MODELLING SECTORAL SPILLOVERS FOR REGIONAL CAPITAL SUBSIDIES USING AMOS

Transcription

1 European Regonal Scence Assocaton 36th European Congress ETH Zurch, Swtzerland August 996 Erc P. McVtte Aberdeen Busness School, The Robert Gordon Unversty Aberdeen, UK Emal: Peter G. McGregor, Km Swales, Ya Png Yn Fraser of Allander Insttute, Unversty of Strathclyde Glasgow, UK Fax: MODELLING SECTORAL SPILLOVERS FOR REGIONAL CAPITAL SUBSIDIES USING AMOS ABSTRACT: Captal subsdy polces have been central to regonal development strateges n the UK and elsewhere. Such polces are complex n ther effects partcularly where they ncorporate a sectoral as well as a regonal bas. Ths paper wll examne the effects of regonal captal subsdy polces usng a CGE model of the Scottsh economy (AMOS). The paper wll concentrate on the spllover effects of subsdy polces whch are drected at partcular ndustral sectors on other sectors of the regonal economy. The ssue of sectoral spllovers from regonal polces has often been addressed through the use of sectoral demand multplers such as those based on nput-output models. Ths approach gnores potentally mportant mechansms through whch subsdy polces effects may be dstrbuted throughout the economes of recpent regons, n partcular through ther effects on nput and output prces. Relatve prce effects are explctly ncorporated by Computable General Equlbrum analyses.

2 MODELLING SECTORAL SPILLOVERS FOR REGIONAL CAPITAL SUBSIDIES USING AMOS INTRODUCTION In general, regonal polcy polcy n the UK (and elsewhere) has provded assstance only to selected frms or ndustral sectors wthn the asssted regons. The regonal polcy regmes used pror to the reforms of the 980s, whch were prmarly based on 'automatc' factor subsdes (partcularly captal subsdes), usually ncorporated a sectoral as well as a spatal bas. Subsdes and other forms of regonal assstance were made avalable only to frms n specfed ndustral sectors (prmarly manufacturng). The schemes of dscretonary assstance whch have formed the core of regonal polcy snce 988 are desgnedly selectve. To analyse the effects of regonal assstance whch apply n such a selectve manner on the asssted regon as a whole we must take account of the spllover effects of assstance on other (unasssted) frms and ndustres. Only very lmted attenton has been gven to such spllover effects n the regonal polcy evaluaton lterature, at least when compared to the effort expended n dervng estmates of the effects of polcy on asssted frms and ndustres. Thus, n dervng cost-perjob estmates, the standard measure of regonal polcy effectveness presently adopted n UK, the prmary emphass s placed on accurately dentfyng the effects of polcy on employment wthn asssted frms and ndustres. Consderaton of the effects of the polcy on employment elsewhere n the regon s generally lmted to the applcaton of fxed multplers, the source of whch s not always clear, to the estmates of employment generated n the asssted sectors. 2 Ths focus appears unwarranted snce an error of x % n estmates of the multpler wll have dentcal mplcatons for the accuracy of total employment and cost-perjob estmates as does an x % error n estmates of the multplcand. Ths mbalance suggests a belef that dffcultes arse only n accurately estmatng the multplcand, the multpler effects of polcy beng smple and fully understood. Ths paper examnes the employment multplers assocated wth regonal captal subsdy polces whch are appled to only some ndustres wthn the asssted regon. 3 The central argument s that employment multplers are consderably more complex than has been mpled by ther treatment n the polcy evaluaton lterature. The paper consders the relevance of fxed Consumpton, Economc Base (EB) and Input Output (IO) multplers to the analyss of the spllovers assocated wth captal subsdy polces. A broadly neoclasscal approach s used, ncorporatng substtuton behavour n producton and consumpton. We beleve that ths approach s more approprate n the context of captal subsdy polces snce such polces operate largely through ther effects on relatve prces. The remander of the paper s organsed as follows. Secton presents a general dscusson of neoclasscal multplers. Ths s followed, n Secton 2, by an analyss of captal

3 subsdy multplers based on a smple two-sector neoclasscal economc base model. Neoclasscal sectoral multplers have prevously been dscussed by Mutt (98) and Merrfed (987, 990). Whereas these authors consdered the determnants of output multplers, we examne employment multplers, snce these have been the prmary focus of polcy evaluaton. Our model s rather smpler than that n Merrfeld (987, 990) and has the beneft of provdng more readly nterpreted results, whlst capturng the central features of neoclasscal analyss. However, ts smplcty nvolves gnorng several addtonal spllover mechansms whch may be of practcal mportance. We nclude these addtonal lnkages by usng a smulaton approach based on an emprcal model of an actual regonal economy. Sectons 3 and 4 provde an analyss of employment multplers for a captal subsdy polcy based on a computable general equlbrum (CGE) model of the Scottsh economy - AMOS. A bref outlne of AMOS s gven n Secton 3, followed by an analyss of smulaton results n Secton 4. Secton 5 provdes concludng remarks.. NEOCLASSICAL MULTIPLIERS Input-Output (IO), Keynesan, and Export-Base (EB) multplers are the standard tools for measurng the system-wde effects of shocks to one sector of a regonal economy. They are wdely used n analysng the effects of sectoral demand shocks on output and employment. They have also provded the bass for estmates of the system-wde effects of regonal polces, ncludng captal subsdes. Ther great strength les n ther ease of use and nterpretaton. Such technques have, however, mportant lmtatons. They are derved from very rudmentary general equlbrum models whch omt consderaton of the effects of prce changes whch may accompany the ntal shock. The standard treatment of regonal multplers based on these approaches s essentally Keynesan. Increases n demand to one sector generate ncreases n output and employment n that sector and a derved ncrease n actvty elsewhere wthn the regon through ts effect on demand for ntermedate goods and on ncome and consumpton demands. Excess capacty and/or perfect factor moblty ensures an nfntely elastc supply of all productve factors. Ths mples that the demand shock has output effects but no prce effects. Substtuton behavour does not take place, and so the structure of the regonal economy (ndustry output and employment shares) s unaltered by the shock. To the extent that there are factors whch nhbt the adjustment of supply to demand, they are seen as slowng-down the multpler process rather than changng ts fundamental nature. An alternatve vew on sectoral spllovers s provded by the general equlbrum tax ncdence lterature (Harberger, 962) and the trade polcy lterature (Jones, 965). Here the emphass s the response of supply to demand shocks and on the role of substtuton behavour by transactors n response to changes n relatve product and factor prces. The mplcatons of such behavour for regonal sectoral multplers are dscussed by Mutt (98) and Merrfeld (987, 990).

