Working Paper Series. Costs of Inflation in Japan: Tax and Resource Allocation

Transcription

1 Working Paper Series Coss of Inflaion in Japan: Tax and Resource Allocaion Kozo Ueda Working Paper 0-0 Research and Saisics Deparmen Bank of Japan C.P.O BOX 03 TOKYO JAPAN Views expressed in his Working Paper Series are hose of auhors and do no necessarily reflec hose of he Bank of Japan or Research and Saisics Deparmen.

2 Coss of Inflaion in Japan: Tax and resource allocaion November, 00 Kozo Ueda * Absrac This paper ries o shed ligh on he opimal inflaion rae by invesigaing he effecs of changes in inflaion on resource allocaion via changes in he effecive ax raes. Given ha some axes are no lump-sum bu subjec o he proporional/progressive ax schedule, and ha axes are levied on nominal income insead of real income, an increase in he inflaion rae has a disorional effec because i raises he effecive ax raes. This paper ries o esimae ha effec by aking Japan s insiuional background fully ino accoun and by applying he general equilibrium framework of Abel [997]. The curren coss of he higher inflaion are found o be larger in Japan compared wih hose in oher indusrial counries, because of he lower rae of corporae capial reurn. I would like o hank Professors Nobuo Akai, Shinichi Fukuda, Yasushi Iwamoo, Yukinobu Kiamura, Toshiji Miyakawa and Messrs. Hiroshi Fujiki, Masahiro Higo, Kenji Nishizaki, Toshiaka Sekine, and many ohers for heir helpful commens and suggesions. I am of course responsible for any errors. * Research and Saisics Deparmen, Bank of Japan, <kouzou.ueda@boj.or.jp>

3 I. INTRODUCTION Wha inflaion rae should he cenral bank aim a? Researchers have looked ino he various coss associaed wih paricular aspecs of inflaion in aemps o shed ligh on his quesion. They include inflaion uncerainy (Kimura and Tanemura [000]); relaive price variabiliy (Ueda and Osawa [000], Shirasuka [000]); and inflaion ineria (Kasuya and Oshima [000]). This paper is anoher aemp o answer he above quesion by invesigaing he long-run coss of inflaion in view of ax and resource allocaion. Inflaion affecs resource allocaion because he governmen levies axes proporionally or progressively. I also levies axes on nominal income. Lump-sum axes are desirable for he efficiency of resource allocaion because hey are neural o he opimum behavior of economic agens. However, in realiy, proporional or progressive axes on income and consumpion are ofen used as a means of income redisribuion, and as a buil-in sabilizer, a he expense of heir disorional effecs on resource allocaion. Furhermore, because income subjec o ax is no real bu nominal, an increase in he inflaion rae raises he effecive ax rae in spie of he unchanged preax real income. As a resul, he shif of he inflaion rae induces some changes in disorional effecs on resource allocaion hrough changes in he effecive ax raes. A wealh of sudies have ried o esimae he disorional effecs of inflaion hrough axes see, for example, conribuions in Feldsein [999], which covers he Unied Saes (Feldsein), he Unied Kingdom (Bakhshi, Haldane and Hach), Germany (Töder and Ziebarh) and Spain (Dolado, González-Páramo and Viñals). In Japan, he Economic Planning Agency (EPA, currenly, he Cabine Office) [999] esimaes such disorional effecs. However, all of hese sudies use daa ha conains relaively high raes of inflaion and corporae profis. For insance, he EPA uses daa from 975 o 997, which spans he periods ha were affeced by wo oil crises. I is ineresing o see wheher hese esimaes have been, in he curren Japanese siuaion, quie accurae; he average inflaion rae has been almos zero (or negaive depending on he periods) and he reurn on capial has been low. This paper esimaes he effecs of inflaion on resource allocaion by aking he following wo seps: The firs sep is o calculae he changes in he effecive ax raes caused by inflaion. This paper esimaes changes in he effecive ax raes on (i) corporae capial reurn, (ii) housing invesmen, and (iii) labor income, as consisenly as possible wihin Japan s insiuional background. The esimaed resuls show ha an increase in he inflaion rae raises he effecive ax rae on corporae capial reurn by a larger amoun han hose on housing invesmen and labor income. The second sep is, in a general equilibrium framework of Abel [997], o calculae he impacs on consumpion semming from he above esimaed changes in he effecive ax raes. Abel provides he seup o measure he disorional effecs on resource allocaion as a decrease in levels of household consumpion, which leads o a decline in household uiliy. Mainly due o he low corporae capial reurn, which implies larger changes in is effecive ax, he curren coss of inflaion in Japan are Lump-sum ax can affec he resource allocaion in he long-run model where he populaion is endogenous. Furhermore, he EPA migh overesimae he rae of capial reurn because is calculaion of corporae capial is based on book values.

4 found o be relaively high compared wih hose in he exising sudies. This paper is organized as follows: Secions II, III, and IV focus on he firs sep. The impacs of inflaion on corporae capial reurn, housing invesmen, and labor income are discussed, in urn, in each secion. Secion V proceeds o he second sep by inroducing Abel s model, which leads o he numerical calculaions of he coss of inflaion in Secion VI. Finally, Secion VII summarizes he resuls and provides several caveas. II. IMPACT OF THE SHIFT OF INFLATION ON CORPORATE CAPITAL RETURN This secion analyzes changes in he effecive ax rae on corporae capial reurn. In doing so, i akes ino accoun more deailed informaion of corporae finance han Feldsein [999] and he EPA [999]. A. Corporae finance and ax on capial reurn Households receive reurns from firms who issue deb and/or equiies for heir invesmens, bu hese reurns are subjec o various axes (Char ). In Japan, he following axes are levied: (i) ineres income ax mus be paid when households receive ineres; (ii) corporae income ax is levied on corporae profis afer deducing he above ineres paymens; (iii) dividend income ax mus be paid when households receive dividends as a porion of corporae reurn afer corporae ax paymens; and (iv) capial gains ax mus be paid when households realize capial gains by selling equiies his can be hough as he ax on he reained profis which increase sock prices. The above relaionship can be expressed as follows. Suppose ha households inves in firms whose preax reurn is equal o R. The pos-ax reurn, r, which he households receive (whie areas in Char ) becomes r = R [B(- b )+(-B)(- corp ){(-D)(- cg )+D(- d )}], (-) where B is he share of ineres paymens o capial reurn; corp is he ax rae on corporae income; b is he ax rae on ineres income; d is he ax rae on dividend income; cg is he ax rae on capial gains; and D is he dividend payou raio. The effecive ax rae on capial reurn,, is hen defined as he difference beween he preax and he pos-ax raes of reurn: = r/r. (-) B. Effecs of he change in he inflaion rae on ax Because income subjec o ax is no real bu nominal, is effecive ax rae changes depending on he inflaion rae. Tha is, he shif of he inflaion rae affecs he effecive ax rae hrough changes in he following nominal values: (i) corporae depreciaion allowances; (ii) corporae ineres paymens; (iii) household ineres receips; and (iv) household holding sock. These effecs will be examined below in line wih Feldsein [999]. 3

