[[alternative]]Bequest Motives, Bequest Behavior, Estate Tax and Inequality of Distribution

行政院國家科學委員會專題研究計畫 成果報告

遺贈動機、遺贈行為、遺產稅與分配不均

計畫類別： 個別型計畫 計畫編號： NSC93-2415-H-032-003- 執行期間： 93 年 08 月 01 日至 94 年 07 月 31 日 執行單位： 淡江大學經濟學系 計畫主持人： 江莉莉 報告類型： 精簡報告 處理方式： 本計畫可公開查詢

中 華 民 國

94 年 10 月 31 日

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…dq¨Ö³WÑD•˘íFH æ”þ}íøOÌ©_, 1YW_Aí²µ œ, }qA‚ ‚FD>qú²µ_, J«n³ß˘í½}º^‹…d êÛ, ÄO³œí.°, {³˘í½}º^‹.° 9ÿ àj²7k, Ì ‚í³uÊA‚í8”-C|k‚FC>qœ,{³˘DÖbã‚ó˝, ‹½˘(F)í}º.Ì5^‹Í†,Ê>qœí8”-,à‹‚íF‚H 4'×,†³˘í½}º^‹˛w ÉœÈ_:³œ³ßDD˘ .Ì Abstract

The paper sets up a heterogeneous, overlapping, and general equilibrium bequest model incorporating estate taxation to examine the redistribution effect of estate tax. In the part of individual’s lifetime decision, three kinds of bequest motives are considered, that is selfishness, altruism and exchange. The main finding is that the effects of estate tax on the distribution of dispos-able lifetime income depend on transfer motives. However, the quality results all point to the unfavorable effect of the imposition of estate tax on distribu-tion inequality. The paper also reveals that in the exchange framework, the redistribution effect of estate tax is minor, if the elasticity of intertemporal substitution is large enough.

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qúG-, {³ß˘úùHlzí à, !‹óç}t à‹,øHuA‚í, †{³ß˘ú,øHlzWÑí àe˘YíT}7ì, 7-øHílzÌàS ·}Áý à‹,øHu‚Fí,†{³ß˘úùHlzí à,e,øHíwÛ? ´fÛJ£˘YíT}7ì à‹,øHíž|k>qœ, †{˘ú,øHlz í àEe˘YíT}7ì, ú-øHílz·³ à 9úk.°³œ-{ ³ß˘í½}º^‹5ªœ}&, d.Gšà úkFHí³œ, ®jínjÌ m%íû˝{T|ûFHžíWÑ

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I _c1t D c2t }H[ t H‚ù‚í¾‘, st uwlz, lzí˘(„Ñ{0 u R∗_t+1 wF)VÄ2, F)²ìk’˙?‰ (at) DÒ´ ’0 (wt∗) cq F)˘˘0 ìÑτ, ³˘˘0 ìÑτbR∗t+1 = (1−τ)Rt+1, wt∗ = (1−τ)wt, w2 _Rt+1 D wt }u’…˘‡í„Ñ{0D˘‡ ’0 ¢cq°ø0Hí’˙ ×Ì}º (uniform distribution), at ∈[0,1] t H‚í²µ½æÑ max c 1−γ 1t 1−γ +p c1₂−_tγ 1−γ s.t. c1t= (1−p)(1−τb)st−1R∗t +atw∗t −st c2t=stR∗t+1. (1) j5, )ƒ t H‚ù‚í¾‘ƒb c1t = αs1ty ∗ t, c2t = αs2ty ∗ tR ∗ t+1, y ∗ t Ñ™´ F), k (1−p)(1−τb)st−1Rt∗+atw∗tαs1t Dαs2t }Ñ αs_1t = R ∗ t+1 R∗_t+1+ (pR∗_t+1)1/γ, (2) αs_2t = (pR ∗ t+1)1/γ R∗_t+1+ (pR∗_t+1)1/γ. (3) α₁s_t+αs_2t = 1 ®‚¾‘´™´F)íª0§’…˘‡í„Ñ{0F)˘0D ù‚æº0í à à‹F‚íH 4×kø (γ < 1), †’…˘‡í„Ñ{0B òCF)˘˘0BQ, ø‚í¾‘Bý, ù‚í¾‘BÖ ¤Õ, ù‚íæº0 Bò, ø‚í¾‘Bý_, ù‚í¾‘BÖ B. ‚F cqúäÞíDòQ#‚^à(Andereoni (1990)),J θa _[ýäÞY§í DÊ‚^àƒbힽ I BtH[t H‚kù‚úäÞíž, Bt∗ †upÎ ³˘(äÞí´Y§ ¤‚F‚í²µ½æÑ max c 1−γ 1t 1−γ + c1₂−_tγ 1−γ +θ a Bt1−γ 1−γ s.t. c1t=Bt∗−1+atwt∗−st c2t=stR∗t+1−Bt. (4) t H‚ù‚í|_¾‘DúäÞíž, ·Dw™´F)AøìíªWÉ[, ¹ c1t = αa1ty ∗ t, c2t = αa2ty ∗ tR ∗ t+1, Bt = αa3ty ∗ tR ∗ t+1 ™´F) y ∗ t k

