1 DYING TO SAVE TAXES: EVIDENCE FROM ESTATE-TAX RETURNS ON THE DEATH ELASTICITY Wojciech Kopczuk and Joel Slemrod* —This Abstract paper examines data from U.S. federal tax returns to shed of responsiveness, lies the timing of transactions with re- light on whether the timing of death is responsive to its tax consequences. spect to anticipated changes in the tax structure.^ The classic We investigate the temporal pattern of deaths around the time of changes example, detailed in Burman, Clausing, and O'Hare (1994), in the estate-tax system periods when living longer, or dying sooner, could some evidence that there is find significanlly affect estate-tax liability. We is the increase in capital-gains realizations in 1986 in a small death elasticity, although we cannot rule out that what we have anticipation of increased taxation beginning the next year. uncovered is ex post doctoring of the reported date of death. Realizations increased from $167 billion in 1985 to $322 billion in 1986, only to fall back to $137 billion in 1987. I. Introduction Long-term capital-gains realizations of corporate stock in December of 1986 were nearly seven times their level in the reported that The New York Times N January 15, 2000, O same month of 1985. Other examples of large timing re- in the first week of the new millennium local hospitals sponses include exercise of stock options (Goolsbee, 2000), had recorded an astonishing 50.8% more deaths than in the charitable contributions (Burman and Randolph, 1994), and last week of 1999.' The suggested that this phenom- rimes firms' shifting of taxable income through deferred income enon was due to infirm people willing themselves to stay recognition and accelerated expense recognition (Scholes, alive long enough to witness the dawning of the new age. Wilson, and Wolfson, 1992). Apparently, the anticipation of momentous events can mo- tivate people to live longer. This evidence raises the intriguing question of whether on the Timing of Evidence on the Effect of B. Taxation the timing of death responds to economic factors. Could the " Decisions "Noneconomic decision? timing of death be. to some extent, a rational Economists presume that the timing of other important There is also evidence that financial considerations affect events, such as childbearing or marriage, may be so affected— the timing of decisions that are not generally thought of as why not dying as well? being economic. For example, Sjoquist and Walker (1995) In this paper we examine data from U.S. federal estate- conclude from an analysis of Census data that the marriage tax retums to shed light on this question. We investigate the penalty embedded in the U.S. income tax has a significant temporal pattem of deaths around the time of changes in the negative effect on the timing of marriages: as the penalty estate-tax system—periods when living longer (or dying increases, fewer couples marry in the months of November sooner) could significantly affect estate-tax liability. These and December relative to the number of marriages during periods provide ideal natural experiments enabling us to test the first few months of spring in the new year. Aim and for the presence and strength of this particular kind of Whittington (1995). using data from the Panel Study on behavioral response to taxes. Income Dynamics, also find that taxes have a significant effect on the probability of a couple delaying marriage from the last quarter of one year to the first quarter of the next Taxation on the Timing of Evidence on the Effect of A. year. They find no evidence, though, of taxes having an Economic Decisions effect on speeding divorce to the current year to avoid a There is a vast literature, briefiy summarized in Auerbach year's marriage penalty. Gelardi (1996) reports a significant and Slemrod (1997), conceming the impact of taxation on drop in the percentage of marriages occurring in the last economic decisions ranging from labor supply to business months of the tax year following tax-law amendments in organization to exercise of stock options. Slemrod (1990) Canada, as well as in England and Wales, designed to characterized the magnitude of behavioral response as fit- eliminate the tax benefit of marrying just prior to the tax ting a hierarchy, at the top of which, with the largest degree year-end. Dickert-Conlin and Chandra (1999) find that the timing Received for publication February 14. 2001. Revision accepted for of births is sensitive to tax incentives. Under the U.S. tax publication January 25, 2002. system, the tax benefits of having a child are (fully) realized * University of British Columbia and University of Michigan, respec- tively. only if the birth takes place before midnight, January 1. We are grateful to the Statistics of Income Division of the Internal Using a sample of children from the National Longitudinal Revenue Service for allowing access to confidential estate-tax return data under a data disclosure agreement. We especially thank Barry Johnson of SOI for patiently explaining the data structure and facilitating our analy- - The second rung of the hierarchy includes accounting and renaming Alex Fisher. Robert Greebel. and Cassie Stone provided assistance on sis. responses, such as the shift from Subchapter C to Subchapter S corpora- the history of estate-tax provisions. David Lenter provided assistance with tions after the Tax Reform Act of 1986 inverted the long-standing mortality data. We thank David D. Jones, David Joulfaian, Janet McCub- relationship of the top corporate and top individual tax rates. The third bin. and Antonio Rangel for valuable comments. rung, the least responsive, comprises "real" decisions such as labor supply ' Hershey (2000). or saving. The Review of Economics and Statistics, May 2003. 85(2): 256-265 O 2003 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology
2 DYING TO SAVE TAXES: EVIDENCE FROM ESTATE-TAX RETURNS ON THE DEATH ELASTICITY 257 writing a will whose terms are contingent on heirs' behavior. Survey of Youth, Dickert-Conlin and Chandra find that the Even under this scenario, observing a death elasticity may probability that a child is born in the last week of December, be considered as evidence against the pure life-cycle model, rather than the first week of January, is positively correlated and in favor of a model with a strategic bequest motive. with tax benefits from so doing; they estimate that increas- ing the tax benefit by $500 raises the probability of having a child in the last week of December by 26.9%. Institutional Background II. Estate Tax A. C. The Timing of Death The modem U.S. estate tax was introduced in 1916. If birth, why not death? Of course, barring a future Initially, the highest marginal tax rate was just 10%, on technological advance, any effect of tax policy on death estates above $50,000,000. The tax rates were increased only could be a timing response. There is certainly a large twice during 1917, and then they were reduced in 1919 and literature on how average longevity responds to changes in, Starting in 1932, a series of five consecutive tax 1926. for example, health care, but we know of no evidence about reforms increased the top marginal tax rates to 77%. At that its high-frequency response to pecuniary incentives. In the level the tax rates stayed until 1976. Between 1977 and introduction we referred to the millennium-end evidence 1987 the exemption level changed every year. The Tax that the timing of death is responsive to nonpecuniary Reform Act of 1976 and the Economic Recovery Act of incentives. There is a substantial body of evidence corrob- 1981 also modified the rate structure (the latter was phased orating this phenomenon in other contexts. Phillips and in over three years). King (1988) report that, among Jews, the number of deaths was lower than expected in the week before Passover and Estate-Tax Changes B. higher than expected in the week after; the pattem was most pronounced in years when the holiday fell on a weekend, We examine the timing of deaths resulting in taxable when it is most likely to be celebrated by the largest number estates in the period surrounding 13 major changes in the of people. Phillips and Smith (1990) find that mortality estate tax." Eight of them (3/3/1917, 10/4/1917, 6/2/1924, among Chinese dips by 35.1% in the week before the 6/6/1932, 5/10/1934, 8/30/1935, 6/26/1940, 9/20/1941) Harvest Moon festival and peaks by the same amount in the were tax increases, and five of them were tax decreases week after. Anson and Anson (1997) find a similar effect (2/24/1919, 2/26/1926, 10/21/1942, 1/1/1983, 1/1/1984). related to the timing of Ramadan for Moslems living in These tax reforms involved changes in the tax structure, and Israel, and note that the effect was larger for women than for occasionally also in the exemption level (but always with men, refiecting their different roles in the celebration of the the same direction of changes in tax liability for all estates). holy-day rites. Phillips and Feldman (1973) claim that the The chronology of events leading to the tax changes— same phenomenon occurs around birthdays and presidential and therefore the degree to which the effective date might elections, although Schulz and Bazerman (1980) argue that have been anticipated—varied somewhat. The pre-1980s this analysis does not withstand close scrutiny. The consen- reforms took effect on the day they were signed by the sus of this literature is that death can be briefly postponed president. Our reading of newspaper accounts of the time until after the occurrence of a significant occasion.