5 (i) Corporae depreciaion allowances In calculaing corporae ax, firms can deduc depreciaion allowances from heir axable income. Because a rise (fall) in he inflaion rae does no affec he nominal values of depreciaion allowances, heir real values become smaller (larger) and axable income increases (decreases). When he inflaion rae rises (falls), he effecive ax rae rises (falls) and he pos-ax real rae of reurn falls (rises). Auerbach [978] derives he change in he pos-ax real rae of reurn (which households receive) resuling from he shif of he inflaion rae ( π) as follows: d r = corp π { ( D d + ( D) cg )}, N + π + d where N is capial cos, and d is he rae of depreciaion. The par in braces corresponds o he share of he ne household receips afer deducing capial gains ax and dividend income ax. (ii) Corporae ineres paymens On he assumpions ha (a) he fuure inflaion rae is perfecly foreseeable and (b) boh he nominal rae of reurn and he nominal ineres rae change by he same amoun as changes in he inflaion rae (he Fisher effec), corporae ineres paymens increase (decrease) and axable income decreases (increases), reflecing a rise (fall) in he inflaion rae. Tha is, he effecive ax rae falls (rises) and he pos-ax real rae of reurn rises (falls). The change in he pos-ax real rae of reurn ha households receive becomes r = corp b π {(D d +(-D) cg )}, where b is he raio of debs o asses. (iii) Household ineres receips As he oher side of he coin, he rise (fall) in he inflaion rae causes he nominal values of household ineres receips o increase (decrease). The effecive ax rae on ineres income rises (falls) and he pos-ax real rae of reurn falls (rises). The assumpion ha household porfolio (deb share) is equal o he corporae deb share yields he change in he pos-ax real rae of reurn by r = - b b π, where b is ax rae on ineres income. (iv) Household holding sock The rise (fall) in he inflaion rae raises (reduces) sock prices. Even if he real values of households holding sock do no change, he nominal capial gains increase (decrease). The effecive ax rae on capial gains rises (falls) and he pos-ax real rae of reurn falls (rises). Suppose ha he rise (fall) in he inflaion rae, π, raises (reduces) corporae asses (capial sock) by he same amoun, bu does no affec corporae deb. This causes he nominal values of corporae equiy, whose raio o asses is (-b), o increase (decrease) 4

6 by π/(-b), and he pos-ax real rae of reurn o fall (rise) by cg π/(-b). Assuming ha he household invesmen raio of sock is (-b) as in (iii), he change in he pos-ax real rae of reurn amouns o r = cg ( b) π. b Summaion of he above four facors yields he change in he pos-ax real rae of reurn ( r) and he change in he effecive ax rae ( ), caused by he shif of he inflaion rae ( π), as d r = corp π + corpb π { ( D d + ( D) cg )} bb π cg π (-3) N + π + d r =. (-4) R C. Esimaions of he reurns on corporae capial and he effecive ax raes This paper inroduces wo quaniaive mehods o esimae he raes of reurns and he effecive ax raes 3. The firs mehod (Mehod ) obains hem as he average preax rae from 985 o 998. The oher (Mehod ) calculaes hem from he average pos-ax ineres rae for he same periods wih an assumpion on he risk premium. Mehod As a baseline, i is necessary o have he rae of reurn, which is neural o cyclical movemens and largely consisen wih he zero inflaion rae. The sample period from 985 o 998 is chosen on hese grounds, since he period covers several business cycles and observes reasonably sable inflaion raes he average inflaion rae in erms of he consumer price index (CPI) during he period was.08 percen, which can be regarded as almos zero inflaion rae given he similar size of inflaion bias (0.9 percen in Shirasuka [999]). 4 Based on he daa of he non-financial secor in he SNA 5 (Sysem of Naional Accouns), he preax rae of reurn is calculaed as 6 : R = (receips 7 dividend incomes) / (asses corporae shares). (-5) This paper uses he ax raes in fiscal year 000 (see Char for furher deails) o calculae he pos-ax rae of reurn and he effecive ax rae. From equaions (-5), (- ) and (-) respecively, he following values can be obained: preax rae of reurn R: 4.5%, pos-ax rae of reurn r:.83%, effecive ax rae : 37.7%. 3 This paper assumes ha a change in inflaion does no affec corporae finance behavior such as he raio of deb o equiy. 4 As menioned above, he sample period of he EPA [999] is 975 o 997, which yields he higher average inflaion rae. 5 Based on he SNA68 insead of he more recen SNA93. 6 Since he receips in he numeraor do no include capial gains from sock, dividend incomes and corporae shares (sock which corporaions hold) are subraced. 7 The sum of operaing surpluses and propery income. 5

