The elasticity of taxable income: evidence and implications

Transcription

1 Journl of Public Economics 84 (2002) locte/ econbse The elsticity of txble income: evidence nd implictions Jon Gruber,c, *, Emmnuel Sez Deprtment of Economics, Msschusetts Institute of Technology, MIT E52-355, 50 Memoril Drive, Cmbridge, MA , USA b Deprtment of Economics, Hrvrd University, Littuer Center, 1575 Cmbridge Street, Cmbridge, MA 02138, USA c NBER: Ntionl Bureu of Economic Reserch, 1050 Msschusetts Avenue, Cmbridge, MA 02138, USA Received 31 Mrch 2000; received in revised form 6 September 2000; ccepted 3 Jnury 2001 b,c Abstrct A centrl tx policy prmeter tht hs recently received much ttention, but bout which there is substntil uncertinty, is the overll elsticity of txble income. We provide new estimtes of this elsticity which ddress identifiction problems with previous work, by exploiting long pnel of tx returns to study series of tx reforms throughout the 1980s. This identifiction strtegy lso llows us to provide new evidence on both the income effects of tx chnges on txble income, nd on vrition in the elsticity of txble income by income group. We find tht the overll elsticity of txble income is pproximtely 0.4; the elsticity of rel income, not including tx preferences, is much lower. We estimte smll income effects of tx chnges on reported income, implying tht the compensted nd uncompensted elsticities of txble income re very similr. We estimte tht this overll elsticity is primrily due to very elstic response of txble income for txpyers who hve incomes bove $ per yer, who hve n elsticity of 0.57, while for those with incomes below $ per yer the elsticity is less thn one-third s lrge. Moreover, high income txpyers who itemize re prticulrly responsive to txtion. Our estimtes suggest tht optiml tx structures my feture tightly trgeted trnsfers to lower income txpyers nd flt or even declining mrginl rte structure for middle nd high income txpyers Elsevier Science B.V. All rights reserved. JEL clssifiction: H21; H31; J22 *Corresponding uthor. Tel.: ; fx: E-mil ddress: gruberj@mit.edu (J. Gruber) / 02/ $ see front mtter 2002 Elsevier Science B.V. All rights reserved. PII: S (01)

2 2 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) 1 32 One of the most importnt fetures of economic policy-mking during the 1980s were series of tx reforms which drmticlly lowered mrginl income tx rtes in the US, prticulrly for higher income fmilies. The top mrginl income tx rte t the federl level fell from 70% in 1980 to 28% by 1988, s the income tx schedule ws reduced from 15 brckets to four. There were prllel chnges in stte income tx systems over this decde s well; New York, for exmple, moved from system in 1980 with 13 brckets nd top mrginl rte of 14% to one in 1989 with five brckets nd top mrginl rte of 7.875%. The intellectul weight behind this drmtic reduction in mrginl tx rtes ws the logic of supply side economics. A number of influentil rticles, such s Husmn (1981) nd Boskin (1978), rgued tht behviors such s lbor supply nd svings were very elstic with respect to their prices, nd s result lower tx rtes could generte importnt increses in economic ctivity. A lrge body of subsequent literture, however, suggested tht these behviorl elsticities were ctully rther modest (Slemrod, 1990). While this subsequent literture my not be driving fctor, it is noticeble tht the 1990s hve seen reversl of the tx reductions of the 1980s, with mrginl rtes rising to 39.6% t the top tody. Over the pst few yers, however, new literture hs emerged which hs pointed out tht these stndrd behviorl responses re only one component of wht drives txble income; other responses such s the form of compenstion, unmesured effort, nd complince lso ultimtely determine txble income income, nd these my be more elstic with respect to txtion. Feldstein (1995) in prticulr observed tht it is the overll elsticity of txble income which is relevnt for ssessing the implictions of tx chnges for revenue rising. His seminl rticle found tht this elsticity ws very high for the Tx Reform Act of 1986 (TRA86), in excess of one for his centrl estimtes. This striking conclusion hs generted substntil body of work on this centrl prmeter. Unfortuntely, this subsequent work hs generted wide rnge of estimted elsticities, rnging from Feldstein s estimte t the high end to close to zero t the low end. This extreme vrition reflects vriety of differences between the pproches in these ppers, long dimensions such s the definition of income (rnging from brod Hig-Simons type definitions to nrrower txble income definitions), the smples used (rnging from just focusing on high income txpyers to using full rnge of incomes), nd, perhps most importntly, the source of identifiction. As emphsized by Slemrod (1996) nd Goolsbee (2000,b), mny of the studies hve essentilly shown tht high income txpyers, whose mrginl rtes were flling in the 1980s, incresed their txble income during this er. But there ws generl widening of the income distribution during the 1980s, nd disentngling the role of txtion, s opposed to other fctors such s interntionl trde nd skill-bised demnd shocks, is quite difficult. Our pper mkes three contributions to this empiricl literture. First, we drw on the entire set of stte nd federl tx reforms during the 1980s to estimte the

