The Effects of Taxation on Income-Producing Crimes with Variable. Leisure Time

Transcription

1 The Effects of Txtion on Income-Producing Crimes with Vrible Leisure Time Avrhm D. Tbbch I. INTRODUCTION The existing literture on the effects of txtion on income-producing crimes lys clim to severl importnt results: first, tht pure income tx regime under which legl nd criminl income re txble nd fines re fully deductible mintins the level of crime with respect to risk neutrl offenders; second, tht tx regime such s the current U.S. income tx lws under which legl nd criminl income re txble but fines re nondeductible reduces criminl ctivities unmbiguously; third, tht shift from pure income tx to the current U.S. income tx lws will lso unmbiguously reduce crime (Png nd Zolt (1989), Zolt (1989), Tbbch (2003)). 1 Bsed on these results, Png nd Zolt (1989) nd Zolt (1989) rgue tht efficient deterrence requires the deductibility of fines nd cll for the repel of section 162(f) of the Internl Revenue Code, which prevents such deductions. 2 Their work plyed mjor role in policy discussion on orgniztionl snctions. 3 In ddition, in relted work, Polinsky nd Shvell (1998) John M. Olin Scholr in Lw nd Economics University of Chicgo Lw School. I would like to thnk Willim Lndes, Jcob Nussim, Dvid Weisbch, nd n nonymous referee, s well s prticipnts t tx workshop t Northwestern University Lw School nd t lw nd economics workshop t Tel Aviv University Lw School for helpful comments nd suggestions. 1 The first two clims re mde in comprison to world with no txtion or for different tx rtes. The ltter two clims re obtined regrdless of offenders version or indifference to risk. 2 Png nd Zolt recognize tht nondeductibility rule will lso chieve efficient deterrence if fines re djusted ccording to the formul f n = f ( 1 t), but they rgue tht deductibility rule my be superior on the bsis of dministrtive considertions. 3 Png nd Zolt s (1989) pper ws the bsis of testimony on orgniztionl snctions before the United Sttes Sentencing Commission on December 2,

2 rgue tht the current tx rule llowing deductions for punitive dmges is desirble. 4 The ppers obtining these results nd those mking these strong policy suggestions ssume either implicitly or explicitly tht txtion does not ffect the level of mrket ctivities, but only the choice between legl nd criminl income-producing ctivities. Put differently, they ssume tht the mount of time offenders devote to leisure ctivities is fixed. 5 The im of this pper is to exmine the robustness of these results nd the vlidity of their policy suggestions when leisure time cn vry. 6 This inquiry is importnt becuse the ssumption tht txtion does not ffect the level of mrket ctivities (or leisure time) is unrelistic nd restrictive. It is lso nturl given tht the criminl choice problem is usully constructed s lbor supply, time-lloction decision under uncertinty. As is well known, the key insights from models of txtion nd lbor supply (nd indeed of optiml txtion literture) hinge on the effects of txtion on the lborleisure choice. 7 Thus, nlyzing the effects of txtion on income-producing crimes while ssuming tht leisure is predetermined sheds doubt on the results nd policy recommendtions. 4 Revenue Ruling , C.B. 57 snctions deductions for punitive dmges. Needless to sy, but these recommendtions pply only if the income ssocited with the ctivity leding to the imposition of fines or punitive dmges is txed. 5 See Tbbch (2003). In Png nd Zolt (1989), Zolt (1989), nd in Polinsky nd Shvell (1998) the ssumption tht txtion does not ffect the level of production is implicit nd, s suggested, it is equivlent to ssuming tht leisure (or income-producing ctivities) time is fixed. Moreover, becuse this ssumption is implicit in their work, neither Png nd Zolt nor Polinsky nd Shvell discuss the implictions of relxing it, let lone, limit their conclusions nd policy recommendtions. Note tht illmn nd Ktz (1984) ccount for vrible leisure time in their nlysis of the effects of txtion on crime, but their nlysis does not del with pure income tx regime or with the current U.S. income tx lws, but with tx imposed solely on legl ctivities. 6 In this respect, this pper joins long line of ppers in the economic literture tht exmine how the results nd recommendtions obtined in simple models re ltered once the utility function is expnded to include two rguments (such s income nd leisure) or the gent s choice is expnded two include two vribles (such s how much to work nd how much to underreport income). In the tx evsion literture, for exmple, Andersen (1977), Bldry (1979), nd Pencvel (1979) exmine how the results of the bsic model of tx evsion chnge when the lbor supply decision is explicitly incorported in the model. In the txtion nd risk tking literture, Cowell (1981) exmines similr question. On the reltionship of this pper to these relted works see the Concluding Remrks. 7 See, for exmple, usmn (1985). See lso Atkinson nd Stiglitz (1980). 2

