FURTHER EVIDENCE ON THE DYNAMIC IMPACT OF TAXES ON CHARITABLE GIVING

Transcription

1 IMPACT OF TAXES ON CHARITABLE GIVING FURTHER EVIDENCE ON THE DYNAMIC IMPACT OF TAXES ON CHARITABLE GIVING * KEVIN STANTON BARRETT, ANYA M. MCGUIRK, ** & RICHARD STEINBERG *** Abstract We estimate the impact of taxes on donations using a large panel of middle-class taxpayers. Our specification allows estimation of the effects of habits, time shifting, and consumption smoothing on the time path of adjustment and produces plausible simulated adjustment paths to permanent and temporary anticipated tax reforms. We find that taxes determine both the longrun level and the timing of donations, so that, even though taxes appear to have long-run behavioral effects, estimates of these effects are exaggerated if one fails to estimate the rescheduling of giving in response to tax regime shifts. Our results challenge the view that tax deductions for charitable giving are efficient. * Department of Accounting, Walker College of Business, Appalachian State University, Boone, NC ** Department of Agricultural and Applied Economics and Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, VA *** Department of Economics, Indiana University-Purdue University at Indianapolis, Indianapolis, IN In this paper, we estimate the effects of tax policy on charitable donations using a panel of 1,382 individual tax returns from the years We do so in order to provide additional evidence on the efficiency of tax incentives for giving, to better understand the time path of adjustment to new tax regimes, and to better reconcile observed giving behavior and the predictions of econometric models. The relation between charitable donations and federal tax policy has been explored by dozens of authors (as surveyed by Clotfelter (1985a) and Steinberg (1990). Almost all of these studies find that giving is price-elastic, so that tax expenditures (such as the charitable deduction or a similarly fashioned credit) dominate direct federal expenditures in support of charitable outputs. More recent studies using panel data strongly challenge that conclusion (Broman, 1989; Daniel, 1989; Frischmann and Lin, 1990; Ricketts and Westfall, 1993; Randolph, 1995), estimating price elasticities that are much smaller. Panel data estimates 321

2 NATIONAL TAX JOURNAL VOL. L NO. 2 are generally more persuasive than estimates derived from cross sections or time series for three reasons. First, panels contain sufficient information to allow one to control for a variety of unobserved but nonetheless confounding influences. Second, panels that span statutory tax changes allow one to better untangle the independent effect of price and income on giving. Finally, panels allow one to estimate timing and other dynamic effects that are lost in cross sections and overly aggregated in time series. A panel study conducted by one of us and reported in this journal (Barrett, 1991a) appears to salvage the argument in favor of tax expenditures, with a point-estimate price elasticity of 0.78, insignificantly different from the traditional critical value or its more recent refinements (Roberts, 1987). 1 In this paper, we reanalyze that panel using a more fully dynamic specification. We find that the question remains open, as the revised long-run price elasticity is 0.47, with standard error of Our new point estimate suggests that tax expenditures would be preferred only if a dollar of government spending crowds out more than cents of charitable donations, although our confidence interval includes price elasticities that justify tax expenditures for more realistic levels of crowding out. Econometric analyses of giving have been controversial because predicted impacts of tax reforms often appear inaccurate. Davie (1985) notes that, despite reductions in the capital gains tax rate in 1978 and in the marginal rate on ordinary income in 1981 (and, hence, increases in the tax price of giving appreciated assets and cash, respectively), itemized contributions increased dramatically between 1973 and 1983 (see also Clotfelter (1985b) and Bristol (1985) for a continuing debate on Davie s position). A more sophisticated analysis by Auten, Cilke, and Randolph (1992) finds some large disparities between actual donations in each of the years and the level of donations predicted by a crosssectional regression using 1979 data. To some extent, these disparities are due to changes in the age, marital status, family size, taxpayer profile (type of taxpayer who itemizes), and the definition of adjusted gross income (AGI) across the included tax years, but after adjusting for these factors, large disparities remain. They conclude (p. 289): The typical cross-section regression model does not fully predict some of the observed systematic taxpayer behavior. Most notably, the regression does not account for the short-term timing effects observed in 1981 and The regression also does not distinguish between single-year income and permanent income. Most prior studies portray giving as a static activity, with this year s giving determined by this year s tax-price and income level. Clotfelter (1980) takes the first step toward estimating a more dynamic specification, introducing habit persistence. This estimation technique allows giving to adjust slowly to changes in donor circumstances, either because donors form habits or learn of tax and income changes in tax laws with a lag. Broman (1989) takes the next step, adding a variable reflecting the expected future price of giving on the theory that tax changes may affect the timing as well as the level of giving. Barrett (1991a), like Broman, incorporates habit persistence and price expectations but uses the more efficient two-way fixed- and random-effects panel estimators. In this study, we take the next steps, adding consumption 322