3 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) elsticity of txble income. The use of multiple yers of chnges llows us to ddress the identifiction problem fced by previous work by controlling in rich wy for the reltionship between income chnges nd lgged income levels. Tht is, since for every income group over this time period there re different chnges in tx policy in different yers, we cn control for ny generl tendencies towrds (for exmple) widening income distribution over this period while identifying the impct of tx policy chnges. Second, while the previous literture hs, in most cses, ignored the decomposition of behviorl responses into substitution nd 1 income effects, our empiricl frmework llows us to mke this decomposition. Third, by using this brod set of reforms, which ffected not just txpyers t the top of the income distribution, we cn extend the literture by exploring the vrition in this criticl prmeter long the income distribution. Since we hve vrition not just t the top of the distribution but throughout, we cn exmine the heterogeneity by income clss in how txpyers respond to tx chnges. These dvnces generte number of importnt findings. We find tht the overll elsticity of txble income is 0.4, well below the originl estimtes of Feldstein but roughly t the mid-point of the subsequent literture. This response is much lower, however, for broder definition of totl income tht does not exclude tx preferences such s exemptions nd itemized deductions; this prtly rises from the mechnicl effect tht the bse for clculting the elsticity is lrger, nd prtly from responsiveness of tx preferences to tx rtes. We estimte smll income effects of tx chnges on reported income, implying tht the compensted nd uncompensted elsticities of txble income re very similr. We lso find tht this response is driven lrgely by the behvior of high income txpyers; the elsticity of txble income for those with incomes bove $ is 0.57, while it is less thn one-third tht for other income groups. High income txpyers who itemize pper to be prticulrly responsive to tx chnges. Finlly, we drw on the frmework of Sez (2000) to show tht our estimtes suggest tht the optiml system for most redistributionl preferences consists of lrge demogrnt tht is rpidly txed wy for low income txpyers, with lower mrginl rtes t higher income levels. Our pper proceeds s follows. Section 1 provides review of the literture on the elsticity of txble income, highlighting the vrition in the estimtes, nd the differences in pproch cross these ppers. Section 2 discusses our dt nd methodology. Section 3 presents our bsic results. Section 4 considers heterogeneity by income nd itemizing sttus. Section 5 briefly discusses the implictions of our finding for optiml tx structures. Section 6 concludes. 1 Feldstein (1995) rgues tht he estimtes compensted elsticities becuse the TRA of 1986 ws brodly revenue neutrl tx reform. However, this rgument is correct only when the reform is neutrl for ll income clsses. This is very unlikely to be the cse with the TRA of See Footnote 12.

4 4 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) Previous work As noted in the introduction, there is long trdition of work on the behviorl elsticities of lbor supply nd svings which determine the responsiveness of rel behvior to txtion. The literture on lbor supply hs recently been reviewed in Blundell nd MCurdy (1999), nd they conclude tht the responsiveness of mle lbor supply to fter-tx wges is low, lthough it is higher (nd perhps much higher) for femle/ secondry erner lbor supply. There is less consensus on the responsiveness of svings to txtion, but Hll (1988) concludes tht there is little evidence from time series dt to suggest n importnt correltion between svings nd rtes of return. There is lso lrge literture on the responsiveness of other elements of txble income to txtion, such s chritble giving nd the form of compenstion (s well s tx evsion), which suggests tht these elements re firly sensitive to txtion (Slemrod, 1990). But these litertures hd proceeded in piecemel fshion, ech pper considering the response of prticulr rel or reporting behvior, but with little effort to integrte the findings. The first rticle to ttempt such n integrtion ws Lindsey s (1987) study of the response of txble income to the Economic Reform Tx Act of 1981 (ERTA 81), which significntly reduced tx rtes on high income erners. He used series of cross-sections of txpyers to project wht the distribution of ernings would hve been like in 1982 hd there been no chnge from 1979, other thn uniform overll income growth. He then interpreted chnge in the distribution of incomes towrds the welthy s evidence of responsiveness to txtion, estimting n elsticity of txble income with respect to txtion of But, s highlighted by Nvrtil (1995), criticl problem with this pproch is tht the income distribution is not sttic, nd if there is ny growing skewness of incomes for other resons, then the use of constnt rel income cutoff will nturlly led to finding tht tx cuts for the welthy re leding to higher txble incomes in tht group. Feldstein s (1995) influentil rticle ddressed this problem by turning to pnel dt, llowing him to ssess whether given individuls ctully sw income chnges, rther thn simply whether income chnged on verge in given income group. He studied the experience of the Tx Reform Act of 1986 (TRA 86), which further reduced tx rtes t the top of the income distribution. He exmined groups of txpyers bsed on their pre-tra income levels, nd found tht for those txpyers for whom rtes fell the most, txble income incresed the most. He estimted elsticities of txble income with respect to txtion rnging from 1 to over 3, with centrl estimte of Feldstein s rticle generted significnt mount of interest in this question, nd led to the series of dditionl studies reviewed in Tble 1. As is immeditely pprent, there is significnt disgreement mong these studies bout the pproprite elsticity estimte, with results rnging from zero to 0.8. But s is lso

5 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) Tble 1 Previous studies Author Dt Tx Smple Controls for men Income Elsticity (dte) (yers) chnge (4) reversion nd income definitions results (1) (2) (3) distribution (6) (7) (5) Lindsey (1987) Repeted tx ERTA 81 AGI.$5K None Txble income Elst.: cross-sections Centrl estimte: 1.6 ( ) Feldstein (1995) NBER tx pnel TRA 86 Mrried, non-ged None AGI Elst. of AGI: (1985 nd 1988) non-s corp creting Txble income Elst. of txble income: Income.$30K Nvrtil (1995) NBER tx pnel ERTA 81 Mrried, Use Averge Income Txble Income Elst. of txble income: (1980 nd 1983) income.$25k 0.8 Auten nd Crroll (1997) Tresury tx pnel TRA 86 Single nd mrried Include Log Income Gross Income Elst. of gross inc.: 0.66 (1985 nd 1989) ge 25 55, inc..$15k in bse yer Txble Income Elst. of txble income: Non-S corp creting 0.75 Smmrtino nd Weiner (1997) Tresury tx pnel OBRA Less thn 62 yers None AGI Close to zero permnent ( ) 1993 old response of AGI Goolsbee (1998) Pnel of corp. exec. OBRA Corporte executives Use Averge Income Wges, Bonus Short run elst.: 1 ( ) % with income.$150 K nd Stock Options Long run elst.: 0.1 Crroll (1998) Tresury tx pnel OBRA Mrried ged Use Averge Income Txble Income Elst.: 0.5 (1987 nd 1996) 1993 Income.$50 K Sez (1999) NBER tx pnel Brcket Mrried nd singles Include Log Income AGI Elst. of AGI: 0.25 ( ) Creep only nd Polynomils Txble Income Elst. of txble income in Income 0.4 Moffitt nd Wilhelm (2000) SCF pnel TRA 86 High incomes Use vrious Sets AGI Elst. of AGI: 0 to 2 (1983 nd 1989) oversmpled of Instruments depends on instruments Goolsbee (1999) Tx sttistics tbles Vrious Incomes.$30 K None Txble Income Elst. from 21.3 to 2 ( ) tx ref. depending on tx reform