^ suggests that once the House and Senate conference agreed on the tax bill, that the president would sign it was a tmplications for Bequest Motives D. foregone conclusion. As the chronology in Table shows, A1 the elapsed time between the two dates ranged from 2 to 18 A nonzero death elasticity is consistent with the notion of days, and averaged 6.6 days. The time between the passage a bequest motive. Altruistic individuals should consider of a tax bill in the Senate and presidential signature ranged adjusting the timing of their death if by so doing it will from 5 to 63 days, and averaged 19.1 days. The generally benefit their heirs. There is, however, another possibility. swift procedure strongly suggests that the effective date of Decisions about prolonging the life of a critically ill person the prewar tax bills could to some varying extent be antic- (e.g., regarding whether to continue with life support) are ipated. The timing and content of reforms of the 1980s were often made not by the dying person but by others, including known in advance, because they were part of legislation the potential heirs themselves. For this reason, observing a nonzero death elasticity would not definitively establish the * These are the reforms that involved significant changes in the tax rate presence of an altruistic bequest motive on the part of the structure, as identified by McCubbin (1990) and Luckey (1995). Because decedent. Note, however, that a parent anticipating the of the incomplete coverage of our data detailed in section ni, we cannot possibility of self-serving behavior by potential heirs might analyze a few tax reforms, such as the changes in the rate structure and exemption level between 1977 and 1982. Because of data deficiencies at an earlier time alter his or her behavior, perhaps by related to inconsistent sampling rules across years, we also do not examine changes in the exemption level between 1985 and 1987 and a small modification of the tax rate structure introduced by the Omnibus Budget ^ There is also a literature on the pattern of suicides around major public Reconciliation Act of 1987 that applied only to very large estates (above holidays, but the contentious findings on this topic are related to the theory $10,000,000). of the effect. broken-promise
3 258 THE REVIEW OF ECONOMICS AND STATISTICS designed to gradually increase the tax credit and phase out tax refonn. Because for later years the sampling procedure high marginal tax rates. changed exactly at the time when tax reforms were imple- The changes in tax law usually involved more than just a mented, we analyze in this way only the pre-1945 reforms. change in the tax rate structure. On a few occasions the In order to make this comparison meaningful, tax returns definition of taxable estate changed, and we take account of before and after a tax reform need to be drawn from the that in the analysis below. Occasionally, the definition of same population. For that reason we investigate only those gross and net estates changed as well. This is relevant retums with a reported net worth above the larger of the pre- because the filing requirement is expressed in those terms, and postreform filing thresholds. Implicitly, this amounts to so that some size classes of estates would appear in the data treating net worth around the tax reform as exogenous. This before but not after a tax refonn, or vice versa. As men- assumption would be unacceptable for analysis over a tioned below, we deal with this issue by considering only longer period, but it seems to be reasonable to make it for an those returns with a reported net worth that is above the analysis of the decisions regarding a short of period as we larger of the pre- and postreform thresholds. do here.^ Some of the pre-1945 tax reforms did not take effect at midnight. Instead, the law specified a precise time of day other than midnight when the new law started to apply. As III. Data a result, retums filed for decedents who passed away on the Our analysis makes use of an extraordinary sample of day of the refonn may be subject to either of the two estate-tax returns filed from the inception of the modem statutes.* For this reason, for these reforms' we exclude U.S. tax until very recently. This database contains most of from the analysis retums that report the reform date as the the information from estate-tax returns filed in every year date of death. between 1916 and 1945, as well as returns filed in 1962, Table 1 summarizes this data. As a basis of comparison, 1969, 1972, 1976, and all years between 1982 and 1965, it first gives the number of tax retums filed reporting the 1996. the returns actually all For the years 1916 to 1945, date of death to be the day of the tax reform. Then it reports filed in those years (provided they were not missing at the number of retums with date of death within 1, the average time the data were entered in the database) are included. The 3, 7, and 14 days of the tax reform. The averages do not postwar data are a stratified sample of all returns filed, with include the day of the reform. The table contains /-statistics sampling probabilities available to enable us to statistically and /7-values for the mean of the number of retums filed represent the unsampled returns as well. McCubbin (1990) within a given number of days from the tax refonn in the describes the origin and structure of the data in detail. lower-tax regime to be greater than of those filed in the The information requested on the tax return changed over higher-tax regime.'" Note that reforms of 1919, 1926, and time, as did the items from the returns that were placed in 1942 are tax decreases (denoted by D in the third column of the data set. In one key respect, the data for the pre-1945 the table) and the others are tax increases (denoted I). period are better: infonnation on the day of death is avail- There is some evidence for the presence of a death able for every individual, so that it is possible to identify a elasticity for the 14-day window. The tests for differences in complete population of individuals dying close to any tax the means are significant at the 10% level, and in the reform. The postwar tax reforms coincide with the begin- expected direction, for the reforms of 3/3/1917, 1926, 1934, ning of the year, and thus in every case also correspond to and 1942. This includes two out of the three tax decreases differences in the sampling for this period. This pattem is particularly interesting in that one might expect the behavioral response to tax decreases to be stronger: it is more plausible that people live longer to rv. Aggregate Analysis lower estate taxes than that they die sooner to save taxes. The evidence for shorter windows is less clear, which is not We begin with the simplest possible approach for detect- surprising in light of the small number of observations. ing the effect of estate-tax changes on the reported dates of The foregoing analysis of dates of death makes no use of deaths: observing the number of returns filed that report dates of death within a period of days before and after the ' In other work (Kopczuk & Slemrod, 2001), we examine the effect of the estate tax on the value of reported estates. ' As noted earlier, there may also be nontax behavioral responses with * It was not possible to ascertain precisely which law wa.s applicable regard to end-of-year deaths. We return this issue later. from the magnitude of the estate and the reported tax liability, because the The sampling procedure used in choosing estates filed in 1985 differed * tax-liability variable available in the data set was reduced by certain from those for other years. In particular, no individuals who were older credits whose magnitude is not known. than 45 and had estates below $5 million were sampled. Most tax returns 'These are the reforms of 1919, 1924. 1926. 1932, 1934, 1935, 1940, are filed within 3 years of decedent's death (more than 99%, according to 1941, and 1942. Johnson. 1994), so that it is unclear if data between 1982 and 1985 are '" This is a standard one-sided /-test for equality of the means of two representative. For this reason and we do not include this data in the populations (here, the average numbers of deaths before and after the tax pooled specification. reform), with standard deviations calculated based on a 30-day window.