7 Equaions (-3) and (-4) hen yield he following impacs of he changes in he inflaion rae. Rise in he inflaion rae (from 0 o %) Fall in he inflaion rae (from 0 o %) Pos-ax rae of reurn.4% (-0.60%) 3.43% (+0.60%) Effecive ax rae 50.36% (+3.9%) 3.98% (-3.9%) Figures in parenheses indicae he level changes (% poins). If he inflaion rae rises by wo percenage poins, he effecive ax rae on reurn rises by around 3 percenage poins and he pos-ax rae of reurn falls by 0.60 percenage poins. The decomposiion of he rae of reurn shows ha he effecs are (i) 0.56 percenage poins by he decrease in corporae depreciaion allowances, (ii) percenage poins by he increase in corporae ineres paymens, (iii) 0.0 percenage poins by he increase in household ineres receips and (iv) 0.0 percenage poins by he rise in household holding sock. Mehod Mehod goes he oher way round i firs calculaes he pos-ax rae of reurn from he average ineres rae from 985 o 998 wih an assumpion on he risk premium, and hen derives he preax rae of reurn (Char 3). The pos-ax rae of reurn, which households receive, can be expressed as: r = b i b + (-b)(i b +ρ), where i b is he pos-ax ineres rae, and ρ is he risk premium. Mehod obains he preax rae of reurn in he following ways. () deb: he preax reurn o debs is equal o b i b (+ b ) () equiy: he preax reurn o equiy is equal o X which saisfies X(- corp ){D(- d ) + (-D)(- cg )} = (-b)(i b + ρ). Summaion of () and () yields: R =b i b (+ b ) + (-b)(i b + ρ)/{(- corp ){ D(- d ) + (-D)(- cg )}}. Assuming he risk premium is one percen, he average pos-ax ineres rae of 4.4 percen gives (see Char 3 for more deails) preax rae of reurn R: 8.7%, pos-ax rae of reurn r: 4.90%, effecive ax rae on reurn : 40.06%. From equaions (-3) and (-4), he pos-ax rae of reurn and he effecive ax rae afer he shifs of inflaion become as follows: 6

8 Rise in he inflaion rae (from 0 o %) Fall in he inflaion rae (from 0 o -%) Pos-ax rae of reurn 4.38% (-0.5%) 5.4% ( 0.5%) Effecive ax rae 46.39% (+6.33%) 33.73% (-6.33%) Figures in parenheses indicae he level changes (% poins). The change in he effecive ax rae,, in Mehod (abou 3 percen) is more han double compared wih ha in Mehod (a lile more han six percen). This is because he raes of reurns are esimaed lower in Mehod han Mehod. The same size shif in he inflaion rae (i.e., wo percenage poins) brings roughly same size shifs in he pos-ax rae of reurn, r. However, in Mehod becomes larger owing o he lower level of R in equaion (-4). Alhough i is very difficul o judge which of he above wo mehods is more plausible, his paper akes Mehod as more reasonable. This is mainly because here seems o be no reason o assume ha he risk premium is one percen. In addiion, he calculaed ineres rae of 5½ percen (preax basis) migh be overesimaed because he rae of reurn migh no have fully refleced he recen rend of disinflaion and low growh. D. Inernaional comparison The rae of corporae capial reurn in Japan (4½ percen, Mehod ) is much lower han hose in oher indusrial counries (Char 4). For example, Feldsein [999] esimaes abou 9 percen for he Unied Saes, which is more or less in line wih hose in he Unied Kingdom, Spain, and Germany. This implies ha he same amoun of change in he inflaion raes (say, from zero o wo percen) lead o a larger change in he effecive ax rae in Japan han hose in oher counries. The wide gaps of he raes of reurns beween Japan and oher indusrial counries are hough o be due o he combinaion of several facors: Japan has suffered from he long-lasing recessions of he 990s and he rae of reurn has been progressively lowered. However, he household secor has been insensiive o such changes in he reurn and has kep is high savings raio. Furhermore, even afer financial liberalizaion including ha on capial ouflows Japan s massive savings has no flowed ou from he counry (semming, perhaps, from he so-called home bias regarding global invesmen). This has prevened he inernaional arbirage of real ineres raes among hose counries. As a resul, Japan has a lower rae of corporae capial reurn. III. IMPACT OF THE SHIFT OF INFLATION ON THE COST OF HOUSING INVESTMENT As seen above, inflaion reduces he corporae capial reurn (i.e., reurn on nonhousing invesmen), and hen makes housing invesmen relaively favorable. Consequenly, inflaion may lead o excessive demand for housing. A. Cos of housing invesmen The cos of housing invesmen consiss of (i) he corporae capial reurn, which households could earn unless hey invesed in housing sock (opporuniy cos), (ii) he 7

9 cos of mainenance, and (iii) depreciaion of housing sock. The coss wih/wihou axes hen become: he cos of housing invesmen wihou axes: RH, RH = R + m + δ, he cos of housing invesmen wih axes: rh, rh = µ(i-θ) + (-µ)(r+π) + + m + δ π, (3-) where m is he mainenance cos of housing sock; δ is he rae of depreciaion of housing sock; µ is he raio of he morgage o housing sock; i is he ineres rae on he morgage; θ is he raio of ax credi o he morgage; and he rae of propery ax (see Char 5 for furher deails). The governmen adops ax incenive (such as ax credi o he morgage) o promoe owner-occupied housing invesmen, which may end up excessive invesmen. Tax incenive for housing differs across counries. In Japan, he governmen allows o deduc a cerain porion of he morgage balances from income ax of households (ax credi). B. Change in he cos of housing invesmen due o he shif of inflaion The rise in he inflaion rae affecs he cos of housing invesmen hrough wo channels in equaion (3-). One is a rise in he ineres rae of he morgage. The oher is a change in revenues from corporae capial invesmen ha households could earn if hey did no inves in housing sock. The ax incenive remains consan under he Japanese ax credi sysem. The effec of he shif of inflaion is d(rh)/dπ = µ di/dπ + (-µ ) d(r+π)/dπ, where di/dπ= (he Fisher effec). Denoe he raes of he corporae capial reurn before and afer he shif of inflaion (say, from zero o wo percen), r and r, dr/dπ = (r -r)/ π. The cos of housing invesmen afer he shif of inflaion, rh, is calculaed as rh = rh + {(d(rh)/dπ} π = rh + (-µ)(r -r). The rise in he inflaion rae decreases corporae capial reurn (r < r), and hen makes housing invesmen more favorable (rh < rh). Based on he parameers in Char 5, he cos of housing invesmen becomes 4.98 percen under he zero inflaion rae in Mehod. Compared wih he cos of 5.3 percen under no axes, his implies ha he ax incenive rae amouns o.6 percen (=( )/5.3). When he rae of inflaion rises (falls), he cos of housing invesmen and he ax incenive rae change as described in he following able. 8

