Technical Paper Series

Congressional Budget Office

Washington, DC

CHARITABLE BEQUESTS AND THE REPEAL OF THE ESTATE TAX

Robert McClelland

Tax Analysis Division

Congressional Budget Office

Washington, D.C.

(Email: robm@cbo.gov)

July 2004

2004-8

Technical papers in this series are preliminary and are circulated to stimulate discussion and critical

comment. These papers are not subject to CBO’s formal review and editing processes. The analysis and

conclusions expressed in them are those of the authors and should not be interpreted as those of the

Congressional Budget Office. References in publications should be cleared with the author. Papers in this

series can be obtained at www.cbo.gov/tech.cfm
The author would like to thank Jon Bakija, David Joulfaian and Bob Williams for their helpful comments, 1

especially regarding section II.

1

I. INTRODUCTION

1

Recent years have seen tremendous changes in tax law. For example, the Economic

Growth and Tax Relief Reconciliation Act of 2001 (EGTRRA 2001) phases out the estate tax

over 10 years until it is fully repealed in 2010. Those changes reduce federal revenues but also

alter various incentives. For example, the deductibility of charitable bequests from one’s taxable

estate provides an incentive to make these bequests so that eliminating the estate tax would

eliminate this incentive. 

Recently, two important articles have presented substantially different estimates of the

effect of estate tax repeal on charitable bequests. Joulfaian (2000) estimates the relationship in

1992 between charitable bequests and variables such as the price of giving and after-tax wealth. 

With those estimates, he calculates that estate tax repeal would cause charitable bequests to

decline by about 12 percent. Bakija, et al. (2003) analyze simulated panel data and find that

charitable bequests exhibit much less sensitivity to the tax price than is suggested by Joulfaian’s

estimates. In spite of this lower estimate, when Bakija and Gale (2003) use that estimate to

calculate the effect of estate tax repeal they conclude that charitable bequests would fall by about

37 percent.

This paper re-examines the results of the aforementioned papers by applying their

methods to 1999 and 2000 data. Once the differences in methodologies and variable definitions

are reconciled, the estimates are quite close. Further, confidence intervals can then be formed

around the estimated decline in charitable bequests.
2

II. THEORY

This section graphically reviews the concepts behind two variables that are critical to the

study of charitable bequests and the estate tax: the share of wealth charitably bequeathed and the

increase in wealth from estate tax repeal. Although written specifically about the case at hand, it

holds generally for any tax system that imposes a piecewise linear budget constraint.

In this example a decedent’s estate may be dispersed in one of two ways: it may be given

to heirs or it may be given to charity. The tradeoff between the two is defined by a budget

constraint, and in the absence of the estate tax an extra dollar contributed reduces the bequests to

he PT 1irs by one dollar (see figure 1). Heirs could receive at most W , and if C is given to charity 

1 PT

the budget share contributed S is C /W . 

e

If estates were taxed at a single rate M above some exempt amount W , then heirs could

no PT longer receive W (see figure 2). The maximum available to heirs is after-tax wealth with

no char 2 0 PT 2itable contributions W , at which point the estate tax is T = W - W . Given

contributions C2 2 , the heirs will receive H , but the loss to heirs will no longer be simply the

amount contributed. 

Instead, we must account for the decrease in taxes caused by the deductibility of

cha 0ritable contributions. Without charitable contributions the estate tax is T , but with

con 2 2 2 0 2tributions C the tax is only T . The loss to heirs is thus C - [T - T ], which is identical to

W2 2 - H , the difference between what the heirs could receive and what they actually receive. 

Because taxes decrease by M for every dollar given away the loss may also be written as 

2 2 2 2

[C - M C ] = (1-M) C or P C , where P is the “tax price” of a contribution. 
3

The appropriate 2 0 2 2 measure of the budget share contributed is then (C - [T - T ])/W , or

P C2 2 2 PT 0/W . The denominator W equals W - T , the amount potentially available to heirs. Taxes

here must be estimated in the absence of charitable bequests. Using the actual taxes paid would

define PT 2 the denominator as W - T , which would overestimate the amount available to heirs and

thus would underestimate the budget share contributed.

