STRATHCLYDE DISCUSSION PAPERS IN ECONOMICS. The Impact of the Barnett Formula on the Scottish Economy: A General Equilibrium Analysis

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1 STRATHCLYDE DISCUSSION PAPERS IN ECONOMICS The Impact of the Barnett Formula on the Scottsh Economy: A General Equlbrum Analyss BY Lnda Ferguson, Davd Learmonth, Peter G McGregor, J Km Swales and Karen Turner No DEPARTMENT OF ECONOMICS UNIVERSITY OF STRATHCLYDE GLASGOW

2 The Impact of the Barnett Formula on the Scottsh Economy: A General Equlbrum Analyss* 21st March 2003 by Lnda Ferguson** Davd Learmonth** Peter G McGregor+ J Km Swales** and Karen Turner** ** Fraser of Allander Insttute, Department of Economcs, Unversty of Strathclyde + Department of Economcs, Unversty of Strathclyde * The authors acknowledge the support of the ESRC (grant L ) under the Devoluton and Consttutonal Change Research Programme. We are grateful to Alex Chrste, Scottsh Economc Polcy Network, for dscussons on a number of aspects of the Barnett formula. We are also ndebted to partcpants n semnars at Aberdeen and St. Andrews Unverstes; the Internatonal Regonal Scence Assocaton Annual Conference, Brtsh and Irsh Secton, Brghton, August 2002 and Davd Hume Insttute, December,

3 1. Introducton The Barnett formula s the offcal bass upon whch publc funds are allocated to the UK devolved terrtores - Northern Ireland, Scotland and Wales - for those parts of the budget that are admnstered locally. In the past, actual allocatons have dffered markedly from the Barnett benchmarks. However, the recent moves towards devoluton n the UK have both sgnfcantly ncreased the level of nterest n the formula and further fuelled the controversy surroundng ts mplcatons for the regons of the UK. The exstng lterature on the Barnett formula has mproves our understandng of ts operaton. However, ths lterature s extremely crcumscrbed, focusng prmarly on the equty mplcatons of the spatal changes to government expendture per head that would accompany the strct mposton of the Barnett formula under varous scenaros. There has been no correspondng analyss of the lkely spatal mpact on wder economc and demographc varables. Ths s despte the fact that the Barnett formula effectvely determnes the geographc dstrbuton of a sgnfcant element of exogenous demand n the devolved terrtores. In ths paper we begn to redress ths mbalance. In ths paper we attempt to provde theoretcal and emprcal analyses of the systemwde effects of the operaton of the Barnett formula n one of the devolved regons of the UK, Scotland. We use a sectorally dsaggregated verson of the Layard et al (1991) regonal model. The emprcal results are derved through numercal smulaton wth an approprately parametersed verson of our Scottsh computable general equlbrum (CGE) model, AMOS. Further we employ ths analyss to explore the mportance of the recent swtch to the regular up-datng of the populaton weghts n the Barnett formula. Secton 2 presents a schematc account of how the Barnett formula allocates the devolved budgets and Secton 3 brefly descrbes the way n whch the operaton of the formula has changed over tme. Secton 4 defnes the noton of a Barnett equlbrum. Ths s a dstrbuton of publc expendture whch, f reached, would be 2

4 subsequently replcated through the acton of the Barnett mechansm. In ths secton we focus partcularly on the nteracton between populaton and publc expendture mpled by the acton of the Barnett formula together wth a flow-equlbrum mgraton process. In Secton 5 we outlne the Scottsh Computable General Equlbrum model, AMOS, whch s used to smulate Barnett equlbra over a number of conceptual tme perods. Secton 6 reports the smulaton results and Secton 7 s a short concluson. 2. Devolved Budgets under Barnett For our purposes, t s suffcent to know that the Barnett formula s used to determne any ncrease (or decrease) to the assgned budgets of the devolved authortes. These cover those elements of UK Department Expendture Lmts (DEL) for whch there s equvalent expendture n the devolved authortes. DEL covers spendng under headngs such as Health, Socal Work, and Educaton n the devolved authortes. It does not fnance spendng on departmental programmes whose provson s ncluded n the vote of the UK Parlament, such as, for example, the Common Agrcultural Polcy or spendng on teachers pensons. 1 In modellng the mplcatons for aggregate economc actvty n Scotland of the strct mplementaton of the Barnett formula, we focus on the consequences for the level of government fnal demand n Scotland and the subsequent product and labour market mpacts. In these smulaton exercses we take 1999 as our base year. 2 In that year, 77% of the government fnal demand dentfed n the Scottsh Input-Output accounts s funded from the assgned budget, that s DEL expendtures. The remander conssts of fnal demands attrbutable to programmes reserved to the UK government or fnanced by local authorty expendtures. The Barnett formula allocates a populaton-based share of any ncrease (or decrease) n comparable Englsh DEL expendture to the devolved authortes of the UK. At 1 More detal of the dfferent publc spendng aggregates that apply to the devolved authortes s gven n Appendx s the last year for whch Scottsh Input-Output accounts are avalable. These accounts are requred to parameterse our model. 3