10 Rise in inflaion (from 0 o %) Fall in inflaion (from 0 o %) Cos of housing capial invesmen 4.7% (-0.7%) 5.5% (+0.7%) Tax incenive rae % (-.79%) -0.37% (+.79%) Figures in parenheses indicae he level changes (% poins). The rise (fall) in he inflaion rae makes housing invesmen more (less) favorable. However, he size of he changes in he ax incenive rae of housing invesmen is small compared wih ha in he ax rae on corporae capial reurn. C. Inernaional comparison Compared wih oher indusrial counries, he ax incenive rae of housing invesmen in Japan is relaively small (Char 6). The ax incenive rae under he zero inflaion rae amouns o only a lile more ha wo percen in Japan, in comparison wih abou 0 percen in he U.S. and abou 5 o 40 percen in European counries. The change in he ax incenive rae resuling from he shif of inflaion (from zero o wo percen) is abou ¾ percenage poins, smaller han hose in oher counries: more han hree percenage poins in he U.S. and wo o hree percenage poins in European counries excep for Germany. These differences are aribuable o wo reasons. Firs, he scale of ax credi (ax incenive) is smaller in Japan. Second, he ax incenive in Japan is neural o a change in inflaion rae 9. The reason for he laer: in Japan, he ax credi is applied o a cerain porion of he morgage balance, which is no alered by a change in he curren inflaion. Meanwhile, in he U.S., for example, ax deducion depends on nominal ineres paymens for he morgage a rise in inflaion increases boh nominal ineres paymens and he amoun of ax deducion, and hen reduces boh real ineres paymens and he cos of housing invesmen. IV. IMPACT OF THE SHIFT OF INFLATION ON LABOR INCOME TAX A change in nominal labor income (due o inflaion) alers he effecive ax rae on labor income because of he following wo reasons: Firs, is ax schedule is progressive (i.e., he higher he nominal income becomes, he higher ax rae is applied). Second, here exis several ax deducions (e.g. basic allowance, allowance for spouse, allowance for dependans and deducion for employmen income). This secion esimaes he effec of inflaion on labor income ax in accordance wih Mishan and Dicks-Mireaux [958] and Hayashi [995]. A. Model of he progressive srucure of income ax and he effec of inflaion To esimae he effec of inflaion on labor income ax, he following exponenial form is assumed o approximae he progressive srucure of income ax: = a y b, 8 Negaive ax raes mean incenive o housing invesmen in view of he ax sysem. 9 In Japan, he ineres rae paid on he morgage is no much lower han corporae capial reurn. Therefore, housing invesmen becomes less advanageous. This could be anoher reason, in addiion o he above wo menioned in he ex. 9

11 where y is labor income and (y) is he amoun of ax paymens. Labor income, y is ordered so ha i becomes a coninuous funcion of n, where he nh individual is arranged from he lowes income o he highes: y = f(n). The aggregae income, Y, and he aggregae income ax paymens, T, are where N is he populaion in he counry. Y T = = 0 0 N N f ( n) dn, a[ f ( n)] Because he shif of he inflaion rae changes labor income o (+ π)y, he aggregae income, Y, and he aggregae ax paymens, T, become Y' = T' = 0 0 N N b dn, ( + π ) f ( n) dn = ( + π ) Y, b b a[( + π ) f ( n)] dn = ( + π ) T. The following equaion shows he average ax rae afer he shif of he inflaion rae: T /Y = (+ π) b- T/Y T/Y + (b-) π T/Y. (4-) Because he marginal ax rae mar can be expressed as: N N b mar = dn = ab( f ( n)) dn, 0 y 0 he marginal ax rae afer he shif of inflaion becomes N N ' ' mar = dn = ab{( + π ) f ( n)} 0 y = ( + π ) b mar 0 mar + ( b ) π b mar dn. (4) B. Esimaion of a facor of he exponenial form Following Nishizaki and Nakagawa [000], his secion esimaes he relaionship beween ax paymens 0 and labor income, aking accoun of he progressive ax schedule and he ax deducions. Tax paymens are based on he sauory ax raes in FY000. The esimaion is based on a family consising of wo parens wih wo children. Char 7() shows he relaionship beween preax labor income and he average/marginal ax raes. Esimaion based on he ax schedule in Char 7() yields he following resuls (Char 7()). log(paymens of labor income ax) = log(preax labor income), (-7.68) (.6) where adj.r =0.93 and he figures in parenheses are -values. Thus, he facor of he exponenial form, b, becomes.4. 0 Sum of naional and local axes. 0

12 C. Esimaion of he effec of inflaion on he labor income ax rae The change in he average/marginal ax raes resuling from he shif of inflaion by π is (b-) π, from equaions (4-) and (4-), where is eiher he average or marginal ax rae. The shif of he inflaion rae from zero o wo percen bring an increase in he labor income ax rae by = (.4-)*0.0*0. = (0.%), which is much smaller han he change in he ax rae on corporae capial reurn (abou 3 percen). Thus, he effec of inflaion on he labor income ax is almos negligible. V. ESTIMATION OF THE COST OF INFLATION BY A GENERAL EQUILIBRIUM MODEL This secion discusses he disorional effecs of an increase in he inflaion rae hrough a rise in he effecive ax rae by applying a general equilibrium model of Abel [997], which is an exension of Sidrauski s [967] model. By means of a general framework, Abel models he behaviors of households, firms, and he governmen. The main idea of Abel s model is summarized in Char 8. Consider he case where he inflaion rae rises. Because he rise in he inflaion rae increases he ax rae on corporae capial reurn, household invesmen decreases, and boh capial sock and producion decline. This in urn decreases household income and consumpion in he long run. Furhermore, an increase in he cos of holding money balances reduces household uiliy. Meanwhile, an increase in he governmen revenue is supposed o parially offse he above negaive impacs on he household uiliy. The firs par in his secion inroduces Abel s model o describe he behaviors of households, firms, and governmen. The nex par discusses how household behavior changes by he shif of he effecive ax rae (resuling from he shif of he inflaion rae). A. Seup of a general equilibrium model As menioned above, Abel s model consiss of he hree secors: households, firms and he governmen. Each secor is modeled as follows: Household secor The household secor is assumed o have he following uiliy, which comprises consumpion, money balances, and labor supply: ρ δ + η = c m l u ( c,, ) β + φ ψ m l, (5-) = ρ δ + β η = 0 0 The 0 percen labor income ax rae is consisen wih boh he weighed average of he marginal ax raes by persons and he weighed average of he average ax raes by ax paymens in Char 7(3). See foonoe for furher discussion. In fac, a parial equilibrium model of Feldsein [999] appears more popular han Abel s model among empirical economis. However, his paper uses Abel s model because of is clariy. See Appendix B for he esimaed resuls of Feldsein s model and he comparison wih hose of Abel s model.