4 DYING TO SAVE TAXES: EVIDENCE FROM ESTATE-TAX RETURNS ON THE DEATH ELASTICITY 259 AVERAGE OF DECEDENTS DYING WITHIN 1, 3. 7, AND 14 DAYS OF TAX REFORMS TABLE 1.— NUMBER Within Standard Within Within Within Day of Reform 14 Days Deviation 7 Days 3 Days Reform Date 1 Day Before 23.86 24.67 03/03/1917 5.61 28 27 24.93 22.21 4.55 20.57 23 23.00 After 1.41 1.20 0.40 0.55 /-Stat. 0.12 0.08 0.35 0.29 p-Value 5.06 20.00 21.14 23 19.33 Before 12 10/04/1917 4.79 15.67 18.86 20 19.43 After 0.61 0.65 0.91 0.43 r-Stat. 0.27 0.26 0.18 0.33 p-Value 28.21 7.53 27.14 29.67 36 Before 21 D 02/24/1919 5.33 29.93 31.00 33.00 35 After 0.70 l.U 0.11 0.63 f-Stat. 0.24 0.14 0.27 p-Value 0.46 30.64 5.02 33.29 31.67 35 Before 36 06/02/1924 31.64 5.60 33.57 29 31.00 After 0.50 0.10 0.15 0.80 r-Stat. 0.44 0.31 0.21 0.46 p-Value 4.08 18.57 18.43 23 20.33 Before 16 02/26/1926 4.65 20.86 19.71 19.00 After 17 1.47 0.37 0.49 0.97 r-Stat. 0.07 0.31 0.17 0.36 p-Value 9.14 3.46 10.14 7.67 9 10 Before 06/06/1932 3.42 9.50 9.57 10.33 15 After 0.49 -0.23 -1.23 -0.95 /-Stat. 0.31 0.59 p-Value 0.89 0.83 26.71 4.94 24.67 28.00 20 26 Before 05/10/1934 24.29 24.86 5.02 23.67 24 After 0.70 1.97 0.25 0.57 /-Stat. 0.24 0.03 0.40 0.29 ;»-Value 25.29 26.29 4.07 28.00 26 Before 28 08/30/1935 26.64 5.39 24.00 25.29 21 After -0.75 0.74 0.39 /-Sut. 1.03 0.77 0.23 0.35 0.15 p-Vaiue 35.00 35.67 5.36 35.00 36 Before 40 06/2.V1940 36.57 6.90 36 35.00 35.07 After -0.48 0.13 -0.03 /-Stat. 0.00 0.51 0.68 p-Value 0.50 0.45 37.21 7.40 34.67 35.86 30 Before 31 09/20/1941 40.67 37.57 38.86 6.33 After 35 -0.47 -1.07 -0.63 /-Stat. -0.51 0.84 0.68 0.73 p-Value 0.70 5.09 2.'i.33 28.50 29.14 33 Before 32 10/21/1942 6.07 38.67 34.43 34.79 After 43 2.97 1.77 2.92 1.26 /-Stat. 0.00 0.04 0.00 p-Value 0.11 Note: I or D in die itecond column refcni to whether the tax reform was an incrciuc or a decrease in tax liability. The last column reports the standard deviation of the daily number of deuthn during the 30 days und p-ytSua are obtained using test for equality of meant using standaid deviation^i bailed on a 30-day window. ntotm. r-slatistici before and aftes a The included." It is clear that the potential tax saving is much the fact that the financial incentive to postpone or accelerate the tax changes, in particular 1932, 1934, higher for some of death or its reported date varies greatly across the reforms, and across individuals for a given reform. To investigate this 1935, and 1942. In some cases (1935,1941,1942), the mean issue we calculate, for every individual with a reported date tax savings before and after the tax change are statistically of death close to a tax reform, the tax liability under the old significantly different. In 1935 and 1942 the mean tax and new tax systems; one of these figures is a counterfac- saving is higher in the low-tax regime, but in 1942 it is tual, or hypothetical, tax liability. (Details of the calculation are presented in the appendix.) The difference between " Most of the reforms affected almost everyone subject to tax. Excep- tions are: the refonns of 1924 and 1934, which each increa.sed only the top these two tax liabilities is our measure of the tax incentive rates without affecting tax rates for smaller estates (30% and 38% of our regarding the time of death. sample had potential tax savings, respectively) and the 1980s reforms, Table 2 presents some summary information about the sample when the unlimited marital deduction was in place (60-70% of our had positive savings). During the remaining nine reforms, more than 98% average and median tax incentive, or potential savings, for of our sample had potential changes in tax liability. In the regression people who died before and after a given tax reform. Only analysis that we report later in the paper, we include individuals with zero individuals who could have saved a positive amount are potential savings.