3 IMPACT OF TAXES ON CHARITABLE GIVING smoothing to the menu of estimated dynamic effects and correcting the method for estimating the time-shifting aspect of taxation. We include consumption smoothing because spending need not take place in the year that income is generated. Consumer theory suggests that past income increments will be spent over the consumer s remaining lifetime so as to equate the marginal utility of consumption (and, in particular, of donating) across time periods. Thus, lagged income should have a positive effect on current giving. Fully anticipated future income will also be spent over the consumer s lifetime, suggesting that expected future income should also have a positive impact on current giving. However, because the future is less certain than the past, one expects a smaller current reaction to future income than to past income. Like Broman (1989) and Barrett (1991a), we include the expected future price of giving, because those who expect the price of giving to drop will time shift some donations to the future. However, the logic of time shifting (intertemporal substitution) suggests that the lagged price of giving should enter the estimation 1 as well. If last year s price were higher than average, all else held equal, then this year s giving should be larger than average. Thus, we expect a positive coefficient 1 on lagged price. In summary, we extend Barrett by incorporating lagged income and price and a measure of expected future income into the estimation of a habit-persistence specification. Other authors have taken alternative approaches to estimate the dynamics of taxpayer adjustment. Auten and Rudney (1990) estimate separate equations for permanent donations (where an individual s long-term average giving is explained by that individual s long-term average price and other variables) and transitory donations (where the deviation of an individual s giving in a particular year from its long-term average is explained by the deviation of that individual s current tax price from its long-term average). This is more restrictive than our approach. 2 Alternatively, Randolph (1995) identifies the effects of observed temporary variations in prices and income as transitory, and the effects of other variations in price and income as permanent price and income elasticities. However, he does not specify an explicit dynamic-adjustment 2 process. Similarly, in their study of capital gains realizations, Auten, Burman, and Randolph (1989) 2 identify statutory tax changes with permanent effects and individualspecific tax changes with transitory effects. Clotfelter (1980) separates income into permanent and transitory components using the estimated income trend of each individual. These approaches are enormously useful in reconciling and interpreting crosssectional and time-series estimates and in projecting the impact of certain taxpolicy changes, but do not allow one to project the time path of response to anticipated tax changes that are neither one time nor permanent (such as a phased-in change). Our approach allows us to project the time path of adjustment for any time path of tax changes. While more general than much of the literature, our approach does not capture all aspects of dynamic response to tax-rate changes. We have no data on bequests, and so we cannot study the dynamic relation between inter vivos giving and charitable gifts upon death (Watson, 1984). Although we allow for the time shifting of donations in 323