4 Mutt (98) examnes how the general equlbrum models used n nternatonal trade theory can be adapted to use n analysng regonal problems. Constant sectoral multplers n economc base and nput-output modes are seen as dervng from the abstracton n such models from changes n relatve prces. Ths, n turn, assumes (mplctly or explctly) "ether large ntal levels of unemployed labor and captal wthn the regon or an nfntely elastc supply of factors of producton whch can mmgrate nto the regon" (). In contrast, the general equlbrum model adopts the assumpton of regonally mmoble labour, gvng rse to sectoral output multplers whch are non-constant and whch may even be negatve at the margn. Merrfeld (987, 990) presents a more detaled analyss of economc base multplers from a neoclasscal perspectve, ncorporatng prce endogenety, resource restrctons and substtuton behavour by producers and consumers. Hs ams are to trace the lnks between basc and non-basc sectors n a neoclasscal settng, and to show how one could calculate a neoclasscal economc base multpler and the relatonshp between ths and the average (EB) multpler. Hs analyss suggests that margnal output multplers (the rato of the change n total to the change n basc output) generally dffer. Where prces are fxed, however, average and margnal multplers are equal. The essence of the neoclasscal multpler s the effect of prce changes on the patterns of product and factor demands. We can llustrate ths by consderng a neoclasscal economcbase system n whch captal s nfntely elastcally suppled but where labour s regonal specfc and the labour market clears through varatons n the wage. A shock to the export sector whch ncreases export sector output and labour demand tends to ncrease the real wage and stmulate an expanson n labour supply. Regonal ncome ncreases whch stmulates expendture on non-basc goods. The neoclasscal employment multpler depends on how ths expendture ncrease s dstrbuted between commodtes and on the effects of changes n output on employment. Substtuton s possble n consumpton (changng the pattern of commodty demands) and n producton (changng the pattern of factor demands). The neoclasscal multpler wll equal the standard EB multpler only where such substtuton does not take place, leavng the pattern of employment unaltered. 2. CAPITAL SUBSIDY MULTIPLIERS IN A SIMPLE NEOCLASSICAL ECONOMIC- BASE MODEL Consder a regonal economy wth two sectors - an export sector (sector ) and a nontraded sector (sector 2), whch produces goods for domestc consumpton. Total consumpton comprses non-traded goods and mports. Traded goods from dfferent regons are mperfect substtutes, wth demand for exports and mports dependng on ther prces relatve to the prces of substtute goods n other regons and sector 2 prces respectvely.

5 Thus, the sectoral composton of product demands depends on relatve product prces. Both goods are produced under condtons of perfect competton. Producton n both sectors uses captal and labour. All producton and expendture functons are lnear homogeneous. The small regon assumpton s adopted for captal markets - captal s n nfntely elastc supply at exogenously determned rental rates. The regonal captal stock s externally owned. Labour supply to the regon s an ncreasng functon of the real consumpton wage - the nomnal wage deflated by the regonal consumer prce ndex. The model dffers from that used by Merrfeld (987, 990) n three ways. Frst, Merrfeld ncludes a thrd factor, regonally mmoble land, n addton to captal and labour. A smpler two-factor model s used here for pedagogc reasons. Our model provdes more easly understood results whlst stll retanng a regon specfc factor, labour. Second, we relate labour supply to the regonal real wage rather than to the nomnal wage, as n Merrfeld s model. Our approach s more consstent wth neoclasscal theory. Thrd, whereas Merrfeld mposes the law of one prce n the export market, we use the Armngton (969) trade assumptons by whch goods produced n dfferent regons are mperfect substtutes. Ths allows greater flexblty and ncorporates law-of-one-prce as a specal case. It s also consstent wth the approach adopted n the computable general equlbrum analyss dscussed n Sectons 3 & 4. The hghly smplfed nature of our model should be noted. There s no government expendture, taxaton, savng or nvestment and the assumpton of perfectly moble captal mples a long-run nterpretaton. We relax some of these assumptons n the CGE analyss. We wsh to analyse the effect of the ntroducton of a captal subsdy (s) to the export sector. The followng nne equatons - expressed n terms of proportonal changes n the relevant varables - descrbe the response of the regonal economy to the captal subsdy polcy. Export Demand q = ηp η > 0 () Demand for labour from the export sector Output prce n the export sector n = q ζ w + ζ p ζ > (2) 0

6 p = α w ( α ) s 0< α < (3) Demand for labour from the non-traded sector Prce n the non-traded sector Aggregate labour demand n = q ζ w + ζ p (4) p Aggregate labour supply Consumer prce ndex = α w (5) 2 2 Expendture on non-traded output n = βn + ( β) n 0 < β < (6) 2 n = γw γc γ > 0 (7) c = λp 2 (8) q + p = θ p + n + w (9) where q s output, p output prce, n employment, w the nomnal wage, and c the consumer prce ndex, dots represent proportonal changes (dx/x) and subcrpts and 2 refer to the export and non-traded sectors respectvely. All parameters are assumed fxed. Equaton () s a conventonal demand functon for sector output, where ncome and prces n export markets are constant. Equaton (2) s a cost-mnmsaton labour demand functon for sector, where ζ s the elastcty of substtuton between captal and labour n producton, 4 whle equaton (3) specfes the prce change for sector output, based on costmnmsaton under perfect competton (zero profts) wth an nfntely elastc supply of captal. The equvalent expressons for sector 2 are (4) and (5). Equatons (6) and (7) specfy changes n aggregate labour demand and labour supply. The proportonate change n aggregate labour demand s the weghted sum of the changes n the two sectors (β s the ntal share of traded employment n total regonal employment). Aggregate labour supply s an ncreasng functon of the real consumpton wage, where the change n the consumer prce