5 260 THE REVIEW OF ECONOMICS AND STATISTICS STATISTICS FOR THE ESTATE-TAX REFORMS DESCRIPTIVE 2.— TABUE Number of Individuals Tax Saving (current dollars) Reform Date Weighted Unweighted Median Mean Dev, Std. 3/3/1917 I Before 349 349 285,8 1.114 4,456 After 318 318 4.471 225.9 1.608 10/4/1917 Before 280 4,142 280 256,8 783 I 260 After 260 186.1 3.271 1,406 02/24/1919* Before 392 392 3,560 417,5 419 D After 416 416 632,6 3.609 391 I 02/06/1924* Before 132 132 1,071,3 77.122 62.153 After 126 126 1.102,4 12.110 7,319 257 02/26/1926* D 257 Before 18,674 1.389,2 7.352 After 288 288 1,313,9 21.761 7,183 06/06/1932* I Before 141 141 14.056 5.788,7 2.332 5.851,7 132 132 After 15.895 2.392 05/10/1934* I Before 3.247,1 156 156 35.360 11.869 124 124 After 4,235,3 21.059 8.366 Before 1 08/30/1935* 348 348 8.032 2.732.0 829 After 366 366 6,345 2.037,5 618 I 06/25/1940* Before 483 140.4 324 483 1.599 After 483 2,417 192.4 483 1.066 1 09/20/1941* 508 Before 508 10,017 1.929,6 965 After 535 535 8.235 1.563,6 1.120 5,211,4 10/21/1942* 390 390 Before D 4,630 95 After 482 482 4.404 79 4.688,1 Reforms of the 1980s D 01/01/1983 557 Before 1512,3 16.500,0 16.146 810 After 1672,9 53 16.500,0 2.949 17.895 01/01/1984 D Before 40 1345,4 17,000.0 17,070 6,489 After 1870.8 17.000.0 49 23,131 23.786 * Day of the reform is excluded. 1: The pre-t943 data are based on a 100% sample of esule-lax are based on stratified nmdom samples, for which the sampling probabilities change from year to data from the 1980s returns: Note Ihe ycoi. 2: Only individuals with positive savings are included. See footnote 11 for di.scussion Note for individuals dying within 14 days of the tax reform. Note 3: The nutnhetx are higher in the high-tax regime. Overall, means and medians different. This suggests that one has to be careful to make of tax savings do not suggest that the behavioral response, sure that outliers do not unduly affect the conclusions. if any, should be concentrated among the richer part of the Table 3 contains more information about the potential tax sample. saving of different tax reforms. Mean savings in constant 1945 A comparison of means and medians in table 2 suggests dollars (multiplying by 9.63 yields 2000 dollars) are shown, as that the distribution of potential tax saving is highly skewed. well as the average ratio of the potential tax saving to the individual's net worth. The reforms vary significantly in the This is especially obvious for the reform of 1924, when the medians are very close, but mean tax savings are very magnitudes of potential savings, ranging firom $2,577 in 1940 MEAN AND MEDIAN POTENTIAL TAX SAVING. OVERALJ. AND BY TAX REFORM TABL£ 3.— Mean Tax Saving Saving Median Tax Share in Net Value Value Share in Net Reform Date Worth (%) Worth (%) (1945 $) (1945$) 10.772 1,8 All (except 1980s) 0,9 1.532 By Reform 358 I 3/3/1917 6.265 0.5 0,3 308 10/4/1917 5.226 I 0,2 0,5 D 2/24/1919 0.5 3,731 505 0,8 I 0.4 6/2/1924 1,129 0,8 47,765 D 0,7 2/26/1926 1.2 20.650 1.378 I 3.4 6/6/1932 19.696 3,7 7.629 5/10/1934 I 4,701 2,0 1.4 39,015 3.133 2,5 2,3 9,399 I 8/30/1935 1 0.4 2,577 0,2 6/25/1940 211 9/20/1941 1 2.106 11.126 3.5 2,4 10/21/1942 4,976 3,4 D 5.302 3,6 Reforms of the 1980s 1/1/1983 D 2,9 3,130 3.078 1,6 1/1/1984 3,583 D 3,1 3.073 2,5 * See notes to table 2.
6 DYING TO SAVE TAXES: EVIDENCE FROM ESTATE-TAX RETURNS ON THE DEATH ELASTICITY 261 TABLE DYING IN THE LOW-TAX REGIME AS A FUNCTION OF OF TAX SAVING 4,— PROBABILITY POTENTIAL Independent Variable Relative Tax Absolute Tax Log of Absolute Deaths in High- and Reform Constant Constant Saving (1945 $) Saving $) Constant Saving (1945 Low-Tax Regimes Date All (except -0.0109 1.3857** 0,0173** 1980s) 0,0004 3954 0.0280** 0,0098 (0,0141) (0,0176) (0,0003) (0.6976) (0.0074) (0.0228) 4155 Reform-Specific Regressions 0,0584 6,9134 0,0246 0,0000 0.0281 318 03/03/1917 0.0018 I (0,0493) (0,0014) (0,0790) (0,0633) (0.0310) (8,3583) 349 0.0587* 0,0011 -0.0687 0,0407 -0,0320 I 16.4911* 260 10/04/1917 (0,0704) 0.05533 (0.0861) (0,0025) (0.0342) (9,5632) 280 0,0436 0,0353 -0,0092 5,6060 0,0005 -0,0597 D 395 02/24/1919 (0.0480) (0,0631) (0,0052) (0.0770) (0,0286) (5.5281) 419 06/02/1924 -0.0333 -0,0231 -0,0407 5.4666 443 0,0244 1 0,0003 (5.0264) (0.0005) (0,0442) (0,0425) (0,0480) 429 (0,0265) 0,0001 0,1847 0,0891 -0,0344 -0,9970 0,0750 258 02/26/1926 D (0.0543) (3.5177) (0,0377) (0.0671) (0,0005) 292 (0,1289) -0.0345 -3,3180 0,1952 0,0633 0,1617 -0.0011 133 I 06/06/1932 (4,1634) (0,0865) (0,0022) (0,0607) 142 (0,2820) (0,1695) 0,0005 0,0566 0,0815* 05/10/1934 4,3427 I 0.0295 340 0,0459 (0,0512) (0,0468) (0.0005) 392 (0.0557) (2,8996) (0.0210) -0.1437 4,6057 0.0044 -0,0729 0.0503 -0.2092* I 08/30/1935 373 (0,0027) 354 (0,0527) (3,3223) (0,0321) (0,1218) (0,0925) 491 06/25/1940 -0,0016 0,0027 0,0772 I -13,9118* -0.0506* 0,0567 (0,0014) (0.0518) (0,0402) (7,9534) (0,0276) (0,0586) 490 09/20/1941 -0,0432 544 -0,0890 1,7881 0.0291 -0,1179 1 0,0015 (1,2409) (0,0577) (0,0416) (0,0015) (0,0204) 521 (0,0745) 6.0601* 0,0786 10/21/1942 -0,0266 D 0,2554** -0.0782 0,0122 399 (0.1093) (0,1288) (0,2480) 487 (3,6403) (0,0648) (0,0205) Reforms of the 1980s -0,2424** 0.0529 2457,0 0,2212*** -0.3008*** 8.3163*** -0,6699*** 01/01/1983 D (0.1197) (0,0536) (2.1572) (0,0268) (0,0596) 2013.7 (0,0787) -0,2337 01/01/1984 0.0261 0,0096 2697.9 17.2686*** -0.2160 D 0.1412** (0,1473) (0.1208) (0,0367) 2891.5 (6,3250) (0.1582) (0.0640) level, respectively. ••*, ••, and " denote significance at the 1%. 5%. and 10% Note: We compute and examine three different measures of tax to $47,765 in 1924. The medians also vary quite a bit, from saving: (1) the absolute value of the potential tax saving (in $308 in 1917 to $7,629 in 1932. In most cases, the medians are significantly smaller than the means. The mean ratio of saving 1945 dollars); (2) the tax saving expressed as a fraction of to net worth also varies significantly, fix)m 0.4% to 3.7%. The the decedent's net worth, and (3) the logarithm of the medians range from 0.2% to 3.6%. absolute tax saving (in 1945 dollars) plus $100.'