B_t∗₋₁+atw∗t7®‚í¾‘ª0DúäÞힴ™´F)íª0}Ñ αa_1t = R ∗ t+1 R∗_t+1+ (R∗_t+1)γ_{+ (θ}a_R∗ t+1)1/γ , (5) αa_2t = (R ∗ t+1)1/γ R∗_t+1+ (R∗_t+1)γ_{+ (θ}a_R∗ t+1)1/γ , (6) αa_3t = (θ a_R∗ t+1)1/γ R∗_t+1+ (R∗_t+1)γ_{+ (θ}a_R∗ t+1)1/γ . (7) à‹F‚íH 4×kø, †’…˘‡í„Ñ{0Bò (CF)˘0BQ), ø‚ í¾‘ª0BQ_, ù‚í¾‘ª0Džª0Bò¤Õ_, ‚í‚F˙Bò_, žª0Bò, 7‚A™ù‚¾‘íª0BQ C. >q cq‚Ѧ)äÞÊù‚íÎe, wÛDäÞ Ä¤, ‚ø‚ílzÎ7 Xù‚í¾‘Õ_, ÿu˛äÞ퐎 _(Zt) óúí, äÞÊø‚Î7ÊÒÿ “:¦‹’Õ, ÿuTXŽ#‚, ©ÀPª×) P_zt∗ í´Ñ{ Ì©v, P_zt∗ = at+1w∗t+1Ñ“}&,cq©_ðêíäÞÞúó°íΈŽí´Ñ{,¹P ∗ zt= ¯ at+1w∗t+1, ¯at+1 ut+ 1 0HíÌ’˙‚ʪpù‚¹âÞú-í²µ½ æ: max c 1−γ 2t 1−γ +θ e Zt1−γ 1−γ s.t. c2t=stR∗t+1−PztZt. (8) cJ Zt>0,†‚ù‚í¾‘DúäÞíž}Ñ c2t = (1−ρt)stR∗t+1, (9) PztZt = ρtstR∗t+1, (10) 2, ρt = ((θe)1/γP γ−1/γ zt )/(1 + (θe)1/γP γ−1/γ zt ) ku, ‚Þúí™|_“½æÑ max c 1−γ 1t 1−γ + c1₂−_tγ 1−γ +θ e Zt1−γ 1−γ s.t. c1t =atwt∗+P ∗ z,t−1Zt−1−st, c2t = (1−ρt)stR∗t+1 PztZt=ρtstR∗t+1. (11)