7 ndex s specfed by equaton (8). Equaton (9) determnes the demand for sector 2 output. The change n expendture on sector 2 goods s related to the endogenous change n regonal ncome and to changes n the prce of sector 2 output. Equatons () - (9) together determne the 9 endogenous varables: the proportonate changes n sectoral output, employment and prces ( q, q2, n, n 2, p, p2 ) and the proportonate change n total employment, the cp and the nomnal wage ( n, c, w ). The value of each of these varables can be specfed analytcally as a functon of the exogenous varable (s) and the model parameters ( η, ζ, ζ 2α, β, γ, λ, θ). We begn by analysng the effect of the subsdy on the export sector gnorng spllover effects between export and non-traded sectors. Usng equatons ()-(3) and (7) (wth n and c = 0 ) we can solve to gve the followng expressons for w and n n terms of s: = n ( η ζ )( α ) w = γ + α η + ( α ) ζ s ( )( ) γ η ζ α n = γw = s γ + αη + ( α ) ζ (0) () Equaton () ndcates both postve and negatve effects of the subsdy on export sector employment, referred to as output and substtuton effects n the partal equlbrum lterature (Lucas, 969; Swales, 98; Holden & Swales, 993). The output effect depends upon the senstvty of product demand to prce reductons, measured by the prce elastcty of demand η. The substtuton effect depends upon the senstvty of labour demand to changes n factor prces, measured by the elastcty of substtuton n producton ( ζ ). The subsdy polcy ncreases export sector employment whenever the output effect domnates the substtuton effect ( η > ζ ). Where postve, the employment effect s larger the hgher s the elastcty of demand ( η ), the lower s the elastcty of substtuton ( ζ ), the hgher s the elastcty of labour supply (γ ) and the larger s the share of labour n the producton of the export good ( α ). These results correspond to those n Holden & Swales (993). Let us now consder the lnks between the export and non-traded sectors n the model. In ths smple model all sector lnkages occur through changes n the wage and n labour ncomes. Changes n the wage affect producton costs and output prces, shftng output supply and factor demand functons. Wage changes also affect labour supply and ncome and

8 so consumpton expendtures on non-traded output. Ths shfts the demand curve for nontraded output. The resultng changes n labour demand from the non-traded sector alter the wage and so produce feedback effects on the export sector. Our system can be reduced to gve the followng three equatons: Export sector product market equlbrum [equatons ()-(3)]: [( ) ] [( )( )] n = α ζ + α η w + η ζ α s (2) Domestc non-traded product market equlbrum [equatons (4)-(6) & (9)] α 2 ( θ ) ( α 2) ζ 2 + n2 = w + n β (3) Labour market equlbrum [equatons (5)-(8)] ( ) βn + ( β) n = γ α λ w (4) 2 2 whch, for smplcty, we wrte as n = Γ w + Ψ s (2) n = Γ w + n (3) 2 2 βn + ( β) n = Γ w (4) 2 3 Equatons (2), (3) and (4) solve to gve: w = Ψ Γ ( β) Γ + Γ 2 3 s (5) n Γ = s Γ ( β) Γ2 + Γ 3 Ψ (6) n 2 Γ2 Γ = + s Γ ( β) Γ2 + Γ 3 Ψ (7) We consder each of these expressons n turn. The Wage Consder frst equaton (5). The numerator n (5) s

9 ( η ζ )( α ) Ψ= whch may be ether postve or negatve, and s postve where η > ζ. Ths s the condton for the ntal (partal equlbrum) effect of the subsdy on export sector labour demand to be postve. At frst sght t appears that the denomnator n (5) may also be ether postve or negatve. If, however, we restrct attenton to cases where the system s stable, then the denomnator must be postve. Stablty for the system requres that an ncrease n the wage must reduce any excess demand for labour,.e. a wage ncrease must result n an ncrease n labour supply whch s greater than any ncrease n labour demand arsng from ncreased real ncome. From equatons (2), (3) and (4) ths requres that Φ = Γ ( β ) Γ + Γ > 0 (8) 2 3 Thus, for stable cases, the regonal wage wll ncrease whenever the subsdy polcy has a postve effect on labour demand n the subsdsed sector. Employment From equaton (6) export sector employment depends on the sgns of Ψ and Γ Γ ( β) Γ + Γ 2 3 The former determnes whether the subsdy has a postve or a negatve effect on export sector labour demand and on the wage. The latter determnes the response of non-traded labour demand and of aggregate labour supply to ths wage change. A captal subsdy polcy whch rases labour demand n the export sector (Ψ > 0) wll ncrease export sector employment f Γ < Γ ( β) Γ + Γ 2 3 or, defnng a new varable, Φ 2, f Φ = Γ ( β ) Γ > 0 (9) Ths requres than an ncrease n the wage produces a labour supply response ( Γ 3 ) whch exceeds an ncrease n labour demand n sector 2 ( ( β) Γ ). Ths s the condton that the 2 labour market for sector 2 shows partal equlbrum stablty. Equaton (9) s not, however, bndng n the general equlbrum system snce excess labour demand n one sector can be met by labour released from the other sector. In partcular, Γ 2 may be postve (f θ s postve or