6 6 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) 1 32 pprent, there is significnt difference cross the studies in how the question is pproched, long t lest two importnt dimensions. The first, nd most importnt difference, is whether the studies ttempt to control for men reversion nd, reltedly, for other trends in the income distribution which might confound the results. While pnel dt reduces the problem noted bove with the Lindsey (1987) study, it introduces new problem: if there is men-reverting trnsitory component to income in given yer, then it cn cuse high income txpyers in 1 yer to pper low income in the next, side from ny true behviorl response. At the sme time, counterviling fctor is the fct tht the distribution of income hs been continully widening since the mid-1970s, with prticulrly lrge gins t the very top of the income distribution in the 1980s nd 1990s. This corresponds to series of tx reforms which hve trgeted their tx cuts (ERTA 81 nd TRA 86) nd increses (the 1993 tx increses studied by Goolsbee (2000) nd Crroll (1998)) t the top of the income distribution. It is possible tht these tx policies re themselves cuslly relted to this widening of the pre-tx income distribution, but there re vriety of lterntive explntions s well, rnging from the impcts of interntionl trde to skill-bised technologicl chnge (see Ktz nd Murphy (1992)). While severl of the studies reviewed here recognized the men reversion problem, only Auten nd Crroll (1997) nd Sez (1999) delt with it in mnner tht lso potentilly ddressed concerns bout omitted determinnts of the income distribution (by including explicit controls in the regression for bse yer income group). A second mjor issue is the definition of income used. Most studies reviewed here use txble income s the income definition, in mny cses excluding cpitl gins income. Whether this is the right definition depends very much on the question being sked; for locl reforms, this is probbly pproprite, but for thinking bout lrger reforms or optiml tx systems, it would be more pproprite to use more comprehensive income definition. There is some suggestion in the literture of sensitivity to the income definition; Feldstein s estimte is significntly lower (lthough still bove most of the subsequent literture) when broder definition of income is used. 2. Dt nd methodology 2.1. Dt Our dt source for this exercise is the NBER pnel of tx returns over the period. This pnel, known s the Continuous Work History File, contins most of the individul line items from form 1040, s well s numerous other items from the other forms nd schedules. The pnel is constructed from ll tx returns filed in given yer by selecting certin four-digit endings of the socil security number of the primry txpyer listed on the form. From 1979 to 1981,

7 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) five such endings were chosen, nd the pnel is quite lrge, with roughly observtions. However, in 1982 nd 1984, only one ending ws chosen, nd in other yers only two, so tht the size of the pnel ws drsticlly reduced. Appendix A describes in more detil this dt source nd the definitions of our key vribles. The empiricl strtegy is to relte chnges in income between pirs of yers to the chnge in mrginl rtes between the sme pirs of yers. This pir of yers re clled yer 1 nd yer 2. The time length between yer 1 nd yer 2 cn be of 1, 2 or 3 yers. In our bsic specifiction, the time length is 3 yers, following Feldstein (1995). In tht cse, we relte yer 1982 to yer 1979, yer 1983 to yer 1980,... nd yer 1990 to yer These nine differences re stcked to obtin single dtset of bout observtions. We then exclude txpyers whose mritl sttus chnges from yer 1 to yer 2, for whom we expect lrge reported txble income chnges unrelted to tx policy. It is unlikely tht tx chnges ffected specificlly mrrige strtegies nd therefore discrding those observtions should not bis the results. We use two different types or definitions of income: brod income nd txble income. Brod income is n extensive definition of gross income tht is consistent cross the yers It includes most of the items tht re summed to rrive t Totl Income on Form 1040: wge income, interest income, dividends, business income, etc. The precise definition of brod income is given in Appendix A. Brod income is grosser income definition thn Adjusted Gross Income (AGI) becuse Brod Income does not incorporte the vrious djustments such s IRA or retirement plns deductions tht re substrcted from Totl Income to obtin AGI. Cpitl gins re excluded becuse their tx tretment is specil. Before the TRA of 1986, only 40% of cpitl gins were included in txble income nd thus the mrginl rte on cpitl gins ws much lower thn on other income. After the TRA, full cpitl gins were included in txble income but the top rte for cpitl gins ws limited to 28%. Becuse of these specil rules for cpitl gins, most previous studies hve lso excluded cpitl gins from their nlysis (see Tble 1). The Txble Income definition we use is close to the ctul definition of txble income. Our definition is consistent over the yers It includes ll the items nd djustments tht cn be computed from the dt for ll the yers For exmple, the secondry erner deduction tht ws in plce from 1982 to 1986 is not included becuse it cnnot be computed for the other yers. As for Brod Income, Cpitl Gins hve lso been excluded from our Txble Income definition. See the ppendix for the precise definition of Txble Income; 2 this definition is similr to wht hs been used in previous work. Using constnt definition of txble income cn be seen s nturl counterprt of wht previous studies hve done using only 2 yers of dt. 2 Contrry to Feldstein nd Auten nd Croll, we do not dd bck losses to our income definitions becuse we find tht dding bck losses does not ffect the results.

