = 0 

Current 

Transitory, dP* = 0 

Notes: 

Full model Full model 

1.27 1.12 1.17 

(0.02) (0.01) (0.02) 

0.82 

(0.09) 

0.05 0.57 0.60 

(0.03) (0.01) (0.01) 

-0.06 -0.49 

(0.10) (0.06) 

-1.37 -1.29 

(0.09) (0.07) 

-2.35 -1.57 

(0.13) (0.06) 

/a Mean share = 0.04; mean tax price= 0.56 

/a Mean share = 0.089; meantax price = 0.66 

i 
Table 4: Comparison of Elasticities of Giving With Respect to a 

Proportional Change in all Marginal Tax Rates 

Progressivityof Marginaltax rate 

marginal tax rates /a 20% [ 40% I 60% 

1 .o 0.12 0.33 0.73 

1.5 0.19 0.54 1.33 

2.0 0.22 0.62 1 SO 

Basedon full-model parameterestimates /c 

1.o -0.19 -0.39 -0.55 

1.5 -0.09 -0.08 0.30 

2.0 -0.04 0.03 0.54 

Notes: 

/a Ratio of marginaltax rate to average tax rate 

/b Incomeelasticity = 0.78;Price elasticity = -1.27 

/c Permanent income elasticity = 1.12;Price elasticities are -0.38,-0.53, 

and -0.75at marginaltax rates of 20,40, and 60percent, respectively 
Table 5: Additional Sensitivity Experiments, Elasticity Estimates 

Income elasticities I Price elasticities 

Sensitivity experiment Permanent I Transitory I Permanent I Transitory 

Evaluated at giving-weighted means la 

Full model (for comparison) 1.12 0.57 

1. Two-stage least squares 1.19 0.60 

2.Tobit (otherwise same as 1) 1.20 0.60 

3.Age pattern as a step function 1.14 0.57 

4.Alternative definition of exemptions 1.12 0.57 

5.Includeall years of panel 1.16 0.53 

6.Capital gains excluded 1.09 0.58 

Evaluated at a lower tax price lb 

Full model (for comparison) 1.12 0.57 

1. Two-stage least squares 1.19 0.60 

2.Tobit (otherwise same as 1) 1.20 0.60 

3.Age pattern as a step function 1.14 0.57 

4.Alternative definition of exemptions 1.12 0.57 

5.Includeall years of panel 1.16 0.53 

6.Capital gains excluded 1.09 0.58 

Notes: 

la share = 0.089;tax price = 0.66 

/b share = 0.089;tax price = 0.40 

-0.49 -1.57 

0.39 -1.55 

0.36 -1.56 

-0.46 -1.55 

-0.50 -1.56 

-0.28 -1.63 

-0.83 -1.65 

-0.76 -1.70 

-0.66 -2.07 

-0.66 -2.07 

-0.75 -1.70 

-0.76 -1.69 

-0.62 -1.80 

-0.81 -1.64 
Table 6: Random vs. Fixed Effects Estimates 

(reducedmodels; standarderrors in parentheses) 

Randomeffects I Fixedeffects 1 Randomeffects 

Variable 

Intercept 

Age la 

Age squared 

Married 

Exemptions 

Dummy, 1980 

Dummy, 1983 

Dummy, 1984 

Dummy, 1985 

Dummy, 1988 la 

Log( Y') 

WY) 

Log(P) 

Log(P) squared 

Elasticities /b 

Currenttax price 

Current income 

Permanent income 

Transitory income 

(1) I (2) I (3) I (4) 

0.16 -0.14 

(0.01) (0.02) 

-0.00044 0.00062 0.0016 -0.0015 

(2.6E-04) (3.5E-04) (3.5E-04) (2.6E-05) 

2.IE-05 8.5E-06 1.2E-05 2.4E-05 

(2.4E-06) (3.4E-06) (3.4E-06) (2.4E-06) 

0.0004 0.0029 -0.0021 -0.0021 

(0.001) (0.002) (0.002) (0.001) 

0.0020 0.00062 4.8E-05 0.0010 

(0.0003) (0.0004) (0.0004) (0.0003) 

0.0032 0.0026 0.0099 0.0071 

(0.001) (0.001) (0.001) (0,001) 

0.0091 0.0048 0.022 0.020 

(0.001) (0.001) (0.001) (0.001) 

0.009 0.0040 0.020 0.020 

(0.001) 0.001 (0.001) (0.001) 

0.0084 0.0040 0.018 0.020 

(0.001) (0.001) (0.001) (0,001) 