5 present the formula operates n nomnal terms. Therefore, n so far as the Barnett formula s scrupulously adhered to, margnal changes n DEL n Scotland are determned by the dfference equaton: G = α G (1) St, t Et, where: G S,t (G E,t ) s the nomnal level of DEL expendture n Scotland (England) n perod t, s the frst dfference operator, and α t s a parameter based upon the rato of Scottsh to Englsh populaton. A factor central to the debate concernng the operaton of the Barnett formula n Scotland s that at present the proporton of UK DEL expendture that s allocated to Scotland s much greater than Scotland s populaton share. 3 Therefore under strct adherence to the Barnett formula, the margnal allocaton of UK DEL expendture to Scotland s lower than ts average allocaton. Much of the Scottsh lterature surroundng the Barnett formula therefore focuses on the fact that wth ncreasng nomnal publc expendture n England, the proportonate publc expendture advantage at present enjoyed by Scots wll declne. Ths s the so-called Barnett squeeze (see, for example, Bell et al 1996; Cuthbert, 2001; Heald, 1996; Heald and McLeod, 2002; Kay, 1998; McCrone, 1999; Mdwnter, 2000, 2002; Twgger 1998.) 3. A Hstory of the Barnett Formula The account so far gves the prncples underlyng the operaton of the Barnett formula. However, the detals have changed over tme. Ths partcularly apples to the populaton weghts used n the formula, that s the populaton numbers that determne the value of the parameter α t n equaton (1). In the 1960s and early 1970s, publc expendture plans for Scotland, Wales and Northern Ireland were determned by the same departmental barganng that characterses the rest of spendng allocatons among Whtehall departments (HM 3 For example, n the md 1970s HM Treasury (1979) estmated Scotland s per capta publc expendture to be 22% hgher than the correspondng Englsh fgure. 4

6 Treasury, 1997a). The Barnett formula - named after the then Chef Secretary of the Treasury - was used for the frst tme n 1978 n Scotland and two years later for Northern Ireland and Wales, and has been n contnuous use ever snce. 4 The populaton proportons used at the tme of the formula's ntal mplementaton were estmates for Under the Barnett formula Scotland then receved 10/85 ths of any ncrease or decrease n comparable Englsh programmes (HM Treasury, 1999). There have been a number of subsequent changes to the Barnett allocaton mechansm. Frst, up untl 1985 the formula was appled n real terms wth fgures rollng forward from one year to another wth an n-bult allowance for nflaton. However, post-1985 expendture changes have been allocated n nomnal terms only (UK Treasury, 1999). Second, n 1992, Mchael Portllo, as Chef Secretary to the Treasury, revsed the formula to reflect the populaton fgures gven n the 1991 Census. Scotland s share n the UK populaton had fallen, so that margnal change n Scottsh nomnal DEL for any change n margnal Englsh DEL - the value of α t n equaton 1 - was reduced from 11.76% to 10.66% (McCrone, 1999). Fnally n 1997 a rather more fundamental modfcaton was ntroduced. Chef Secretary to the Treasury, Alastar Darlng, commtted the government to an annual revson of the Barnett populaton weghts, based on the latest populaton estmates for England, Scotland and Wales, publshed each year by Natonal Statstcs (HM Treasury, 1997b). Ths was to take effect from It s mportant to say that durng much of the perod snce 1979, bypass and adjustment of non-formula-drven expendtures have meant that actual DEL expendtures n Scotland have dffered, to Scotland s advantage, from those whch would have emerged from the strct applcaton of the Barnett formula (Mdwnter, 2002). However, the formula has been accepted as the bass for determnng the DEL of the Scottsh Parlament (and the budgets of other devolved terrtores). Further, the 4 The formulac approach to allocatng publc expendture between the countres of the UK goes back to Chancellor Goschen n He ntroduced a formula to allocate probate dutes between countres n support of local government expendture, based on each country's overall proportonate contrbuton to the Exchequer. Ths formula was also used as a bass for allocatng some elements of publc expendture (e.g. educaton grants). 5