Introducing a progressive rate structure complicates the analysis (see figure 3). As

before, wealth g e1 reater than W is taxed, but now there are several marginal tax rates. In figure 3

3 3 e2 e2 the applicable rate is M because H exceeds W . However, wealth in excess of W is taxed at a

highe 3r marginal rate M , leading to a steeper slope. At any point on the budget constraint, the

total tax consists of two parts: a lump sum amount L equal to the tax due from all lower brackets

and a ma 3 3 e2rginal amount equal to the tax due from the highest applicable bracket, M [H - W ]. 

The maximum 3 PT 0 amount available to heirs is W , which is total wealth W minus T , the estate tax

in the absence of charitable bequests. If charitable bequests are sufficiently small, as is the case

a 3t C , the amount lost to heirs is still P C. 

But if charitable e2 bequests lower the tax rate by decreasing taxable wealth below W , then

4 4 that rule no longer applies (see figure 4). With charitable bequests C and bequests to heir H the

4 4 3 4 formula P C will overestimate the loss to heirs as W - H . The loss to heirs is actually W - H

or equiva 4 0 4lently C - [T - T ]. The budget share contributed to charity would then be 

4 0 4 3

(C - [T - T ])/W .

Repeal of the estate tax would affect charitable bequests through changes in both wealth

and the change in price. From figure 3 the estate tax consists of a lump sum amount L plus the

tax from the highest applicable bracket. Then repeal increases wealth by L and increases the tax
4

pr 3ice from P to 1 (see figure 5). Equivalently, repeal results in a lump sum increase from W to

W5 5 PT and the change in tax price results in an increase from W to W . Measuring the change in

wea PT 3 5 3 5lth as W - W instead of as W - W would obviously double count the increase from W to

WPT 5. Similarly, measuring the change in wealth as taxes actually paid (T ) in figure 5 would also

partially double count some of the change in wealth.

The appropriate definitions for several variables used in the analysis of the estate tax and

charitable bequests can now be summarized. Wealth W should be defined as gross wealth minus

T0, which is the estate tax in the absence of charitable bequests. The share of wealth contributed

S should be defined a 0s (C - [T - T])/W, where C is charitable bequests and T is the actual level

of the estate tax. When simulating estate tax repeal, the change in wealth should be L, the tax

due from all lower brackets, and the change in tax price should be from P=(1-M) to 1. P should

be defined as 1-M; M is the applicable marginal tax rate and not the marginal rate in the absence

of charitable bequests.

III. PREVIOUS ANALYSIS

Joulfaian (2000) estimates the relationship between charitable bequests and tax price and

wealth with 1992 data using a budget-share model of the form:

S = lnP + lnW + ’X + u (1)

where X is a vector of variables such as dummy variables for age ranges, region, marital status,

and gender. The share of wealth made up of business assets is used as a proxy for the desire of 

business owners to leave the business to their heirs. The deductibility of charitable bequests
For a small number of estates, estate taxes may be deferred up to 15 years. The price for these estates is 2

then 1-(1- )M - θδM where is the percent of the estate that is deductible and is discount. Joulfaian shows that

the inclusion of tax deferrals barely changes the average tax-price: 0.7743 with the deferral versus 0.7721 without

the deferral. A small number of estates elected to use the special-use valuation method (e.g., value of land as a farm

rather than the market value). See Joulfaian (2000) for more details.

5

implies that the after-tax cost of an additional dollar in charitable bequests is P=1-M. 

2

Joulfaian addresses problems caused by the large number of non-contributors by using a

maximum likelihood method similar to the tobit method. The well-known endogeneity of the tax

price is addressed by essentially using an instrumental variable estimator. Both of these methods

may be expressed as a full information maximum likelihood model (FIML):

S = L 1 lnP + lnW + ’X + u

L P F W x 2

lnP = lnP + lnW + ’X + u (2)

where PL F is the last-dollar price – the marginal cost of the last dollar contributed – and P is the

first-dollar price – the marginal cost of the first dollar contributed. After-tax wealth suffers from

an endogeneity 0 0 problem similar to the last-dollar price, but it is addressed by using W =W - T

as the de 0finition of after-tax wealth. Because W subtracts taxes under the assumption that there

are no charitable bequests, it is exogenous.