4 NATIONAL TAX JOURNAL VOL. L NO. 2 response to exogenous tax-rate differences, we do not allow time shifting designed to alter tax rates themselves. Our data cannot be used to estimate bunching effects, where contributions are made in alternating years when there is a statutory floor on deductibility (Feldstein and Lindsey, 1981). Our functional form does not uncover other forms of bunching, such as that resulting from a desire to make a major gift and so to maximize one s prestige and influence over the recipient or that resulting from capital campaigns that span several years (Auten and Rudney, 1990). The impact of these omissions is probably not so severe for our sample of mostly middle-income taxpayers as it would be for studies of the wealthy. However, as the wealthy supply the bulk of donations, it would be valuable for future researchers to explore these issues. DATA AND SPECIFICATIONS We employ the Statistics of Income (SOI) panel of returns from the Ernst and Young Tax Research Database to study a panel of 1,382 individual taxpayers filing itemized returns in each of the years The sample contains primarily middle-class taxpayers; the mean (median) AGI of respondents is $45,845 ($37,953) in 1982 dollars. Itemized donations were reported by 96 percent of sample taxpayers. Further details on sample selection criteria and the variables generated from these data appear in Barrett (1991a), who uses an identical sample and identical methods to construct those variables common to both studies. We then explain donations using income, the tax price of giving, marital status, number of dependents, and claims for the old-age exemption. The three most important variables are those measuring donations, the tax price of giving, and taxpayer income. Donations are the sum of itemized cash and asset gifts, restated in terms of 1982 dollars. The tax price of giving measures the after-tax cost to the taxpayer of contributing one dollar of pretax income. We compute this price separately 3 for cash and for asset gifts, and then use the contribution-weighted average of these prices to explain total individual donations. Following the common practice in this sort of study, we approximate the cash-gift price by unity minus the marginal tax rate that would apply if the taxpayer had contributed one dollar. Thus, for example, a donor in the top (39.6 percent) marginal tax bracket could contribute a dollar, receive 39.6 cents in reduced tax payments, and incur a net cost of 60.4 cents per dollar contributed. We use the tax rate that would apply to the first dollar of donations (the first-dollar price ), because this approximation removes endogeneity as a source of possible bias (some donors might lower their tax rates, and hence raise their tax price of giving, by making a large enough gift) while remaining well correlated with the actual price of giving (Clotfelter, 1985a). First-dollar prices are obtained from a tax spreadsheet, using all the relevant financial data to calculate the difference between each taxpayer s federal tax liability if donations had been zero and if donations had been $100, and then dividing by 100. In addition to the charitable contribution deduction, donations of appreciated assets avoid capital gains taxation on the appreciation portion of their value, further lowering the tax price for this type of gift. The appreciation portion of the value of asset gifts is not contained in tax data, so we make the standard assumption (justified by evidence presented in Feldstein and Clotfelter (1976) and in Auten and Rudney (1986)) that 50 percent of asset value represents appreciation. Dispos- 324

5 IMPACT OF TAXES ON CHARITABLE GIVING able income is measured by AGI minus tax liability. Again, to remove the possible biasing effect of donations on disposable income, we use a first-dollar measure of tax liability (calculating the tax liability that would be incurred if the taxpayer had instead contributed exactly one dollar). Several new variables were constructed for this study. Lagged income and price are defined in the same way as the corresponding current variables used in the previous study. These variables are known by donors with certainty, but expected income is both uncertain and unobservable. We approximate expected future income by using realized future income, a presumably unbiased proxy. All continuous variables were expressed as logs, and we estimated the following basic equation: 1 ln Contribution it = α 0 + β 1 (ln Contribution it 1 ) + β 2 (ln Income it 1 ) + β 3 (ln Price it 1 ) + β 4 (ln Income it ) + β 5 (ln Price it ) + β 6 (Marital Status it ) + β 7 (Age it ) + β 8 (Dependents it ) + β 9 (ln Income it+1 ) + β 10 (ln Price it+1 ) + ε it where the subscript i indexes individuals; t indexes time; marital status takes the value of 1 if the taxpayer s filing status is either married, filing jointly or qualifying widow(er), and 0 otherwise; age takes a value of 1 if an old-age exemption is taken, and 0 otherwise; and dependents is the number of exemptions for children living at and away from home. Habit persistence is incorporated in this basic model through the inclusion on the right-hand side of lagged contributions. The coefficient on lagged contributions can be used to calculate the percentage of the long-term response to a change in any of the other exogenous variables that will occur in one year. Time shifting is incorporated through the inclusion of the expected future price and lagged price of giving. Consumption smoothing is incorporated through the inclusion of lagged and expected future income. We estimate several variants of the above in order to exploit the panel nature of our data. The one-way fixedeffects model postulates that there is an unobserved something that is constant over time and particular to each taxpayer and that influences the taxpayer s average giving (for example, the taxpayer s religion). These individualspecific effects are captured, in effect, by regressing the deviation of a taxpayer s contributions in a particular year from that taxpayer s average donations across the sample years on similarly constructed deviations in price and income. The two-way fixed-effects model postulates that, in addition to these individual-specific fixed effects, there are year-specific fixed effects representing the influence of unobserved variables that influence every taxpayer s giving in a particular year but vary across years (for example, the level of federal expenditures on social welfare). We also estimate a one-way randomeffects model. In this model, the individual-specific effects are assumed to be drawn from a distribution of individual effects found in a larger population (there were insufficient degrees of free-dom in the time dimension to estimate a meaningful two-way random-effects model). In 325