0.0097 0.017 

(0.002) (0.002) 

0.098 0.050 

(0.006) (0.003) 

-0.016 -0.027 -0.039 -0.035 

(0.001) (0.001) (0.001) (0.001) 

-0.057 0.012 -0.034 -0.054 

(0.01) (0.01) (0.005) (0.01) 

-0.038 -0.01I -0.00021 -0.025 

(0.005) (0.005) (0.0005) (0.005) 

-1.29 -0.76 -1.39 -1.37 

(0.07) (0.06) (0.06) (0.09) 

0.82 0.70 

(0.09) (0.01) 

1.66 1.17 

(0.06) (0.02) 

0.56 0.60 

(0.01) (0.01) 

la Age and time dummies not separately identified in fixed-effects model 

Ib Evaluatedat giving-weightedmeans; 
Table A.l: Estimates from First Step of Estimation 

(standarderrors in parentheses) 

Depende variable 

Regressors Log modified income (Y) Logtax price (P) 

(11 (2) (3) (4) 

Intercept 2.7 1.3 2.5 3.0 

(0.04) (0.01) (0.01) (0.01) 

8.5E-03 3.4E-03 -5.9E-03 -3.1E-03 

(1.1E-03) (3.1E-04) (3.7E-04) (2.8E-04) 

Age A2 -9.2E-05 4.8E-05 3.7E-05 1.9E-05 

(1.OE-05) (2.9E-06) (3.4E-06) (2.6E-06) 

Married 0.082 0.027 0.022 0.032 

(0.008) (0.002) (0.003) (0.002) 

Exemptions 0.0043 0.0066 0.0034 0.0040 

(0.002) (0.0005) (0.0006) (0.0005) 

Dummy, 1980 -0.14 -0.15 -0.044 -0.039 

(0.008) (0.002) (0.003) (0.002) 

Dummy, 1983 -1.6 -0.53 -1.5 -1.9 

(0.05) (0.01) (0.01) (0.01) 

Dummy, 1984 -1.6 -0.52 -1.4 -1.9 

(0.05) (0.01) (0.01) (0.01 

Dummy, 1985 -1.6 -0.50 -1.4 -1.9 

(0.05) (0.01) (0.01) (0.01 

Dummy, 1988 -2.6 -1.2 -2.4 -3.0 

(0.06) (0.02) (0.02) (0.02) 

Log(meany) 0.72 0.86 -0.25 -0.31 

(0.003) (0.001) (0.001) (0.001) 

Log(meany) 0.13 0.038 0.14 0.18 

x period2 (0.004) (0.001) (0.001) (0.001) 

Log(meany) 0.23 0.10 0.23 0.28 

x period 3 (0.005) (0.001) (0.002) (0.001) 

Log(y / meany) 0.82 -0.30 

(0.002) (0.002) 

Log(y/ meany) 0.058 0.15 

x period 2 (0.003) (0.002) 

Log(y/ mean y) 0.13 0.25 

x period 3 (0.003) (0.003) 

Observations 53,703 53,703 53,703 53,703 

R-square(Adj.) 0.84 0.99 0.76 0.86 
Table A.2: Share Equation Estimates from the Second Step 

(nominal standard errors in parentheses) /a 

Variable 

Intercept 

Age 

Age squared 

Married 

Exemptions 

Dummy, 1980 

Dummy, 1983 

Dummy, 1984 

Dummy, 1985 

Dummy, 1988 

Notes: 

Coefficient 

-0.092 

(0.01) 

-0.0013 

(0.0002) 

2.4E-05 

(1.6E-06) 

-0.0059 

(0.0011) 

0.0015 

(0.0003) 

0.0068 

(0.001) 

0.011 

(0.001) 

0.008 

(0.002) 

0.007 

(0.002) 

-0.017 

(0.002) 

Variable Coefficient 

0.017 

(0.0007) 

Log(YM*) -0.036 

(0.001) 

0.20 

(0.01) 

Log(P/P*) -0.010 

(0.005) 

Log(PIP*)A2 0.16 

(0.009) 

Var(delta) /b 0.0035 

Var(epsi1on) 0.0029 

Total error variance 0.0064 

Var(dependent variable) 0.0071 

Observations 53,703 

/a Estimatesfrom two-stage least squares; Standard errors uncorrectedfo 

error-term correlations caused by individual-specificrandom effects. 

/b Variance of individual-specificrandom effect 
Figure 1. Age Pattern of Giving as a 

Fraction of Modified Income (PgN) 

0.12 T 

-From estimates in Table 2 -Alternative model with age brackets