ʤ_2_, ù‚í¾‘Dú-øHힷu™´F)íøìMç_, ¹ c1t = αe 1ty ∗ t, c2t = αe2ty ∗ tR ∗ t+1, PztZt = αe3ty ∗ tR ∗ t+1 y ∗ t D αeit(i = 1,2,3) í ì2à-: y∗_t = P_z,t∗ −1Zt−1+atwt∗, (12) αe_1t = (1−ρt)R ∗ t+1 (1−ρt)R∗t+1+ (R∗t+1)1/γ , (13) αe_2t = (1−ρt)(R ∗ t+1)1/γ (1−ρt)R∗t+1+ (R∗t+1)1/γ , (14) αe_3t = ρt(R ∗ t+1)1/γ (1−ρt)R∗t+1+ (R∗t+1)1/γ . (15) Ê>qœ-, ‚ù‚í¾‘ª0Džª0°š§ƒ’…˘‡í„Ñ{0DF) ˘0í àF.°íu, F)˘0Î7Z‰F‚í¾‘²ÏÕ,6 àäސŽíg  Ê>qœ-,‚í¾‘ª06DäÞí ’0£D˘˘0É à‹F‚í H 4×kø, äÞí ’0 (CD˘˘0) Bò, äސŽígBò, *7 ‚úøO¼¹í¾‘ª0Bò,úäސŽíX|ª0BQ Τ5Õ,‚BÊ<ä Þ퐎v, úäސŽí¾‘X|ª0Bò

2.2

ÞßÞ cqrþ}í,Þ߃buCobb-Douglas$,† t ‚(óçkt 0Hø‚)í ,ß|Ñ Qt=KtβL 1−β t . (16)

w2_, ^_{(effective labor) Lt=N¯at, N} u®0Hí‚€A¨bBk’…_,

cqwUà‚ÌÑø‚, †t ‚í’…êrVAk‡ø‚ílz, ¹ Kt = Z 1 0 st−1h(at−1)dat−1 = (αj2t+α j 3t)Ny¯ ∗ t−1, j =s, a, e. (17) α₃s_t= 0_h(a)u’˙}ºíœ0òƒbÑp–c, ÎαÕ_,wì‰bí-™j Ì8JôI t+ 1 ‚í’…„Ñ{0D ’0}Ñ Rt+1 = β(αj2t+α j 3t) β−1_(¯a t)1−β(¯y∗t−1) β−1_{, (18)} wt = (1−β)(αj2t+α j 3t) β_(¯a t)−β(¯yt∗−1) β_{. (19)}

t Hí´F)¨Žr¶í˘( ’F)D˘(ížF) ÊA‚ ‚FD>q ùžœ-, t Hí´F)}Ñ Ny¯_t∗ = (1−τ)(1−β)Qt+ (1−p)(1−τb)R∗t+1Kt = (1−τ)[(1−β) + (1−p)(1−τb)β)](αs2,t−1) β_¯a1−β t N(¯y ∗ t−1) β_{, (20)} Ny¯_t∗ = (1−τ)(1−β)Qt+ αj_3,t−1 α₂j_,t−1+α j 3,t−1 (1−τb)Rt∗Kt = (1−τ)[(1−β) + α j 3,t−1 αj_2,t−1+αj_3,t−1(1−τb)β)](α j 2,t−1+α j 3,t−1) β ¯ a1_t−βN(¯y_t∗₋₁)β, j =a, e. (20’) cq%ÈñÍu ìí, /®HíÌ’˙ó° (¹ ¯at = ¯a,∀t), †ÊìG5-, Rt+1 = R, wt = w,y¯t∗ = ¯y∗,∀t, *7 α j it = α j i, i = 1,2,3, j = s, a, e,∀t ñ ÍÌ©ªâ-ä…•: ¯ y∗ = (1−τ)1/(1−β)[(1−β) + (1−p)(1−τb)β]1/(1−β)(αs2)β/(1 −β)_{¯a, (21)} R =β(1−τ)−1[(1−β) + (1−p)(1−τb)β]−1(αs2) −1_{, (22)} w= (1−β)(1−τ)β/(1−β)[(1−β) + (1−p)(1−τb)β]β/(1−β)(αs2)β/(1 −β)_, (23) ¯ y∗ = (1−τ)1/(1−β)[(1−β) + α j 3 αj₂+αj₃(1−τb)β] 1/(1−β)_(αj 2+α j 3) β/(1−β)_¯a, (21’) R =β(1−t)−1[(αj₂+αj₃)(1−β) +αj₃(1−τb)β]−1, (22’) w= (1−β)(1−t)β/(1−β)[(αj₂+α₃j)(1−β) +αj₃(1−τb)β]β/(1−β), j =a, e. (23’) ‚à (22) ( C (22’)) D(23) ( C (23’)) TªœÓG}&, )øÌ‚ uA‚C‚Fí,±QF)˘˘0C³˘˘0,·ø±Q’…˘‡í„Ñ{0, 1T ò ’0 à‹‚úäÞížu!k>qœ, †±Q³˘˘0°šU)’… ˘‡í„Ñ{0±Q, ’0,¯ Bk|±F)˘˘0úbÖÑ{0í à†.ø ì à‹γ > β(1−τb)/2(1−βτb), †F)˘0±Q(,’…í„Ñ{0±Q, ’ 0,¯