8 8 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) 1 32 As our definition of txble income is similr to the definition in plce in 1990, our estimtes cn be viewed s the impct of txes on 1990-style txble income definition. A limittion of this constnt-definition pproch is tht we potentilly understte the responsiveness of txble income to txtion, even from the perspective of This is becuse if the 1990 definition were in plce in erlier yers, individuls my hve undertken different ctivities to void txes tht would hve shown up in this definition; tht is, if the voidnce venues vilble in erlier yers were mde unvilble, other venues might hve been used insted tht would hve shown up in our dt. Slemrod (1998) describes this point in detil. Offsetting this, however, is the problem tht, like ll other ppers in this literture, we focus solely on the individul income tx bse. A growing wedge between the individul nd corporte tx rte could led some individuls to shift their income genertion from the non-corporte to corporte sectors; see Gordon nd McKie-Mson (1994) nd Gordon nd Slemrod (2000) for evidence of this type of shifting. Thus, we re overstting the totl cost to the tx system from rising tx rtes, since some of the reduced individul income tht we estimte will show up in rising corporte sector income. We lso exclude txpyers whose income is below $ in yer 1, to void very serious men reversion t the bottom of the income distribution. In fct, s our elsticity results re weighted by income, including txpyers with lower incomes does not significntly ffect the results. We select txpyers ccording to their Brod Income in yer 1, even when looking t Txble Income. Therefore, potentil differences between Brod Income nd Txble Income estimtes do not come from selection. In Tble 2, we present the mens of the dt for the 3-yer difference cse; the tble shows tht verge Brod Income is equl to bout $ nd verge Tble 2 Summry sttistics Men S.D. (1) (2) Brod income $ Txble income $ Mrried dummy Single dummy 0.28 Itemizer sttus 0.41 Federl tx rte Stte tx rte Averge net-of-tx rte Federl tx libility $ Stte tx libility $ Number of observtions Summry sttistics given for ll observtions with Brod income bove $ All dollr vlues re expressed in 1992 dollrs.

9 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) Txble Income equl to $ Sixty-four percent of our smple consist of mrried txpyers nd 28% of singles. All our dollr figures re expressed in terms of 1992 dollrs Empiricl strtegy Our gol is to mesure the impct of chnge in the tx schedule fced by given individul on his income. To do so, we use the bsic micro-economic frmework with two goods (consumption nd income). From this bsic model, we derive regression specifiction nd we then discuss the identifiction ssumptions The model The budget constrint of txpyer on liner prt of the tx schedule is given by c 5 z(1 2 t) 1 R, where z is before tx income, t is the mrginl rte nd R is virtul income. Utility mximiztion leds to n income supply function which depends on the slope of the budget line nd on virtul income: z 5 z(1 2 t, R). As depicted in Fig. 1, for given individul, tx chnge cn be seen s chnge in both virtul income R nd mrginl rte t. Chnges in R nd t ffect income supply z s follows, z z dz 52]]] dt 1] dr. (1 2 t) R Introducing the (uncompensted) elsticity of income with respect to the net-of-tx u rte z 5 [(1 2 t)/z] z/ (1 2 t) nd the income effect prmeter h 5 (1 2 t) z/ R, we get, u dt dr dz 52z z]] 1h ]]. 1 2 t 1 2 t Using the compensted elsticity of income z 5 [(1 2 t)/z] z/ (1 2 t)u c u Slutsky eqution z 5 z 2h, we obtin finlly, c u nd the dz c dt dr 2 z dt ] 52z ]] 1h ]]]. (1) z 1 2 t z(1 2 t) dr 2 z dt is the chnge in fter-tx income due to the tx chnge for given before tx income z. It is thus lso equl to the chnge in tx libility for txpyers with income z. This is illustrted by the verticl segment between the two schedules on Fig Regression specifiction Eq. (1) displys the behviorl response in income induced by the smll tx chnge (dt, dr). This eqution could be estimted by replcing z by z (yer 1 1

10 10 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) 1 32 Fig. 1. Income nd substitution effects of tx chnge. income), dz by z22 z 1 (chnge in income between yer 1 nd yer 2), dt by T 92(z 2) 2 T 19(z 1) (chnge in mrginl tx rtes), nd dr 2 z dt by [z22 T 2(z 2)] 2 [z12 T 1(z 1)] (chnge in fter-tx income). However, for lrge tx chnges, it is perhps more nturl to use log log specifiction tht is lso closer to previous studies specifictions. Therefore using (1) nd replcing dz/z by log(z 2/z 1), 2 dt/(12 t) by log[(1 2 T 92)/(12 T 19)] nd (dr 2 z dt)/(z(1 2 t)) by log[(z 22 3 T (z )) /(z 2 T (z ))], we obtin the following specifiction, log (z 2/z 1) 5 z log[(1 2 T 29)/(12 T 19)] 1h log[(z 22 T 2(z 2)) /(z12 T 1(z 1))] 1 e, (2) where z is the compensted elsticity prmeter nd h is the income effects prmeter. zi is rel income in yer i, T i9 is the mrginl tx rte in yer i nd T i(z i) is the tx libility in yer i. This specifiction resembles tht used in previous studies, with n importnt difference: the inclusion of income effects. Fig. 1 illustrtes empiriclly how one cn decompose tx chnge into tx rte 3 Here, we use the pproximtion z(1 2 t). z 2 T(z).