13 where β: discoun rae; ρ, δ, η: coefficiens of relaive risk aversion on consumpion, money, and labor (reciprocals of he elasiciy of ineremporal subsiuion); φ, ψ: posiive consans; c, m, l: consumpion, real money balances, and labor supply (per capia); and subscrip denoes he ime period. The household secor faces he following budge consrain, where household income consiss of labor income, capial income, and ineres income from holding governmen bonds: c ( + c ) + ( + n)( k,+ + k,+ ) + ( + n)p + m+ + ( + n)p + b+ = (- ) w l + R k + R k + { + i ( )} b + m, w,,,, b, b (5-) where n: populaion growh rae; k, k, b: corporae capial sock, housing sock, and real sock of governmen bonds (per capia); w, c,, w : real wage, consumpion ax rae, labor income ax rae; R : pos-ax rae of corporae capial reurn; R : pos-ax rae of reurn o housing invesmen; i b, : preax ineres rae of bonds; b : ineres income ax rae; and π + : inflaion rae (=p + /p ). The following equaions represen a soluion ha maximizes he uiliy of equaion (5- ) subjec o (5-) wih he Lagrange muliplier of β λ : ρ ( c ): c = ( + ) λ ( k i, ): βλ R ( m ): βφ m ( b ): βλ { + i ( l ): ψ l η i, δ = λ b, + βλ ( + λ ( c ( + n) = λ b )} = λ w ) w ( + n) π = 0 ( + n) π (5-3) In a seady sae, equaions (5-3) become as follows 3,4,5 : + n Ri =, where i =, β + i ( b b + n ) = π β δ φ m ( + c ) = ib ( b ) ρ c η ψ l ( + c ) = ( w ) w ρ c (5-4) Corporae secor 3 I is necessary o saisfy π > β/(+n) from he zero ineres rae consrain of he nominal ineres rae. 4 The second equaion in (5-4) represens he Fisher effec regarding he pos-ax ineres rae. Assuming he ax rae on ineres income is equal o 0 percen, he rise in he inflaion rae by wo percenage poins raises he pos-ax nominal ineres rae by he same amoun and he preax nominal ineres rae by wo and a half percenage poins. However, because debors borrow heir funds by he paymens of he preax ineres rae, i may no be realisic ha he preax nominal ineres rae makes greaer changes han he inflaion rae by he effecs of ax. 5 In his model, ax on ineres income does no affec esimaed resuls since he ax is assumed o be lump-sum.

14 3 A Cobb-Douglas ype producion funcion of labor, corporae capial and housing sock is assumed, where y is per capia producion 6. = l k Ak y, (5-5) where and are shares of corporae capial and housing sock respecively. In a compeiive marke, maximizaion of corporae profis yields: l y w / ) ( = (5-6) / ) ( + = i i i i k y R, where i=,. (5-7) Governmen Suppose a cenral back is a par of unified governmen 7. The governmen finances is expendiures by axes (on corporae capial reurn, labor income, and consumpion) and seigniorage. The governmen levies a negaive ax (ransfer) o households for housing invesmen. This model does no ake progressive ax on labor income ino accoun. Given almos negligible impac on he effecive ax rae (Secion IV), he simplificaion mus no aler he esimaed resuls below much. Budge consrain of he governmen is, } ) ( ) ( { } ) {( ) ( b n i g m n y y y c b b w c π π = (5-8) where g is per capia governmen expendiure. Eliminaing i b from equaion (5-4), equaion (5-8) becomes. / ) )( ( / / } ) {( ) ( / y b n y g y m n y c c w π β π + + = (5-9) B. Seady sae equilibrium From equaions (5-4) o (5-7) and (5-9), he following equaions can be derived: y y g k k n c ) / ( ( ) = + + (5-0). ) )( (, ), ( ) / (,, ) ( ) ( ) ( η ρ δ ρ ψ π β φ β + = + + = + = = + = + c w c c l y l c n m B nk l k AB y g c Bk k B where l, AB n k (5-) 6 I migh be beer o include housing sock no in he producion funcion bu in he uiliy funcion. However, his does no make difference in his model, as an increase in housing sock raises producion and enhances household consumpion as a consequence. 7 In his model, he inflaion rae is deermined exogenously.

15 Subsiuion of he iniial exogenous values of m 0, y 0, and l 0 gives he ax rae on labor income, w, and parameers φ, A, ψ. This analysis assumes l 0 = wihou loss of generaliy. C. Change in he household consumpion level due o he shif of inflaion Suppose each effecive ax rae changes by when he inflaion rae changes. The effecive ax raes on corporae capial reurn and on housing invesmen are hose obained in Secions II and III. The governmen needs o increase or decrease axes o saisfy is budge consrain. If he governmen muliplies all he ax raes by he same facor, θ, hen he effecive ax raes afer he shif of he inflaion rae become as follows: = θ c w c = ( = ( = ( w + ) θ + ) θ + ) θ w (5-) Subsiuion of equaion (5-) o equaions (5-7) o (5-) gives he value of θ and he values afer he shif of he inflaion rae such as c new, m new, l new and k new. Denoe he consumpion level c* which yields he same level of uiliy as ha in he new seady sae. 0 0 new new new u ( c*, m, l ) = u( c, m, l ) (5-3) From equaion (5-), c* can be expressed as c* = ( ρ) u( c new, m new, l new 0 ( m ) ) φ δ δ 0 ( l ) + ψ + η + η ρ. (5-4) Then, (c*-c 0 )/c 0 can be used as a measure of he cos of inflaion, where c 0 is he iniial consumpion level. VI. ESTIMATED RESULTS A. Esimaed resuls of he cos of inflaion Subsiuion of he parameers 8,9,0, in Char 9 o he previous equaions provides 8 This esimaion assumes β (he discoun rae) is 0.97, almos he same as he reciprocal of he pos-ax rae of reurn. The inflaion rae mus be above minus hree percen o saisfy he zero ineres rae consrain of he nominal ineres rae (because n, he populaion growh rae, is se o be zero). η (he reciprocal of he elasiciy of labor) is assumed o be 0, alhough here is lile consensus in academia regarding how much i is. For insance, Shimada [986] obains nearly zero elasiciy of labor o wages for housewives, while Higuchi [99] obains.9 elasiciy of labor o wages, which appears higher han ha in he U.S. δ (he reciprocal of he elasiciy of money) is supposed o be 0, in accordance wih Shirasuka [000] who esimaes he elasiciy of money o ineres raes around 0.. ρ (he reciprocal of he elasiciy of consumpion) is se o be 4, as Abel [997]. 9 Noe ha per capia producion, y, is ne naional produc because his esimaion uses ne capial socks. 0 This paper calculaes and o saisfy k /k ={(- ) /(- ) } under he condiion of + =0.3 and k /k =0.58 (FY998, Naional Accouns ). The heoreical meaning is differen beween he ax raes in equaion (5-) and equaions (5-8) and (5-9). However, he acual values are almos idenical. The labor income ax rae in equaion (5-) corresponds o he weighed average of he marginal ax rae by persons and amouns o 0.7 percen 4