The price and wealth elasticity formulas for the budget share model in equation (1) are 

p = αΦ(z)(1/S) - 1 (3)

w

 = βΦ(z)(1/S) + 1

where z = [ LlnP + $lnW + (’X ]/F, is the standard normal cdf, and F is the estimated variance ^ ^ ^ ^

of 1 u . Because those elasticities vary across estates with z and S, estimation of the aggregate

change in contributions from estate tax repeal requires one of two approaches. Either

representative elasticities may be calculated and applied to representative changes in tax price

and wealth, or individual changes in contributions are calculated and aggregated across all
6

estates. I Lf the elasticity formulas were linear in P ,W, X, and S, both methods would lead to the

same answer. However, (z) and 1/S are nonlinear, and the nonlinearity of 1/S is accentuated

by its distribution: in 2000, 5 percent of estates gave away more than 95 percent of their assets

(1/S is less than 1.05) while 5 percent of estates gave away less than 6/100 of 1 percent (1/S is

greater than 1,700). Therefore, different methods for calculating elasticities may lead to

substantially different estimates.

Joulfaian uses the first method and calculates arc elasticities at the mean budget share and

the mean value of z: the price elasticity is estimated as about -1.7 and the wealth elasticity is

about 1.2. The percentage change in tax-price (%∆P) is the difference between the mean taxprice and unity, and the percentage change in wealth (%∆W) is calculated using the mean values

of T0 0 p w and W . The percentage change in charitable bequests is then η ×(%∆P) + η ×(%∆W),

leading to an estimated decline of 12 percent. 

Joulfaian calculates the elasticities and the percentage change in wealth without use of the

sampling weights. Because the estate tax file is stratified by wealth, use of weighted means

could lead to a substantially different result.

Bakija et al. use data from 39 years: 1924-1945, 1969, 1976, 1982 and 1985-1998. Estate

records of widows and widowers are aggregated into five wealth categories (defined in 1996

dollars). The tax-price of a charitable bequest includes federal and state estate taxes and state

inheritance taxes. The addition of state taxes helps to increase the independent variation of taxprices and wealth. Using this simulated panel Bakija et al. estimate equation (1) where X now

consists of dummy variables for wealth class, year, and state. 

The aggregated nature of their data ensures that charitable bequests are positive for most,
7

if not all, of the cells. This means that tobit or FIML – and possible inconsistency from a misspecified likelihood function – is not necessary. Further, the use of panel data avoids possible

bias caused by unobserved heterogeneity. Finally, the authors estimate their model with twostage least squares, instrumenting for both tax price and after-tax wealth. 

Their estimated price coefficient is substantially smaller than Joulfaian’s while the wealth

coefficient is about the same, suggesting that predicted effects of estate tax repeal which use

these coefficients will be smaller than Joulfaian’s. 

Instead of calculating elasticities at the mean, they derive the total change in charitable

bequests by calculating elasticities for each observation. Dividing by total charitable bequests

creates an estimate of the aggregate elasticity. Although the price coefficient is lower in absolute

value than Joulfaian’s, the price elasticity of -2.1 is greater in absolute value. The wealth

elasticity of 1.6 is a third larger than the 1.2 found by Joulfaian.

Bakija and Gale (2003) estimate the decline in charitable bequests induced by repeal for

2000. Rather than use a representative elasticity, they calculate each estate’s predicted level of

charitable bequests after repeal and sum over all estates. They also point out that elasticities vary

not only across estates but also within each estate as the tax-price and wealth change. For that 

reason they do not use individual price and wealth elasticities to calculate the effect of estate tax

repeal. 

Instead, they calculate the new level of contributions as the new level of wealth

multipl PT ied by the new budget share. The new level of wealth is defined as W . The new budget

share equals the old budget share plus the change induced by estate tax repeal. The change in

wealth is a function of the change in log tax price, ln(1) - ln(P) = - ln(P), and the change in log
8

wea PT PT lth. That change is defined as ln(W -T) - ln(W ), where T is the actual amount of taxes

paid rather than taxes due if there are no charitable bequests. Using equation (2), the new level

of contributions is calculated as 

C* = W[S -  PT PT ln(P) + ${ln(W ) - ln(W -T)}], (4) ^

whe PT re S is defined as P C/(W -T) and predicted bequests are not allowed to fall below zero. 