6 NATIONAL TAX JOURNAL VOL. L NO. 2 some regards, the random-effects model is more satisfactory, for it enables one to project how the regression would apply out of sample. However, the distributional assumptions necessary for this generalization are sometimes not satisfied (and, in particular, are not satisfied for our data), so, although we report results using both models, we prefer the more robust consistency of the fixed-effects estimates. Results We tested a variety of specifications, described in full in Barrett (1991b). One specification dominated on the grounds of specification adequacy (best explanation of the data), statistical adequacy (allowing the best statistical inference), and consistency with a priori theoretical expectations the two-way fixed-effects model incorporating habit persistence and all the lag and lead variables discussed above. Table 1 reports results from the preferred specification and four alternatives: a version without habit persistence but otherwise identical to the preferred specification; a version without timespecific intercepts (the one-way fixedeffects model) but otherwise identical to the preferred specification; a version that assumes that individual effects are random (the one-way random-effects model); 3 and a version identical to the TABLE 1 ESTIMATED COEFFICIENTS Preferred Model No Habits One-Way Fixed Effects One-Way Random Effects Preferred Model, 1986 Excluded Intercept (0.593) (0.600) not estimated (0.257) (0.717) Contributions (0.012) not estimated (0.012) (0.006) (0.013) Income (0.042) (0.042) (0.043) (0.035) (0.049) Price (0.111) (0.112) (0.101) (0.093) (0.126) Income (0.044) (0.044) (0.042) (0.039) (0.048) Price (0.116) (0.117) (0.109) (0.106) (0.125) Income (0.040) (0.041) (0.038) (0.034) (0.046) Price (0.121) (0.123) (0.110) (0.102) (0.130) Married? (0.059) (0.059) (0.058) (0.025) (0.069) Old Age Exemption? (0.070) (0.071) (0.070) (0.031) (0.083) Dependents (0.018) (0.018) (0.039) (0.006) (0.021) Adjusted R