11 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) effect (chnge in the slope of the budget constrint) nd n income effect (chnge in tx libility). Any tx chnge genertes both shifts in the slope of the income/ tx reltionship, s well s chnges in fter-tx income. In principle, since the shift in the slope ffects eqully ll those on segment of tx/ income reltionship, but the income effect vries by how fr one is from tx kink, nd both income nd substitution effects cn be seprtely identified. In order to simplify the discussion, let us ssume first tht there re no income effects (h 5 0). The term cpturing the tx rte chnge log[(1 2 T 92)/(12 T 19)] is correlted with e becuse if there is positive shock to income (e. 0) then, due to progressivity, the tx rte increses mechniclly. Therefore, n OLS regression of Eq. (2) would led to bised estimte of the behviorl elsticity. The strtegy to build instruments for this vrible is to compute T 9p which is the mrginl tx rte tht the individul would fce in yer 2 if his rel income did not chnge from yer 1 to yer 2; tht is, to just use chnges in tx lws to provide identifiction of the prmeter of interest. The nturl instrument for log[(1 2 T 9)/(12 T 9)] is thus 2 1 log[(1 2 T 9p )/(12 T 19)] which is the predicted log net-of-tx rte chnge if rel income does not chnge from yer 1 to yer 2. Running the IV regression of Eq. (2) might lso led to bised estimte of the elsticity if e is correlted with z. There re two different resons why individuls 1 t different points in the income distribution might experience different income growth rtes, side from tx chnges. The first is men reversion: high incomes in yer 1 tend to be lower in the following yers, producing negtive correltion between e nd first period income. The second is chnge in the distribution of income. For exmple, if the income distribution widens, there will be positive correltion between e nd z. As noted in the introduction, these opposing forces 1 re both very likely to operte in the 1980s, nd there is no reson to expect tht they will cncel. If e depends on z, then the instrument (which is lso function of z ) will be 1 1 correlted with the error term, producing bised estimtes. It is for this reson tht Auten nd Crroll (forthcoming) nd Sez (1999) include lgged income s control in their regression models. Auten nd Crroll show tht there is significnt increse to their coefficient when this control is dded. But the problem with this solution is tht the two effects do not necessrily operte linerly, prticulrly in combintion with ech other. Thus, in principle, richer controls for period 1 income might be clled for. But, in prctice, with only 2 yers of dt (nd therefore only one tx chnge), much richer set of controls for period 1 income my destroy identifiction. This problem is especilly cute when the size of the tx rte chnge is directly correlted with the income level s in the TRA of As highlighted by Goolsbee (2000b), wht is required is number of yers of 4 Note tht the Auten nd Crroll results re in principle lso identified by stte tx chnges round TRA86, by the non-linerity introduced by the 33% bubble rte under TRA86, nd by chnges in deduction rules.

12 12 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) 1 32 dt, where there re different chnges in fter-tx shres over time. In this frmework, one cn control in very rich wy for lgged income nd still identify tx effects. As we will demonstrte below, we use vriety of reforms tht ffected different points in the income distribution in different wys over time. As result, we cn dd, in ddition to log income, 10-piece spline in log first period income (nd our results re not sensitive to even richer splines in first period 5 income). We lso control for time (by including yer dummies) nd mritl sttus. Of course, even in this richer frmework, we still rely on n identifying ssumption: tht men reversion or chnges in inequlity re not chnging yer-to-yer in wy tht is correlted with yer-specific chnges in tx policy. In other words, we re llowing the reltionship between e nd z1 to be non-liner, but we re imposing tht it is constnt over time. Given the stedily widening income distribution over the time period we study, this identifiction ssumption is likely to be innocuous. We present specifiction tests below tht show tht this ssumption is robust to llowing in limited wys for yer-specific vrition in the reltionship between e nd z. 1 Following this sme discussion, the term log[(z 22 T 2(z 2)) /(z12 T 1(z 1))]inEq. (2) which cptures the income shock, is mechniclly correlted with e nd needs to be instrumented. A nturl instrument is the log chnge in rel fter-tx income if there were no behviorl response: log[(z 1 2 T p)) /(z12 T 1(z 1))] where Tp is the rel tx libility in yer 2 tht the txpyer would fce if his income did not chnge in rel terms from yer 1 to yer 2. Additionl income controls lso remove the residul correltion between the error term e nd the income effect instrument. Once gin, for identifying the income effect it is importnt to control for bse yer income. In prctice, rich controls for bse yer income mke it very difficult to seprtely identify income nd substitution effects with only one tx chnge. But since we re using mny tx reforms, the two effects cn be seprtely identified, s we show below. The regression setting is thus the following, log(z 2/z 1)501z log[(12t 29)/(12T 19)]1h log[(z 22T 2(z 2)) /(z12t 1(z 1))] 1 log(z ) 1O mrs 1O YEAR 11O SPLINE (z ) 1 e k k 3j j 4i i 1 k j i51 10 (3) 5 Another pproch to controlling for men reversion is to control for verge income, rther thn simply using bse period income, s in Crroll (1998). While this my help with men reversion, however, it does not ddress our joint concern with omitted vribles bis through income distribution chnges. Moreover, if verge incomes from only the yers before the tx chnge re used, then slowly moving men reversion is still problem; if verges tht include the yers fter the tx chnge re used, then the income control becomes endogenous to the response of incomes to txtion. We hve estimted models using income verging in plce of our richer income controls, nd the results re much weker thn those reported below.