16 he esimaed effecs of he shif of inflaion, which is summarized in Char 0. The columns from () o (3) indicae individual effecs of changes in seigniorage (money demand), he ax rae on corporae capial reurn, and he cos of housing invesmen. Column (4) combines all hree effecs. Column (4) in Char 0 shows ha he rise in he inflaion rae from zero o wo percen reduces he consumpion level by 3½ percenage poins and he fall in he inflaion rae from zero o minus wo percen raises he consumpion level by 4¼ percenage poins. Changes in he ax rae on corporae capial reurn have much larger impacs han he oher wo effecs (seigniorage (money demand) and housing invesmen). This esimaion supposes no change in he labor income ax rae due o inflaion, as he rise in he labor income ax rae by 0.5 percenage poins (Secion IV) does no have large effecs (Char -(3a)). The rise in he effecive ax rae on corporae capial reurn reduces corporae capial socks and producion. Household income and consumpion decrease. In he meanime, he increase in governmen revenue from corporae capial reurn allows governmen o reduce he ax rae. In his model, he fall in he labor income ax rae induces he labor supply o increase. Dominance of he impacs from changes in he ax rae on corporae capial reurn leads o a much larger cos of inflaion (i.e., he fall in he consumpion level caused by he rise in he inflaion rae) in Japan han hose in oher counries (Char ). As seen above (Secion II.D), a change in he effecive ax rae on corporae capial reurn is larger in Japan reflecing he low rae of corporae capial reurn. B. Robusness of he esimaed resuls Overall, Chars - and - show ha he above obained resuls are reasonably robus agains differen assumpions on he parameers. In paricular, he changes in he corporae deb raio, he coefficiens of relaive risk aversion (on consumpion, labor and money) and he level of governmen deb have lile effec on he previous resuls (Char - and -()). However, he esimaed resuls are sensiive o he following facors: (i) he preax rae of corporae capial reurn, R; (ii) he change in he governmen expendiure afer he shif of inflaion; and (iii) he choice regarding which ax o cu. These facors are explained a lile more fully below 3,4. (Char 7). On he oher hand, he labor ax rae in equaions (5-8) and (5-9) corresponds o he weighed average of he average ax rae by ax paymens and amouns o. percen (Char 7). The difference beween he ax rae (4. percen) obained endogenously from Abel s model and he above ax raes (0.7 and. percen) can be aribued o several ax iems (e.g. ax on oil, revenue-samp duy, and so on) oher han labor income ax. Column () in Char 0 is consisen wih Mankiw [987] who poins ou he meri of inflaion. However, he effec is small compared wih he adverse effec of he ax on corporae capial reurn. 3 Though he effec due o change in he capial gains ax rae (from 0. o 0.6) is also large, his case should be considered as exreme in a sense, he 0.6 ax rae may look unrealisic because axpayers can selec he opion o pay he axes of.05 percen on oal proceeds insead of he ax of 6 percen on capial gains, and he governmen levies ax only when households sell he sock. 4 Char - (3d) is he case in which a negaive relaionship is assumed beween he labor share of income and he rae of inflaion as in Char 3, insead of he consan share of labor. In ha case, he rise in he effecive ax rae caused by inflaion heighens he preax share of capial, which moderaes he decrease in capial sock due o he higher inflaion. Thus, he consumpion level falls by smaller amoun depending on he parameer values, i migh increase. As indicaed in Char - (3d) if he share of he non-housing capial,, increases by 0.00 or wih he rise in inflaion by wo 5

17 (i) Preax rae of corporae capial reurn Mehod obains he rae of corporae capial reurn as 4½ percen from he daa of 985 o 998. However, he rae migh be underesimaed because of cross-share holdings in Japan. Furhermore, once Japan undergoes srucural reforms, including changing managemen syles o aim a higher profiabiliy, he rae migh rise in he fuure. If he long-run rae of reurn rose o seven percen 5 or 0 percen, he fall in consumpion level would be lile more han wo percenage poins or around ½ percenage poins, which is smaller in absolue value han he previous resul of 3½ percenage poins (Char -). (ii) Change in he governmen expendiure Suppose he governmen does no reduce axes bu increases is expendiure afer governmen revenue increases due o inflaion. If he governmen increases he raio of is expendiure o GDP by one percenage poin due o he wo-percenage-poin rise in he inflaion rae, he cos of inflaion jumps o 5.63 percen (Char -(3b)). This is because his model assumes ha governmen expendiure does no increase he household uiliy in iself. On he conrary, he ax cu, as seen above, somewha offses he rise in he effecive ax raes and hence conribues oward an increase in is uiliy. (iii) Choice of ax cus This model supposes ha he governmen reduces all ax raes uniformly when he governmen revenue increases due o inflaion. If he governmen reduces only he ax on consumpion and labor income, wih he excepion of he ax on corporae capial reurn, he coss of inflaion become larger (Char -(3c)). On he oher hand, if he governmen can cancel he rise in he ax rae on capial reurn by means of acceleraed depreciaion or cus of ax raes, he cos of inflaion becomes almos zero. VII. CONCLUSION This paper shows ha a rise in he inflaion rae increases he effecive ax rae and disors resource allocaion. Conversely, he fall in he inflaion rae provides benefis o he sociey. The coss and benefis in Japan are found o be larger han hose in oher indusrial counries, because of Japan s low rae of corporae capial reurn. Consequenly, if he oher condiions are idenical across counries, Japan s opimum inflaion rae may be lower. However, he acual benefis of deflaion (disinflaion) may well be much smaller han he above esimaed resuls. Several imporan caveas seem worhwhile o menion here. Firs, all he effecs due o he shif of he inflaion rae and he ax raes are aribued o only household behavior (consumpion and invesmen) in Abel s model. A firm is supposed o be jus a mediaor in he capial and he labor markes and be enirely conrolled by households. In oher words, a firm is somehing like a veil. The fall in he inflaion rae causes he rae of reurn (which is fully disribued o households) o rise and hen corporae invesmen o increase. percenage poins, hen change in he consumpion level becomes.5 percen or +.08 percen. 5 The rae of corporae capial reurn amouns o 6.3 percen when i is defined as corporae operaing surplus divided by ne fixed asses + invenories + land (average from 985 o 998, real, Naional Accouns ). 6