2.3

ìGÌ©íF)}º â_)ø, t 0Hø_Ôì‚í´F)Ñ y∗_t =atwt∗+ (1−p)(1−τb)αs2,t−1y ∗ t−1R ∗ t, (24) y∗_t =atwt∗+ (1−τb)αj3,t−1y ∗ t−1R ∗ t, j =a, e. (24’) ¤ùéýFHÈF)í:û Ê‚uA‚í8”-,cà 1−(1−p)(1−τb)(1− t)αs₂R >0, †F)Y¹BøìGí}º, ìGÌ©-íÌ´F) (E(y∗)) D´F )í‰æ[b5j(SCV(y∗)) }Ñ E(y∗) = (1−τ)w¯a 1−(1−p)(1−τb)(1−τ)αs2R , (25) SCV(y∗) = 1−(1−p)(1−τb)(1−τ)α s 2R 1 + (1−p)(1−τb)(1−τ)αs2R SCV(a), (26) 2, SCV(a) u’˙í‰æ[b5j °Ü, ç‚u‚FCæÊ>qœv, à‹1−(1−τb)(1−t)αj3R > 0, j = a, e,†æÊìGíÌ´F)J£´F)í‰æ[b5j, !‹à-: E(y∗) = (1−τ)w¯a 1−(1−τb)(1−τ)αj3R , (25’) SCV(y∗) = 1−(1−τb)(1−τ)α j 3R 1 + (1−τb)(1−τ)αj3R SCV(a), j =a, e. (26’)

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;WìGÌ©íÌ´F)J£´F)í‰æ[b5j, ªWªœÓG}& (dE(y∗)/dτ, dE(y∗)/dτb, dSCV(y∗)/dτ, dSCV(y∗)/dτb),J«nÊ.°í³ œ-_, F)˘D³˘í{ú%È‚í à1 _{íl, ç‚uA‚v, à‹ 1−} (1−p)(1−τb)(p(1−τ)R)1/γ >0,†±QF)˘˘0øTòÌ©Aí˘(F) ¢à‹ β < 1/2, †±Q³˘˘06ªTòÌ©Aí˘(F)Bk}º^‹j Þ, |±³˘˘0øU}º.Ìí˙ (J _SCV(y∗_{) ©¾) ±Q ŸÄu³˘} 1_{ĪœÓG}&!‹õµ,Ñô¹Ù,.8| àÛb,ª²T6ئ}