13 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) YEARj denote bse yer dummies nd mrsk dummies for mritl sttus in bse yer. This eqution is estimted by 2SLS using log[(1 2 T 9p )/(12 T 91 )] nd log[(z 12 T 2(z 1)) /(z12 T 1(z 1))] s instruments. The first stge of this regression is very strong. The F sttistics for the coefficient of the tx rte instrument in the first stge regression re lwys bove 20 nd often round 100. The F sttistics for the coefficient of the income effect instrument in the first stge regression re weker but lwys bove 6 nd often round 20. Since we stck observtions from nine pirs of yers to form our estimtes, we re using multiple observtions on mny of the sme individuls. If there is individul-specific correltion in how income chnges over time, then stndrd 2SLS will understte our ssocited stndrd errors. We therefore present estimtes tht correct the stndrd errors for intr-personl correltion Computtion issues nd sources of vritions All tx rte nd tx libility vribles re computed using the TAXSIM 6 clcultor developed t the NBER. The tx computtion includes federl nd stte tx rtes. At the federl level, the Erned Income Tx Credit nd vrious other chrcteristics of the tx rules re tken into ccount when computing the tx rtes. In order to compute the predicted tx rte T 9p nd predicted tx libility T p, ll sources of incomes in yer 1 re first inflted using nominl growth defltor (see Appendix A for more detils). Then, the TAXSIM clcultor pplies the income tx lw of yer 2 to this inflted observtion. All income levels re expressed in rel terms in 1992 dollrs. During the decde there hve been two mjor tx reforms, ERTA 1981 nd TRA In 1981, the Economic Recovery Tx Act (ERTA) decresed mrginl rtes in 3 yers from 1982 to The top-rte ws reduced from 70 to 50%. In 1986, the Tx Reform Act (TRA) introduced the lrgest chnges in the income tx since World Wr II. The number of brckets ws drsticlly reduced nd the top-rte ws further reduced to 28%. The TRA lso incresed substntilly the stndrd deduction nd personl exemption levels in order to be roughly redistributionlly neutrl (see Slemrod (1990) for more detiled description of the TRA). In 1987, the Erned Income Tx Credit ws lso significntly expnded, producing significnt chnges in the tx rtes fced by low income households with children. There hve lso been numerous stte tx reforms during tht decde, with mny sttes decresing the number of brckets nd reducing the top tx rtes. At the sme time, few sttes incresed their income tx rtes. And bout hlf of the 7 sttes hve experienced very little vrition in their tx rules. 6 Feenberg nd Coutts (1993) provide n overview of the TAXSIM clcultor. 7 The biggest tx cuts hve been in Alsk (from top rte equl to 14.5% to no txtion t ll), Delwre (top rte decresed from 16.7 to 7.7%), Minnesot (from 17 to 8%), New York (from 14 to 7.8%) nd Wisconsin (from 10 to 6.9%). Ohio nd North Dkot experienced the biggest tx increses.

14 14 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) 1 32 Tble 3 shows the extent of vrition in our dt. We provide informtion for ech yer in our smple on the vlue of our instrument for the elsticity of txble income, the predicted log chnge in the net-of-tx rte, for the full smple nd for three different income groups, defined by brod income: $ ; $ ; nd $ nd bove. The instrument is negtive for tx rte increse nd positive for tx rte cut. We show the results for 3-yer difference between yers; we discuss further below the implictions of different lengths of differences. We show both the verge vlue of the instrument, nd, in squre brckets, the stndrd devition in this vlue. As the results show, there is substntil vrition in the men vlues of this instrument, over time, cross income group, nd within group over time. Over the period, the vlues re negtive (except for the top group), due to the brcket creep explored by Sez (1999). Then, from 1980 to 1983, the first effects of ERTA 1981 re felt, with lrge rise in the fter-tx shre t the very top of the Tble 3 Vrition in fter-tx shres log(1 2 T9 p/12 T91) Yer $10 K nd $10 K to $50 K to $100 K nd (1) bove (2) $50 K (3) $100 K (4) bove (5) [0.058] [0.055] [0.045] [0.118] [0.059] [0.050] [0.052] [0.111] [0.063] [0.052] [0.060] [0.109] [0.050] [0.047] [0.053] [0.057] [0.082] [0.041] [0.115] [0.210] [0.077] [0.074] [0.070] [0.108] [0.092] [0.085] [0.076] [0.113] 11,918 8,589 2, [0.091] [0.084] [0.075] [0.105] [0.057] [0.053] [0.052] [0.060] Men, stndrd devition nd number of observtions reported. Income cuts bsed on Brod income definition.

15 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) income distribution, while it is close to zero t the bottom due to continued brcket creep. By the next yer, there re increses in the fter-tx shre for most of the income distribution, nd they persist to Then, in , the vlues become smll gin, before rising in nd s result of TRA Once gin, these increses re lrgest t the top of the income distribution. By , the instrument vlues re smll once gin (except t the very top becuse of the phsing in of the TRA 86). Clerly, the most sizeble vrition in the mens is t the top of the income distribution. But there re non-trivil movements in mny yers t the bottom nd middle income levels s well. Moreover, there is enormous heterogeneity within groups, s is illustrted by the stndrd devitions. This heterogeneity rises from numerous federl nd stte tx reforms during the period. 3. Overll results 3.1. Bsic results Since the focus of the previous literture hs been solely on the elsticity of txble income, we first estimte (3) without income effect controls; we return to discussion of income effects in the next section. We include in ll models controls for bse period mritl sttus, nd dummies for ech bse yer; the ltter re not reported. Our bsic results from doing so re reported in Tble 4. The tble hs six columns, expressing three lterntive methods for deling with the issue of men reversion/ income distribution chnges, for our two income concepts. In the first two columns, we do not include ny control. In the second two columns, we control for log income, s in Auten nd Crroll (forthcoming). Finlly, in the third set of columns, we further include 10-piece spline in income, to llow for non-linerities in the widening of the income distribution; our results re insensitive to higher order spline terms. We show the results for both definitions of income, brod nd txble. All estimtes re weighted by income to reflect the reltive contribution to totl revenues. As sketched in Section 5, the importnt prmeters for optiml txtion or dedweight burden computtions re the elsticities weighted by income becuse the income response to chnge in 8 mrginl rtes is proportionl to the elsticity times the income level. However, to void the undue influence of few very high income observtions, we censor our weights t $1 million; this ffects only 13 observtions. We lso censor the chnge in log income t 7, so tht the 11 observtions who report chnges income rtios cross the 2 yers of more thn 1000 or less thn 1/1000 re censored t those 8 It should be noticed tht, if one ssumes tht elsticities re constnt cross income levels, weighted estimtes re less efficient thn unweighted estimtes. However, s we will see, the ssumption of constnt elsticities is rejected by the dt.