3 Although llowing leisure time to vry dds more relism to the model, it complictes the nlysis. In generl, unless some strong restrictions re imposed on the utility function, the effects of txtion on crime become more complex nd the results more mbiguous. This occurs becuse vrible leisure time dds to the nlysis two well-known tx effects. On the one hnd, txtion reduces time llocted to both legl nd criminl ctivities becuse it mkes leisure reltively cheper thn mrket ctivities (substitution effect). On the other hnd, becuse txtion reduces welth, it increses time llocted to mrket ctivities s long s leisure is norml good (income effect). If, however, offenders re ssumed to be risk neutrl nd the utility function is ssumed to be seprble in income nd leisure, then the income effects essentilly dispper nd unmbiguous results emerge. Contrry to existing results, pure income tx regime will no longer mintin the bsolute level of legl nd criminl ctivities, but rther it will unmbiguously reduce both crime nd work. owever, becuse the reduction is not necessrily proportionte, pure income tx regime will not even mintin the reltive level of work nd crime. On the other hnd, the current U.S. income tx lws will reduce crime, but they will hve n mbiguous effect on work. Lstly, shift from pure income tx regime to the current U.S. income tx lws will hve its expected effects of reducing crime nd incresing work. The pper proceeds s follows. Section II develops the model of txtion nd crime with vrible leisure time. Section III exmines the effects of different income tx regimes on legl nd criminl ctivities. Section IV provides some concluding remrks. 3

4 II. TE MODEL To nlyze the effects of txtion on crime while llowing leisure time to vry, the model found in Tbbch (2003) is employed but modified to include leisure time s n rgument in the utility function. Following Schmidt nd Witte (1984), it is ssumed tht there is no disutility ssocited with either legl or criminl ctivities, side for the reduction in leisure time. Assume then tht individuls optimlly llocte their time between three ctivities: crime, work, nd leisure, t the beginning of given period. A frction of totl mount of time T, normlized to one, is llocted to criminl ctivities, frction b to legl ctivities, nd the reminder, frction 1 b to leisure, where 0 1 nd 0 b 1. The fter-tx returns from legl ctivities re sfe in the sense tht they re given with certinty by the function W ( b, t) = (1 t), where t is the proportionl tx in plce. These returns re ssumed to be mrginlly decresing with time llocted to legl ctivities, so W b > 0 nd W bb, where s usul subscripts indicte prtil derivtives. The fter-tx returns from crime, on the other hnd, re risky in the sense tht they re conditionl upon two sttes of the world: punishment t the end of the period with (subjective) probbility p, nd non-punishment, with (subjective) probbility 1 p, where p is constnt nd exogenously determined. 8 If successful, offenders receive the fter-tx returns from their crime tht tke monetry or monetry-like form, nd re given by the function C(, t) = (1 t) c(, ssumed to be mrginlly decresing with time llocted to criminl ctivities so C > 0 nd C. If offenders re punished, the fter-tx 8 See generlly Schmidt nd Witte (1984). See lso Png nd Zolt (1989). 4