˘0±Q_, ¬V<Õ×)í´žÓ‹_,HÈíF)Ïòü_, Å‚5-í}º.ÌZ ¾ ÇjÞ, ‚0-± (à‹ γ < 1), U)FHžDw„Ñ{0ÌÁý, ú}º. ÌØ×í^‹;9w à.J‡6× Í7, F)˘í{ú}º.Ì˙º³ à wŸ, ç‚u‚Fv, à‹ β < 1/2, †±Q³˘˘0°šªTòÌ©A í˘(F) à‹ 1−(1−τb)(θa(1−τ)R)1/γ >0,†±QF)˘˘0?øTò Ì©Aí˘(F)Bk|±³ß˘í˘0_,°š}±Q}º.Ìí˙;¤ø!X M Stiglitz íõ 7|cF)˘˘0í½}º^‹, Ê˘0D‚0íTàóJ 5(, ¾Üw` |(, à‹‚í³œu|k>q, †{F)˘D³˘ú%È‚í à̶‡ì DwFù8”.°, Ê>qœ-, |±³˘˘0CF)˘˘0(, J ’0,¯,‚úäÞížøÁý;Ó¼}º.ÌíÄÖD^‹Ñnjs˘í ½}º^‹, …d4SàbM_Òj¶,Êqì(γ, θj_{, β) ¡bM(,_Ò.°˘0} -, ìGÌ©íÌ´F)J£´F)í‰æ[b5j [ 1 í_Ò!‹éý, Ê ¤øÕ”-, F)˘í{à°ã‚Oí±QÌ´F), OºÁQ}º.Ì˙ íTàÇjÞ, {³˘ú%È^0 (?¹Ì´F)) Ù{Qí^‹, ú} º.̆‹½í^‹9J‚íF‚íH 4Ó×(, ³˘ú^0D}ºí àMÚÁQ

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ÄO³œí.°, {³˘í½}º^‹.° 9ÿ àj²7k, Ì‚ í³uÊA‚í8”-C|k‚FC>qœ, {³˘DÖbã‚ó˝, ‹ ½˘(F)í}º.Ì5^‹Í†,Ê>qœí8”-,à‹‚íF‚H 4 '×,†³˘í½}º^‹˛wF)˘í{†Ì“í^‹,9wú%È ^0íaï6œ³˘Ñ×

ÉkFHž, A‰’…íI’u.ªeíáñ d. (à Caball´e (1995))

éý,‚úùžjí²ÏÉ[øÅí%ÈAÅ Y¤R¿,øï‹pA‰’… íI’²µ, ɳ˘DF)˘í½}º^‹, C.°í!DyÖí\µ°2

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¤Õ, ;W…dFqí¨Ö³WÑ5LH_, ²ì%Èþ}Å‚í}º. Ì5ÄÖ, YO‚í³œ7.° Ĥ, à‹„VÅqód’e5r, †ª

YW…û˝í!, ³íõ„_, JìÅq‚í³œ °v, cJª J¦)‹\¶í˙˘’e, †)Jªø¥Ç,³ß˘í½}º^‹ [1. F)˘D³˘íìGÌ©_Ò: >qœ τ R w Q K E(y∗) SCV(y∗) (γ, θe_{, β, τ} b) = (0.4, 0.1, 0.3, 0) 0.4 1.460 0.355 25.374 5.212 0.110 0.311 0.3 1.267 0.378 26.970 6.387 0.136 0.317 0.2 1.117 0.398 28.462 7.643 0.163 0.320 0.1 0.998 0.418 29.866 8.974 0.191 0.323 τb R w Q K E(y∗) SCV(y∗) (γ, θe_{, β, τ) = (0.4, 0.1, 0.3, 0)} 0.4 0.911 0.435 31.061 10.228 0.218 0.331 0.3 0.909 0.435 31.089 10.258 0.219 0.330 0.2 0.907 0.436 31.119 10.292 0.219 0.328 0.1 0.905 0.436 31.154 10.331 0.220 0.327

¡5

d.

[1] rpœ(2001),BųߣD˘˘„5«n˚,\µ×狢û˝Fî=d

[2] Barro, R.J. (1974), Are Government Bonds Net Wealth? Journal of

Political Economy 82, 1095-117.

[3] Becker, G.S. (1974), Theory of Social Interactions, Journal of Political

Economy 82, 1063-93.

[4] Becker, G.S. (1991),A Treatise on the Family, Cambridge, MA: Harvard University Press.

[5] Becker, G.S. and N. Tomes (1979), An Equilibrium Theory of the Dis-tribution of Income and Intergeneration Mobility, Journal of Political

Economy 87, 1153-89.

[6] Bernheim, B.D., A, Shleifer and L.H. Summers (1985), The Strategic Bequest Motive, Journal of Political Economy 93, 1045-76.

[7] Caball´e, J. (1995), Endogenous Growth, Human Capital, and Bequests in a Life-Cycle Model, Oxford Economic Papers 47, 156-81.

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