7 IMPACT OF TAXES ON CHARITABLE GIVING preferred model but excluding data from the 1986 tax year. This last specification was included in order to determine whether the unusual tax reforms passed, but not implemented, in our final sample year were influencing our results. In terms of specification adequacy, the one-way fixed-effects dominated the one-way random-effects specification at better than the significance level (using a Hausman test for the correlation between donorspecific effects and the regressors). In turn, the two-way fixed-effects specification dominates one way at better than the 0.01 level (using a conventional F test). 4 All but one of the baseline elasticity estimates have the expected sign and are highly significant. The lone exception is next year s income, which nonetheless has the proper sign and is nearly significant (P = ). The same can be said of the alternative model estimates, with the exception of the significant and wrongly signed coefficient on lagged income in the one-way random-effects model. Thus, our estimates provide stable support for the importance of habits, consumption smoothing, and time shifting as determinants of middle-class giving. Although habits are important, we find, like Broman (1989) and Barrett (1991a) (but unlike Clotfelter, 1980), that adjustment is fairly rapid. For example, our baseline estimates imply that roughly 85 percent of the change in current giving due to the change in any of our explanatory variables occurs within one year; 98 percent within two years. Similarly, the one-way fixedeffects model implies that 83 percent of adjustment occurs within one and 97 percent within two years of a price or income change. A very different picture emerges from the one-way randomeffects estimates, with only 22 percent of adjustment occurring in the first year and 71 percent after five years. However, as noted above, the random coefficients specification is dominated by the others. Finally, excluding 1986 led to a more rapid estimated adjustment, with 91 percent of the adjustment occurring during the first year following the change. Incorporating habit formation to derive long-run elasticities (Table 2), 5 we find that the long-run elasticity of, say, current price on current donations is not very different from the short-run elasticity for all specifications except the one-way random effects. Please note that the elasticities in Table 2 are long run only in the limited sense of measuring the ultimate impact on donations of a change in one period s price or income, holding price and income constant in all other periods. In particular, no account is taken of the fact that, for example, a change in price this period becomes a change in lagged price during the next period, so we label these as partial long-run elasticities. We report the full long-run elasticities for the preferred model in the text below. Also, it is important to note that the long-run elasticities are not normally distributed, because they are calculated as the ratio of two normally distributed parameter estimates (in the habit-persistence framework, partial long-run elasticities are the ratio of the price or income coefficient to unity minus the coefficient on lagged giving). Instead, long-run elasticities are Cauchy distributed, so that confidence intervals must account for the relatively thin tails in this distribution. To calculate the full long-run elasticities, we must sum the partial long-run elasticities for lagged, current, and future values of the variable of interest. 6 Doing so for the preferred model, one 327

8 NATIONAL TAX JOURNAL VOL. L NO. 2 Preferred Model b TABLE 2 PARTIAL LONG-RUN ELASTICITIES a No Habits One-Way Fixed Effects b One-Way Random Effects b Preferred Model, b 1986 Excluded Income 1 Price 1 Income Price Income (0.050) (0.131) (0.052) (0.138) (0.048) Price (0.144) a These represent the ultimate impact of a proportional change in each independent variable, accounting for the adjustment of habits but not for the fact that one cannot change this year s current price without simultaneously changing that donor s lagged price in the subsequent year. b Standard errors are simulated using 5000 draws from the relevant Normal distribution. Standard errors, which are tedious to calculate, were not computed for the less-preferred models. obtains a long-run income elasticity of 0.495, with a standard error equal to 0.103, which is similar to what most other authors obtain from panel estimators. For example, Daniel (1989) obtained an income elasticity of 0.48 (0.03) when applying a two-way fixedeffects estimator to our tax panel (restricted to the years ) with neither lags, leads, nor habit persistence. However, our income-elasticity estimate is noticeably smaller than those obtained from cross sections and from that obtained by Randolph (1995) when he distinguished permanent- from transitory-income effects using panel data. Perhaps the explanation for this difference is that the individual-specific effects we include implicitly control for an individual s permanent income, so that the estimated coefficient on income is largely picking up the impact of transitory income, which has a smaller effect on giving. Additional evidence in support of this theory is provided by Barrett (1991b), who obtained an income elasticity estimate of 0.87 (0.04) in a static specification without individual effects versus an elasticity of 0.62 (0.03) in a static one-way fixed-effects or 0.34 (0.04) in a static two-way fixedeffects specification. Full long-run elasticities also measure the proportional change in steady-state giving when taxes or income change permanently, 7 and so, the long-run price elasticity is the relevant parameter for testing the efficiency of tax incentives for giving. In the preferred model, the long-run price elasticity is 0.471, with a standard error of This point estimate of the price elasticity does not suggest that tax incentives for giving are efficient, as it is far from the critical values in the case of zero crowding out ( 1), 1 percent crowding out ( 0.99), 10 percent crowding out ( 0.84), or 35 percent crowding out ( 0.53). Figure 1 presents the empirical distribution of the long-run price elasticity that we used for hypothesis testing. 8 Accounting for the 328