5 returns from crime re reduced by n fter-tx fine, given by the function F(, δ, t) = (1 δt) f (, where δ ( 0 δ 1) is the degree of deductibility of fines. This fter-tx fine is ssumed to exhibit incresing mrginl severity, so F > 0 nd F > 0. It is lso ssumed tht individuls hve initil welth, py ny mount of fines. 9 0 W, tht is sufficient to Assuming full complince with the tx lws nd tht revenues from txtion re used to finnce government spending tht enters the utility function in seprble wy, 10 the criminl choice problem is to choose nd b tht mximize expected utility: (1) E [ U( W, ] = (1 p) U(, pu( Y,. Where: (2) Y = W 0 W ( b, t) C(, t) F(, t, δ ) = W 0 W ( b, t) C(, t ) re terminl welth t the end of the period given punishment nd non-punishment respectively, L =1 b is the time llocted to leisure ctivities, nd U( W, is the individul s von Neumnn-Morgenstern utility function defined over welth nd leisure. It is ssumed tht U W > 0, U WW = 0 or U WW, implying risk neutrlity or risk version respectively, nd U L > 0, U, implying decresing mrginl utility of leisure. It is lso ssumed tht U LW = 0, which mens tht the rte t which the mrginl utility of leisure chnges is independent of welth nd vice vers. This strong ssumption mounts to ssuming seprbility in income nd leisure. As will be shown, 9 This ssumption is required to rule out the need to resort to nonmonetry snctions, nmely, imprisonment. 10 See Atkinson nd Stiglitz (1980), Tbbch (2003), nd the Concluding Remrks. 5

6 without this restriction, no comprtive sttic result of ny interest ppers unmbiguous. The first order conditions for locl mximum (ssuming positive vlues for ll three vribles,b, nd L ) re: EU (3) = = ( 1 p)[ U(, C UL(, ] p[ U ( Y, ( C F ) U ( Y, ] = 0 EU (4) b = = ( 1 p)[ U (, Wb UL(, ] b Y p[ U ( Y, W U ( Y, ] = 0 Y These first order conditions imply tht in equilibrium offenders choose the optiml nd b, denoted, * nd b *, simultneously, so tht the net fter-tx mrginl returns to time spent in legl nd criminl ctivities is zero. These net fter-tx mrginl returns include the mrginl disutility of decresing leisure time, which in turn depends on both nd b. For risk neutrlity nd seprbility, these first order conditions reduce to: (3 ) = U (, ( C pf ) U (, = 0 (4 ) = U (, W U (, = 0 b Which lso imply tht 11 : (5) C pf = Wb b L L It is ssumed throughout tht the prmeters of the model tke on vlues tht result in n interior solution. 12 b L L 11 Note tht (5) holds by virtue of risk neutrlity lone. 12 The second order conditions re stisfied by ssuming decresing mrginl returns from legl nd criminl ctivities, incresing mrginl severity of punishment, decresing mrginl utility of leisure, nd risk neutrlity or risk version with income. See lso discussion below. 6

7 III. COMPARATIVE STATIC RESULTS A. The Effects on Crime of Pure Income Tx Regime Exmine first the effects on crime of pure income tx regime -- tx regime under which legl nd criminl income re txble nd fines re fully deductible -- for risk neutrl offenders. Such regime is cptured by setting δ = 1, so expected welth becomes: (6) EW = W 0 (1 t)( c( pf ( )) The effects on crime of imposing pure income tx regime or of incresing tx rtes under such regime cn be investigted by differentiting the first order conditions (3 ) nd (4 ), understood to hold for δ = 1, with respect to t nd solving for obtin: * 1 b (7) = b bb Where: *. We (8) = b b bb The second order conditions for locl mximum imply tht > 0, bb, nd. owever, to determine the sign of * requires knowledge of the vlues of b, bb, b, nd. Direct clcultions of these terms yields: (9) = U (, b, 7

8 (10) = U (, (1 t) w''( U (, bb, (11) b = U (,, nd (12) = U (, ( pf '( ). Inserting these terms bck to (7) yields: * ( U 2 (, ) (1 t)( c' ( pf '( ) w' '( (13) = which implies tht pure income tx regime reduces crime. The economic explntion of this result is simple. Becuse the reltive expected returns from legl nd criminl ctivities re not ltered by pure income tx regime, there is no substitution effect between legl nd criminl ctivities. In ddition, the risk effects of pure income tx or its effects on the willingness of offenders to ber risk re irrelevnt for risk neutrl offenders. 13 Moreover, becuse of risk neutrlity nd seprbility, the chnges in welth ssocited with txtion do not ffect the demnd for legl, criminl, or leisure ctivities. The only effect tht pure income tx regime cretes is substitution effect between leisure nd income-producing ctivities due to the fct tht leisure is not txed. This substitution effect leds to reduction in time llocted to both legl nd criminl ctivities nd, therefore, to reduction in the level of crime, s indicted by (13). 14 It is importnt to note tht this result criticlly depends on the ssumption of seprbility nd risk neutrlity. 15 If, for exmple, we ssume tht U LW > 0, which 13 On these effects see Tbbch (2003). 14 The explicit effect of pure income tx on legl ctivities is given in eqution (B2) in ppendix B. 15 With respect to risk version, Tbbch (2003) shows tht pure income tx regime results in indetermincy even when leisure time is predetermined due to conflicting risk nd income effects. 8