The weighted sum of these new contributions is 37 percent less than the initial amount of total of

contributions. Thus, the estimated decline in charitable bequests is much greater than

Joulfaian’s, even though the estimated price coefficient is substantially lower. 

The difference between declines of 12 percent and 37 percent stems from five significant

differences. First, different coefficient estimates are used to simulate the response to estate tax

repeal. Second, repeal is simulated for different years. Third, weights are used only in the Bakija

and Gale study. Fourth, different methods for simulating repeal are used. Finally, different

definitions of S and the change in wealth from estate tax repeal are used.

IV. DATA

This paper uses data drawn from 1999 and 2000 estate tax filings. Table 1 lists the years

of death for each filing year. The 1999 file was limited to deaths after 1995, and the 2000 file

was limited to deaths after 1996. Those limits leave 20,763 records in the 1999 file and 10,931

records in the 2000 file, representing 103,279 and 106,602 decedents, respectively. The samples

are stratified by wealth, and the probability of selection increases with estate size.

Using sampling weights that account for wealth stratification noticeably affects the

variation in the estimated means of several variables (see table 2. Definitions of selected
9

variables are described in the appendix). For example, the unweighted mean charitable bequest

in 2000 is $873,000, substantially more than the 1999 mean of $493,000. However, the weighted

mean bequests of $150,000 and $141,000 are about the same. Weights have a smaller impact on

charitable bequests as a share of wealth: the unweighted shares are 3.08 and 3.77 for 1999 and

2000 respectively, but the weighted shares are 2.77 and 2.73, respectively.

Oversampling large estates means that the sampling weights also dramatically lower the

estimates of terminal wealth from $3.45 million to $1.54 million in 1999 and from $5.71 million

to $1.69 million in 2000. Perhaps surprisingly, the weights have almost no effect on the tax

prices: 0.76 versus 0.77 in 1999 and 0.74 versus 0.77 in 2000. The difference is small because

the tax price is sharply bounded between 0.4 and 1.0, which makes the mean tax-price less

sensitive to changes in weights just as it makes the mean price less sensitive to the removal or

addition of individual records.

V. NEW ANALYSIS AND RESULTS

This section applies the estimation and simulation strategy of Joulfaian (2000) to 1999

and 2000 data and the simulation strategy of Bakija and Gale (2003) to 2000 data. It also shows

that although the resulting estimates of the decline in charitable bequests appear to be quite

different, with modifications the two strategies produce similar results. 

The coefficients in equation (3) are estimated using the same FIML method as Joulfaian. 

Weights are not used in the regression for the standard reason: they do not affect consistency in a

properly specified model, but they lower precision. 

The L 1999 and 2000 coefficients on ln(P ) are larger in absolute value and significantly
10

dif 0ferent from the 1992 estimate while the coefficient on the ln(W ) in 1999 and 2000 is

significantly lower than in 1992 (see table 3). Together these results suggest that the drop in

charitable bequests from repeal of the estate tax will exceed 12 percent.

By calculating the elasticities in equation (3) as Joulfaian does, differences in the

estimated effect of estate tax repeal may be decomposed into differences in coefficient estimates

and differences in the use of sampling weights. The use of weights magnifies the price effect,

which further separates the 1999 and 2000 estimates from the 1992 estimates (see table 4). The

1999 price elasticity of -1.999 is almost 20 percent larger than the 1992 elasticity of -1.698. 

Comparing these estimates with the unweighted 1999 estimate, use of the weights increases the

price elasticity by about 0.15. The 2000 price elasticity of -2.1 is more than 25 percent larger

than the 1992 elasticity, and again the weights increase the price elasticity by 0.15. On the other

hand, because the 1999 and 2000 wealth elasticities are lower than the 1992 elasticity, weights

decrease w the difference in elasticities. - 1 in 1999 is half of the 1992 value, but is even lower

if weights are not used.