10 weakly negatve and f ζ 2 s small), so that a wage rse may ncrease excess labour demand n sector 2, wth ths excess beng met by labour transferred from sector. An ncrease n labour demand n sector can generate a reducton n employment n that sector. The effect of the subsdy on employment n the non-traded sector s gven by equaton (7). The drecton of the non-traded employment effect depends on the sgns of Ψ and of Γ2 Γ + Γ ( β) Γ + Γ 2 3 Usng the aggregate labour market stablty condton (equaton 8), n 2 s postve f Ψ > 0 and Φ = βγ + Γ > or (20) Ψ < 0 and Φ < 0 3 and s otherwse negatve. Γ 2 (and so Φ 3 ) may be ether postve or negatve. If Φ 3 s negatve then a demand stmulus from sector ( Ψ > 0 ) results n a reducton n sector 2 employment. The ncrease n export sector labour demand rases the wage. Ths ncreases regonal ncomes and so stmulates consumpton demand for non-traded goods. However, f there s strong substtuton of mports for domestc goods n consumpton (θ s negatve and takes a large value) and/or f there s strong substtuton of captal for labour n producton of good 2 (ζ 2 s large) then non-traded employment wll fall. In general, the subsdy polcy may ether rase or lower non-traded employment, even n cases where labour demand ncreases n the export sector. Conversely, the subsdy may reduce export sector labour demand yet ncrease employment n the non-traded sector. It s clear from the above that complex sectoral spllover effects can occur even n ths smple model. Even the effects on the subsdsed export sector are not straghtforward. That a captal subsdy may ether rase or lower labour demand n the subsdsed sector s clear from the partal equlbrum analyss. The above analyss suggests that a rse n labour demand could be assocated wth ether a rse or a fall n subsdsed sector employment and wth ether a rse or a fall n employment elsewhere n the regon (and smlarly for a fall n labour demand). There s, therefore, consderable complexty concernng both the own-sector effect of the subsdy polcy and ts effect on employment n other sectors.

11 The Multpler We are partcularly nterested n the relatonshps between export and non-traded employment effects resultng from the captal subsdy polcy. We wll dscuss possble combnatons of export and non-traded employment effects n terms of the the margnal employment multpler for the regon n response to a captal subsdy to the traded sector: M 2 dn N n m n = = = dn N n n 2 where N and N 2 represent employment n sectors and 2 respectvely and m s the average employment multpler (the economc-base multpler) m = N = 2 β N β. Thus, the margnal employment multpler s M 2 m n 2 β = = n β Γ Γ3 + βγ2 2 = β Γ + ( β) Γ β Γ ( β) Γ (2) Fgure : Varatons n the Multpler for changes n Γ 2 M 2 m Γ 3 β Γ 3 β Γ + Γ β 3 Γ 2 - Fgures and 2 llustrate the relatonshps between the margnal employment multpler and our summary parameters, Γ and Γ. Note that the nterpretaton of a gven value of M 2 2 3

12 depends on the sgn of the export sector employment effect ( n ) and, n partcular, on the sgn of the drecton of the ntal mpact of the subsdy on export sector labour demand (Ψ). For smplcty of exposton, we focus our dscusson on cases where Ψ > 0, so that the subsdy rases export sector labour demand and the wage. The relatonshp between M 2 and Γ 2 (the response of non-traded labour demand to changes n the wage) s shown n Fgure. Frst consder the case where Γ 2 = 0, so that the demand for non-traded output s completely nsenstve to changes n the wage and n nontraded prces. Shocks to the export sector affect the non-traded sector only through changes n ncome, whch are proportonal to the change n export sector employment. Employment n each sector changes n the same proporton and the margnal multpler equals the economc base multpler. As Γ 2 becomes negatve the margnal multpler falls below the EB multper. The wage ncrease tends to reduce labour demand n sector 2 so that n < n. For small negatve 2 values of Γ 2 the multpler remans postve: employment n the two sectors rses or falls together. Where Γ 2 s strongly negatve ( Γ < Γ / β ), however, a rse n export sector 2 3 employment and the wage s assocated wth a fall n non-traded employment, so that the multpler s negatve. As Γ 2 we approach a stuaton of complete crowdng out: a rse n export sector employment s assocated wth a fall of equal magntude n non-trade employment (M 2 = -). Any tendency for the wage to ncrease due to the subsdy polcy s suffcent to ensure a reducton n non-traded employment whch exactly matches the ncrease n export employment. For postve values of Γ 2 the pattern of response s more complex. Γ 2 > 0 mples that a rse n the wage results n an ncrease n sector 2 employment. The wage effect of the subsdy on non-traded employment supplements ts ncome effect so that n > n. The 2 value and sgn of the multpler depends on the drecton of the export sector employment effect, whch n turn depends on the relatve szes of the wage effect on non-traded labour demand and on labour supply. If a wage ncrease rases non-traded labour demand by less than labour supply (( β) Γ < Γ ) then export sector employment rses and the multpler s 2 3 postve. If, however, the wage ncrease rases non-traded labour demand by more than labour supply (( β) Γ > Γ ) then ncreased employment n non-traded more than absorbs the 2 3

13 Fgure 2: Varatons n the Multpler for changes n Γ 3 a. Γ 2 < 0 M 2 M 2 m 0 -βγ 2 Γ 3 - b. Γ 2 > 0 M 2 m 0 ( β) Γ2 Γ 3 - ncreased labour supply and the gap s made up from labour transfered from the export sector. Export sector employment falls and the multpler s negatve. For ( β) Γ = Γ any 2 3 addtonal labour supply s entrely absorbed by the non-traded sector, so that export sector employment does not change. Around ths value of Γ 2 we have a relatvely large non-traded