9 mounts to ssuming tht the mrginl utility of leisure is incresing with income nd vice vers, or, in other words, tht the richer you become the more you vlue leisure t the mrgin, while mintining the ssumption of risk neutrlity, (13) becomes (see ppendix A): (13 ) * U (, (1 t) w' '( b = ) Becuse cnnot be signed (see ppendix A), neither cn *. The reson why the effects of pure income tx regime on risk neutrl offenders become mbiguous once the ssumption of seprbility is dropped for the ssumption U > 0 is rther simple. Now, in ddition to the substitution effect between leisure LW nd income-producing ctivities, there is lso n income effect in ply: txtion mkes offenders, t lest in expected terms, poorer. This income effect reduces the demnd for leisure nd therefore increses the demnd for legl nd criminl ctivities to the extent tht leisure is norml good, which is gurnteed by the ssumption U LW > 0. As shown, pure income tx regime does not mintin the bsolute level of legl nd criminl ctivities for risk neutrl offenders when leisure time cn vry. Seemingly, pure income tx regime will mintin the reltive level of legl nd criminl ctivities, tht is, the proportion *, becuse the reltive expected returns from legl nd criminl b * ctivities re not ltered. This, however, is true in only the unlikely event tht the rtio of the rtes t which the expected mrginl returns from legl nd criminl ctivities chnge equls the rtio of the optiml time lloction between criminl nd legl ctivities. Tht is, where (see ppendix B): 9

10 (14) w' '( b*) c' '( *) pf ''( *) = * b* If the former rtio is greter (smller) thn the ltter rtio, then the reltive time llocted to criminl ctivities will increse (decrese) nd correspondently the reltive time llocted to legl ctivities will decrese (increse). The economic explntion of these results is s follows: fter the imposition of pure income tx regime, the new equilibrium still requires tht the expected mrginl returns from legl nd criminl ctivities will be equl, but this equlity tkes plce for higher vlue (becuse txtion reduces the mrginl utility from mrket ctivities). Thus, the reltive chnge in the optiml lloction of time between criminl nd legl ctivities will depend on the rte t which the expected mrginl returns from legl nd criminl ctivities chnge, nd it will remin the sme only if tht rtio equls the rtio of the optiml time lloction between criminl nd legl ctivities, s indicted in (14). B. The Effects on Crime of Txing Legl nd Criminl Income nd Disllowing Deductions for Fines Consider next tx regime such s the current U.S. income tx lws under which legl nd criminl income re txble but fines re nondeductible. 16 This regime is cptured by setting δ = 0, so terminl welth becomes: (15) Y = W 0 (1 t)( c( ) f ( ) 16 See Jmes v. United Sttes 366 U.S. 213 (1961) (txble income ccrues if the txpyer cquires ernings, lwfully or unlwfully, without the consensul recognition, express or implied, of n obligtion to repy nd without restriction s to their disposition) nd section 162(f) of the Internl Revenue Code (2003) ( no deduction shll be llowed for ny fine or similr penlty pid to the government for the violtion of ny lw ), which codified the decision in Tnk Truck Rentls, Inc. v. Commissioner 356 U.S. 30 (1958). See in generl Bittker (1974); nd Colliton (1989). 10