Given the elasticities and the estimated percentage changes in wealth and the tax price

from repeal of the estate tax, it is now possible to estimate the change in charitable bequests (see

table 5). Because the elasticities and estimated percentage changes are calculated using the same

method in all columns of table 5, differences in the estimated decline in charitable bequests must

come from other sources. The first column reproduces the results of Joulfaian (2000). The 1999

and 2000 data suggest a substantially more serious decline: 26% and 30% respectively for the

weighted data. About 2/3 of the difference between the weighted 1999 estimate and the

unweighted 1992 estimate is due to the use of weights. The remaining difference is due to the
11

differences in estimated coefficients and differences in the unweighted distributions. 

In contrast, the sampling weights are relatively unimportant to the 2000 results: the

unweighted decline is 28 percent and the weighted decline is 30 percent. Just as there is more

variation in the unweighted sample means than in the weighted sample means, so too the

estimates from unweighted data of -12, -17, and -28 percent show more variation than the

estimates on weighted data of -26 and -30 percent. This difference is due to variation in the

estimated coefficients in table 3 and to variation in the sample means used to calculate the

decline in charitable bequests.

To identify the differences in the results arising from differences in the variables z, S,

%∆P and %∆W, the 1992 coefficients were applied to 1999 and 2000 variables (see table 6). 

Because the same coefficients are used everywhere in table 6, the difference between the

resulting estimates and 12 percent is due solely to changes in the four variables. The simulated

decline in charitable bequests using unweighted 1999 data is similar to the 1992 decline but is

lower than the 2000 estimate. However, at 19 percent and 20 percent, the weighted estimates are

very similar. 

By applying the 1992 elasticities to the 2000 percentage changes rather than applying the

1992 coefficients to z, S, %∆P and %∆W, one can further distinguish between the variables used

in the elasticity calculations (z and S) and the percentage changes in P and W. In this case the

elasticities created from 1992 coefficients and 2000 data are so close to the 1992 elasticities that

the predicted decline is the same as in table 6: 20 percent. Therefore, the difference between the

12 percent estimate and the 20 percent estimate in table 6 is due to the difference in %∆P and

%∆W and the difference between the 20 percent estimate in table 6 and the 30 percent estimate
The author would like to thank Jon Bakija for making his code available for this analysis. 3

12

in table 5 is due to difference in the coefficient estimates.

Applying the elasticities in Bakija et al. (2003) to the weighted 2000 data, the predicted 

decline is 22 percent, which is remarkably close to the 19 percent and 20 percent estimates in

table 6. However, as described in section II Bakija and Gale (2003) estimate the decline more

rigorously by calculating the effect of estate tax repeal on individual estates and then aggregating

to estimate the total change.

Calculating the percentage change in charitable bequests using their method and

parameters on the weighted 2000 data yields the same predicted decline: 38 percent. That result 3

may be sensitive to both the definition of the change in wealth and the definition of the share S. 

Section II describes the appropriate change in wealth as the lump sum amount due from all tax

brackets below the applicable rate (L in figure 5) rather than as T, the variable in equation 4. In

this application however, the difference in estimates from using one or the other definition is so

small as to disappear when the estimated percentage declines are rounded to whole numbers.

The results are more sensitive to the definition of S (see table 7). As mentioned, using

P C PT /[W -T] as the definition of S leads to a predicted 38 percent decline in charitable bequests. 

But from section I PT I, P C overstates the budget share while [W -T] understates the budget share.

PT 0

 If the denominator of S is changed to W - T , charitable bequests are actually predicted to

increase by four percent. That one difference causes a 42 percentage point swing in the predicted

change in charitable bequests. Alternatively, changing the numerator leads to a more severe

decline of 53 percent; in other words the differences in the numerator and denominator somewhat
13

offset each other. If both the numerator and the denominator are adjusted, the predicted decline

is 22 percent, which is well within the range of estimates in tables 6 and 7.

The range of estimates described so far is suggestive but does not constitute an actual

confidence interval. The data used to estimate the coefficients are different from those used to

simulate estate tax repeal and they separately create sampling variation in the estimated effect of

estate tax repeal. Those two sources of variation lead to a confidence interval for variation in the

coefficient estimates and another for the sampling variation in year 2000 data. 

If the coefficient estimates in Bakija et al. are independently normally distributed, then

the variation in C* in equation (4) will be a weighted sum of the variations in those estimates. 