14 employment effect combned wth a small export employment effect so that the multpler becomes very large (ether postve or negatve). Wth ( β) Γ > Γ + Γ the labour market 2 3 s unstable. The relatonshp between the multpler and the aggregate labour supply parameter ( Γ 3 ) s shown by Fgure 2. There are two separate cases dependng on the sgn of Γ 2. For Γ 2 < 0 (part a) the pattern s relatvely straghtforward. A wage ncrease reduces labour demand n sector 2. Where the labour supply s completely nelastc ( Γ 3 = γ = 0) ncreases n employment n one sector must be met by equal reductons n employment n the other sector. There s complete crowdng out of non-traded employment by export employment (for Ψ > 0), and the multpler s -. At the opposte extreme, where labour supply s nfntely elastc the subsdy polcy has no effect on the wage, and hence on the prce of non-traded output. The subsdy polcy affects the non-traded sector only through ts effect on ncome and the EB multpler apples ( M = m). Between these two extremes there s a postve relatonshp 2 between M 2 and Γ 3. The mportant factor s the drecton of the non-traded employment effect whch determnes the sgn of the multpler. For low values of Γ 3 (< -βγ 2 ) the subsdy reduces non-traded employment and the multpler s negatve. For hgher values non-traded employment ncreases and the multpler s postve.part (b) of Fgure 2 examnes the relatonshp between M 2 and Γ 3 for Γ 2 > 0. For extreme values of Γ 3 the multpler s as for Γ 2 < 0, although the nterpretaton s rather dfferent. Where labour supply s completely nelastc the crowdng-out s now n the opposte drecton: export sector employment declnes whle non-traded employment ncreases. We can nterpret ths as a terms-of-trade effect. The regon exports only to fnance mports. Wth Γ 2 > 0 an ncrease n wage ncome s used to buy non-traded domestc goods whch are substtuted for mports. Ths allows the regon to reduce ts exports, transferrng labour from export to non-traded sectors. As Γ 3 rses, aggregate labour supply responds to a wage ncrease so that crowdng-out s ncomplete. The sze of the declne n export employment s reduced whch, combned wth a relatvely large non-traded effect results n an ncreased (negatve) multpler. As noted above, wth Γ = ( β ) Γ the export sector employment effect s zero: ncreases n non-traded can be met 3 2 from ncreased labour supply wth no transfer of labour from the export sector. Around ths value the multpler ncreases wthout bound (ether postve or negatve). Above ( β) Γ 2, the labour supply response s suffcent to permt an ncrease n employment n both sectors,

15 so that the multpler s postve. An ncreased labour supply response then allows a larger ncrease n export employment and the multpler declnes towards the value of the EB multpler (whch agan apples where labour supply s perfectly elastc). The above dscusson has llustrated the potental complexty of captal subsdy effects wthn even a very smple neoclasscal system. In our model, sector spllovers occur only through the effect of the subsdy on the wage and on labour ncomes. The nature of the spllover depends on the drecton of the wage change (Ψ), ts magntude (γ and Γ 3 ), and on the effect of the wage change on labour demand n the unsubsdsed sector ( Γ 2 ). The system acts as a standard EB model ( M = m) where the subsdy does not affect the wage ( γ ) 2 or where wage changes do not affect non-traded labour demand ( Γ 2 = 0). In ether of these cases the sole lnkage between sectors s through wage ncomes and consumpton demands whch change n proporton to the change n export sector employment. In general, however, the margnal multpler dffers from the EB multpler and can take any value, ether postve or negatve. Whle the analyss presented above gves some nsght nto the nature and complexty of sectoral multplers n a neoclasscal economy, the model does exclude sectoral lnkages whch may be of substantal practcal mportance. The captal market assumptons adopted are common n regonal models and serve to focus the analyss on the effects of subsdes on wages and labour ncomes. The treatment of ownershp also rules out any fscal njecton effects on regonal ncome assocated wth externally fnanced subsdy polces. If captal was not n perfectly elastc supply and/or some of the regonal captal stock was owned by resdents of the regon then the effect of the subsdy on captal rentals and captal employment would nfluence employment multplers. Such consderatons wll be of partcular mportance where we are concerned wth short-run multplers. Also of mportance n the short-run s the treatment of nvestment. By focusng on the long-run the model abstracts from the effects of the subsdy on nvestment demands. For the subsdy to operate, however, frms must alter ther captal stocks through nvestment. Investment demands wll, n general, be spread across dfferent sectors of the regonal economy, producng spllover effects on output and employment outsde the subsdsed sector. In addton, there are no nput-output lnkages n the model so that multpler effects assocated wth demands for ntermedate products are not consdered.

16 Incorporatng even some of these addtonal sectoral lnkages would greatly complcate the analytcal model and the results. Rather than proceed by ths route we may nvestgate regonal polcy multplers n a more realstc settng by usng smulatons of a model representatve of an actual regonal economy (AMOS), whch captures the addtonal lnkages outlned above. 3. CGE ANALYSIS: AN OVERVIEW OF AMOS AMOS s a CGE modellng framework parametersed on data from Scotland based on a 989 Socal Accountng Matrx. We provde here only a very bref descrpton of AMOS: more detals can be found n the Appendx and n Harrgan et al (99). AMOS has four domestc (.e. Scottsh) transacton groups (households, the nonhousehold personal sector, corporatons and government); three commodtes and actvtes (manufacturers, non-manufacturng traded and non-traded); and two productve factors (captal and labour). 5 The market for fnancal captal s not explctly modelled, the assumpton beng made that Scotland s a prce-taker n compettve UK fnancal markets. Ths mples an nfntely elastc captal supply n the long-run. The supply-sde of AMOS adopts a representatve transactor approach n whch aggregate producton actvty s descrbed as f t were the result of sutably constraned optmsng behavour. Producton behavour s descrbed n terms of a set of mult-level producton functons and ther dual cost functons. AMOS allows a hgh degree of flexblty n the choce of key parameter values and functonal forms. The smulatons reported below mpose cost-mnmsaton wth CES producton functons and constant returns to scale. 6 There are four major components of fnal demand: consumpton, nvestment, government expendtures and exports. Aggregate consumpton s related to real dsposable ncome. Investment demands are determned n accordance wth a smple partal adjustment specfcaton based on captal demands. In multperod smulatons sectoral captal stocks are held constant n each perod and nvestment equals deprecaton plus some fracton of the gap between the desred level of the captal stock and ts actual level. 7 In long-run equlbrum smulatons, captal stocks are determned endogenously on cost-mnmsaton crtera and nvestment equals deprecaton at the optmal captal stock. Aggregate government expendtures are fxed. The model ncorporates prce senstvty n the dstrbuton of all