18 However, he decision of corporae behavior may depend on firms hemselves raher han on households. Managers are ofen observed o make heir decisions on invesmen so as o maximize heir nominal accouning profis. When he inflaion rae declines deeply below zero, heir profis plunge. In ha case, corporae invesmen shrinks. Thus, he acual increase in invesmen caused by disinflaion migh be much smaller han he previous esimaed resuls. Second, i is imporan o recognize he comparaive saic naure of he analysis. Abel s model compares wo long-run equilibrium saes before and afer he shif of inflaion. I is beyond he scope of his model o analyze a quesion regarding dynamic adjusmens; a quesion like wheher here is a single and sable pah oward a new equilibrium sae or how much shor-run coss are incurred in a ransiional sage. Alhough i is rue ha deflaion enails a emporary decline in producion and employmen, as shown in he Phillips curve, hose sors of shor-run coss are ignored in his analysis. Third, he assumpion of he Fisher effec migh no hold. The paper assumes he perfec foresigh and he Fisher effec (ha is, when he inflaion rae changes, boh he nominal rae of reurn and he nominal ineres rae change by he same amoun). These assumpions seem appropriae in he long run, bu may be improper in he shor run. Moreover, given he zero bound of he nominal ineres rae, a case may arise in which he ineres rae canno be lowered as much as he Fisher effec proclaims. In ha case, he cos of deflaion migh be larger. Indeed, he opimum inflaion rae depends no only on ax bu also on oher facors, including he rigidiy of nominal wages and prices, he uncerainy of inflaion, he relaive price variabiliy, and he zero ineres rae consrain of he nominal ineres rae. The cos/benefis of deflaion aside, however, his paper reveals ha, from he viewpoin of ax and resource allocaion, here is a considerable cos associaed wih inflaion. Furhermore, he paper highlighs he imporance of he rae of corporae capial reurn and he ax sysem wih respec o he corporae ax. These are policy implicaions of his paper. 7

19 (APPENDIX A) Tax Rae on Dividend Income Calculaion of he naional and local ax raes on dividend income based on he FY000 ax schedule, aking he dividend ax credi ino accoun. There are four ypes of dividend income axes depending on he amoun of dividend income: (i) comprehensive ax; (ii) opional wihholding ax; (iii) wihholding ax; and (iv) ax on invesmen rus ec. In he case of comprehensive axaion, he ax wihheld on disribuion is credied agains personal income ax liabiliy. () Marginal ax rae in comprehensive axaion oal income people dividend income ax credi ax rae ax levied on dividend income housand yen per capia persons million yen million yen % million yen below , ,500, ,000 8, ,500,878, ,000 4,959, ,000 30,76 3, ,000 7,903 4, ,000 4,776 4, ,000,94 5, ,000 9,47 5, ,000 3,03,694, ,70,000,44, ,54 5,000 9,39,389, ,498 0,000 33,487 37,76, ,8 30,000 3,3 56,978, ,09 50,000,650 7,08 3, ,755 above 50,000,976 45,699 7, ,64 oal 346,79 385,44, ,04 Noes:. Tax levied on dividend income = (dividend income)*(ax rae) - ax credi. The ax rae is weighed average of he marginal ax rae by axable income. A similar calculaion of he local ax raes on dividend income gives an average effecive ax rae of.07%. () Dividend income axes ax rae weigh naional local oal ax rae comprehensive ax wihholding ax, opional wihholding ax on invesmen rus % Noe: Weighs are calculaed from Saisics of Naional Tax Adminisraion. 8

20 (APPENDIX B) FELDSTEIN S MODEL This Appendix calculaes he coss of inflaion by a model developed by Feldsein [999]. In comparison wih Abel s model, Feldsein s model can be characerized as follows: The coss of inflaion are represened by deadweigh losses, whereas in Abel s model hey are measured by a change in he household consumpion. Since Feldsein s model is based on a parial equilibrium framework, four effecs of changes in inflaion (i.e., consumpion, housing invesmen, money demand and deb service) are separaely esimaed and added ogeher wihou invesigaing he consisency among hem. On he oher hand, Abel s model assesses all hese effecs in a consisen manner by a general equilibrium framework. The model conains boh young and old periods. In conras, Abel s model is based on he Ramsey economy, in which he household lives for an infinie ime horizon. The ime frame of Feldsein s model is hough o be shorer han ha of Abel s model. I akes accoun neiher producion nor labor ino accoun, and hence accumulaion of capial does no increase producion. Preax reurn is predeermined. Pos-ax reurn varies, depending on he inflaion rae and he ax rae. In Abel s model, pos-ax reurn is predeermined by deep parameers such as he discoun rae of he household secor. Char 4 summarizes he esimaed resuls of Feldsein s model. A rise in he inflaion rae by wo percenage poins leads o a cos of.40 percen of GDP. On he oher hand, a decrease in he inflaion rae by he same amoun yields he benefi of 0.3 percen of GDP. The esimaed coss of inflaion in Feldsein s model are smaller han hose in Abel s model. Moreover, deflaion can be cosly depending on a parameer of ax policy (a parameer of he deadweigh loss coefficien), λ. These differences of he esimaed resuls are rooed in he characerisics of hese wo models. Abel s model akes he effecs of corporae producion ino accoun, whereas Feldsein s model does no. Because a decrease in he effecive ax rae due o disinflaion increases capial sock and producion, he esimaed resuls of he benefis of deflaion in Abel s model are much larger han hose in Feldsein s model. Moreover, he resuls of Feldsein s model hinge upon a raher ad hoc assumpion on λ, whose equivalence canno be found in Abel s model. Ineremporal subsiuion of consumpion A. Seup of Feldsein s model An individual is supposed o live for wo periods (young and old). When he is young, he receives income and saves par of i, s. He reires afer T years, and consumes c=(+r) T s from he ineres income of his saving. In his framework, saving a he young period can be regarded as he expendiure on he fuure goods/services a a price of p=(+r) -T. The individual s consumpion level afer reiremen is a funcion of he price, p. The figure below shows a compensaed demand curve. Tax and inflaion reduce he pos-ax 9