^ We pursue the last two measures in order to reduce the influence of Regression Analysis Micro V. large outlying values, and because we suspect that the incentive of any dollar amount of tax saving may be smaller If the (reported) date of death responds to tax changes, the larger is the overall size of the estate. one should observe that the probability of dying in the We first pool all of the data, and then separately analyze low-tax regime is a function of the tax saving from so doing. the data for each tax change.*^ Table 4 reports the results for To test this hypothesis, we run a series of probit regression deaths that occurred within 14 days of the tax reform. The analyses spanning a short window around estate-tax third column of this table shows the number of individuals changes, with the sole right-side variable being a measure of who died in the high and low tax regimes for each reform, the potential tax saving from dying in the low-tax regime, respectively. The pooled regressions suggest that there may which may be before or after the tax law change.'^ Thus, we be a significant death elasticity. When the tax saving is are examining whether the probability of dying in the measured either in log terms or as a fraction of net worth, low-tax regime, whether that is before or after a tax change, depends on the tax saving from dying then rather than dying '•' More precisely, this variable is defined as log(100+saving)-log(100), during the high-tax regime. so that it equals zero when there is no potential tax saving. We use sampling weights in the regressions. This matters only for the '* '^ reforms of 1983 and 1984, The results when weights are not used share the For each refomi. taxes for all individuals change in the same direction. qualitative features of the ones presented here. We report the robust Therefore, for each refonn it is unambiguous to refer to one of the tax regimes as the high-tax one and to the other as the low-tax one. For standard errors. In the regressions the tax savings are expressed in real individuals whose tax liability is the same under either regime, we set the (1945) dollars. The pooled regression does not include the reforms of the low-tax dummy according to the time of their death. In a sense, people 1980s, The results when they are included show stronger behavioral with zero tax saving constitute a natural control group. response than what is reported in the pooled results excluding the 1980s,
7 262 THE REVIEW OF ECONOMICS AND STATISTICS 5.— PROBABIUTY OF DYING IN THE LOW-TAX REGIMES AS A FUNCTION TABLE there is a statistically significant relationship between the POOLED OF POTENTIAL TAX SAVING: REGRESSIONS DIFFERENT FOR ALLOWING probability of dying in the low-tax period and the tax saving SEASONAL PATTERNS ACROSS REFORMS iFrom so doing. The probit coefficients imply'^ that a 1% Independent Variable increase in the ratio of tax saving to wealth would increase Log of Absolute Relative Tax Absolute Tax the probability of dying in the low-tax period by 0.6%. In Tax Refomi Saving (1945 $) Saving Saving (1945 $) the logarithmic specification, a $10,000 tax saving (using Tax saving 2000 dollars, which corresponds to $1034 in 1945) is coefflcient 0.0004 0.0175** 2.1459** associated with an increase of 1.7% in the probability of 0.0087 (0.9043) (0.0003) dying in the low-tax period. We find no significant relation- Reform Dummies I 03/03/1917 0.0560 0.0478 0.0230 ship for the absolute tax saving specification, which we (0.0488) (0.0516) (0.0486) suspect is due to the noise introduced by large outlying 10/04/1917 0.0120 I 0.0362 0.0446 values of the potential tax saving. (0.0541) (0.0566) (0.0540) D 02/24/1919 0.0289 0.0499 0.0663 The results for individual tax refonns are not nearly as (0.0475) (0.0440) (0.0434) strong, although most of the estimated coefficients have the 06/02/1924 I -0.0840** -0.0720* -0.0743* (0.0423) (0.0417) (0.0417) "right," that is, positive sign. Of the thirteen tax reforms we 0.0566 02/26/1926 0.0864 0.1038* D study, the coefficients are of expected sign in ten cases for (0.0530) (0.0593) (0.0538) each of the specifications. If the coefficient is truly zero, 06/06/1932 -0.0824 I -0.0828 -0.0115 (0.0813) (0.0839) (0.0744) estimated coefficients should be positive and negative with I 0.0172 05/10/1934 0.0267 0.0379 equal probability. The probability of observing at least that (0.0206) (0.0461) (0.0457) many positive coefficients is 4.6%. Treating these thirteen I -0.0814* -0.1297** 08/30/1935 -0.1394** (0.0549) (0.0457) (0.0505) reforms as draws from the same distributions, for each of -0.0594 06/25/1940 I -0.0778* -0.0513 the three measures of potential tax saving the hypothesis of (0.0416) (0.0394) (0.0393) no effect may be rejected at a 5% level of significance, 09/20/1941 -0.1167** I -0.1363*** -0.0657* (0.0467) (0.0493) (0.0380) the although for many reforms the magnitude of effect is not 0.0984* D 0.0927* 10/21/1942 0.1628*** statistically different from zero. (0.0514) (0.0530) (0.0416) The measured behavioral response is most pronounced Note: ••*. ••. and * denote significance at the 1%. 5%. and 10% respectively. level, Each column contains results of a separate regression of the iow-tax indicator on one of the tax for the two reforms of the 1980s, when the sampling dummies. measures and reform procedure was not consistent in adjacent years. The retums were sampled every year, but the procedure was designed to achieve a representative sample of decedents dying in 1982 and 1986, so that retums filed in these years were over- pooled regression essentially forces these constants to be sampled. Although the population weights for other years identical, which amounts to ignoring the seasonal pattem. were constructed to replicate the actual distribution of net As a robustness check on the importance of seasonality, in worth of decedents, tlie precise sampling properties for table 5 we report the results of reestimating the pooled those years are not known. In particular we are not sure if specification while allowing reform-specific dummies that the sample is representative of the individuals dying during could allow for seasonal effects. It is reassuring that the the short period we consider. This problem is not present for estimated tax saving coefficients are very close to the ones the pre-1945 reforms.'