9 IMPACT OF TAXES ON CHARITABLE GIVING FIGURE 1. Smoothed Empirical Distribution of the Long-Run Total Price Elasticity sampling variation of our price-elasticity estimate, there is only a 9.2 percent chance that deductions are efficient if crowding out is 10 percent, and a 42.1 percent chance of efficiency if crowding out is 35 percent. Viewed another way, if our point estimate captures the true price elasticity, then tax deductions are efficient only if crowding out exceeds 40.5 percent. Although other studies find evidence suggesting that middle-class taxpayers are less responsive than wealthy taxpayers to the charitable deduction (see the summary in Clotfelter 1985a), we do not believe this is the reason we (but not earlier researchers) reject the efficiency of the charitable donations deduction. Broman (1989) also uses the SOI tax panel. Estimating the price elasticity for middle-class taxpayers using only the 1982 cross section, she obtains a value of 1.03; estimating the same elasticity using a one-way fixedeffects habit-persistence specification over data from , she obtains a value of Daniel (1989) uses data from from the same panel, estimating the price elasticity at 1.31 when he pools the data and takes no account of individual effects, and estimating the price elasticity at 0.03 when he applies the one-way fixedeffects model. Frischmann and Lin (1990) use SOI panel data from , the same years we chose for this study, and estimate the pooled price elasticity and two-way fixed-effects price elasticities at 0.95 and 0.39, respec- 329

10 NATIONAL TAX JOURNAL VOL. L NO. 2 tively. Thus, the low price elasticities estimated here appear to be due to our panel specification, rather than the middle-class nature of our sample. In order to assess the implications of various specifications for the time path of adjustment, we simulate the adjustment of donations to an anticipated temporary increase in the price of giving occurring in two years (Figure 2). In all cases, the simulations are obtained by selecting initial values of the exogenous variables (including the lag and lead variables), calculating fitted levels of donations, and then recursively substituting fitted donations for the nextperiod value of lagged donations. We compare the dynamic adjustment path generated by our preferred model with those generated by Barrett s (1991a) preferred estimates and by Broman s (1989) most-dynamic estimates using, respectively, estimates derived from data and estimates derived from data, following a normalization that leads to approximately the same initial steady state. Specifically, we find a set of initial values for the exogenous variables such that this year s forecast donations will exactly equal last year s realized donations, choosing modelspecific initial values so that the steady states generated by the four models are approximately the same in year zero. In each case, we set the initial steady-state price equal to 0.7, corresponding to an initial 30 percent marginal tax rate, and project initial per capita donations of just under $650. We then let the anticipated future price increase to 0.8 in year 2, returning to 0.7 for years 3 FIGURE 2. Adjustment of Donations; Temporary Anticipated Price Increase, Yr2 330

11 IMPACT OF TAXES ON CHARITABLE GIVING and happily ever after, while holding the after-tax income of simulated donors constant. All the dynamic models predict an announcement effect, where donations increase in year 1 to beat the price increase. All also predict a dramatic drop in donations the year the price increase is implemented. Thus, if one looked only at the change in donations during the implementation year, one would get an exaggerated estimate of the price elasticity, confounding price, and timing effects. All the models predict an increase in donations in year 3, following the revocation of this price increase. Thus, one would also get an exaggerated notion of the price elasticity if one looked only at the change in donations between years 2 and 3, as year 2 donations are artificially low due to time shifting into year 1. The only qualitative difference here between our preferred model and the earlier dynamic models is that donations overshoot their long-run equilibrium in year 3 using the new estimates. This is because the new estimates incorporate a lagged price term that is absent from previous work. Year 3 contains some donations that were shifted forward from year 2 to minimize the impact of the price increase, and so donations are higher than the steady state. We also project the impact of a permanent and anticipated increase in the tax price of giving. Again, we normalize to produce the same initial steady state and let the price increase in year 2 from 0.7 to 0.8, but this time, the price remains, eternally, at 0.8 (Figure 3). All FIGURE 3. Adjustment of Donations; Anticipated Price Increase, Yr2 331