17 elements of domestc fnal demand between actvtes. Exports (and mports) are determned va an Armngton lnk (Armngton, 969) and are therefore also relatve-prce senstve. A varety of labour market specfcatons are avalable n AMOS, ncorporatng alternatve perspectves of the spatal ntegraton of labour markets and the regonal wagesettng process. 8 Unless otherwse stated, the smulatons reported n Secton 4 adopt a compettve labour market closure n whch labour supply responds to varatons n the real consumpton wage and the replacement rato and where the real wage adjusts to clear the labour market. In multperod smulatons we ncorporate mgraton between Scotland and other regons based on a mgraton functon n whch net mgraton flows are determned by regonal real consumpton wage and unemployment-rate dfferentals (Layard et al, 99; Treyz, et al, 993). AMOS s closed through the mechansms that determne goods and factor prces. All markets clear through changes n prces. Assumng perfect competton n goods markets, n equlbrum the total demand for each commodty equals supply at a prce equal to the margnal cost of producton. The real wage mpled by the labour market closure determnes the level of employment and the dstrbuton of factor and nsttuton ncomes. The model, whch comprses several hundred non-lnear smultaneous equatons, s solved n levels form usng a functon-mnmsaton approach. 9

18 4. SIMULATION RESULTS Ths secton presents the results of polcy smulatons nvolvng the ntroducton of a 0% captal subsdy to the traded actvtes wthn AMOS. It s assumed that ths subsdy s funded outwth the regon. For ease of comparson wth the results n Secton 2 we aggregate the manufacturng and non-manufacturng traded actvtes nto a sngle traded sector. Most of the smulatons adopt a long-run equlbrum closure n whch captal supples are nfntely elastc. Unless otherwse stated, smulatons are for the compettve labour market specfcaton, n whch the regonal labour market clears through changes n the real wage. We examne the senstvty of results to changes n key model parameters suggested by the analyss of Secton 2. We fnsh wth a bref dscusson of the tmng of captal subsdy multplers based on multperod smulatons of the model. 0 Table presents the results for a benchmark verson of the model ncorporatng default producton and trade elastctes and labour supply specfcaton. These nvolve CES aggregaton functons wth substtuton elastctes of 2.0 n trade and 0.3 n producton (at all levels), and a labour supply elastcty of 0.4. The effect of the subsdy polcy s to reduce the cost of captal n the traded sectors and to reduce output prces stmulatng export demands, outputs and ncome. Ths tends to ncrease labour demand. The reducton n the prce of captal relatve to that of labour tends, however, to nduce substtuton of captal for labour n producton of value added. Wth the default parameters the output effect domnates the substtuton effect and employment n traded ncreases. The ncrease n traded labour demand results n an ncrease n the wage. The resultng ncreases n regonal ncome and n demands for ntermedate goods spllover nto the non-traded sector. The changes n factor prces also nfluence non-traded producton, as does the effect of the ncreased captal stocks on deprecaton nvestment n the long-run. The overall effect s that non-traded output and employment also rse, but by proportonately less than output and employment n the traded sectors. The non-traded employment multpler s 0.23 and the total employment multpler.23, compared wth average (Economc Base) multplers of and.395 respectvely. The comparable output multplers (based on value added) are 0.80 and.80 (wth EB multplers of 0.48 and.48). The subsdy results n a shft n expendture patterns away from non-traded and towards traded actvtes, but also substtuton of captal for labour n producton of traded goods.

19 Table : The percentage change n key varables for a 0% captal subsdy to traded actvtes. Base Soluton % Change GDP Output: Value Added Traded Non-Traded Employment ( 000) Total Traded Non-Traded Nomnal Wage Real Consumpton Wage Prces: Value Added Traded Non-Traded.068 Consumer Prce Index Captal Rental Rates: Traded Non-Traded Captal Stock: Traded Non-Traded We now examne the senstvty of the employment multpler to changes n the model specfcaton. Frst consder the effects of changes n the elastcty of labour supply. A zero supply elastcty s gven by the Fxed Labour Supply closure, and an nfnte elastcty by mposng a fxed real wage (the Real Wage Resstance closure). All other parameters and functonal forms are unchanged. The results are presented n Fgure 3. They correspond to those for the model n secton 2 (for Γ 2 < 0). The multpler s - for the zero elastcty case and approaches the EB multpler as the labour supply elastcty ncreases. We next consder the effects of changes n the elastcty of substtuton n producton of non-traded value added, whch nfluences the value of Γ 2 n the model of secton 2. The results are presented n Fgure 4. As the elastcty of substtuton n non-traded ncreases, the employment multpler declnes and eventually becomes negatve. Ths agan corresponds to the results n secton 2 (Fgure ) for negatve values of Γ 2, snce there s a negatve relatonshp between Γ 2 and ζ 2 n the smple model.

20 0.4 Fgure 3: Varatons n Multpler for Changes Elastcty of Labour Supply Elastcty of Labour Supply Emp Fgure 4: Varatons n Multpler for Changes Non-Traded Elastcty of Substtuton Emp Elastcty of Substtuton Fgure 5: Varatons n Multpler for Changes n Traded Sec Armngton Elastcty Emp Elastcty of Substtuton Emp -0 Fgure 6: Varatons n Multpler for Changes Traded Sector Elastcty of Substtuton Elastcty of Substtuton