11 = W 0 (1 t)( c( )) The response of offenders to imposing (or incresing tx rtes under) such tx regime cn be investigted by differentiting the first order condition (3 ) nd (4 ), understood to hold for δ = 0, with respect to t nd solving for ddition to (8), (9), (10) nd (11) we hve: (16) = U (, Inserting these terms to (7) nd simplifying yields (17): * ( U = 2 (, ) (1 t) w''( U (, U *. We obtin (7), where now in (, ( ) The economic interprettion of this result is lso simple. Imposing tx regime tht disllows deductions for fines cretes two substitution effects. It reduces the expected returns from criminl ctivities proportionlly more thn it reduces the returns from legl ctivities, thus inducing offenders to substitute work for crime. In ddition, the tx reduces the reltive price of leisure, thus inducing offenders to substitute lso leisure for crime nd work. These two substitution effects imply then tht tx regime tht disllows deductions for fines will reduce crime. 17 As cn be expected, this result lso depends upon the ssumption of seprbility (see ppendix C). The reson gin is simple. Assuming U LW > 0 implies tht leisure is norml good, so txtion genertes 17 The effect of such tx regime on legl ctivities, however, is mbiguous becuse the two substitution effects re conflicting. This cn be mthemticlly seen from the following eqution, where the first term is negtive while the second term is positive. 2 b * ( U (, ) ((1 t) c''( pf''( ) U(, U (, ( ) (18) = 11

12 n income effect s well tht opertes to reduce the demnd for leisure nd increse the demnd for legl nd criminl ctivities. This income effect works in the opposite direction to the substitution effects discussed bove, so the net result is indeterminte. This result lso depends upon the ssumption of risk neutrlity (see ppendix D). The reson is similr, but little bit more complicted. Becuse of seprbility, the income effect generted by txtion does not ffect the mrginl utility of leisure. owever, even ignoring its effects on the willingness of offenders to ber risk nd other potentil effects, the income effect increses the mrginl utility of income ssuming the utility function is concve with respect to income thus incresing the mrginl utility of mrket ctivities. This increse mens tht the demnd for legl nd criminl ctivities will rise. Under seprbility nd risk version (with constnt bsolute risk version), the income effect works gin in opposite direction to the substitution effects, so the net effect is still indeterminte. 18 C. The Effects on Crime of Chnges in the Degree of Deductibility δ (Punishment) Lstly, nlyze the effects on crime of switching from deductibility regime to nondeductibility regime, which mounts to nlyzing the effects on crime of chnges in the degree of deductibility δ. Terminl welth for some positive δ becomes: (19) Y = W 0 (1 t)( c( ) (1 δt) f ( ) = W 0 (1 t)( c( )) 18 It should be noted tht if the multi-ttribute bsolute risk version function is decresing, the income effect with respect to criminl ctivities itself becomes mbiguous. On the one hnd, the reduction in the level of welth increses the mrginl utility of mrket ctivities, leding to n increse in the demnd for crime. On the other hnd, the (equl) reduction in the level of welth reduces the willingness of offenders to ber risk, thus reducing the demnd for crime. Disregrding other possible effects, these two effects lone operte in opposite directions, so the net income effect is mbiguous. 12

13 Differentiting the first order conditions (3 ) nd (4 ), understood to hold for 0 < δ < 1, with respect to δ nd solving for *, we obtin: δ * 1 b (20) = b bb δ δ δ Where now: (21) = 0 δ b. (22) = pu (, tf '( > 0 δ The second order conditions for locl mximum imply tht > 0 nd * > δ we cn conclude tht The economic explntion for this result is similr to the one given bove nd need not be repeted here. Somewht surprisingly, this result lso depends on seprbility nd risk neutrlity (unless the uncommon ssumption of constnt or incresing bsolute risk version is dopted). If we ssume tht U LW > 0, while mintining risk neutrlity, then: (20 ) b = pu ( Y, tf ( LY δ (21 ) = pu (, tf '( pu ( Y, tf ( δ LY bb, so b * < δ 19 Similrly, with respect to legl ctivities we cn esily obtin 0. 13