7 recent concern wth adjustng the formula populaton weghts, together wth the greater transparency produced by devoluton, has led to a belef that the Barnett formula wll play a more central role n the actual allocaton n the future (Goude, 2003). However, the Barnett formula takes no account of the relatve need between Scotland and England, apart from ther relatve populaton szes. Alternatve methods of allocatng expendture between regons have been nvestgated usng the needs assessment approach (Chrste, 2002). Ths takes the vew that the budget to the Scottsh Executve should reflect the dfferng expendture needs of the Scottsh people as aganst ther Englsh counterparts. Scotland's hgher morbdty rates, sparse populatons n remote areas and greater poverty are thought to warrant hgher expendture (Mdwnter, 2000). In the md 1970s, the Treasury led an nterdepartmental study to assess the level of per capta spendng n Scotland and Wales that would be requred n order to provde a level of servces comparable to that n England (HM Treasury, 1979). It estmated a requred level of Scottsh expendture per head of 16% above the correspondng Englsh level. Ths compared wth the actual fgure that showed Scottsh expendture per head 22% hgher than the correspondng Englsh fgure. It s thought that the Barnett mechansm was ntroduced n order to affect a short-run adjustment towards these needs based fgures. 4. Barnett Equlbra In the analyss n ths secton we focus on the mpact of the operaton of the Barnett formula wthn a sngle devolved terrtory. We take the case of Scotland but the analyss can be replcated for any other regon. Exstng work on the Barnett formula s organsed around the followng relatonshp: 5 The populaton proportons used n the 1998 Comprehensve Spendng Revew related to 1996 mdyear populaton estmates that reported Scotland s populaton as 10.45% of the Englsh value. 6

8 G G / P St, St, / P Et, Et, = BG ( 0, G 0,..., G, P 0,..., P, P 0,..., P ) (2) S, E, E, t E, E, t S, S, t where P s populaton. Ths work attempts to reveal the evoluton of Scottsh DEL per capta expendture under a strct Barnett regme and alternatve scenaros concernng the exogenous growth n nomnal Englsh DEL and exogenous populaton changes. As such, ths analyss smply charts the publc fnance mplcatons of the operaton of the Barnett allocaton formula and requres no addtonal nformaton. In partcular, where the relevant explanatory varables are taken to be exogenous, the results are wholly ndependent of other economc varables, such as the level of actvty, output or employment. The analyss s therefore rather restrcted. Perhaps more mportantly, t s also conceptually flawed f the changes n devolved publc expendture have drect demographc mplcatons. Such a lnk operates most straghtforwardly through mgraton. If changes n aggregate economc actvty brought about through changes n government expendture nfluence mgraton flows, then populaton becomes endogenous. In ths paper we wsh to model the effect of the strct applcaton of varants of the Barnett formula on economc actvty through ts mpact on devolved government expendture. We lmt our analyss to the mpact on a sngle regon and adopt the small-regon assumpton. Ths takes the regon to be so small relatve to the rest of the economy that changes n the regon s actvty, fscal arrangements and populaton do not have mpacts on the rest of the naton large enough for there to be perceptble postve or negatve feedback to the regon tself. Further, we do not track the perod by perod changes. Rather we focus on the economc mplcatons of achevng Barnett equlbra. We desgnate a Barnett equlbrum to be a spatal allocaton pattern of devolved DEL expendture whch, once reached, would be replcated by the subsequent operaton of the Barnett formula. 7