21 The above results are broadly n lne wth those for the smple model of secton 2. The addtonal sectoral lnkages ncluded n AMOS do not appear to greatly nfluence the relatonshp between the employment multpler and the varables wthn the multpler expresson, at least for negatve values values of Γ 2. Rather dfferent results arse, however, when we examne the relatonshp between the employment multpler and the sze of the traded sector labour demand effect n AMOS. In our smple model, the varables whch determne the ntal effect of the subsdy on export sector labour demand ( η and ζ ) do not affect the sze of the multpler. Ths s not the case n AMOS, as can be seen from Fgures 5 and 6. Fgure 5 shows the relatonshp between the employment multpler and the traded sector Armngton elastcty n AMOS. The hgher s the Armngton elastcty, the hgher s the elastcty of demand for traded output. An ncrease n the Armngton elastcty, ceters parbus, gves a larger traded sector employment effect but a smaller non-traded employment effect due to the ncreased real wage. The multpler therefore falls. Fgure 6 llustrates the sze of the employment multpler for dfferent values of the elastcty of substtuton of producton n the traded sector. The most nterestng feature s the dscontnuty for values of the elastcty around.2. Ths result drectly reflects the addtonal lnkages ncluded n AMOS but not n our smple model. In the smple model sectoral spllovers occur only through labour market varables (wages and labour ncomes). If the subsdy has no effect on export sector labour demand, then t can have no effect on ether wages or labour ncome and so no effect on the non-traded sector. Thus, where Ψ = 0 ( η = ζ ) the export and non-traded employment effects and the multpler are all zero. In AMOS the presence of addtonal spllover mechansms (through the effect of the subsdy on captal ncomes, nvestment and ntermedate demands) mples that employment n the nontraded sector can vary even f traded employment s unaffected by the subsdy. The pattern observed n Fgure 6 reflects varatons n the multpler around the pont where the traded sector employment effect s zero, combned wth a postve effect on non-traded employment. The equalty of IO/EB and neoclasscal multplers for demand shocks under condtons of nfntely elastc factor demands has been wdely noted. 2 The analyss of Secton 2 and the above smulaton results suggest that the result s of broader applcaton. The mplcatons of ths result depends on the ratonale for perfectly elastc factor supples, n

22 partcular wth regard to labour. One possble nterpretaton s that the regonal labour market fals to clear due to wage-rgdty gvng rse to persstent unemployment. Labour supply may then be perfectly elastc n the short-run. There s, however, substantal evdence to suggest that regonal wages do respond to varatons n labour demand even n the presence of unemployment (Layard et al, 99; Blanchflower & Oswald, 994). An alternatve nterpretaton s that labour supply s perfectly elastc n the long-run as a result of mgraton behavour. Ths vew s emphassed by McGregor et al (996). We can llustrate the long-run nterpretaton usng multperod smulatons of AMOS wth a neoclasscal-type mgraton functon whch enforces a compensatng-dfferentals mgraton equlbrum n the long-run (Harrs & Todaro, 970; Hall, 970, 972). The multperod smulatons also ndcate the mportance of nvestment expendtures and the mplcatons of mperfectly-elastc captal supples n determnng short-run multplers. Fgure 7 shows the value of the non-traded employment multpler over a 60 perod smulaton of the model. 3 2 Fgure 7: Employment Multplers for Multperod Smula Emp Perod The sequencng of multperod solutons n AMOS mples fxed captal stocks n the frst perod. The effect of the captal subsdy under ths assumpton s very dfferent from when captal stocks are varable. Wth fxed captal stocks the man effect of the captal subsdy s to stmulate nvestment expendtures by the traded sector whch seeks to ncrease ts captal nputs. Ths produces a demand shock whch s not confned to the traded sector but s spread throughout the regon. The short-run effect of a demand shock s to rase prces. Ths tends to reduce sales of traded output and traded employment. The negatve multpler n perod therefore reflects a fall n traded employment and a rse n non-traded employment. Once new captal s n place, traded sector prces fall and output and employment grow n

23 both sectors. Employment effects are stll relatvely concentrated n the non-traded sectors so that the margnal multpler exceeds the average multpler. Over tme, however, the multpler converges to the long-run soluton wth nfntely elastc labour supples. In perod 60, the margnal multpler equals the EB/IO multpler (0.395). 5. CONCLUSIONS Ths paper has consdered the nature and extent of sectoral spllover effects assocated wth regonal captal subsdy polces. We began by questonng the approprateness of usng fxed sectoral multplers based on economc-base or nput-output models n estmatng the effects of regonal assstance on unassssted sectors and frms. The nature of factor subsdes, n partcular, would seem to argue for an approach whch explctly allowed for the effects of changes n relatve prces on the allocaton of expendtures and the pattern of factor demands. Our theoretcal analyss suggested consderable complexty n sectoral lnkages even n a hghly smplfed neoclasscal model. Both ths analyss and the computable general equlbrum analyss whch followed dd, however, suggest that IO/EB multplers may be approprate n an mportant specal case where factor supples are perfectly elastc. The most reasonable nterpretaton of ths specal case s as a long-run equlbrum poston wth labour mgraton. Ths s not generally how IO/EB multplers have been used n the evaluaton lterature, where they have generally been nterpreted as applyng over a much shorter tme-scale than the longrun result would mply. A lmted analyss of the tmng of multplers suggest that radcally dfferent results may apply n the short-run. Ths s an ssue to whch we ntend to return n future research.

24 NOTES For a bref hstory of regonal polcy n the UK see, for example, Armstrong & Taylor (993). 2 See the ex post evaluatons of regonal selectve assstance n Kng (990) and PA Cambrdge Economc Consultants Ltd (993) based on the offcal gudelnes presented by HM Treasury (99, 995). PA Cambrdge Economc Consultants, for example, use an employment multpler of 0.3, calculated by addng a consumpton multpler of 0. to a backward lnkage (nput-output) multpler of Captal subsdes have played a domnant role n UK regonal polcy n the past. At present regonal polcy n the UK nvolves project rather than captal assstance. It s not unreasonable to assume, however, that project-based assstance generally nvolves a captal subsdy element. We focus on pure captal subsdes for smplcty. 4 5 The fxed parameters assumpton mples that the producton technology s CES. Both captal and labour can be treated as ether moble or mmoble between sectors. In addton, the new verson of the model allows for a dsaggregaton between sklled and unsklled labour. The smulatons reported n Secton 4 under the long-run closure adopt the smplest two-factor case. The multperod smulaton has sectorally moble labour but mmoble captal wthn each perod The smulatons use default elastctes of substtuton of 0.3 n all sectors (Harrs, 989). The captal stock adjustment parameter s taken to be 0.3 n each sector. See Harrgan et al (992, 996). The procedure used n based on the Levenberg-Marquardt algorthm. See Harrgan et al (99). 0 Issues of the tmng of multplers wll be examned more fully by future research. In order to ad comparsons wth the analyss of secton 2 we set the elastcty of labour supply wth respect to the replacement rato to zero, and vary only the elastcty wth respect to the real consumpton wage. 2 The result s an extenson of Samuelson s (966) general non-substtuton theorem (Johansen, 972; Stgltz, 970). Ths nterpretaton of IO was orgnally formulated n the early 950s by Arrow (95), Cameron (95-2), Georgescu-Roegan (95), Koopmans (95) and Samuelson (95). Mutt (98) and Merrfeld (987, 990) note that the result obtans n ther model for other types of shocks. 3 Other features of the model specfcaton are as for the benchmark long-run smulaton reported n Table.