14 Becuse δ cnnot be signed (the first term is positive while the second term is negtive), * δ cnnot be signed either. If, however, 0 δ, which follows if UY ( Y, f (, then becuse U ( Y, f '( YL b, bb *, we cn conclude tht > 0. If, δ on the other hnd, δ, which follows if UY ( Y, f ( <, then U ( Y, f '( YL * δ will be indeterminte. If we relx the ssumption of risk neutrlity nd ssume insted risk version, while mintining the ssumption of seprbility, then, in ddition to bb : (22) = puyy ( Y, ((1 t) (1 δt) f '( ) tf ( δ (23) b = pu ( Y, (1 t) tf ( YY but, δ 2 (24) = (1 p) U (, (1 t) b pu Y ( Y, tf '( > 0 pu ( Y, (( 1 t) (1 δ t) f '( )( 1 t) U (, YY * > δ is not signed. It is pprent tht if b, then 0, but tht otherwise * δ cnnot be signed. b is negtive, however, only if the multi-ttribute function of bsolute risk version is constnt or incresing with income (see ppendix E). One cn 14

15 conclude then tht for risk version nd seprbility shift from deductibilty regime to nondeductibility regime will reduce crime unmbiguously only if offenders exhibit constnt or incresing bsolute risk version. If, however, the common ssumption of decresing bsolute risk version is employed, the effects of chnges in the degree of deductibility cnnot be unmbiguously determined. IV. CONCLUDING REMARKS The im of this pper hs been to exmine the robustness of the results nd the vlidity of the policy suggestions mde in the literture on txtion nd crime when the mount of time llocted to leisure (or income-producing ctivities) is vrible. As shown, unless strong restrictions re plced on the utility function -- in prticulr tht offenders exhibit risk neutrlity nd tht the utility function is seprble -- no cler results cn be obtined. In prticulr, in contrst to previous results, pure income tx regime no longer mintins the level of crime with respect to risk neutrl offenders. Tht is, pure income tx regime is not neutrl to efficient deterrence. Similrly, the current U.S. income tx lws no longer reduce crime unmbiguously in comprison to world with no txtion or for different tx rtes. Moreover, even the effects on crime of shift from deductibility regime to nondeductibility regime (t lest for smll vlues of tx rtes) re no longer unmbiguously determined. This occurs becuse with vrible leisure time, txtion, on the one hnd, reduces time llocted to both legl nd criminl ctivities s leisure becomes reltively cheper thn mrket ctivities, but, on the other hnd, it increses time llocted to mrket ctivities s long s leisure is norml good. If, however, offenders exhibit risk neutrlity nd the utility function is seprble in income 15

16 nd leisure, then the income effects essentilly dispper nd the results become cler. A pure income tx regime then will reduce both legl nd criminl ctivities, but surprisingly the reduction will not necessrily be proportionte. Tht mens tht pure income tx regime will not necessrily mintin the reltive level of work nd crime. On the other nd, the current U.S. income tx lws will reduce crime, but they will hve n mbiguous effect on work. Only shift from deductibility regime to nondeductibility regime will hve the sme, expected effects of reducing crime nd incresing work. The nlysis nd results of this pper re subject to severl importnt limittions, two of which worth emphsis. First, it ws ssumed tht tx revenues re spent on public good tht entered the utility function in seprble nd dditive wy, which implied tht txtion reduces offenders expected welth. It is cler tht government revenues nd spending my ffect offenders behvior. In prticulr, txtion my increse, rther thn decrese, the welth of some offenders if, for exmple, it redistributes income from (rich) non-offenders to (poor) offenders. In such cse, txtion my generte positive income effect tht would tend to discourge, rther thn encourge, mrket ctivities, including income-producing crimes. This income effect then will reinforce, rther thn offset, the substitution effect, leding to n unmbiguous reduction in the level of crime. Second, it ws ssumed tht offenders fully comply with the tx lws. This ssumption seems t first blush restrictive nd unrelistic. owever, in severl importnt cses much illegl income is in fct reported. For exmple, mny offenders who commit white-collrs crimes, such s those who commit frud, those who engge in insider trding, or those who violte the ntitrust lws, re likely to report their illicit gins. In ddition, mny offenses re committed in the course of running n 16