9 Where the Barnett populaton weghts, taken at tme perod 0, are fxed, then the Barnett equlbrum s very straghtforward to determne. In the two-regon case, n tme perod t the Barnett equlbrum rato of DEL government expendture n the two regons, B F, where the F superscrpt stands for fxed populaton weghts, s gven as: B F GSt, = = G Et, P P S, 0 E, 0 (3) Further, ths equlbrum s stable n the sense that n perods of ncreasng nomnal government expendture, the operaton of the Barnett formula wll drve the dstrbuton towards the Barnett equlbrum, ndependently of the ntal dstrbuton. That s to say: G G St, Et, B F asg Et, Our concern s to quantfy the mplcatons of achevng the Barnett equlbrum on the level and composton of actvty n Scotland, A S. In order to solate the mpact of the adjustment n government expendture requred to acheve the Barnett equlbrum, we keep all other exogenous varables fxed. Essentally we mpose the ceters parbus assumpton. As noted above, we are also operatng wth a stand-alone regonal model that gnores nter-regonal feedback effects. These combned exogenety assumptons mean that the analyss smply focuses on the mpact of change n publc expendture n Scotland n a straghtforward comparatve statc manner. Under these crcumstances, economc actvty n Scotland s derved as: F A = A ( A, R, p, z, B ) (4) S S E E E S In ths analyss, we hold constant: Englsh economc actvty (A E ), real government expendture (R E ) and prces (p E ); and Scottsh exogenous demands (z S ) - prmarly 8

10 export demands. But Scottsh nomnal publc expendture s determned by the Barnett equlbrum (B F ). Whlst the exogenety assumptons mposed n equaton (4) gve an approprate focus to the smulatons, how can they be justfed? In partcular, we know that nomnal government expendture n England (and also Scotland) must rse for a Barnett equlbrum to be reached wth exstng populaton weghts. Wll these ncreases not automatcally volate the ceters parbus assumptons that we have mposed? The approach we adopt can be motvated n two ways. Frst, equaton (4) could be thought of as resultng from purely nomnal changes n the UK economy, wth no changes n real varables asde from Scottsh publc expendture. As long as the two economes are homogeneous of degree zero n prces ths nterpretaton s vald. A second nterpretaton for equaton (4) s that t shows the proportonate devatons from the counterfactual that would occur n the Scottsh economy f the Barnett equlbrum were mposed n a UK economy experencng lnear expanson, wth all real exogenous varables ncreasng at the same rate. In ths case, provded that the economes are lnear homogeneous n the real exogenous varables, ths s a reasonable nterpretaton. Up to now we have been consderng the applcaton of the Barnett formula wth fxed populaton weghts. However, as explaned n the prevous secton, under the 1997 Darlng amendment, the populaton weghts used to calculate margnal nomnal changes n DEL publc expendture are, f requred, updated to reflect any changes n the populaton levels. Under ths formulaton a necessary condton for the economy to be n a Barnett equlbrum n tme perod t would be that: B V GSt, = = G Et, P P St, Et, (5) where B V represents the Barnett equlbrum rato where the formula has varable populaton weghts (that s, wth the full updatng of those weghts). Equaton (5) 9

11 ndcates that n ths case, Barnett equlbrum mples that DEL nomnal publc expendture per head wll be equalsed among devolved terrtores. In the sngle-regon analyss, wth Englsh nomnal government expendture, prces and populaton held constant, equaton (5) mples: G S = βp S (6) where β = G PE E. Equaton (6) captures the equlbrum operaton of the Barnett mechansm n the allocaton of expendture. It s shown as the Barnett dstrbuton lne B V n Fgure 1. But wth populaton endogenous, there wll be a second relatonshp between Scottsh populaton and DEL nomnal expendture that operates through the requrement for zero net mgraton n Barnett equlbrum. That s to say, for a gven Scottsh DEL nomnal expendture, there wll be an equlbrum populaton level needed so as to generate no desre for net out- or n-mgraton. Ths can be expressed as: PS = PS( GS, AE, PE, pe, zs) (7) Expresson (7) dentfes the stable Scottsh populaton level supported by a gven level of nomnal DEL nomnal expendture wth Englsh actvty, prces and populaton fxed and wth other elements of Scottsh fnal demand constant at ther ntal values. For equaton (7) we expect P S ( 0) > 0 and dp S > 0. Ths s dg represented as the equlbrum populaton lne, P S, n Fgure 1. Smultaneously solvng equatons (6) and (7) generates the varable-weght Barnett equlbrum populaton and nomnal Government expendtures. Ths s shown dagrammatcally as the ntersecton, E, between the lnes B V and M n Fgure 1. We then determne the level of Scottsh actvty, gven the varable-weght Barnett equlbrum DEL expendture. S 10