* reported in table 4 and with identical pattem of significance. Additionally, we could presumably sharpen our estimates Note that the reform-by-reform regressions allow for not if the values of constants were known.'^ There are data on only reform-specific tax coefficients but also reform- specific constant terms. In fact, there is a significant sea- aggregate mortality experience, and, assuming that the mor- sonal pattem of mortality during a year, with a peak during tality experience of the estate tax filers follows the same the winter months and a trough in August and September. pattem, they can be used to determine the value of the Although the estimated constants in the reform-specific constants when tax savings are not present. In implementing regressions are supposed to take account of this effect, the this strategy, we used the data on the monthly aggregate mortality rates from the U.S. Department of Commerce to The marginal effects are evaluated at zero tax savings. '^ come up with the values of constants representing the "• In order to check the robustness of our results, we experimented with mortality changes during periods under consideration. Our different windows around the tax reform. The pooled results for a procedure is described in the appendix. We pursued this one-week window were insignificant, although with "correct" positive signs in each case, and the results for the second week were just approach only for the pre-1945 refonns, because we are not significant. We suspect that this may be due to significant uncertainty confident that the numbers of deaths in our sample for the regarding the date of enacting the reforra, which makes planning the exact timing more difficult. In order to make sure that we are not simply picking 1980s reforms are representative. The restricted values of up some other permanent effect of changes in tax law, we compared the third week into the low-tax regime with the third week into the high-tax regime. The results were insignificant, and were also of the "wrong" sign " If the true effect is nonlinear, not restricting the constants may be a in two out of three specifications. The same was tme for the fourth week. preferred approach.
8 DYING TO SAVE TAXES: EVIDENCE FROM ESTATE-TAX RETURNS ON THE DEATH ELASTICITY 263 IN THE LOW-TAX REGIME AS A FUNCTION OF POTENTIAL TAX DYING REFORM-SPECIFIC REGRESSIONS WITH A CONSTANT OF TABLE 6.— PROBABILITY SAVING: PATTERN OF DEATHS RESTRICTION BASED ON THE AOOREGATE Deaths in Independent Variable High- and Relative Tax Lx)w-Tax Restriction on Absolute Tax Log of Absolute Reform Saving (1945 Regimes the Constant Saving $) $) Saving (1945 Date 318 0.0002 0.0222 7.2208 0.0209 I 03/03/1917 (0.0190) (0.0044) 349 (6.4184) 0.0092 I 0.0013 12.9885* 10/04/1917 260 0.0346 (0.0214) (7.2738) 280 (0.0081) -0.0167 D 6.0721 0.0306* 395 02/24/1919 0.0027 (0.0163) 419 (3.8512) (0.0151) I 06/02/1924 0.0181 0.0091 0.0003 3.6831 443 (0.0235) 429 (4.7546) (0.0011) 0.00001 0.0768 258 0.0002 0.0551 02/26/1926 D (0.0014) (0.0156) (2.7982) 292 0.0028 0.0157 06/06/1932 133 -0.1014 1 -0.0006 (1.8598) (0.0163) (0.0059) 142 05/10/1934 I 0.0360** 0.0007 5.3273** 0.0150 340 (0.0176) (0.0017) 392 (2.6631) I 0.0090 08/30/1935 -0.0028 373 -0.1324 0.0025 354 (1.6694) (0.0122) (0.0074) -0.0184 -0.0179 06/25/1940 491 I -6.6851 -0.0015 (0.0188) 490 (0.0045) (6.0835) 544 09/20/1941 1 0.4714 0.0030 -0.0070 0.0011 521 (0.8267) (0.0043) (0.0105) 0.0100 10/21/1942 399 3.7099*** 0.0299*** 0.0158 D 487 (0.0110) (0.0252) (1.1932) Note: and 10% level. lespectively. 5%. •**. **. and * denoie signiticance at the 1%. shown are in constants'^" and the corresponding results table 6. For the logarithmic and relative specifications, the AS A RBGDties LOW-TAX IN THE DYING OF 7.—PROBABnjTY TABLE FUNCTION coefficients for 1942 are significant at the 1% level and the TAX SAVING: ALLOWING FOR DIFFERENTIAL OF RESPONSE FOR TAX POTENTIAL SEASONAL DECREASES AND INCREASES AND coefficients for 1934 are significant at the 5% PATTERNS level. There is DIFFERENT 1917 and of also some evidence of an effect for the reforms Independent Variable The coefficients for the 1940 reform remain positive, 1919. Log of Absolute Relative Tax Absolute Tax eleven prewar longer significant. Out are no but they of Tax Reform $) Saving Saving (1945 Saving (1945 $) of the tax-saving coefficients are pos- reforms, all but two 0.0186* Saving 2.0213** 0.0005 the If itive for the logarithmic and absolute specifications. (0.0004) (0.9832) (0.0096) -0.0061 Decrease X saving -0.0005 0.7911 eifect was not present, the probability of estimating at least that (0.0232) (2.5136) (0.0006) be 3.3%. For the relative many positive coefficients would Reform Dummies specification, there are three negative coefficients, but two of 1 03/03/1917 0.0209 0.0484 0.0549 (0.0522) (0.0486) (0.0488) them (1932 and 1935) are extremely close to zero. 10/04/1917 I 0.0100 0.0436 0.0368 In table 7, we reestimated the pooled specification of (0.0541) (0.0540) (0.0571) D 02/24/1919 0.0401 5 while allowing for differential response for tax 0.0445 table 0.0673 (0.0474) (0.0639) (0.0434) relative and tax increases. The results decreases for the -0.0849** I 06/02/1924 -0.0728* -0.0740* and the at the S% specification remain significant level (0.0424) (0.0417) (0.0417) 0.0724 D 02/26/1926 0.0788 0.1093** results for the logarithmic specification are significant at the (0.0841) (0.0535) (0.0589) 06/06/1932 I -0.0875 -0.0779 -0.0150 " Apart from the seasonal