12 NATIONAL TAX JOURNAL VOL. L NO. 2 the dynamic models predict an announcement effect, where gifts rise in anticipation of the rise in price. All predict a decrease in donations the first year of the price increase, and the decrease is so large that one would get an exaggerated idea of the price elasticity from this shift. Notice, however, that year 2 donations are projected to overshoot their ultimate decline when one uses the new estimates. This reflects time shifting around the time of the price increase, where year 2 donations are below their new steadystate level because they were partially shifted into year 1. The simulated effects using the older estimates show a continued but small decline in year 3 and thereafter, as old habits gradually vanish and donors reach a new steadystate level of giving. Conclusions In this paper, we estimate the impact of taxes on donations using a large panel of middle-class taxpayers followed over a period of time containing two major statutory tax reforms. Our dynamic specification allows us to estimate the effects of habits, time shifting, and consumption smoothing on the time path of adjustment and produces plausible simulated adjustment paths to permanent and temporary anticipated tax reforms. We find that taxes determine both the long-run level and the timing of donations, so that, even though taxes appear to have long-run behavioral effects, estimates of these effects are exaggerated if one fails to estimate the rescheduling of giving in response to tax-regime shifts. For example, accounting only for the dissipation of habitual behavior, our preferred specification finds a price elasticity of Accounting for tax shifting reduces our point estimate of the price elasticity to Our results challenge the view that tax deductions for charitable giving are treasury efficient (e.g., that they stimulate an increase in donations that exceeds foregone tax revenues) or that they are efficient in Roberts (1987) sense (that they accomplish a given expenditure level on some good at lowest social cost). Accounting for sampling variation, one can reject the hypothesis that the deduction is treasury efficient at the three percent level. Similarly, one can reject the hypothesis that the deduction is efficient in Roberts sense at the 9 percent level if crowding out is 10 percent, and at the 42 percent level if crowding out is 35 percent. We demonstrate a simple approach to estimating some dynamic effects and find that they are important. The Ernst and Young SOI tax panel provides a treasure trove of data that could extend this line of inquiry. In addition, the approach could be extended to estimate the dynamic impacts of other forms of tax expenditure. ENDNOTES The authors wish to thank Gerald Auten, William Randolph, Partha Deb, Steven Russell, Cherie O Neil, James Yardley, Robert Brown, G. Rodney Thompson, and anonymous referees for helpful discussions. Barrett and Steinberg s research was partly supported by grants from the Indiana University Center on Philanthropy. 1 Roberts presents a formula for determining whether direct federal expenditures dominate tax expenditures on social-welfare grounds. The relevant critical value depends upon three parameters: the price elasticity of giving, the marginal tax rate, and the crowding out of giving by direct government expenditures. Using estimates, summarized in Steinberg (1991), that crowding out is between 0.5 and 35 cents per dollar, and using the current top marginal rate of 0.396, the critical value for (the absolute value of) elasticity is between 0.99 and Picking a value in this range, if there is ten percent crowding out, then tax expenditures dominate whenever the price elasticity of giving is more than Thus, 332