25 Appendx - AMOS The followng table (based on Harrgan et al, 996, Table ) captures the prncpal features of the AMOS model. The summary model gnores some detals of the tax and socal securty benefts system, and suppresses some model features such as the treatment of transport and dstrbuton margns, the dstncton between commodtes and actvtes, the mult-level producton functon specfcaton, and some of the mechansms through whch factor ncomes are transmtted to nsttutonal transactors. Equatons are presented n a general form snce AMOS permts consderable dscreton over functon forms for many equatons - n partcular producton and cost functons, labour supply and labour market clearng condtons, and export demands. Short-Run Equatons () Prce Determnaton p = p( wn, wk ) Long-Run (2) Wage Determnaton d w = w( L, cp) (3) Consumer Prce Index RUK RUK ROW cp = θ cp = θ p + θ p + θ p j j j j j ROW j = m, nmt, nt; j = m, nmt (4) Captal Supply s s s s K = ( d ) K + I K = K ( w, kp), t t,, t j j j j (5) Captal Prce Index RUK RUK ROW kp = γ p + γ p + γ p = m, nmt, nt; j = m, nmt (6) Labour Demand d d L = L ( Q, w, w ) n k (7) Captal Demand d d K = K ( Q, wn, wk ) (8) Labour Market clearng s d L = L = L (9) Captal Market clearng s d s d K = K K = K = K (0) User Cost of Captal uck = uck( kp, sk, d,, t ) j k ROW j 23

26 () Desred Captal Stock * K = K * ( Q, wn, uck ) (2) Investment Demand RUK I I p p p ROW d = (,,, bj I j ) for = m, nmt and j = m, nmt, nt j (3) Household Income d * I = λ ( K K ) + d K j I nt = b I d j j j = m, nmt, nt j j j Y = Ψ Lw + Ψ k c K w k j _ + T d I j = d jk Y = Ψ Lw + c Ψ Kw k k j _ + T (4) Commodty demand Q = C + I + G + X RUK ROW (5) Consumpton demand C = C ( p, p, p, Y, cp) = m, nmt C = C ( Y, cp) (6) Government Demand G G nt nt = _ RUK ROW RUK ROW (7) Export Demand X = X ( p, p, p, D, D ) = m, nmt X nt = 0 Notaton: Actvty-Commodtes m = Manufacturng nmt = Non-Manufacturng Traded nt = Non-Traded Transactors RUK = ROW = Rest of the UK Rest of the World Functons p(.) Cost functon (CES, Cobb-Douglas, or Leontef) K s (.), L s (.) Factor supply equatons K d (.), L d (.) Factor demand equatons (CES, Cobb-Douglas, or Leontef) C(.), I(.), X(.) Armngton consumpton, nvestment and export demand functons (wth CES aggregaton). 24

27 Varables b Elements of Captal matrx d Physcal deprecaton of captal stock cp, kp consumer and captal prce ndces p prce of commodty/actvty output uck user cost of captal s k captal subsdy rate dscount rate t company tax rate w n, w k Wage, captal rental rate C Consumpton D Exogenous export demand G Government demand for local goods I Investment demand for local goods I d Investment demand by actvty K d, K s, K*, K Captal demand, Captal supply, Desred captal stock and captal employment L d, L s, L Labour demand, Labour supply and labour employment Q Commodty/actvty output T Nomnal transfers from outwth the regon X Exports Y Household nomnal ncome Ψ Share of factor ncome retaned n regon θ Consumpton weghts γ Captal weghts l Captal stock adjustment speed parameter 25

28 REFERENCES Armngton, P.S. (969) A theory of demand for products dstngushed by place of producton, Internatonal Monetary Fund Staff Papers, 6: Armstrong, H. & Taylor, J. (993) Regonal Economcs and Polcy, 2nd. ed., Harvester Wheatsheaf, London. Arrow, K.J. (95) Alternatve Proof of the Substtuton Theorem for Leontef Models n the General Case, n Koopmans, T.C. (ed.) Actvty Analyss of Producton and Allocaton, Yale Unversty Press, New York. Blanchflower, D.G. & Oswald, A.J. (994) The Wage Curve, MIT Press, Cambrdge, Massachusetts. Cameron, B. (95-52) The constructon of the Leontef System, Revew of Economc Studes, 9: Georgescu-Roegan, N. (95) Some propertes of a generalsed Leontef model, n Koopmans, T.C. (ed.) Actvty Analyss of Producton and Allocaton, Yale Unversty Press, New York. Hall, R.E. (970) Why s the unemployment rate so hgh at full employment?, Brookngs Papers on Economc Actvty, 3: Hall, R.E. (972) Turnover n the Labor Force, Brookngs Papers on Economc Actvty, 3: Harberger, A.C. (962) The ncdence of the corporaton ncome tax, Journal of Poltcal Economy, 70: Harrgan, F., McGregor, P.G., Dourmashkn, N., Perman, R., Swales, J.K. & Yn, Y.P. (99) AMOS: A macro-mcro model of Scotland, Economc Modellng, 8: Harrgan, F., McGregor, P.G., Swales, J.K. & Dourmashkn, N. (992) Imperfect competton n regonal labour markets: A computable general equlbrum analyss, Envronment and Plannng, A, 24: Harrgan, F., McGregor, P.G. & Swales, J.K. (996) The system-wde mpact on the recpent regon of a regonal labour subsdy, forthcomng n Oxford Economc Papers. 26