17 otherwise legitimte business, for exmple, trucking compny tht overlods its trucks, so the income ssocited with these offenses is ctully reported. 20 Moreover, ssuming full complince with the tx lws llows us to concentrte on the effects of txtion on crime without the dditionl compliction of secondry violtions of the tx lws. In this respect, it provides rough estimte of the miniml level of overll crime. If one llows for the possibility of tx evsion of either legl or criminl income, one should expect tht the level of crime would be higher thn the one indicted in this pper. 21 The indetermincies regrding the effects of txtion on crime ssocited with model with vrible leisure time re not surprising. In prt, they re relted to the work of illmn nd Ktz (1984) who showed tht with vrible leisure tx imposed solely on legl income does not necessrily reduce the level of criminl ctivities. 22 They re lso relted to indetermincies regrding the effects on tx evsion of chnges in tx rtes or in punishment prmeters obtined in the tx evsion literture when the lbor supply decision is incorported into the model. 23 As this pper shows, however, these indetermincies lso persist even if offenders re ssumed to be risk neutrl, s long s the utility function is not seprble in income nd leisure. 24 The results obtined in this pper cll into question the policy suggestions mde on the bsis of models with fixed level of income-producing ctivities (or leisure time). 20 Even in serious crimes one should tke into considertion the possibility tht offenders would report, t lest, prt of their criminl income s mens of money lundering. 21 It is worth lso emphsizing tht leisure ctivities include not only legl but lso criminl non-mrket ctivities. Therefore, n increse or decrese in leisure time does not necessrily men decrese or n increse in the level of criminl ctivities in generl, but rther potentil decrese or increse in the level of income-producing crimes. 22 It should be noted, however, tht Tbbch (2003) demonstrted tht tx imposed solely on legl income might hve n mbiguous effect on criminl ctivities even if leisure is fixed. 23 See, for exmple, Andersen (1977), Bldry (1977), Pencvel (1979). 24 Note tht the work of illmn nd Ktz (1984) nd the relted work in the tx evsion literture obtin mbiguous results with respect only to risk-verse offenders. Thus, it is uncler whether the indetermincy is the result of risk version or of vrible leisure time. 17

18 In prticulr, the recommendtion to repel section 162(f) of the Internl Revenue Code nd to llow deductions for fines nd the relted justifiction for llowing deductions for punitive dmges. This critique dds to previous critique showing tht even if leisure is fixed, llowing deductions for fines is not necessrily desirble, becuse it my ctully increse the level of crime if offenders re risk verse. 25 Becuse this pper shows tht unmbiguous results cnnot be obtined in generl setting, it concludes tht n empiricl work tht will exmine the reltionship between txtion nd crime is required. Empiricl reserchers cn tke dvntge of historicl chnges of tx rules, of the different tx tretment between fines nd punitive dmges, nd of the frequent chnges in tx rtes in their work. Such empiricl work will be most vluble to policymkers in deciding between different tx rules nd between different levels of monetry snctions nd tx rtes. APPENDI A To derive (13 ), insert to (7) the following terms (clculted for risk neutrlity nd U > 0 ): LW (A1) = U (, (1 t) w''( 2U (, (1 t) bb L ( 1 p) U (, pu ( Y, (A2) = 2 U (, (1 t) (1 p) U (, pu ( Y, b L (A3) b = U (, U (, ( c( pf ( ) t L 25 See Tbbch (2003). 18

19 (A4) = U (, ( pf '( ) U (, ( c( pf ( ) t L It is pprent tht cnnot be signed becuse the first term is negtive while the second term is positive, so * cnnot be signed either. APPENDI B A pure income tx regime will hve no effect on the reltive time lloction between legl nd criminl ctivities if: * b* * b* b* * t t b* (B1) = 0, which implies tht: * t * = t (B1 ) b* b* Where: 2 = * ( U 2 (, ) (1 t)( c' ( pf '( ) w' '( (13) =, 2 b * ( U (, )) (1 )( '' ( ) '' ( )) ' ( ) (B2) = L t c pf w b 19

20 Inserting these terms bck to (B1 ) we obtin (14). 26 APPENDI C We exmine the chrcteristics of * 1 b (7) = b bb for the cse of risk neutrlity nd U LW > 0, ssuming tx regime with no deductions for fines is in plce. Direct clcultion of b, bb, b, nd yields: (C1) = U (, (1 t) w''( 2U (, (1 t) bb L ( 1 p) U (, pu ( Y, (C2) = 2 U (, (1 t) (1 p) U (, pu ( Y, b L (C3) U (, U (, ( c( ) t = L (C4) U (, U (, ( c( ) t = L It is pprent tht b nd cnnot be signed (the first term in ech is negtive while the second term is positive), therefore it is likely tht either. Inserting these terms bck to (7) yields: * will not be signed 26 The sme will be true if * nd b* were clculted for U LW > 0 insted of seprbility. 20