12 AS = AS( AE, PE, pe, zs, β ) (8) In consderng the stablty of the varable-weght Barnett equlbrum, Fgure 1 suggests that f there s one or more equlbra, then at least one wll be stable n terms of the equlbrum relatonshps dentfed here. The Barnett dstrbuton curve, B V must cut the equlbrum populaton curve M from below. If the ntal government allocaton s above G V* S, then the subsequent populaton adjustment s nsuffcent to mantan that nomnal government expendture. Smlarly, f the ntal populaton s above P * S, subsequent changes n the allocaton of nomnal expendtures are not large enough to mantan ths populaton. The varable weght Barnett equlbrum s therefore stable, subject to exogenous shocks. The Barnett dstrbuton and stable populaton curves llustrated n Fgure 1 can be used to dentfy the mplcatons for nomnal DEL expendture and populaton of mposng Barnett equlbra. Fgure 2 s agan drawn n nomnal DEL expendture (G) and populaton (P) space. The ntal equlbrum that s before the ntroducton of the Barnett formula - s at A, wth populaton and DEL expendture P 0, G 0. There are two stable populaton curves, M L and M M that pass through pont A. These curves represent the long- and medum-run relatonshps between populaton and nomnal DEL mposed va the zero net mgraton constrant. We expect populaton wll be more senstve to changes n DEL expendtures n the long run, when captal stocks are allowed to fully adjust, than n the medum run, when they are assumed fxed. Captal fxty, together wth prce flexblty, cushons the mpact on populaton. As DEL expendture falls, prces fall as the captal rental rates declne. Ths means that the real expendture reducton s less than the nomnal reducton. Also the unchanged real wage requred by the zero net mgraton constrant mples a fall n the nomnal wage and therefore ncreased compettveness and potental crowdng n for some sectors. M L s therefore steeper than M S. 11

13 Barnett equlbra wth fxed populaton weghts Imposng the Barnett equlbrum mples for Scotland a reducton n DEL expendture. Begn wth the Barnett equlbrum wth fxed weghts. The new nomnal DEL expendture would be the ntal populaton tmes the Englsh per capta nomnal DEL, β. Wth fxed populaton weghts, ths gves a new Scottsh nomnal DEL expendture that s ndependent of subsequent changes n populaton. It s represented n Fgure 2 by the vertcal lne at B F. In the short run, when populaton and captal stocks are fxed, the equlbrum s at B. Populaton s at ts orgnal value P 0 and the nomnal DEL expendture falls to G F. The reducton n nomnal government expendture wth populaton and captal stocks fxed mples that the unemployment rate wll rse. Wth the regonal barganng functon adopted n ths varant of the AMOS model (Layard et al, 1991), Scottsh real wage wll fall. Captal rental rates wll also tend to fall as commodty demand falls. However, these prce reductons wll cushon the declne n Scottsh GDP because they generate crowdng n of actvty as a consequence of ncreased Scottsh prce compettveness. In the medum run, where populaton s allowed to fully adjust but captal stocks held fxed, the new equlbrum s dentfed by pont C n Fgure 2. Gven the flowequlbrum regonal net mgraton functon we use here (Layard et al, 1991), together wth the regonal barganng functon, out-mgraton wll reduce the Scottsh populaton up to the pont where the orgnal unemployment rate and real wage are renstated (McGregor et al., 1995). The populaton adjustment lmts the fall n the nomnal wage generated by the fall n government expendture, reducng crowdng n. The negatve mpact on GDP s therefore larger n ths case. In the long run, wth full captal adjustment, the populaton declne s even greater. In ths case the Barnett equlbrum s at D wth populaton P F L. Ths represents the Input-Output adjustment to the reduced government expendture (McGregor et al, 12

14 1996). 6 Output n all sectors wll fall wth a correspondng proportonate reducton n employment. Because the zero net mgraton condton mples no change n the unemployment rate, the proportonate fall n populaton wll equal the proportonate fall n total employment. Barnett equlbra wth varable (constantly up-dated) populaton weghts In Fgure 2, at pont B the Scottsh per capta DEL expendture equals the ntal Englsh fgure. If there s to be constant updatng of the Barnett weghts, the equlbra must le on the straght lne from the orgn through B. Ths s smply a representaton of equaton (6) and the slope of the lne s 1 β. In the short run there s no populaton change, therefore the ssue of updatng the weghts n the Barnett formula smply does not arse. However, n the medum and long run, the adjustment of the stable populaton level to changes n nomnal DEL expendture wll mean that unless the weghts are amended, Barnett equlbrum DEL expendture per capta wll contnue to vary across space. In the medum run wthout correctons to the weghts the equlbrum s at C, wth populaton and DEL nomnal expendture P F M and G F respectvely. Adjustng the weghts leads to lower DEL expendture but also further falls n populaton and DEL expendture as part of a downward multpler process. The new equlbrum s at E, where populaton and DEL expendture stands at P V M and G V M. A smlar relatonshp s apparent n the long-run adjustment. Wth a full adjustment of the populaton weghts, the Barnett equlbrum shfts from D to F. From nspecton of Fgure 2, t s clear that the expected adjustment to populaton as a result of updatng the Barnett weghts wll be larger n the long run than the medum run. Populaton s more responsve to changes n DEL expendture n the long run, so that the multpler effects wll be larger. 6 The analytcal characterstcs of the medum- and long-run results are dscussed n greater detal n Secton 5. 13