However, the progressive nature of the tax structure creates a negative correlation between tax

price and wealth and therefore a negative correlation between  and $ when estimating equation ^

(1). Strong negative price responses are then likely to be estimated with strong positive wealth

responses. These two responses will tend to cancel out when calculating equation (4), leading to

a narrower confidence interval. Thus, estimating a confidence interval under the independence

assumption represents an upper bound on the interval’s width. 

Alternatively, one could ignore sampling variation in the coefficient estimates and focus

on sampling variation in the data used to simulate the change in bequests. That process can be

accomplished through the use of a bootstrap: new samples are created by drawing with

replacement from the existing data and calculating the percentage change in charitable bequests

in that sample. That method can not only estimate confidence intervals; it can take account of

bias in the estimated decline in bequests (see Hall (1992)).

The estimated bias is b = p* - p, where p is the estimated percent change in charitable ^ ^
14

bequests and p* is the estimate averaged over the simulated samples. The bias-adjusted estimate

p’ is found by subtracting the bias from p, so that p’ = 2p - p*. Using the ‘percentile method’ of ^ ^

Ha .975 .025 ll (1992), the confidence interval around this bias corrected estimate is [2p - p ,2p - p ], ^ ^

where pa is the a-th percentile in the set of bootstrapped estimates. 

To incorporate both sources of variation into a single confidence interval new coefficient

estimates are independently drawn from the appropriate normal distributions and then a new

sample is drawn from the estate tax data. The decline in charitable bequests is then estimated by

applying the new coefficient estimates to the new sample. Repeating this procedure 1,000 times

yields a bias-corrected estimate of -22 percent and a 95 percent confidence interval of 

[-16%, -28%]. Because the new coefficient estimates are drawn under the assumption of zero

covariance between the price and wealth coefficients, this interval represents an upper bound on

the size of the actual interval.

VI. CONCLUSION

Two recent articles offer drastically different estimates of the decline in charitable

bequests that would be caused by repeal of the estate tax: 12 percent in Joulfaian (2000) and 37

percent in Bakija and Gale (2003). However, with modifications the estimates are actually quite

close and a variety of methods yield estimates in the range of 20 percent to 30 percent. Using the

coefficients from Bakija et al. (2003) and the best measure of the change in wealth from estate

tax repeal implies a 22 percent decline with a 95 percent confidence interval around this estimate

of 16 percent to 28 percent.
15

Table 1. 

Number of filers by year of death and filing year

Year of Death Filing Year

1999 2000

1996 203 0

1997 2,635 0

1998 14,750 2,521

1999 3,175 7,171

2000 0 1,239

Total 20,763 10,931
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Table 2. Means of selected variables, 1992, 1999, 2000. (Dollar figures in millions)

Variable

1992

unweighted

1999

unweighted

1999

weighted

2000

unweighted

2000

weighted

Charitable Bequests 0.463 0.493 0.141 0.873 0.150

Charitable Bequests as a

Share of Wealth

3.56 3.51 3.44 4.22 3.35

Terminal Wealth 2.91 3.45 1.54 5.71 1.69

Pre-tax Wealth 3.80 4.40 1.83 7.20 1.99

First-dollar price 0.75 0.76 0.77 0.74 0.77

Last-dollar price 0.77 0.78 0.80 0.76 0.79

Percent Widowed 24.53 29.14 43.35 30.79 42.91

Percent Never married 9.48 8.49 7.81 8.96 8.08

Percent Divorced/Separated 6.72 6.62 5.15 5.91 4.67

Percent Male 66.15 61.58 53.16 60.73 52.31

Percent under 45 years old 8.00 5.25 1.11 6.82 1.02

Percent 45 or older, under 55 13.44 10.46 3.36 8.82 3.34

Percent 55 or older, under 65 20.85 17.47 7.54 13.74 7.86

Percent 65 or older, under 75 23.01 23.81 18.48 21.11 17.92

Percent 75 or older, under 85 17.35 19.91 32.90 23.40 33.90

Percent over 85 years old 17.36 23.09 36.60 26.10 35.96

Business Share of Estate 8.50 8.18 3.85 9.00 3.81

Observations 11,915 20,763 103,279 10,931 106,602

SOURCE: 1992 data from Joulfaian (2000) table 3.
17

Table 3. Estimated Coefficients

(Standard errors in parentheses)