13 IMPACT OF TAXES ON CHARITABLE GIVING Vickrey s (1962) heuristic rule that deductions are treasury efficient whenever the price elasticity is greater than one is numerically close to the formally derived rule of Roberts (1987). Note that Roberts rule does not provide a complete assessment of the efficiency of tax expenditures, for he considers only efficiency in provision of a homogenous good. Because donors and governments differ in the allocation of their support, an aggregate elasticity is insufficient to fully assess efficiency. 2 If the true model is a two-way static fixed-effects model (neglecting, for simplicity, habit persistence, lagged income and price, and future income and price), but one instead estimates the permanent giving model of Auten and Rudney (1990), then coefficients will suffer from omitted variable bias unless there is no sample variation in the individual effects. In contrast, the transitory giving equation implicitly controls for individual-specific constants and so is unbiased regardless of the sample variation in individual effects. Auten and Rudney s finding that the estimated price and income elasticities in the permanent giving equation are significantly different from their estimated values in the transitory giving equation can be taken as evidence that individual effects matter. Relaxing the simplification, one can interpret Auten and Rudney s transitory giving equation as the special case of our dynamic two-way fixed-effects model when the true coefficients on lagged and future prices and income are zero. 3 To account for the possibility that lagged contributions are correlated with this year s error term, we also estimated an instrumental-variables model using fitted lagged contributions. None of the estimated coefficients was significantly different from the preferred model, in either a statistical or numerical sense. See Barrett (1991b) for details. 4 Barrett (1991b) provides complete details on these tests and for the tests for statistical and a priori dominance for the first three alternatives. Similar tests, available from the authors, detail the statistical dominance of the preferred specification excluding 1986 over one-way fixed effects and a no fixed-effects alternative. 5 Because long-run elasticities are calculated as the ratio of two consistent and asymptotically normal regression coefficients, they are Cauchy distributed. The Cauchy distribution has no mean (although there is a well-defined median and the distribution is symmetric about that median) and has thin tails, so that the relevant confidence intervals are of different size than the familiar Normal and t distributions. The means and standard deviations presented in Table 2 are finite sample means and deviations calculated via a Monte Carlo simulation containing 5,000 draws from a Normal distribution whose mean and standard deviations are the point estimates of the betas and the covariance of the betas, respectively, obtained from our regression. The simulation sample size is sufficient to ensure that our finite sample mean is reasonably close to the Cauchy median. We also computed the approximate means and standard deviations using formulas presented in Lindley (1965) and following Clotfelter (1980), obtaining fairly similar results. By this method, the approximate standard deviation of the coefficient on lagged income was 0.030, on lagged price 0.120, on income 0.048, on price 0.124, on lead income 0.044, and on lead price Suppose that, in period t, it is announced that the price will change by z percent in year t +1, returning to its previous value thereafter. Then, during this year, giving will change by z times the elasticity of giving with respect to future price. Next year s giving will go up by z times the elasticity of giving with respect to current price, and the following year s giving will go up by z times the elasticity with respect to lagged price, so that the sum of these elasticities produces the desired long-term impact. Technically speaking, we should compute the present value of induced changes in giving. However, as all variables are expressed in constant dollars, and the long-term real interest rate is only slightly above zero (Mehra and Prescott, 1985), discounting makes a negligible difference and we report the simple sum of long-run elasticities. 7 The proof is tedious but straightforward. See Barrett (1991b). 8 The empirical distribution was smoothed via nonparametric density methods, using a kernel distributed as N(0,1) and a bandwidth of evaluated at 128 points. This method simply makes the graph of the distribution smoother (as it would be with more than 5,000 draws). See Silverman (1986) for details. REFERENCES Auten, Gerald E., Leonard E. Burman, and William C. Randolph. Estimation and Interpretation of Capital Gains Realization Behavior: Evidence from Panel Data. National Tax Journal 42 No. 3 (September, 1989): Auten, Gerald E., James M. Cilke, and William C. Randolph. The Effects of Tax Reform on Charitable Contributions. National Tax Journal 45 No. 3 (September, 1992): Auten, Gerald E., and Gabriel Rudney. Tax Reform and the Price of Donating Appreciated Property. Tax Notes 33 No. 3 (October 20, 1986):

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