16 16 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) 1 32 Tble 4 Bsic elsticity results Income controls None Log income Log income 10-piece spline Brod Txble Brod Txble income income income income Brod Txble (1) (2) (3) (4) income income (5) (6) Elsticity (0.120) (0.194) (0.106) (0.144) (0.106) (0.144) Dummy for mrrieds (0.010) (0.018) (0.014) (0.023) (0.012) (0.021) Dummy for singles (0.012) (0.019) (0.013) (0.022) (0.013) (0.021) Log(income) control (0.015) (0.021) Spline 1st decile control (0.086) (0.039) Spline 2nd decile control (1.13) (0.047) Spline 3rd decile control (0.055) (0.057) Spline 4th decile control (0.051) (0.069) Spline 5th decile control (0.054) (0.075) Spline 6th decile control (0.053) (0.081) Spline 7th decile control (0.056) (0.083) Spline 8th decile control (0.057) (0.083) Spline 9th decile control (0.076) (0.125) Spline 10th decile control (0.041) (0.064) Observtions: Estimtes from 2SLS regressions. Income rnge is $ nd bove. Regressions weighted by income. All regressions include dummies for mritl sttus nd dummies for ech bse yer. endpoints. In prctice, the results re firly sensitive to the first restriction; our overll elsticity is only bout three-qurters s lrge when we use n uncpped weight, nd the elsticity t the top of the income distribution is only bout 60% s 9 lrge. The results re not very sensitive to the second restriction. 9 We hve decided to censor these observtions becuse we did not wnt to llow few outliers to drive our min estimtes. Moreover, when we llow for income-specific time trends in our specifiction check section, we obtin the sme elsticity s in Tble 4 both with nd without this censoring, s the influence of these outliers is cptured by these dditionl time trend terms. So we feel tht the estimte in Tble 4 is the best estimte of the true responsiveness of txble income to txtion.

17 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) Our findings reflect substntil sensitivity to controlling for income, nd to the form of the controls. For the models in the first column tht exclude ny control for men reversion nd income distribution chnges, we obtin lrge wrong-signed elsticities for both brod nd txble income. Once log income is included in the model; however, the results chnge quite rdiclly. For brod income, the elsticity becomes positive 0.17, nd for txble income, the effect is drmtic, with the elsticity rising to This estimte lies in the upper end of the post-feldstein literture discussed bove. Log income itself hs highly significnt negtive coefficient, suggesting tht on verge men reversion domintes income dispersion in our smple period. As noted erlier, the problem with this specifiction is tht it ssumes tht ny chnges in the income distribution re (log) function of lgged income. It is difficult to effectively weken this ssumption with only one chnge, s in most previous work, since it destroys identifiction of the tx effects. But, since we hve number of tx chnges over this period, we cn weken this ssumption in the third column, by including s well 10-piece spline in lgged income. In fct, we find tht dding this spline significntly decreses our txble income estimte, with the elsticity flling to 0.4, nd lowers slightly our brod income estimte, with the elsticity flling to As noted erlier, this estimte is robust to the inclusion of dditionl splines, cubics, or other forms of income controls. The coefficients on the splines themselves support the contention tht bse period income should not be entered in simple log-liner fshion. For brod income, there is positive coefficient on the first spline, presumbly reflecting men reversion, nd then sizeble negtive coefficient on the second spline, perhps reflecting worsening income prospects for low income groups over this time period. The coefficients then demonstrte significnt non-linerities throughout the rest of the income distribution. For txble income, the splines re highly negtive t the bottom of the income distribution, nd then once gin vry non-linerly s income rises. In ll specifictions except with no controls, we find positive coefficients on dummies for mrrieds nd negtive coefficients on dummies for singles implying tht mrried households experience increses in income from yer to yer reltive to single txpyers. The lrge difference between our brod nd txble income elsticities is striking. There re two sources of difference here. The first is mechnicl; brod income hs lrger bse, so tht given dollr response will result in smller 10 elsticity. The second is behviorl; txble income includes itemized deductions, which might respond to chnges in txes (s well s exemptions, which could respond if fmily size is endogenous to txtion). To decompose these effects, we hve estimted some models with pseudo- 10 Another form of mechnicl effect here is tht with txble income, higher stte tx rtes will result in lrger deduction on federl income txes, leding to n mechnicl negtive correltion between stte txes nd federl txble income. We re grteful to Gry Engelhrdt for pointing this out to us.