pattem, there is also significant idiosyncratic (0.0858) (0.0825) (0.0746) variation. For example, mortality was unusually high in late 1918 and 05/10/1934 I 0.0277 0.0156 0.0355 flu epidemic. For that reason, constants for the the to early 1919 due (0.0477) (0.0461) (0.0458) year can differ of the roughly same time at the reforms occurring 08/30/1935 I -0.0830* -0.1267** -0.1431** significantly. In interpreting the constants of table 7, one should also note (0.0514) (0.0566) (0.0458) that they reflect the probability of dying in the low-tax regime, which may I 06/25/1940 -0.0589 -0.0795* -0.0517 be before or after the reform, depending on whether the tax change was an (0.0421) (0.0393) (0.0395) increase or a decrease. I 09/20/1941 -0.1200** -0.0676* -0.1320*** '^ For most reforms and specifications, our restrictions cannot be re- (0.0484) (0.0511) (0.0381) jected using the coefficient and standard-error estimates from table 6. For D 0.1177 10/21/1942 0.1642*** 0.0704 the logarithmic and relative specifications, at a 5% significance level one (0.0901) (0.0880) (0.0416) can only reject restrictions for 1924, 1935, and 1941. For the absolute 10% respectively. Note: *". ". and * denoie significance at the 1%. S%. and level, specification, the restrictions for 1924, 1935, and 1942 can be rejected at Bach cduinn contain!! results or the tax sepanie legression of Ihe low-tax indicator on one of a a 5% level. measures (allowing for difTereni respofue for tax incteases and decreaut) and refonn dummies.
9 THE REVIEW OF ECONOMICS ANfD STATISTICS 264 OF DYING IN THE PROBABILITY REGIME AS A FRACTION 8.— TABLE LOW-TAX $10,(X)0 potential tax saving (using 2000 dollars) increases SAVING; POTENTIAL REGRESSIONS TAX ADDITIONAL USING INDICATORS OF the probability of dying in the lower-tax regime by 1.6%. Relative Saving Log Saving Variable Absolute Saving That there is any effect at all adds to the large body of evidence that taxes affect behavior, and particularly the -0.0304 -1.7838 Saving -0.0190** (0.0869) (7.2830) (0.0081) timing of behavior, including activities such as marriage and -0.0528 -0.0003 0.00016*** Age X saving childbearing, which are not generally thought to respond to (0.0737) (0.0009) (0.00006) financial incentives. Male X saving -1.6300 0.0001 -0.0418* (1.8317) (0.0217) (0.0011) We cannot rule out that what we have uncovered is not a 8.0363 0.0093 Married X saving 0.0988 real death elasticity, but instead ex post doctoring of the (0.0072) (0.0645) (5.4886) reported date of death to save on taxes. Even in that case, 8.1263 Single X saving 0.0095 0.0900 (5.8291) (0.0680) (0.0072) this exercise provides evidence on how the attempt to Widow X saving 7.8955 0.0794 0.0059 collect taxes can engender resource-using avoidance re- (5.5882) (0.0072) (0.0655) sponses that reduce tax revenue. 0.0010 -0.0012 Age 0.0012 (0.0017) (0.0030) (0.0023) 0.0734 Male 0.0098 0.0456 REFERENCES (0.0414) (0.0553) (0.0726) -0.2357 -0.3411 -0.1362 Married Aim, James, and Leslie Whittington, "Does the Income Tax Affect Marital (0.1377) (0.1753) (0.2195) Joumat 48:4 (1995), 565-572. National Decisionsr' Tax -0.1936 Single -0.2949 -0.3739 "Surviving the Holidays: Gender Differences Anson, Anson, Ofra, and Jon (0.2289) (0.1436) (0.1830) Sex Roles in Mortality in the Context of Three Moslem Holidays," -0.2805 -0.1036 -0.2261 Widow 37:5-6(1997), 381-399. (0.1772) (0.2217) (0.1389) Auerbach, Alan J.. and Joel Slemrod, "The Economic Effects of the Tax 0.1272 0.2382 0.1715 Constant Economic Literature 35:2 (1997), Reform Act of 1986," Joumal of (0.1756) (0.2931) (0.2290) 589-632. Burman, Leonard, Kim Clausing, and John O'Hiu-e, "Tax Reform and Note: ••*. •'. and • denote significance at the I"*. 5%. and 10% level, respectively. 47:1 Each column contains results of a separate regression of the low.tax indicator on one of the lax Realizations of Capital Gains in 1986," National Tax Joumal variables. and other measures 1-18. (1994), Burman. Leonard, and William Randolph, "Measuring Permanent Re- sponses to Capital-Gains Changes in Panel Data." Eco- American nomic Review 84:4 (1994). 794-809. level. There is, however, no evidence of 10% a difference in Dickert-Conlin, Stacy, and Amitabh Chandra, "Taxes and the Timing of the strength of effect between tax decreases and increases.^" 107:1 (1999), 161-177. Political Economy Joumal of %\Vibs," Finally, in the results reported in table 8, we allow for a Gelardi, Alexander M. G., "The Influence of Tax Law Changes on the National Tax Timing of Marriages: A Two-Country Analysis," different response by demographic groups. Because of the Joumal 49:\ (1996), 17-30. data limitations (see the appendix), the sample used in these Goolsbee, Austan, "What Happens When You Tax the Rich? Evidence analyses includes only the reforms that occurred between Joumal of Political Economy, from Executive Compensation," 108:2 (2000), 352-378. 1926 and 1942. There is no evidence for the presence of a Hershey, Robert, "Rise in Death Rate after New Year is Tied to the Will differential response by age, gender, or marital status. Al- to See 2000," The New York Times (January 15, 2000). though the coefficient on the interaction of tax saving with Johnson, Barry W., "Estate Tax Retums, 1986-1988," in Barry W. John- of Personal Wealth son (Ed.), Federal Estate Tax and Compendium being a male is significant at the 10% level for the logarith- Studies. Pub. 1773 (4-94), Department of Treasury, Intemal Rev- mic specification (and suggests a weaker response), it is enue Service (1994). insignificant for the other two specifications. Similarly, the Kopczuk, Wojciech, and Joel Slemrod, "The Impact of the Estate Tax on ±e Wealth Accumulation and Avoidance Behavior of Donors," in coefficient on the interaction with age is significant only for William G. Gale, James R. Hines, Jr.. and Joel Slemrod (Eds.), the absolute specification (at the 1% level, however). No Rethinking Estate and Gift Taxation (Washington: Brookings