17 Capital tax competition

Transcription

1 17 Captal tax competton 17.1 Introducton Governments would lke to tax a varety of transactons that ncreasngly appear to be moble across jursdctonal boundares. Ths creates one obvous problem: tax base flght. If moble factors move n response to tax rate dfferentals among jursdctons, then governments should have an ncentve to reduce tax rates. Ths tax competton mght ncrease the cost of taxaton, reduce government spendng, and reduce welfare of taxpayers throughout the world. (Tax base moblty creates another, dfferent problem: tax exportaton: f governments tax factors owned by non-resdents, then tax rates may be hgher than desrable. But ths lecture deals manly wth the former pont.) Much of the lterature, and ths lecture, concentrates on attempts to tax captal ncome on a source bass.e. tax s pad where captal s employed, rather than n the jursdcton where the captal owner resdes. But the same ssues arse n other contexts: e.g. redstrbutve taxaton of moble workers, sales taxaton and cross-border shoppng, etc. Some mportant ssues n the theoretcal and emprcal lterature on tax competton: Do frms and ndvdual nvestors choose the locaton of ther real assets based on tax rate dfferentals? or s nternatonal tax avodance more about fnancal rather than real decsons? Does ncreased economc ntegraton and factor moblty lead to a race to the bottom n tax rates? to a convergence of tax rates to some postve level? Why do some countres appear to choose hgh tax rates for captal whle others choose low rates? What correctve devces are avalable to governments or nternatonal bodes to stop tax competton? Can such measures be Pareto mprovng.e. can they ncrease welfare for ctzens of all countres? 17.2 A model of tax competton n a federaton A federal economy conssts of N regons. In each regon, frms produce a consumpton good (the numerare) wth a lnear-homogeneous technology, usng an mmoble factor, labour, and a moble factor, captal. Snce the labour nput s nelastcally suppled n each regon, we suppress t from notaton and wrte the aggregate producton of regon as f (k ), f k unts of captal are employed there. Captal s pad ts margnal product, and the wages to labour are the resdual amount w(k ) = f (k ) k f (k ). There s a sngle representatve ctzen n each regon who s endowed wth all of the local labour nput and s unts of the captal good. Captal moves freely among regons n the federaton and s allocated to maxmze returns. Accordngly, n equlbrum, t earns an equal net rate of return r n each jursdcton, and agents receve total factor ncomes c = w(k ) + (1 + r)s. To fnance spendng on the local publc good, each local government leves a specfc, sourcebased tax t on captal employed n the jursdcton. Frms n each jursdcton choose nvestment to maxmze proft, takng the gross cost of captal r + t as gven; thus each regon s captal Copyrght c 2003 by Mchael Smart 1 Prnted on: March 25, 2003

2 demand functon s defned by the usual margnal condton k = φ(r + t ) f (k ) = r + t Observe that φ (r + t ) = 1/ f (k ) < 0. Snce taxes are leved on moble captal, ther burden may be borne n equlbrum by landowners wthn the regon, or by captalsts throughout the federaton. Gven tax rates t = (t 1,..., t N ), the captal market n ths economy clears at an nterest rate r (t) such that φ(r + t ) = Ns whch n turn yelds the equlbrum nvestment levels k (t) = φ(r (t) + t ). Implct dfferentaton then yelds the comparatve statc dervatves = φ (r + t ) j φ (r + t j ) < 0 (17.1) k ) = φ (r + t ) (1 + r < 0 (17.2) k j = φ (r + t j ) r > 0 j = (17.3) Thus a unlateral tax ncrease n jursdcton causes a declne n the equlbrum nterest rate, and nvestment declnes at home but rses elsewhere. When all jursdctons levy equal tax rates, we have = 1 N k = N 1 N φ k j = 1 N φ Government behavour. Ctzens also consume a local publc good g. Ctzens n all jursdctons have dentcal quas-lnear preferences over bundles of publc and prvate consumpton c + b(g ), where b s a strctly concave functon. The quantty of publc goods provded n jursdcton satsfes the budget constrant g = t k (t) Each jursdcton s government chooses ts tax rate to maxmze the utlty of ts ctzens subject to the budget constrant, takng as gven the other jursdctons tax rates. Note that c = k f k + s r = k (k s) r Thus the frst-order condton for the government s problem s k + (k s) r = b (g ) [ k + t k ] (17.4) The left sde of equaton (17.4) s the margnal cost, n reduced consumpton of the prvate good, of a tax ncrease n the jursdcton. The rght sde s the margnal beneft of the ncrease n publc good consumpton resultng from the tax ncrease. We look for a symmetrc Nash equlbrum, n whch t = t for all. Wth symmetrc taxes, k = s for all, so that the second term on the left-hand sde of (17.4) drops out. Defnng ɛ = (r + t) k //k as the elastcty of captal demand, and τ = t/(r + t) as the percentage tax rate, the frst-order condtons become b (ḡ) = 1 (17.5) 1 τɛ 2

3 Optmal taxes n a untary state. Now consder the optmum for a central government whch could set each jursdcton s tax rate drectly, and whch could allocate ths tax revenue for publc good provson n each jursdcton. However the central government s not allowed to transfer ncome n a lump-sum fashon among jursdctons. If the central government wshed to maxmze the sum of people s utltes n the federaton, then t would choose the tax rates to max [c(k, r ) + b(g )] subject to the consoldated natonal budget constrant g = t k The untary optmum s therefore descrbed by the frst-order condtons k = b (g ) ( k j k + t j t j ) (17.6) It can be shown that every soluton to the FOCs nvolves equal tax rates t j = t for all j. Then the summaton on the rght-hand sde of the frst-order condtons drops out, and b (g ) = 1 (17.7) Comparng (17.7) and (17.5), we see mmedately that (snce b s concave) spendng on publc goods s lower n equlbrum than s optmal. Each local government regards ts tax base as moble and elastc wth respect to tax rates, whch rases the margnal cost of publc funds and reduces spendng. A central government correctly recognzes that the natonal tax base s nelastc, and t ncreases taxes and spendng accordngly Asymmetrc tax competton Now suppose that jursdctons dffer n ther populaton, but are otherwse dentcal as before. How wll the tax polces of large and small regons dffer n equlbrum? (See Bucovetsky (1991) and Wlson (1991).) Suppose that each regon contans a fracton ω of the natonal populaton. To keep thngs smple, let the captal demand functon n each regon be lnear, so that φ (r + t) = a for some parameter a > 0. Then = ω k = (1 ω )a Snce a large (hgh ω) regon absorbs more of the natonal captal stock, ts tax has a relatvely large mpact on the natonal return to captal r. Thus the cost of captal r + t s less senstve to taxaton n a large regon and the perceved elastcty of the local tax base must therefore be smaller. Ths suggests that a large regon wll compete less vgorously for captal than a small one and wll adopt a hgher tax rate n equlbrum. To see ths, suppose that t = t for all and 3

4 examne agan the frst-order condton (17.4). At symmetrc tax rates, the second term on the left-hand sde wll agan drop out, leavng k = b (g)(k + t k ) Snce the absolute value of the dervatve s decreasng n ω, a large jursdcton would prefer to devate to a hgher tax rate. When regons are asymmetrc n ths (or any other) way, tax competton nduces another knd of neffcency, n addton to the underprovson of publc goods we have already analyzed. Snce jursdctons adopt dfferent tax rates n equlbrum, the pre-tax margnal product of captal s no longer equalzed among regons. Thus captal s msallocated among regons, producton effcency fals to hold, and natonal output s lower than t would be f tax rates were chosen by a utltaran central government. Snce a smaller regon chooses a lower tax rate n equlbrum, t receves more captal per worker than a larger regon; consequently, both GDP per worker and utlty per capta must be hgher n a small country. (A small country could always choose the same tax rate as a large one and obtan the same utlty per capta, so ts equlbrum utlty level can be no lower than that of a large country.) Thus small regons wn the tax competton game. Note the chef emprcal mplcaton of ths model s that larger countres wll have hgher tax rates and as a result they wll export captal to small countres. Thus, f the only dfference among countres s sze, tax rates and net captal mports should negatvely correlated. Ths predcton has some emprcal support: for example, a number of small developed countres (Luxembourg, Ireland) have low taxes on captal and hgh GDP per worker. But t seems nconsstent wth the broader patterns of tax rates and FDI n the world: hgh-tax, ndustral countres do not generally export captal to low-tax developng countres (Baldwn and Krugman, 2002). Terms of trade effects. When regons choose dfferent tax rates, for whatever reason, we no longer have k = s for all : some regons become captal mporters and others captal exporters. Ths gves an addtonal reason for tax polces to dverge. Examnng the frst-order condton (17.4) agan, we see that captal mporters have an ncentve to ncrease taxes, depressng the natonal return to captal r and nducng a transfer to local workers at the expense of captalsts throughout the naton. Ths effect s what DePater and Myers (1994) call the pecunary externalty or terms-of-trade effect of captal tax competton. Usng the same notaton as before, but now lettng the value of publc spendng b (g ) dffer among regons, the frst-order condton n the asymmetrc case can be wrtten b (g ) = 1 (1 s/k ) / 1 τ ɛ For a captal mporter (k > s), the pecunary externalty now reduces the perceved margnal cost of publc funds, leadng to greater publc spendng. If the pecunary externalty outweghs the tax base effect n the denomnator (the fscal externalty), then the MCPF s less than one, and the jursdcton wll choose more publc spendng than the optmal level g. Thus, f jursdctons are suffcently dfferent, tax competton causes the publc good to be over-provded n some jursdctons. (Ths does not seem emprcally plausble, however. As the number of regons grows large, / 0, whereas ɛ remans bounded strctly above zero.) 4

5 Tax competton and convergence. What happens to taxes when competton among jursdctons ncreases? We can represent ths by an decrease n ω, the fracton of the natonal populaton that s n each. Usng the lnear form of captal demands agan, b (g ) = 1 + (1 s/k )ω 1 t (1 ω )a As ω 0, the rght-hand sde approaches (1 t a) 1. (Does ths mply monotone convergence of tax rates? Apparently not.) 17.4 Resdence-based and source-based taxes Thus far we have assumed that each jursdcton leves a tax on captal employed there, but no tax on domestc labour. Equvalently, we have assumed that governments employ only sourcebased, and not resdence-based, ncome taxes. Ths s evdently bad polcy n general: a head tax on labour would have no dstortonary cost n ths model, snce labour s nelastcally suppled. Further, as the sze of a jursdcton becomes small, / 0, mplyng that all of the tax burden on moble captal n a small jursdcton s borne by domestc labour anyway. In a small, open economy, taxes on the moble factor are fully shfted backward to domestc resdents. Thus, n a small, open economy, source-based captal taxes should dsappear, regardless of government s redstrbutve preferences. Ths s an applcaton of the Damond Mrrlees (1971) producton effcency result. What about the general case, where regons are large, and taxes have general equlbrum effects on the natonal return to captal? Let us expand the model to nclude a head tax on domestc labour. If the head tax s chosen optmal, we wll have b (g ) = 1 n all jursdctons. Then the frst-order condtons for the captal taxes reduce to ) (1 sk r k = t The left-hand sde s negatve ff the regon s a captal mporter (k > s). The rght-hand sde has the same sgn as t. Thus when resdence-based taxes are avalable, mportng regons should tax captal, and exportng regons should subsdze captal on a source bass. Ths predcton of the model s clearly counter-factual: all countres tax the use of captal, though to varyng degrees. (Gordon, 1992, makes ths pont, and suggests an alternatve explanaton for why source-based captal taxes reman postve n equlbrum.) 5