21 rae of reurn and increase he price. Thus, consumpion afer reiremen decreases. (Fig. B- ) Reiremen consumpion when he inflaion rae rises price F π %, wih ax p p E C π 0%, wih ax P 0 D B A π 0%, wihou ax c c C 0 reiremen consumpion Case Consumer surplus Tax revenue Deadweigh loss No ax, No inflaion A+B+C+D+E+F 0 0 Tax, No inflaion C+E+F B+D A Tax, Inflaion F D+E A+B+C Denoe he price as P 0 and reiremen consumpion as C 0 under no inflaion and no ax. In his case, consumer surplus is equal o he area from A o F in he above figure. Under no inflaion bu wih ax, he price increases o p and reiremen consumpion decreases o c. Consumer surplus declines o he area, C+E+F, and he governmen receives ax revenue of B+D. If he governmen disribues he increased revenue o consumers in he form of income ransfer wihou disorion (say, by negaive lump-sum ax), hen oal deadweigh loss becomes he area of A. An increase in he inflaion rae raises he price o p and reduces reiremen consumpion o c. Consumer surplus decreases o he area of F and ax revenue increases o he area of D+E. As a whole, he deadweigh loss amouns o he area of A+B+C. Consequenly, he coss of inflaion correspond o he rapezoidal area, -(B+C): -(B+C) = -{(p-p 0 )(c-c )+0.5(p -p)(c-c )}. In realiy, here is no such fricionless income ransfer (or lump-sum ax) in Japan ax revenue and ransfer cause some disorion in resource allocaion. Suppose ha he increase in ax revenue reduces he deadweigh loss by he raio λ. Since he increase in ax revenue due o inflaion is equal o he area of E-B, is benefi becomes λ(e-b). One problem here is ha his model canno derive a paricular value of λ wihou making some arbirary assumpions. 0

22 Housing invesmen Inflaion reduces corporae (non-housing) capial reurn. This reduces he relaive coss of housing invesmen, which may end up as excessive demand for housing sock. The increase in he deadweigh loss amouns o he area of C+D in Figure below. RH, rh and rh are he coss of housing invesmen. H, h and h are housing demand (in he order of no ax and no inflaion, ax and no inflaion, and ax and inflaion ). coss of housing (Fig. B- ) Coss and demand of housing RH rh rh π 0%, wihou ax A C D π 0%, wih ax π %, wih ax H h h housing demand Excessive housing invesmen affecs ax revenue hrough he following hree channels. Firs, ax credi increases because of he increase in housing morgage. Second, he shif of capial from firms (non-housing) o housing reduces ax revenue from corporae (non-housing) capial reurn. Third, propery ax revenue increases. Seigniorage and money demand Inflaion increases he coss of holding non-ineres-bearing money balances and reduces money demand below he opimal level. The area of C+D represens he cos due o inflaion. r + π (Fig. B- 3) Coss of holding money and money demand r + π r π % C π 0% D coss of holding money = 0 (negaive inflaion rae) M M money demand On he oher hand, inflaion affecs fiscal balance in hree ways. Firs, seigniorage increases. Second, he shif from money o corporae capial increases he ax revenue

23 from corporae capial reurn. Third, he rise in inflaion raises governmen ineres paymens since a decline in money demand makes he governmen issue more bonds. Deb service and governmen budge consrain Inflaion increases ax revenue on ineres income, as households receive more governmen deb service. Thus, he real coss of deb service decline. Ineremporal subsiuion of consumpion B. Esimaed resuls The increase in deadweigh loss resuling from inflaion, G (where a negaive sign means an increase in he deadweigh loss), is equal o he area of B+C (Fig. B- ). G = -(B+C) = -{(p-p 0 )(c-c )+0.5(p -p)(c-c )}. Corporae capial reurn, R, r and r, are subsiued o r in he equaion p=(+r) -T, which gives he prices of reiremen consumpion, P 0, p and p. Feldsein s model esimaes reiremen consumpion, c and c, as follows: Change in reiremen consumpion can be approximaed as c-c = -c ε Cp (p -p)/p, where ε Cp is he compensaed elasiciy of reiremen consumpion wih respec o is price. The following equaion represens he Slusky equaion: ε Cp = η Cp + σ, where η Cp is uncompensaed elasiciy of reiremen consumpion and σ is he propensiy o save ou of exogenous income. The relaionship among saving, price and consumpion, s = pc, yields he equaion, η Cp = η Sp, where η Sp is he elasiciy of saving wih respec o he price of reiremen consumpion. Therefore, he following relaion can be obained. p P0 p' p p' p G = s( η Sp σ ) p p p From p=(+r) -T, he elasiciy of saving wih respec o he real rae of reurn, η Sr, becomes η Sr = -rt η Sp / (+r). In a wo-period model, he saving a he young generaion, s, and he ne personal saving, s N, have a relaion of s N = s (+n+g) -T s, where n is he rae of populaion growh and g is he rae of wages per capia. Calculaion from he equaion σ=s/(*gdp), where is he share of labor, gives he propensiy o save ou of exogenous income, σ. From he above formulas and he parameers in he following able, he increase in deadweigh loss becomes G = GDP.