21 (C5) * bu (, ( ) U (, (1 t) w''( b = ) The first term is negtive becuse b. The second term, however, depends on, which cnnot be signed. Therefore, * is mbiguous. APPENDI D We exmine the chrcteristics of (7) for the cse of risk version nd seprbility, ssuming tx regime with no deductions for fines is in plce. By the second order conditions for locl mximum > 0 nd bb. Direct clcultion of, b, nd b revels, however, tht none cn be signed. = ( 1 p) U (, (1 t) ( c( ) (1 p) U (, pu YY ( Y, ((1 t) f '( )( c( ) pu ( Y, The second, third, nd forth terms re negtive, but the first term is positive. Y b = ( 1 p) U (, (1 t) ( c( ) (1 p) U (, pu YY ( Y, (1 t) ( c( ) pu ( Y, The first nd third terms re positive, but the second nd forth terms re negtive. b 2 = (1 p) U (, (1 t) pu ( Y, (1 t) (( 1 t) f '( ) U (, YY The first nd third terms re negtive, while the second term is positive. Y 21

22 APPENDI E We exmine the chrcteristics of (24). Using the multi-ttribute bsolute risk version function R A U ( W, ( W, = WW, the first nd second terms in (24) cn be U ( W, W rewritten s: (E1) Wb (( 1 p) RA(, U(, C pry ( Y, UY ( Y, ( C F )) From the first order condition (3) it follows tht: (E2) ( 1 p ) U (, C pu ( Y, ( C F ) > 0 where the first term is positive nd the second term is negtive. Y It follows then tht for R (, R ( Y,, tht is, for constnt or incresing A A bsolute risk version, the terms in the brckets in (E1) re positive, so tht b. owever, if R (, < R ( Y,, tht is, if bsolute risk version is decresing, then A A (E1) cnnot be signed, so b cnnot be signed either. REFERENCES: Andersen, P Tx Evsion nd Lbor Supply. Scndinvin Journl of Economics, 79: Atkinson, Anthony, nd Joseph E. Stiglitz Lectures on Public Economics. New York: McGrw-ill. Bldry, Jonthn Tx Evsion nd Lbor supply. Economics Letters 3:

23 Bittker, Boris I Txing Income From Unlwful Activities. Cse Western Reserve Lw Review 25: Colliton, Jmes W The Tx Tretment of Criminl nd Dispproved Pyments. Virgini Tx Review 9: Cowell, Frnk A Txtion nd Lbor Supply with Risky Activities. Economic 48: usmn, Jerry A Txes nd Lbor Supply. in 1 ndbook of Public Economic (Auerbch A.J. nd Mrtin Feldstein eds). illmn, Arye L., nd Elikim Ktz Note, Excise Txes, Import Restrictions, nd the Alloction of Time to Illegl Income-Erning Activity. Interntionl Review of Lw nd Economics 4: Pencvel, John., 1979, A note on Tx Evsion, Lbor Supply nd non-liner Tx Schedules. Journl of Public Economics 12: Png I.P.L., nd Eric M. Zolt Efficient Deterrence nd the Tx Tretment of Monetry Snctions. Interntionl Review of Lw nd Economics 9: Polinsky, A. Mitchell, nd Steven Shvell Punitive Dmges: An Economic Anlysis. rvrd Lw Review 111: Schmidt, Peter, nd Ann D. Witte An Economic Anlysis of Crime nd Justice. Orlndo, Fl.: Acdemic Press Inc. [ ]. Tbbch, Avrhm. D Criminl Behvior, Snctions, nd Income Txtion: An Economic Anlysis Journl of Legl Studies 32: Zolt, Eric M Deterrence Vi Txtion: A Criticl Anlysis of Tx Penlty Provisions. UCLA Lw Review 37: