Inter-regional Competition, Comparative Advantage, and Environmental Federalism

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1 Inter-regonal Competton, Comparatve Advantage, Envronmental Federalsm Ida Ferrara, Paul Mssos y Hals Murat Yldz z October 1, 010 Abstract In ts paper, we compare endogenous envronmental polcy settng wt centralzed decentralzed governments wen regons ave comparatve advantages n d erent pollutng goods. We develop a tworegon, two-good model wt nter-regonal envronmental damages perfect competton n product markets, were bot regons produce bot goods. Despte postve spllovers of polluton across regons, te model predcts tat decentralzaton may lead to weaker or strcter envronmental stards or taxes, dependng on te degree of regonal comparatve advantage te extent of transboundary polluton. Ts suggests tat federalsm can lead to eter a "race to te bottom" or a "race to te top," wtout relyng on ne cent lobbyng e orts or captal competton. Keywords: Envronmental polcy, Federalsm, Centralsm. JEL Class catons: H77, Q56, H41 York Unversty, 4700 Keele Street, Nort York, Ontaro, Canada M3J1P3. E-mal: ferrarayorku.ca. y Ryerson Unversty, 350 Vctora Street, Toronto, ON, Canada M5B K3. E-mal: pmssosryerson.ca. z Ryerson Unversty, 350 Vctora Street, Toronto, ON, Canada M5B K3. E-mal: yldzryerson.ca. 1

2 1 Introducton Crtcal to te settng of domestc envronmental polcy s weter a centralzed government would select more or less strngent regulatons tan decentralzed governments. Earler lterature as suggested tat decentralzaton can lead to a race to te bottom, as state, provncal, or regonal governments over-compete for domestc rms /or captal (e.g., Markusen et al., 1995; Rcter Wellsc, 1996; Levnson, 1997; Kunce Sogren, 00, 005; McAusl, 00) or cause rms to over-nvest n unproductve lobbyng actvtes (e.g., Adt, 1998; Fredrksson et al., 006), but may alternatvely lead to no d erence n polcy outcomes (e.g., Oates Scwab, 1988; Fredrcksson Gaston, 000) or to mprovements n envronmental qualty troug better nformaton about local mpacts, te nternalzaton of transboundary polluton spllovers, or te capture of polluton rents by non-local captal owners (e.g., Peltzman Tdeman, 197; Wellsc, 1995). Te results n relaton to envronmental polcy mrror tose of te local publc nance or scal federalsm lterature, were decentralzaton can serve as a dscplnary measure aganst expansonary government taxaton or can pus governments to e cent publc good provson troug te ablty of ndvduals to relocate, but may alternately result n excessve tax competton to attract rms, employment, /or captal (Oates Scwab, 1988). Parallel to ts, te man focus of te envronmental polcy lterature as been on te locatonal decson of rms, wt governments playng te role as actve seekers of employment captal n envronmental polcy settng. Emprcal evdence on te mpact of envronmental polcy decentralzaton as been mxed, altoug tere s a consensus tat decentralzaton does not necessarly lead to a race to te bottom as muc as te teoretcal lterature suggests. For example, Lst Gerkng (000), usng data from before after te Reagan decentralzaton of envronmental polcy enforcement n te early 1980s, found tat real polluton-abatement operatng expendtures per $1000 of value-added ncreased for two of te four ndustres consdered (cemcal/alled products food/kndred products) but declned n te oter two sectors (prmary metals cemcal/appled products). Qute consstent wt ts, Mllmet (003) found tat envronmental decentralzaton n te U.S. n te 1980s led to a sgn cant ncrease n polluton control expendture, but per capta ntrogen oxde sulfur doxde emssons dd not sgn cantly decrease (altoug tere may ave been a reducton n te rate of deteroraton). More on envronmental polcy tan envronmental outcomes, Sgman (005) as suggested tat free rdng by state governments does occur n water polluton control, spec cally, tat states wc control ter Clean Water Act programs free rde on downstream states, mplyng tat centralzaton may be warranted f te cost of free-rdng outwegs te greater exblty nformatonal advantages of decentralzaton.

3 A perusal of recent envronmental ndcators from te World Bank, across d erent pollutants among d erent countres, llustrates a smlar ambguty (see Table 1). For example, among te 30 OECD countres, te 9 countres generally dent ed as federatons ave average carbon doxde emssons per capta of 11.4 metrc tonnes natonally protected area (as a sare of total l area) of 15.7%, 1 wle te countres dent ed as avng centralzed governments ave lower average carbon doxde emssons per capta (9. metrc tonnes) but a lower average percentage of natonally protected area (1.8%). In terms of outcomes, centralzed regmes tus ave better carbon emssons per capta but protect less of ter l area. Fertlzer consumpton (undred grams per ectare of arable l) s also very muc lower among federatons (1341 to 367), but partculate matter emssons (urban-populaton-wegted average, gm 3 ) are vrtually dentcal (5.7 to 5.). Ts nconsstency occurs across pollutants for non-oecd countres as well. It appears, at least on te surface, tat decentralzaton does not even lead to consstent envronmental outcomes wtn a country: some pollutants may by ger wt decentralzaton wle oters are lower. In ts paper, we revst te teoretcal queston about te envronmental mplcatons of polcy decentralzaton, focusng on te role of productvty gaps polluton spllovers, n an attempt to provde a plausble explanaton for te observed polcy nconsstency. Spec cally, we address te followng questons: (1) How does comparatve advantage across regons a ect envronmental polcy damages? () Wat are te d erences n te patterns of envronmental polcy between centralsm federalsm wen regons are relatvely better at producng d erent pollutng goods? (3) How does armonzaton of centralzed polcy mpact te envronment? (4) Wt multple goods multple pollutants ( terefore potentally multple taxes), ow do envronmental damages d er between federalsm centralsm? We use a model comprsng a sngle country wt two regons, two (non-numerare) goods produced by perfectly compettve ndustres a numerare good. Eac regon produces bot non-numerare goods but as a comparatve advantage n one of tem. Te numerare good s assumed to be non-pollutng freely traded wle te two non-numerare goods generate d erent pollutants, wc may be transboundary, are tus subect to envronmental taxes. We consder a two-stage game under two government structures: federalsm (or decentralzaton) centralsm. In te rst stage, eter te centralzed government sets envronmental taxes to levy on te two pollutng goods n eac regon to maxmze natonal welfare (under centralsm), or eac of te two regonal governments sets ts own taxes to maxmze regonal welfare (under 1 Countres are separated by overall government structure, wc may not always be consstent wt tat of envronmental polcy. Te countres categorzed as federatons are Austra, Australa, Belgum, Canada, Germany, Mexco, Span, Swtzerl, te Unted States of Amerca. 3

4 federalsm). Under te centralzed polcy regme, we also consder te case n wc te central government cooses to armonze taxes wtn eac sector between te two regons. In te second stage of te game, gven te envronmental taxes te structure of government (centralsm versus federalsm), producton, nter-regonal transfers of goods across regons, consumpton take place. In te dscusson of te d erences n taxes damages between regmes, we descrbe tree dstnct e ects: an nter-regonal envronmental e ect from cross-border polluton spllovers wc tends to pus up taxes, an ntra-regonal envronmental e ect between sectors wtn a regon wc as an ambguous mpact on taxes, an nter-regonal trade e ect from consumpton n wc tends to lower taxes. Country Natonally Protected Area CO Emssons Per Capta Fertlzer Consumpton Partculate M atter Federal A ustra A ustala B elgum C anada G erm any M exco Span Sw tzerl U SA C entralzed C zec R epublc D enm ark F nl France G reece H ungary Icel Irel Italy Japan L uxem b ourg N eterls N ew Z eal N orway Pol Portugal Slovak R epublc Sout K orea Sweden U nted K ngdom All Federal Countres (mean) All Centralzed Countres (mean) Table 1. Envronmental performance ndcators for te 30 OECD countres, separated nto federatons centralzed groups. Source: World Bank (008). 4

5 Te Model We consder a country wt two regons (A B) tree goods (a numerare good two nonnumerare goods wc we label a b). Regon A as a comparatve advantage n te producton of a wle regon B as a comparatve advantage n te producton of b. We assume perfect competton n all markets but allow for te producton of eac of te two non-numerare goods to generate polluton wc may ave transboundary e ects. Te presence of polluton calls for polcy nterventon we consder non-probtve envronmental taxes (t) tat could be mposed on producers eter by te central government or by te local government. On te dem sde, we ave quas-lnear preferences represented by u(c; c 0 ) v(c) + c 0 ; (1) were c [c a ; c b ] s te consumpton vector for te two non-numerare goods, c 0 denotes te consumpton of te numerare good, v(c) s quadratc addtvely separable n te non-numerare goods. Te dem for good ( a; b) n regon ( A; B) s ten gven by d(p ) p : () On te supply sde, as n Horn et al. (007), labour (l) s te only factor of producton wc s employed n te producton of te numerare good accordng to a constant-returns-to-scale tecnology n te producton of eac of te two non-numerare goods accordng to a decreasng-returns-to scale tecnology. Spec cally, non-numerare good s produced n regon accordng to x q l, were (0; 1] wt 1 f regon as a comparatve advantage n te producton of good wt < 1 oterwse. If te margnal product of labour n te producton of te numerare good s one te supply of labour s su cently large tat producton s postve at all tmes, we ave tat te equlbrum wage s equal to one te total supply of non-numerare good s equal to x p t ; (3) were t denotes te envronmental tax producers of good face n regon. Assumng tat (1) eac unt of producton generates one unt of polluton, () polluton may be transboundary, (3) eac producton process entals a d erent pollutant, (4) envronmental damages are separable n pollutants quadratc n ter levels, we can wrte te envronmental damage functon n regon as x a + s a x a! + x b + s! bx b ; (4) 5

6 for A; B, were s [0; 1] measures te extent to wc polluton generated n te oter ( ) regon travels to regon so tat te ger te s, te more transboundary polluton s. As we ave two pollutng producton processes tus two pollutants, we can allow for te transboundary nature of te two pollutants to d er by ndexng s wt te subscrpt ( a; b). Our framework of analyss nvolves two stages: n te rst stage, envronmental taxes are set to maxmze welfare de ned as te sum of consumer surplus, producer surplus, tax revenues mnus envronmental damage; n te second stage, consumpton producton decsons take place under te assumpton tat markets are perfectly compettve. For te rst stage, we consder two scenaros: n one case, polcy s set centrally so tat te obectve functon ncludes bot te welfare of regon A te welfare of regon B; n te oter case, polcy s set locally at te regonal level so tat te obectve functon ncludes only te welfare of te regon n wc envronmental polcy s beng ntroduced..1 Consumpton Producton Stage In ts subsecton, we look at te second stage of te model solve for equlbrum prces quanttes for gven envronmental taxes. Under zero transportaton costs, p A p B, tat s, te prce consumers pay for good s te same ndependently of were t s produced, we can tus omt te superscrpt express te prce of good smply as p. Market clearng ten requres tat natonal dem equal natonal supply or ( p ) A + B p A t A B t B ; (5) wc gves for a; b. Usng tat A a B b p + A t A + B t B + A + B ; (6) 1, we can express equlbrum prce, producton, export levels as + t x t 3 + p + t x d (p ) d (p ) x t ; (7) x + t 3 + t t ; (8) t ; (9) respectvely, for A (so tat B) wen a B (so tat A) wen b, wc s a labelng strategy we adopt trougout te paper. 6

7 Here we note tat te envronmental tax n te regon wt a comparatve advantage as a stronger prce e ect tan te envronmental tax n te oter regon. Tat s, te tax mposed on producers of good a n regon A, for example, a ects te prce of good a to a greater extent tan te tax on producers of good a n regon B. Furtermore, an envronmental tax reduces producton n te regon n wc t s leved but ncreases t n te oter regon, altoug te latter e ect s weaker (n absolute terms) tan te former e ect. Fnally, nter-regonal exports are decreasng n te envronmental tax mposed n te exportng regon but ncreasng n te envronmental tax mposed n te mportng regon, altoug agan te dependence s weaker n te latter tan n te former. For example, te tax on producers of good a n regon A reduces exports of good a from regon A to regon B but te tax on producers of good a n regon B ncreases exports of good a from regon A to regon B. Gven envronmental taxes, te e ects of an ncrease n, wc amounts to a reducton n comparatve advantage, are less stragtforward but equally unambguous. By partal d erentaton of te above equlbrum prce quantty levels, we ave tat p x 3 + < 0; (10) x x 3 + < 0 x d (p ) x 3x > 0; (11) 3 + x < 0: (1) 3 + As ncreases, prces exports declne wle producton decreases n te regon wt te comparatve advantage but ncreases n te oter regon. Overall, producton n sector ncreases as te producton ncrease n te less e cent regon s larger tan te producton decrease n te more e cent regon.. Envronmental Polcy Stage In ts subsecton, we examne te envronmental polcy settng stage consder two scenaros: rst, we ave te central government determne te envronmental taxes to levy n te two pollutng sectors (a b) n eac of te two regons (A B); second, we allow for eac regonal government to coose te envronmental taxes to mpose n te two sectors. Altoug n bot cases envronmental taxes are welfaremaxmzng, tere are two cannels troug wc envronmental polcy n one regon a ects te oter regon (trade polluton movement) gvng rse to e ects tat are only taken nto account by te central government tus amount to d erent envronmental taxes between federalsm centralsm. Trade 7

8 between regons connects consumers producers n one regon wt te polcy coce n te oter regon generatng an nter-regonal trade e ect tat s ncreasng n te level of trade actvty tus n te productvty gap between te two regons (te lower te gap s, te lower te level of trade actvty te weaker te e ect). Gven te trade possbltes across te two regons, tere also exsts substtutablty n producton across te two regons troug envronmental polcy. Spec cally, envronmental taxes reduce local producton but ncrease producton n te oter regon, a cange n producton as bot an envronmental e ect troug a cange n emssons a tax revenue e ect troug a cange n tax revenues. Te second cannel troug wc envronmental polcy n a regon a ects te oter regon s polluton movement wc generates an envronmental e ect tat s ncreasng n ow transboundary polluton s (te more transboundary polluton s, te stronger te e ect). To sum up, tere are tree e ects explanng any polcy dvergence between centralsm federalsm: an nter-regonal trade e ect, wc depends on te extent of trade, an nter-regonal envronmental e ect wc captures ow a tax ncrease n a regon a ects polluton n te oter regon depends on substtutablty n producton between te two regons as well as on te transboundary nature of polluton, a tax revenue e ect wc depends on substtutablty n producton between te two regons. In tecncal terms, te e ects of t n regon wc a central government takes nto account but a regonal government does not can be expressed as x p d (p ) t {z } trade e ect! + x + s x x 6 4 t {z } own polluton e ect! + s x x s t 7 5 {z } + x spllover e ect {z } nter-regonal envronmental e ect 3 + t x t {z } tax e ect ; (13) for A; B a; b. Provded tat some level of trade actvty s present, te nter-regonal trade e ect ncreases te margnal cost of envronmental taxes n sectors n wc regons ave a comparatve advantage decreases t oterwse. To be clear, a ger tax n regon reduces consumer surplus (troug ger prces lower consumpton) ncreases producer surplus (troug ger prces larger producton) n regon. If regon mports from regon, tat s, x < d (p ), te e ect on consumer surplus prevals so tat overall surplus decreases te margnal cost of taxes ncreases. However, f regon exports to regon, tat s, x tat overall surplus ncreases te margnal cost of taxes decreases. > d (p ), te e ect on producer surplus prevals so Tus, te central government as an ncentve to set lower taxes on goods regons are more e cent at producng but ger taxes on goods regons are less e cent at producng. Gven tat te tax n te 8

9 regon wt te comparatve advantage as a stronger prce e ect tan te tax n te oter regon, te nter-regonal trade e ect wtn a gven sector s larger n te regon wt te comparatve advantage. As te productvty gap between te two regons decreases ( by (1) te trade e ect tus weakens. ncreases), te level of exports/mports falls Te nter-regonal envronmental e ect can also amount to an ncrease or a decrease n te margnal cost of envronmental taxes as ger taxes n regon result n less polluton spllng over nto regon (spllover e ect) but more polluton beng generated troug an ncrease n local producton n regon (own polluton e ect). If polluton s a pure prvate good, tere are no spllovers te envronmental e ect tus ncreases te margnal cost of envronmental taxes gvng te central government an ncentve to decrease taxes. However, f polluton s transboundary, te reducton n spllovers from lower producton n regon may more tan o set te ncrease n polluton from ger producton n regon so tat te margnal cost of envronmental taxes decreases te central government opts for ger taxes. Te more transboundary polluton s, te larger te reducton n spllovers from lower producton n regon te stronger te central government s ncentve to ncrease taxes; altoug te local producton e ect also ncreases wt te extent to wc polluton s transboundary, te cange n te spllover e ect domnates. Furtermore, wen te own polluton e ect domnates so tat, overall, te envronmental e ect s postve (tat s, a ger tax n regon ncreases envronmental damages n regon ), as te productvty gap between te two regons decreases, te envronmental e ect gets stronger n sector but can ncrease or decrease n sector. Correspondngly, wen te spllover e ect domnates so tat, overall, te envronmental e ect s negatve (tat s, a ger tax n regon decreases envronmental damages n regon ), te envronmental e ect as te productvty gap between te two regons decreases gets stronger n sector but can ncrease or decrease n sector. In essence, a decrease n te productvty gap n sector trggers a decrease n producton n regon, wc weakens te spllover e ect, an ncrease n producton n regon, wc strengtens te own polluton e ect; a decrease n productvty gap n sector trggers a decrease n producton n regon, wc weakens te own polluton e ect, an ncrease n producton n regon, wc strengtens te spllover e ect. Fnally, te tax revenue e ect s always postve n tat a ger tax on good n regon mples more producton n regon tus ger tax revenues; te smaller te productvty gap between te two regons s, te more regon produces n sector tus te larger te tax e ect. See Appendx for a formal dervaton of te mpact of a cange n s or on te nter-regonal envronmental e ect. 9

10 ..1 Central Envronmental Polcy Under a centralzed system, a country cooses envronmental taxes as to maxmze ts welfare wc s gven by te sum of te welfare levels of all of ts regons. We can ten express total welfare as X CS (t) + P S (t) + T R (t) X (t) ; (14) W (t) X were t t A a ; t A b ; tb a ; t B b s te vector of envronmental taxes, consumer surplus n regon equals X CS 1 X producer surplus n regon equals X P S X 6 4 p t p 1 ( p a ) + ( p b ) ; (15) x p a t a x a + p b x t b x b x a a + x b b ; (16) tax revenue n regon s gven by X T R t ax a + t b x b ; (17) envronmental damage n regon s gven by (4), for A; B. Wt envronmental polcy centrally set tus maxmzng te sum of regon A s welfare regon B s welfare, we obtan te followng equlbrum envronmental taxes: 8 < 1 + s t + 1 s + 4s : 4 + s s + (3 s ) 9 ; (18) t Upon nspecton of te two taxes, we ave 8 < 4s s 4 : 4 + s s + (3 s ) 9 ; : (19) Proposton 1 Te larger te polluton spllover e ects of producton (s "), te more eavly producton s taxed (t " t "), ndependently of e cency consderatons (.e., for any ). However, a narrowng n te productvty gap between te two regons ( regon (t ") always yelds a tax decrease n te less e cent ") but decreases te tax n te more e cent regon wen polluton s relatvely local (t # for 0 s < 3 p ) ncreases t oterwse (t " for 3 p < s 1). 10

11 Tat an ncrease n s results n tax ncreases n bot regons s farly stragtforward: te more damagng producton s for a country s envronmental qualty (troug larger spllovers from one regon to te oter), te ger te envronmental taxes. Te e ects of canges n on taxes are owever complcated by te presence of two o settng e ects as producton canges ave mplcatons not only for local polluton but also for polluton n te oter regon. A decrease n te productvty gap n sector (tat s, an ncrease n ), trggers a producton decrease n te more e cent regon a producton ncrease n te less e cent regon. Less producton n te more e cent regon means tat less polluton splls over nto te less e cent regon but, overall, polluton does ncrease n te latter regon even n te extreme case wen polluton s a pure publc bad as, by (11), te producton ncrease n ts regon exceeds te producton decrease n te oter regon, te envronmental tax tus always ncreases n te less e cent regon. On te oter, te polluton level n te more e cent regon decreases from lower local producton but ncreases from ger producton n te oter regon troug spllovers; te stronger te spllover e ects, te more lkely te postve e ect on polluton domnates so tat te envronmental tax n te more e cent regon also ncreases; alternatvely, wen spllover e ects are weak, te negatve e ect on polluton domnates so tat te envronmental tax n te more e cent regon decreases. Wen we compare te envronmental taxes te two regons face on a gven good, we obtan Proposton Under centrally set envronmental polcy, a good s taxed more eavly n te regon wc as a comparatve advantage n ts producton, tat s, t A a > t B a t B b > t A b ; te tax d erence s owever smaller n te sector wt a smaller productvty gap between te two regons /or larger polluton spllovers, tat s, t A a t B a < t B b t A b f B a > A b /or s a > s b. We can wrte te d erence n envronmental taxes between te two regons as (1 s ) 1 + t t 4 + s 1 + s + (3 s ) > 0: (0) If s a > s b /or B a > A b, we ave tat ta a t B a < t B b t A b snce t t 4 (1 s ) 1 (4 + s ) s 3 s 4 n s o 4 + s s < 0 (1) + (3 s ) t t (1 s ) 5 + s + s 3 s + s + n 4 + s 1 + s + (3 s ) o < 0: () 11

12 A regonal comparatve advantage results n greater producton wc generates greater polluton ( ger margnal damages) s tus taxed at a ger rate. As spllovers ncrease, te larger producton of a good n te more e cent regon mples tat more polluton splls over nto te less e cent regon so tat te tax on te good ncreases n te latter regon by more tan n te former regon. For example, wen s a ncreases, more polluton from te producton of good a n regon A splls over nto regon B tan from te producton of tat same good n regon B nto regon A; wle envronmental taxes on te producton of good a ncrease n bot regons, te tax n regon A ncreases by less tan te tax n regon B te d erence between te two taxes, tat s, t A a t B a decreases. Wen te productvty gap decreases polluton s su cently transboundary so tat total polluton ncreases n te more e cent regon, te total polluton ncrease n te less e cent regon exceeds tat n te more e cent regon. As a result, te tax ncrease n te latter regon falls sort of tat n te former regon te d erence between te two taxes tus decreases. Tat total polluton ncreases n te less e cent regon by more tan n te more e cent regon follows from te fact tat, unless polluton s perfectly transboundary (tat s, s 1), lower producton n te latter regon as ts strongest e ect n terms of polluton reducton locally, smlarly, ger producton n te former regon as ts stronger e ect n terms of polluton ncrease locally. Wen we compare te taxes on te two goods wtn a regon, we ave Proposton 3 Under centrally set envronmental polcy, te tax n te sector n wc a regon as a comparatve advantage s larger tan te tax n te oter sector wen s a s b s B a A b (e.g., t A a > t A b ). However, f polluton s less transboundary n te more e cent sector tan n te oter sector (e.g., s a < s b ), te tax d erence (t A a t A b ) s smaller; on te oter, f te nter-sectoral productvty gap te regon faces s larger tan tat n oter regon (e.g., A b < B a so tat 1 A b > 1 B a ), te tax d erence s larger. Wen s a s b s < 1 A b B a < 1, t t (1 s) (1 ) (4 + s ) + (1 + s ) + (3 s) > 0; (3) for A wen a (so tat b) B wen b (so tat a). Te postve tax d erental for 0 s < 1 stems from te greater polluton regon generates n sector relatve to sector : te smaller te productvty gap between te two regons s n eac of te two sectors (tat s, te larger te ) /or te more transboundary polluton s n eac of te two sectors (tat s, te larger te s), te 1

13 smaller te tax d erental. In te extreme case n wc polluton s a pure publc bad n eac of te two sectors (s 1), regon faces te same tax n eac sector ndependently of ts relatve e cency n sector (or regon s relatve e cency n sector ). In suc a case, gven tat productvty gaps are te same n te two sectors, natonal producton of good s te same as tat of good so tat te total amount of polluton regon faces from sector s te same as tat from sector even toug regon produces less of tat good. In te absence of nter-sectoral e ects n tax settng, as per (18) (19), we ave tat t t t t t s s t : (4) Usng Proposton 1, we ten obtan tat, f s < s s, te envronmental tax regon faces on good falls relatve to te tax t faces on good,, f < (tat s, regon s more e cent at producng good relatve to producng good tan regon s at producng good relatve to producng good ), te envronmental tax regon faces on good decreases relatve to te tax t faces on good. Wen te polluton from te producton of good n wc regon as a comparatve advantage s relatvely local, t s possble for te tax on good, were t as a comparatve advantage, to be ger tan te tax on good. However, t s also possble for regon to face a ger tax on good tan on good wen good s polluton s perfectly local. In fact, for s 0 < s s, tat s, at values of s wc gve te lowest value for t t, te tax d erental s equal to t t 3s 4 s + s s 4 3s + 18s + 1 s + 16s 8 n o ; (5) (8 + 7) (4 + s ) + (1 + s ) + (3 s) p wc s always negatve for any provded tat 3 < s 1 for 3s 4 3s + 18s + 1 q(3s 4 3s + 18s + 1) + 4 (3s 4 s + s + 7) (s 16s + 8) > (3s 4 s + s + 7) (6) wen 0 s < p 3. Lettng s s s s s, wt 0 < s ; 1, we sow combnatons of s values yeldng a negatve tax d erental (t t < 0) n Fgure 1 for s 0 1, for s 0:5 1, for s 0 0:5; as s (s ) ncreases /or ( ) decreases, te curve sfts to te rgt so tat t becomes less lkely for te tax d erental to be negatve. Wen polluton s perfectly local n sector ( s 0), total polluton regon faces n sector decreases troug lower local producton n response to a decrease n productvty gap n sector (tat s, as ncreases) t Te greater te spllovers n sector, te ger te t so tat t falls sort of t 13 tus decreases. at g values of

14 s wt a ger value of ( tus lower t ) requrng a lower value of s ( tus lower t ) for te tax d erental to be negatve. As s ncreases ( s ncreases), t ncreases relatve to t ; as decreases ( decreases), tat s, te productvty gap n sector becomes larger tan te productvty gap n sector, t decreases relatve to t as total polluton regon faces n sector falls troug a decrease n local producton wc outwegs te producton ncrease n regon. Harmonzed Taxes As central governments do not tend to resort to d erental tax systems, we furter consder central polcy under te constrant tat taxes n a gven sector be equal between te two regons (tat s, taxes are armonzed). Lettng t denote te armonzed tax rate n sector ( a; b), we derve te optmal envronmental polcy maxmzng te country s welfare gven n (14) as comprsng s a + B t a sa B a a 4 + s a + B a 4 + s a B a + 4s a + B (7) a s b + A t b b sb A b 4 + s b + A b 4 + s b A b + 4s b + A : (8) b In comparson to te unarmonzed taxes expressed n (18) (19), te armonzed taxes are lower on goods n wc regons ave a comparatve advantage but ger oterwse, tat s, t B a < t a < t A a t A b < t b < tb b : Under armonzed taxes, te less e cent regon tus subsdzes te more e cent regon; te tax ncrease n te former (t t ) s owever larger tan te tax decrease (t t ) n te latter as long as polluton s not a pure publc bad (see Appendx A). In fact, for s < 1, te margnal envronmental damage of producton n sector s greater n regon tan n regon due to te quadratc nature of te damage functon as regon, beng te more e cent producer n sector, produces more of good tan regon. Hence, a unt tax reducton n sector ncreases polluton n regon by more tan a unt tax ncrease reduces polluton n regon t t but closer to t (.e. so tat te armonzed tax maxmzng a country s welfare s cosen between tan to t. If no productvty gap exsts between te two regons n sector 1), te two regons wll ave te same level of producton n sector face te same margnal envronmental damage of producton ndependently of te transboundary nature of polluton; ence, te armonzed tax wll be exactly equal to te average of te two unarmonzed taxes. In terms of envronmental damages, te unarmonzed polcy always results n a better envronment wen polluton spllovers occur accordng to te same postve rate across sectors (.e., 0 < s a s b < 1) 14

15 productvty gaps are te same across regons (.e., 0 < B a A b < 1).3 Wen movng to armonzaton, te tax canges mply producton ncreases n te comparatve advantage sector but decreases n te oter sector; n te absence of d erences n spllover e ects productvty gaps, te producton ncrease n te comparatve advantage sector domnates so tat, overall, envronmental damages are larger under armonzaton. However, t s possble for a regon to enoy a better envronment under armonzed taxes f te polluton generated n te comparatve advantage sector s more transboundary tan te polluton generated n te oter sector /or f te cross-sectoral productvty gap t faces s smaller tan te crosssectoral productvty gap te oter regon faces. An ncrease n s reduces te gap between polluton under unarmonzed taxes polluton under armonzed taxes n sector (troug a reducton n te tax gap tus n te producton gap) but does not alter te polluton gap n sector. Gven tat polluton from sector s ger n regon but lower n regon (, correspondngly, polluton from sector s ger n regon but lower n regon ) under armonzed taxes, te reducton n sector s polluton gap tat follows te ncrease n s amounts not only to a lower polluton cost of armonzaton n regon but also to a lower polluton bene t of armonzaton n regon. Wle te overall envronmental cost of armonzaton ncreases n regon (tat s, te regon wc does not ave a comparatve advantage n sector ), regon may end up beng envronmentally better o under armonzed polcy as te reducton n te polluton gap n sector may be suc tat te bene t from lower polluton n sector (wc s not a ected by an ncrease n s ) more tan o sets te cost from ger polluton n sector (wc decreases followng an ncrease n s ). In Fgure a, we llustrate te mpact of an ncrease n s on envronmental damages gven, ;, s. regon Te e ect of a devaton n te productvty gap between te two regons (e.g., wen >, tat s, s nter-sectoral productvty gap s smaller tan regon s) s less stragtforward: from a poston of equalty n spllover e ects between te two sectors productvty gaps between te two regons, an ncrease n, ceters parbus, can ncrease or decrease te envronmental cost of armonzaton n regon (as llustrated n Fgure b, te ncrease occurs at low values of decrease ts envronmental bene t n regon values of or n areas Q R) ncrease or (n Fgure b, te ncrease occurs at combnatons of low g values of s or n area Q). By (11), te magntude of te mpact of a cange n depends on te producton level of good n regon : te more regon produces, te stronger te e ects of an ncrease n on good s producton levels n te two regons. As regon s producton level of good s lower under armonzed polcy, an ncrease n ncreases te gap n good s producton 3 In te extreme case n wc polluton s a pure publc bad n bot sectors (.e., s a s b 1), envronmental qualty s te same ndependently of weter taxes are armonzed. 15

16 between unarmonzed armonzed taxes n eac regon. However, a cange n also a ects te tax gaps: a lower productvty gap between te two regons (.e., a ger ) does n fact amount to less varaton between te two regons n te absence of armonzaton tus to a lower tax e ect of armonzaton; a lower tax gap ten mples a lower gap between producton under unarmonzed taxes producton under armonzed taxes. Te lower te productvty advantage tat regon enoys n sector relatve to regon ncreasng regon unarmonzed polcy are. 4 s (tat s, te ger s), te less e ectve an ncrease n s n s producton of good te closer te taxes te two regons face n sector under Hence, at g values of, te e ects of an ncrease n on te tax gaps tend to preval te producton gaps tus tend to decrease, tat s, armonzaton tends to yeld a lower producton ncrease n te e cent regon a lower producton decrease n te oter regon. For a gven s, polluton s ten more lkely to decrease (ncrease) n regon ncrease (decrease) n regon as ncreases at low (g) values of. As s ncreases, te lower polluton ncrease regon experences under armonzaton as a greater mpact on regon s total polluton lower values of are ten requred for regon s polluton to ncrease n response to an ncrease n. At te same tme, te lower polluton decrease regon experences under armonzaton as a greater mpact on regon total polluton ger values of are requred for regon s polluton to decrease n response to an ncrease n. In lgt of te above, t s possble for te regon wt a comparatve advantage n sector to enoy a better envronment under armonzed polcy at g values of s (area S n Fgure b) for te regon wc s less e cent n sector to face less polluton under armonzed taxes at combnatons of low values of g values of s (area Q n Fgure b). In Fgure c, we llustrate te mpact of an ncrease n on envronmental damages gven, s ; s,... Regonal Envronmental Polcy Under a decentralzed system, eac of te two regons (e.g., regon ) cooses te envronmental taxes to levy on te producton of te two goods as to maxmze ts welfare wc s gven by W et X CS e t + P S e t + T R e t et ; (9) were et e t a; et b s te vector of envronmental taxes n regon consumer surplus, producer surplus, tax revenue, envronmental damage n regon are expressed n (15) troug (17) (4), respectvely. 4 Usng (11), we ave tat x x 3 + > 0 x 6 x 3 + < 0: 16

17 Te decentralzed envronmental taxes are tus gven by et en s 4 4s 3 + 3s + 6s 1 + s 3 + 9s 4s s 3s + 1 (30) were et en s 4 4s 3 + 9s s 4 + s 3 + 7s 8s ; (31) en s 4 4s 3 s + 16s 6 + s 3 + 5s + s < 0: (3) Wen we consder te sector n wc a regon does not ave a comparatve advantage (e.g., sector a for regon B sector b for regon A) compare te relevant centralzed taxes gven n (18) (19) wt te correspondng decentralzed taxes gven n (30) (31), we obtan Proposton 4 Te envronmental tax on te good wc a regon s less e cent at producng s always ger under a centralzed system tan under a decentralzed system, tat s, t A b > et A b tb a > et B a. We can express te d erence n te envronmental taxes regon faces on good under te two polcy regmes as t et en n 4 + s s + (3 s ) o > 0; (33) were 1,, 3 are postve parameters. 5 For te sector n wc a regon does not ave a comparatve advantage must tus mport from te oter regon, te nter-regonal trade e ect te tax revenue e ect work n te same drecton to ncrease te margnal bene t of envronmental taxes. Te combned postve e ect on tax settng stems from an ncrease n te value of trade te addtonal tax revenues regon enoys troug ger producton. At low values of s, te nter-regonal envronmental trade e ect works n te opposte drecton to ncrease te margnal cost of envronmental taxes as ger producton n regon yelds ger polluton. However, even n te extreme case wen s 0 (tat s, polluton s perfectly local n sector ), te combned postve e ect from trade tax revenue more tan o sets te negatve envronmental e ect so tat, overall, te central government always opts for a ger tax tan te regonal government n te comparatve advantage sector. For te sector n wc a regon does ave a comparatve advantage, we nstead obtan 5 Spec cally, 1 3s 6 11s 5 + 0s 4 8s 3 1s + 1s > 0, 3s 6 1s s 4 34s 3 5s + 79s > 0, 3 s 6 8s s 4 4s 3 + 9s + 104s > 0. 17

18 Proposton 5 Te envronmental tax on te good wc a regon s more e cent at producng s ger under a centralzed system wen te producton of te good generates substantal polluton spllovers. For su cently low values of s, tere exsts owever a productvty gap between te two regons above wc te tax s ger under a decentralzed system, wt a smaller s requrng a smaller productvty gap for te tax to be ger under a decentralzed system. We can express te d erence n te envronmental taxes regon faces on good under te two polcy regmes as t et en n 4 + s s + (3 s ) + 36s 18 o ; (34) were 1,, 3 are postve parameters. 6 Hence, t et s always postve for s > p 0:5 s postve oterwse, provded tat for t et s not too small; for s < p 0:5, te lower s s, te larger te needed to be postve. Wen polluton arsng from te producton of good s perfectly local (.e., s 0), te envronmental tax on good n regon s larger under te decentralzed regme tan under te centralzed regme for any productvty gap between te two regons (tat s, for any value of ); wen s 0, (34) n fact reduces to et t < 0: (35) In te determnaton of te envronmental tax on te good n wc a regon as a comparatve advantage, te nter-regonal envronmental e ect tax revenue e ect work n te same manner as n te settng of te tax on te ne cently produced good above consdered, ncreasng te tax rate as spllovers ncrease. However, te nter-regonal trade e ect not only works n te opposte drecton as lower taxes generate bene ts to consumers n two regons rater tan one, tus decreasng te tax rate, but s also larger n magntude because of te larger prce e ect of te tax n te more e cent sector. Wen polluton s perfectly local, te nter-regonal envronmental e ect conssts solely of te own polluton e ect tus reenforces te nter-regonal trade e ect n lowerng te central tax relatve to te regonal tax. As polluton becomes less local, te spllover e ect ncreases, counteractng te own polluton e ect eventually cangng te drecton of te nter-regonal envronmental e ect. For a gven productvty gap between te two regons, tere exsts a s above wc te postve nter-regonal envronmental e ect coupled 6 Spec cally, 1 7s 6 1s s 4 14s 3 6s + 45s > 0, s 6 19s s 4 46s 3 43s + 19s > 0, 3 0s 4 36s 3 + 5s + 90s > 0. 18

19 wt te tax revenue e ect more tan o sets te negatve nter-regonal trade e ect te central tax s greater tan te regonal tax. Te smaller te productvty gap between te two regons s, te weaker te nter-regonal trade e ect because of te lower trade volume tus te smaller te spllover e ect tat s necessary for te central tax to be greater tan te regonal tax. We sow te crtcal value of s as a functon of suc tat t et 0, tus solvng (34), n Fgure 3; n te dark grey area, below te crtcal s curve, te centrally set tax on te good n wc a regon as a comparatve advantage s smaller tan te correspondng tax under a decentralzed system. As te case under a centralzed regme, a good s taxed more eavly under a decentralzed system n te regon wc enoys a comparatve advantage n ts producton, tat s, 1 et et 3s 4s s 6s + 11 > 0; (36) en te d erence s owever smaller under a centralzed system, tat s, t < et 4 1 t t e t et en n 4 + s s + (3 s ) t et or o < 0; (37) were 1,, 3 are postve parameters. 7 We can ten conclude tat, wen central taxes are greater tan local taxes n bot sectors, te tax premum under a centralzed system s larger n te regon tat s less e cent at producng te good, tat s, t et > t et. Te presence of te nter-regonal trade e ect n te settng of central taxes s at te core of ts result: a tax ncrease n te sector n wc a regon enoys an exportng poston yelds a prce ncrease tat generates a net cost to te mportng regon as te gan n producer surplus falls sort of te loss n consumer surplus. A tax ncrease n te sector n wc a regon mports yelds a prce ncrease tat generates a net bene t to te exportng regon as te gan n producer surplus more tan o sets te loss n consumer surplus. Hence, te nter-regonal trade e ect serves to curb te central government s ncentve to mpose ger taxes for goods regons export but to re-enforce t for goods regons mport. Wen we compare te taxes wtn a gven regon, we nd tat, as n te central polcy case, te good n wc te regon as a comparatve advantage may be taxed at a ger or lower rate dependng on d erences n te transboundary nature of polluton between te two producton processes as well as d erences n comparatve advantage between te two regons. Te tax d erental, wc s postve equal to te wtn sector tax d erental gven n (36) n te absence of d erences n spllover e ects 7 Spec cally, 1 s 6 5s 5 + 9s 4 3s 3 7s + 1s + 1 > 0, s 6 4s s 4 9s 3 16s + 37s + 1 > 0, 3 s 4 6s 3 8s + 30s + 17 > 0. 19

20 productvty gaps, s owever monotonc n eac of te four parameters, namely, s a, s b, B a, A b ; spec cally, et e t > 0; s et e t < 0; s e t et < 0; e t et < 0: (38) Terefore, te stronger te polluton spllovers of good are relatve to te polluton spllovers of good, te ger te tax regon faces on good, te good wc t produces more e cently tus t exports to te oter regon, relatve to te tax t faces on good. Consstently wt ts result, we ave tat e t et > 0; (39) s were s s s. Altoug a reducton n te comparatve advantage regon enoys n te producton of good as te same qualtatve e ect on te tax d erental as a reducton n te comparatve advantage regon enoys n te producton of good, te latter as a stronger e ect as re ected n e t et < 0; (40) were ; n oter words, a decrease n te productvty advantage regon as n te producton of good (.e., ncrease n ) reduces te tax regon pays on good relatve to te tax t pays on good by a smaller amount tan an equal decrease n te productvty advantage regon as n te producton of good (.e., ncrease n ).8 An ncrease n productvty ncreases producton n te mportng regon by more tan t decreases producton n te exportng regon. Ts d erental e ect on producton as mplcatons for a regon s ncentve to ncrease or decrease ts envronmental tax n te a ected sector. Trade ncreases te cost of taxaton n te mportng regon but decreases t (or, equvalently, ncreases te bene t of taxaton) n te exportng regon; te larger te volume of trade volume s, te ger te cost or bene t of taxaton s dependng on te drecton of trade. A larger ncrease n producton n te mportng regon n response to an ncrease n productvty (wc results n less dependence on mports n spte of te ncrease n local consumpton followng a prce reducton) amounts to a larger reducton n te cost of taxaton, or a stronger weakenng of te ncentve to lower te tax on te mported good, tan 8 Te e ect of on te tax d erence can be wrtten n terms of " 1 et et et as # et < 0: As (0; 1] (e t et ) et > et. See Appendx. et (e t et ) et, te drecton of te e ect for any feasble value mples tat 0

21 te reducton n te bene t of taxaton n te exportng regon from a decrease n producton tus exports. 9 Hence, a decrease n productvty gap as a stronger tax e ect n te mportng regon. 10 In settng taxes, a regon takes nto account te e ects tat tese nstruments ave on total surplus, tax revenues, envronmental damages. Independently of weter te regon as a comparatve advantage n a gven sector, t faces a trade-o between generatng more tax revenues troug greater producton wc requres lower taxes keepng te envronment cleaner troug lower producton tus ger taxes. Te tax e ect on total surplus s owever lnked to te drecton extent of trade terefore to te presence extent of a comparatve advantage; a tax ncrease does n fact generate net bene ts troug ger prces of exports (n te comparatve advantage sector) but net costs troug ger prces of mports (n te oter sector). Te addtonal bene ts of taxes on goods regons are more e cent at producng translate nto ger taxes; conversely, te addtonal costs of taxes on goods regons are less e cent at producng translate nto lower taxes. Clearly, te larger te extent of trade s as a result of a greater productvty gap between te two regons, te greater te revenue from exports or te cost of mports s; ence, as te volume of trade ncreases, te exportng regon faces a stronger ncentve to ncrease ts tax wle te mportng regon faces a stronger ncentve to decrease ts tax. Correspondngly, te smaller te productvty gap s, te smaller te revenue from exports or te cost of mports s te weaker te exportng regon s ncentve to ncrease ts tax or te mportng regon s ncentve to decrease ts tax. Ts convergence of ncentves amounts to a decrease n te tax gap between exportng mportng regons wtn a gven sector between exportng mportng sectors wtn a gven regon. Asde from d erences n te drecton of ncentves stemmng from trade consderatons, tere exst d erences n te strengt of ncentves arsng from envronmental consderatons. As long as polluton generated n a gven sector s not perfectly transboundary, ts level te assocated bene t of a tax ncrease are ger n te regon tat produces more, tat s, te regon wt a comparatve advantage. Te more transboundary polluton s n a gven sector, te smaller te polluton gap between te two regons, correspondngly, te smaller te tax gap. Put d erently, altoug eac regon faces a larger polluton level tus a greater ncentve to ncrease ts tax as polluton becomes more transboundary, te mportng regon (tat s, te regon producng less), faces a larger ncrease n polluton tus a 9 A decrease n productvty gap between te two regons reduces te prce level tus ncreases local consumpton n bot regons. Exports tus fall by more tan local producton. 10 Te tax mplcatons of te d erental e ect on producton of a decrease n productvty gap may also be lnked to envronmental consderatons. In fact, unless polluton n te exportng sector s substantally more transboundary tan polluton n te mportng sector, overall polluton ncreases n te latter by more tan n te former, tus provdng a regon wt addtonal ncentves to ncrease ts tax on te mported good. A decrease n productvty gap n te sector n wc a regon as a comparatve advantage does n fact reduce polluton n tat sector, provded tat ts spllover e ects are not sgn cant. 1

22 greater ncentve to ncrease ts tax. Fnally, wen we compare te above tax d erental under te two polcy regmes, we ave tat t t e t et < 0; (41) tat s, te tax d erental s always smaller under a centralzed system. In fact, as t t e t et t t e t et > 0 > 0; (4) s we obtan te lower bound value of te d erence of te two tax d erentals wen s 0 te upper bound value wen s 1. Te latter turns out to be exactly equal to t t e t et as gven n (37) for s s s t s tus negatve so tat t e t et must be negatve for any combnaton of feasble s values. Tat te gap between te two taxes wtn a regon s narrower under a centralzed regme follows drectly from te presence of te nterregonal trade e ect wc reduces te bene t of taxes for exported good but ncreases t for mported goods..3 Assessng te Envronment: Central versus Regonal Polcy In assessng te envronmental mpact of central polcy versus local polcy, we compare te envronmental damages n regon under te two tax regmes. We ntally consder a stuaton n wc productvty gaps are te same between te two regons spllover e ects are te same between te two goods. Our ntal case nvolves s s te two regons (e.g., regon ). so tat we need only assess envronmental d erences for one of Usng te damage functon gven n (4), te central taxes n (18) (19), te local taxes n (30) (31), we can express te d erence between te envronmental damage under a centralzed system te envronmental damage under a decentralzed system as (; s) e t et X a;b e e 3 + e 3 n t t + et et 4e 1 e + + e 1 e 3 t t e t + et + et e o t ; (43) were A (B) B (A) wen a (b), B a ; A b s [sa ; s b ] are te vectors of productvty gaps spllover e ects, e 1a (1 3s a ), e 1b (s b 3), e a 1 + s a B a, eb A b + s b, e3a s a B a B a, e 3b A b s b A b s b. Upon nspecton of te above d erence, we ave

23 Proposton 6 Wen te two goods ave dentcal spllover e ects (.e., s a s b s) te two regons enoy te same productvty gaps n absolute terms (.e., A a A b B b B a 1 ), envronmental damages from producton can be larger under a centralzed regme. In partcular, for a gven productvty gap (), damages tend to be lower under a decentralzed regme wen polluton from eac of te two goods s relatvely local (at low values of s). Te smaller te productvty gap (te larger te ), te more local polluton as to be (te smaller te s) for damages to be lower under local taxes. Lettng bs satsfy (; s) 0, we ave tat lm!0 bs () 0:5p 0:71 lm!1 bs () 0 (44) tat as dbs () (;s) d (;s) < 0 s < 0.11 We also note tat, for s 0, s < 0; (45) (; s) ( 1) (7 + 8) > 0 (46), for s 1, (; s) (7 + 9) (3 + 5) < 0: (47) Terefore, wen polluton s perfectly local, centrally set polcy always yelds greater damages; wen polluton s perfectly transboundary, locally set polcy always yelds greater damages. Wen te two regons face te same productvty gap between sectors te two producton processes nvolve te same spllover rates, we ten conclude tat damages are always smaller under a central polcy regme for s > 0:5 p ; owever, for s < 0:5 p, weter damages are greater or smaller under one regme or te oter depends on. Spec cally, as dbs() d < 0 (; s) > 0 for s < bs, te larger s, te lower te upper bound of te range of s values over wc damages under central taxes exceed damages under local taxes. Put d erently, te larger te productvty gap between te two sectors, te more lkely t s for a decentralzed system to be preferable to a centralzed system from an envronmental pont of vew. In terms of Fgure 4, damages are smaller wt locally set taxes below (or to te left of) te bs curve. Before we consder te mplcatons of relaxng te assumpton tat s 1, we look at te d erence n envronmental damages relatve to te d erence n taxes between te two regons. To be clear, we are nterested n weter tere exsts consstency between te two d erences wereby ger 11 Tat s < 0 mples tat (; s) > 0 for s < bs (; s) < 0 for s > bs. See appendx for more detal. 3