Variable 1992 1999 2000

Constant -1.2558 (0.0858) -0.8546* (0.0635) -0.9576*(0.0822)

Ln Last-dollar Price -0.2795 (0.0308) -0.3973* (0.0242) -0.4483*(0.0330)

Ln Terminal Wealth 0.0641 (0.0064) 0.0326* (0.0047) 0.0385*(0.0060)

Business share of estate -0.1229 (0.0270) -0.2786* (0.0226) 0.0091*(0.0170)

Under 45 years old -0.2016 (0.0198) -0.1866 (0.0160) -0.3427*(0.0297)

45 or older, under 55 -0.1724 (0.0181) -0.1606 (0.0120) -0.1778 (0.0224)

55 or older, under 65 -0.1730 ( 0.0146) -0.1264* (0.0093) -0.1373 (0.0175)

65 or older, under 75 -0.1501 (0.0122) -0.0961* (0.0081) -0.1358 (0.0143)

75 or older, under 85 -0.0697 (0.0107) -0.0273* (0.0066) -0.0919 (0.0112)

Male -0.0189 (0.0088) 0.0766* (0.0107) -0.0405 (0.0098)

Widowed 0.1280 (0.0133) 0.2923* (0.0108) 0.0563* (0.0153)

Never Married 0.2993 (0.0139) 0.1232* (0.0137) 0.3190 (0.0152)

Divorced 0.1754 (0.0168) 0.0014* (0.0136) 0.0975* (0.0201)

North (east)** 0.0357 (0.0115) 0.0230 (0.0090) 0.0050 (0.0131)

Midwest 0.0433 (0.0121) 0.0318 (0.0094) 0.0230 (0.0132)

South 0.0144 (0.0111) 0.0103 (0.0085) 0.0100 (0.0119)

SOURCE: 1992 results from Joulfaian (2000). 

NOTES: * indicates a statistically significant difference from 1992 estimates (at the 5% significance level).

**Joulfaian uses North, while northeast (as defined in table A) is used here.
18

Table 4. Estimated Elasticities and Components

Year

Price

Coefficient

Wealth

Coefficient 1/S z (z)

Price

Elasticity

Wealth

Elasticity

1992 -0.2795 0.0641 28.09 -1.347* 0.0889 -1.698 1.160

1999 unweighted -0.3972 0.0326 28.42 -1.440 0.0748 -1.845 1.069

1999 weighted -0.3972 0.0326 29.36 -1.374 0.0847 -1.999 1.081

2000 unweighted -0.4483 0.0385 23.70 -1.321 0.0933 -1.991 1.085

2000 weighted -0.4483 0.0385 29.81 -1.369 0.0854 -2.142 1.098

SOURCE: 1992 results from Joulfaian (2000).

NOTES: *Imputed as the residual from equation (3) and the price coefficient and price elasticity.
19

Table 5.

 Percentage Change in Tax-Price, Wealth and Charitable Bequests From Repeal of the Estate Tax

1992

unweighted

1999

unweighted

1999

weighted

2000

unweighted

2000

weighted

Tax-price (elasticity) 25.7% (-1.7) 24.5% (-1.8) 22.6% (-2.0) 26.7% (-2.0) 22.9% (-2.1)

Wealth (elasticity) 26.6% (1.2) 24.3% (1.1) 17.1% (1.1) 23.1% (1.1) 16.2% (1.1)

Charitable Bequests -12% -17% -26% -28% -30%

SOURCE: 1992 results from Joulfaian (2000).
20

Table 6.

Percentage Change in Charitable Bequests Calculated with 1992 Coefficient Estimates and Data

from Various Years

Unweighted Weighted

1992 -12% – 

1999 -11% -19%

2000 -16% -20%

SOURCE: 1992 results from Joulfaian (2000).
21

Table 7.