18 18 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) 1 32 txble income, creted by subtrcting from both period 1 nd period 2 incomes the period 1 level of exemptions nd deductions. Doing so normlizes the income chnge for the mgnitude of the exemptions nd deductions, but does not llow them to respond to txtion, nd thereby cptures the mechnicl but not the behviorl effect of txtion. We hve estimted models using pseudo-txble income, using splines in both brod nd txble incomes s controls. Doing so, we find tht the pseudo-txble income elsticity is 33 45% of the wy between our brod nd txble income elsticities, depending on which controls we use. This is sensible, given tht, s shown in Tble 3, the men of txble income is only 60% s lrge s the men of brod income. Thus, the mechnicl effect ppers to explin bout two-fifths of the gp between brod nd txble income. The reminder is behviorl responses through chnging itemiztion (nd possibly 11 exemption) behvior. To summrize, our most complete specifiction suggests tht there is sizeble response of txble income to tx chnges, with n elsticity of 0.4. This is well below Feldstein s estimtes but is within the rnge of the subsequent literture, despite our bility to include much richer controls for chnges in the income distribution. On the other hnd, we find tht the responsiveness of brod income is much lower thn tht of txble income. Roughly 40% of tht gp is explined by the mechnicl effect tht brod income hs lrger bse so tht elsticities will be clculted to be smller for given dollr response to txtion; the reminder rises through chnges in itemiztion nd exemption behvior Income effects As noted bove, one dvntge of our empiricl frmework is tht we cn seprtely identify the income effects of txtion on txble income. To obtin income effects, we run the regression specifiction (3) including the income effect term nd the full set of control vribles. In fct, it is theoreticlly uncler wht sign to expect for the income effect estimtes for constructs such s brod or txble income. For the lbor component of totl income, we might expect reltively smll negtive estimtes, following on the findings of the lbor supply literture (e.g., Pencvel (1986) nd more recently Blundell nd MCurdy (1999)). But it is fesible tht cpitl income rects positively to positive income shock if svings (nd thus future cpitl income) increse. And it is even more difficult to conceive of how ctivities such s tx evsion or shifts in the form of compenstion rect to income increses. In contrst to the estimtes in Tble 4, our estimtes of this eqution re 11 It is impossible to exmine more directly itemiztion behvior using our methodology, since we would only be ble to include txpyers with itemized deductions in both periods, leding to substntil smple selection bis. Note however tht there is lrge independent literture on the response of items such s chritble contributions to txtion (see, e.g., Clotfelter (1985)).

19 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) unweighted. This is becuse the income effect coefficient h 5 (1 2 t) z/ R gives the direct (nd not the percentge) chnge in reported income due chnge in tx libility. Therefore, the tx revenue effect due to income effects should not be weighted by income. For low txble income levels, the right-hnd side vrible corresponding to the income effect prmeter becomes noisy. As result, when we estimte responses of txble income, we restrict the smple to txble incomes bove $ in yer 1 (insted of restricting the smple to brod income bove $ s we did in Tble 4 nd s we will do subsequently). 12 Tble 5 presents our results. We first show our unweighted overll elsticities. The unweighted txble income elsticity is very similr to the weighted txble income elsticity in Tble 4, while the unweighted brod income elsticity is substntilly lower thn the weighted elsticity in Tble 4. As we will discuss below, this reflects the fct tht most of the response of income to txtion comes from those with high brod but not necessrily high txble incomes, due to the centrl role of itemiztion. Tble 5 Substitution nd income effects Brod Txble income (1) income (2) (A) No income effect included Elsticity (0.066) (0.114) (B) Income effect included Substitution effect (0.069) (0.121) Income effect (0.096) (0.108) N. Obs Estimtes from 2SLS regressions. Regressions re unweighted. Income rnge: brod income bove $ in column (1) nd txble income bove $ in column (2). Regressions include 10 splines in log(income). All regressions include dummies for mritl sttus nd dummies for ech bse yer. 12 It is worth noting tht the elsticities estimted in this model re not necessrily uncompensted elsticities, since with non-liner tx schedule the tx chnges tht we study my chnge both the fter-tx shre nd fter-tx incomes. For exmple, when the tx schedule is flt tx with constnt rte nd the tx reform is simple chnge in the tx rte with no chnge in the intercept then the response is given by the uncompensted elsticity. On the other hnd, if the tx chnge chnges tx rtes without chnging the tx libility then the response is given by the compensted elsticity. Fig. 1 illustrtes this point. Feldstein (1995) rgues tht the TRA of 1986 ws brodly neutrl for redistribution nd thus the response ws compensted elsticity. This is only crude pproximtion becuse tx chnge cnnot ffect tx rtes while keeping tx libilities constnt for everybody.

20 20 J. Gruber, E. Sez / Journl of Public Economics 84 (2002) 1 32 We then show substitution nd income effects from full estimtion of Eq. (3). The income effects re negtive, but they re highly insignificnt in both cses, nd they re quite smll. The Slutsky eqution sttes tht the difference between the compensted nd uncompensted income elsticities is 2h, which is thus pproximtely equl to our empiricl estimte. Our empiricl results show therefore tht the difference between uncompensted nd compensted elsticities is for txble income. This is smll reltive to the mgnitude of the elsticities tht re presented in Tble 4. These smll income effects re perhps unsurprising, given tht income effects on lbor ernings re generlly found to be smll, t lest for primry erners, nd income effects on other forms of income could perhps even be positive. Therefore, we cn sfely ssume tht compensted nd uncompensted elsticity re identicl nd drop the income effect vrible (nd instrument) in specifiction (3). We thus present the reminder of our results, nd our optiml tx simultions, without including income effects Vritions in timing Following the previous literture, we hve used 3-yer difference in computing our mesures of both the chnge in txble income nd the chnge in fter-tx shres. But our frmework llows us to explore the sensitivity of our finding to the length of this differencing window. The implictions of chnging the window of observtion re not cler. If, on the one hnd, individuls rect slowly to tx chnges, then using longer difference might increse the estimted elsticity. If, however, s suggested by Goolsbee (2000) nd Smmrtino nd Weiner (1997), responses to tx chnges re lrgely through the timing of income reporting, then longer difference might reduce the elsticity. We explore these issues of timing in Tble 6. In this nd ll subsequent tbles, we use our richest specifiction from Tble 4, including the splines in first period Tble 6 Vritions in timing 3-Yer 2-Yer 1-Yer lg (1) lg (2) lg (3) Brod income (0.106) (0.104) (0.105) Number of obs Txble income (0.144) (0.138) (0.164) Number of obs Estimtes from 2SLS regressions. Income rnge is $ nd bove. Regressions weighted by income. Regressions include 10 splines in log(income). All regressions include dummies for mritl sttus nd dummies for ech bse yer.