In- additional coefficients are significant when we restrict the stitution Press, 2001). constant to 0, and when we include each interaction term Luckey, John R., "A History of Federal Estate, Gift, and Generation- Skipping Taxes," CRS Report for Congress #95-444A. Congres- separately. (These results are not reported.) sional Research Service, (Washington: The Library of Congress March 16, 1995). McCubbin, Janet G. "The Intergenerational Wealth Study: Basic Estate VL Conclusion (Washington: In- tncome Bulletin Statistics of Data, 1916-1945," temal Revenue Service, Spring 1990). There is abundant evidence that some people will them- Phillips, David P., and Kenneth A. Feldman, "A Dip in Deaths before selves to survive in order to live through a momentous Ceremonial Occasions: Some New Relationships between Social event. Evidence from estate-tax retums suggests that some 38:6 American Sociological Re\iew, Integration and Mortality," 678-696. (1973), people will themselves to survive a bit longer if it will Phillips, David P., and E. W. King. "Death Takes a Holiday: Mortality enrich their heirs. To be sure, the evidence is not over- (1988), 728- Surrounding Major Social Occasions," Lancet2:S6\3 whelming. Nevertheless, our central estimate is that, for 732. Phillips, David P., and D. G. Smith, "Postponement of Death until individuals dying within two weeks of a tax reform, a Symbolically Meaningful Occasions," Joumal of the American Medical Association, 263:14 (1990), 1947-1951. ^ In a working-paper version of this paper, we relied on a zero restric- Scholes, Myron, Peter Wlson, and Mark Wolfson, "Finns' Responses to tion on a constant and found some weak evidence for the presence of such Anticipated Reductions in Tax Rates: The Tax Reform Act of a difference. This result disappeared when we allowed for the seasonal 1986," Joumal of Accounting Research, 30:Suppl (1992). 161- pattem of deaths. 185.
10 DYING TO SAVE TAXES: EVIDENCE FROM ESTATE-TAX RETURNS ON THE DEATH ELASTICITY 265 CHRONOLOGY OF PRE-1945 ESTATE-TAX BILLS TABLE AI.— Conference Conference Bill Passed Bill Passed Conference Bill Signed by President Senate Bill House Bill and Effective Date Agreement Passed by Senate by House Passed D.a. n.a. 3/31/17 n.a. 2/28/17 2/1/17 10/1/17 10/2/17 10/1/17 10/4/17 5/23/17 9/10/17 2/6/19 2/8/19 2/13/19 2/24/19 12/23/18 9/20/18 6/2/24 5/24/24 5/26/24 2/29/24 5/24/24 5/12/24 2/25/26 2/13/26 2/26/26 12/28/25 urvTA mirit 6/4/32 6/6/32 6/6/32 6/1/32 4/1/32 5/3/34 4/17/34 5/1/34 2/2/34 4/30/34 5/10/34 8/22/35 8/23/35 8/23/35 8/5/35 8/16/35 8/30/35 6/21/40 6/22/40 6/22/40 6/11/40 6/20/40 6/25/40 8/4/41 9/8/41 9/16/41 9/15/41 9/18/41 9/20/41 10/20/42 10/20/42 10/19/42 10/10/42 7/20/42 10/21/42 Note: n.ii. mearu that Ihe conference cotnmitlee procedure was bypassed. Schulz, Richard, and Max Bazerman, "Ceremonial Occasions and Mor- and deductions for the property previously taxed, because our data do not 35:3 (1980), 253- American Psychologist tality: A Second Look," contain information on them. For the post-1945 period, we use the actual 261. adjusted taxable estate from the tax returns. We apply to the taxable estate Sjoquist, David L., and Mary Beth Walker, "The Marriage Tax and the the actual tax schedule before and after the tax reform, and define tax 48:4 (1995), Journal Tax Nationat Rate and Uming of Marriage," saving as the difference between them. The infonnation on the estate-tax 547-558. stmcture is obtained from the Intemal Revenue Code. Slemrod, Joel, "The Economic Impact of Tax Reform," pp. 1-12 in J. The decedent's marital status is not present in our data set before the Slemrod (Ed.), Reform Act Do Taxes Matter? The Impact of the Tax 1924 reform. Age is missing for most observations in 1917 and for some (Cambridge, MA: The MIT Press, 1990). of 1986 other observations. For the sample of observations with known age, we U.S. Department of Commerce "Vital Statistics Rates in the United States regress it on the time trend and the constant. For this purpose, all 677,329 1900-1940," Sixteenth Census of the United States (Washington: observations (i.e., not just those close to a tax reform) are used. We impute U.S. Govemment Printing Office, 1943). age for the reniaining observations using predicted values firom this U.S. Department of Commerce, Bureau of the Census, "Vital Statistics of regression. Age is imputed for less than 10% of observations, and the the United States" (Washington: U.S. Govemment Printing Office, results are robust to restricting the sample to individuals with known age. annual issues 1937-1945). The Tax Reform Act of 1924 was repealed in 1926, but we investigate this reform nevertheless, because repeal was unlikely to be anticipated when it was enacted. APPENDIX We used monthly mortality numbers from the U.S. Department of Commerce (1943, 1937-1945) to construct the average daily numbers of For the pre-1945 period (table Al) the value of the taxable estate is not deaths for every month between 1916 and 1945. We assumed that they present in tbe data set. We define it as being equal to the value of net worth accurately describe the number of deaths occurring in the middle of the (gross estate minus debts and mortgages) before 1918, and as the differ- month and interpolated them using a cubic spline. We used the interpo- ence between the value of net worth and charitable bequests for 1918 lated equation to obtain numbers of deaths occurring two weeks before through 1945 (the deduction for charitable bequests was introduced as of and two weeks after refonns that imply certain probabilities of dying in Januaiy 1, 1918). This definition ignores credits against the tax, funeral the low-tax regime. These probabilities were converted to probit coeffi- and administrative expenses, payments for the support of the decedent's cients reported in table 6. dependents required by local law, uninsured losses during administration.
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