Percentage Change in Charitable Bequests Calculated with Weighted 2000 Data and Various

Definitions of the Bequest Share

Definition of budget share Percentage Change

P C PT /[W -T] -38%

P C PT 0/[W - T ]

 4%

0 PT

[C - (T - T)]/[W -T] -54%

0 PT 0

[C - (T - T)]/[W - T ]

-22%
22

Figure 1

Figure 2

Wpt

BEQUESTS TO HEIRS

BEQUESTS TO CHARITY

H1

C1

Wpt

BEQUESTS TO HEIRS

BEQUESTS TO CHARITY

H1

C1

Wpt

BEQUESTS TO HEIRS

BEQUESTS TO CHARITY

We

H2 W2

C2

T2

T0

Wpt

BEQUESTS TO HEIRS

BEQUESTS TO CHARITY

We

H2 W2

C2

T2

T0
23

Figure 3

Figure 4

BEQUESTS TO HEIRS

W3 Wpt

We2 H3

C3

L

T0

BEQUESTS TO CHARITY

BEQUESTS TO HEIRS

W3 Wpt

We2 H3

C3

L

T0

BEQUESTS TO CHARITY

BEQUESTS TO HEIRS

W3 Wpt

T0

BEQUESTS TO CHARITY

C4

T4

H4 W4

BEQUESTS TO HEIRS

W3 Wpt

T0

BEQUESTS TO CHARITY

C4

T4

H4 W4
24

Figure 5

BEQUESTS TO HEIRS

W3 Wpt

C3, H3

L

BEQUESTS TO CHARITY

T5

C1, H1

W5

BEQUESTS TO HEIRS

W3 Wpt

C3, H3

L

BEQUESTS TO CHARITY

T5

C1, H1

W5
Tax price calculations for those deferring taxes (168 estates in the 2000 file) use 1-(1- )e - θδe where and are 4

defined in footnote 1.

25

APPENDIX

After-tax wealth is defined as the total gross estate plus untaxed life insurance minus

debts, expenses and estate taxes. In the cases where the executor elected to use a special use

valuation (78 elections are in the 2000 file), the market value of the estate was substituted for the

total gross estate. Debts are calculated as the sum of medical debts, Schedule L debts (net losses

incurred during the administration of property not subject to claims), and “other debts.” 

Expenses are the sum of funeral expenses, executor’s commissions, attorney fees, and “other

expenses.” Charitable bequests include claimed bequests to all recipients, 

including foundations. 

Pre-tax wealth is the same as after-tax wealth, but without subtracting estate and gift

taxes. The difference between after-tax wealth and pre-tax wealth is therefore the estate and gift

tax in the absence of charitable bequests. 

Charitable bequests as a share of (after-tax) wealth S is the dependent variable in equation

0

(1) and is defined as (C - [T -T ])/W. The last-dollar price of bequests is cost of making an

additional dollar of charitable bequests; the first-dollar price is the cost of making the first dollar

of charitable bequests. Business assets are defined as the sum of closely held stock, farm assets, 4

and “other non-corporate business assets.” Regions are defined in table A. 
26

Table A: Definition of Regions

NORTHEAST MIDWEST SOUTH

Connecticut Iowa Alabama

Massachusetts Illinois Arkansas

Maine Indiana Washington, D.C.

New Hampshire Kansas Delaware

New Jersey Michigan Florida

New York Minnesota Georgia

Pennsylvania Missouri Kentucky

Rhode Island North Dakota Louisiana

Vermont Nebraska Maryland

Ohio Mississippi

South Dakota North Carolina

Wisconsin Oklahoma

 South Carolina

Tennessee

Texas

Virginia

West Virginia
27

REFERENCES

Bakija, Jon and William Gale. “Effects of Estate Tax Reform on Charitable Giving.” Tax Policy

Issues and Options, No. 6. Washington, D.C.: Urban-Brookings Tax Policy Center, July 2003

Bakija, Jon, William Gale and Joel Slemrod. “Charitable Bequests and Taxes on Inheritances and

Estates: Aggregate Evidence from across States and Time.” American Economic Review 93 No. 2

(May 2003): 366-370

Hall, Peter. The Bootstrap and Edgeworth Expansion. New York: Springer-Verlag, 1992

Joulfaian, David. “Estate Taxes and Charitable Bequests by the Wealthy.” National Tax Journal

53 No. 3 (September, 2000)

Randolph, William C. “Dynamic Income, Progressive Taxes, and the Timing of Charitable

Contributions.” Journal of Political Economy 103 No. 4 (August 1995): 709-738