15 Needs assessment We represent the mpact of an allocaton formula based upon a needs assessment n the followng way. Under a needs assessment we take real Scottsh DEL expendture to be: G N S = βφp S (9) where β s defned as for equaton (6) as the Englsh DEL expendture per capta and φ s the needs ndex whch reflects dfferences n needs per capta and ntal dfferences n the cost of provdng the comparable servces n Scotland and England. If φ > 1, then Scotland has a greater per capta need for DEL expendture than England. In the case of the needs assessment, we are assumng another change n the publc expendture allocaton process. Ths s that expendture wll be determned n real terms, rather than nomnal terms as wth the Barnett formula. The analyss of the mpact of a needs assessment allocaton s very smlar to that of the populaton-up-dated Barnett formula. Equaton (9) wll be represented as a straght lne through the orgn n the same way as the updated Barnett formula allocaton s captured n Fgures 1 and 2, except that real, rather than nomnal, DEL expendture wll be on the vertcal axs. The equlbrum wll be where the stable populaton lne cuts ths needs assessment lne. The multpler mpacts runnng from a change n DEL expendture to a change n populaton to further changes n DEL expendture operates here too. However, because Scotland would be expected to have a value of φ > 1, the needs assessment lne wll be less steeply sloped than the populaton up-dated Barnett equlbrum lne. It s thought lkely that a needs assessment would dentfy a real DEL per capta expendture for Scotland above the average for England, but less than the present actual level. If ths s so, we would expect the mpact of the downward adjustment on Scotland s populaton and economc actvty to be less than for the varable-weghts Barnett equlbrum. Ths s unambguously so for the long-run equlbrum where 14

16 prces do not change so that there s no dstncton between real and nomnal expendture changes. 5. AMOS: the numercal verson of the regonal Layard, Nckell and Jackman model We here outlne the numercal, mult-sectoral, varant of the Layard et al. (1991) regonal general equlbrum model employed n producng the smulaton results reported n ths paper. Ths model s captured by a partcular confguraton of the AMOS model, a computable general equlbrum (CGE) modellng framework that s parametersed on data from a UK regon, Scotland. 7 A very bref descrpton s presented n ths secton: more detal s avalable n Appendx 2 and a full lstng of an earler vntage of the AMOS model s provded n Harrgan et al (1991). The current verson of AMOS has 3 transactor groups, namely households, corporatons, and government; 8 25 commodtes and actvtes and two exogenous external transactor groups (RUK and ROW). Throughout ths paper commodty markets are taken to be compettve. 9 We do not explctly model fnancal flows, our assumpton beng that Scotland s a prce-taker n compettve UK fnancal markets and, under the small open economy assumpton, the Bank of England s Monetary Polcy Commttee s nterest-rate-settng decsons are taken to be exogenous to Scotland. Producton s determned through cost mnmsaton wth mult-level producton functons. These are generally of a CES form but wth Leontef and Cobb-Douglas avalable as specal cases. For smplcty, all domestc ntermedate transactons are assumed to be Leontef n ths paper. Otherwse we assume CES technology (notably 7 AMOS s an acronym for A Macro-mcro model Of Scotland. For revews of CGE modellng see Greenaway et al, (1993) and Partrdge and Rckman (1998). 8 At present, AMOS treats Scotland as a self-governng economy, n the sense that there s only one consoldated government sector. Central government actvty s parttoned to Scotland and combned wth local government actvty. Ths s adequate for the present paper but a more sophstcated treatment of the publc sector s part of the work plan under the ESRC Devoluton project. 9 Ths assumpton s also made for the regonal model n Layard et al. (1991). 15

17 for the producton of value-added from captal and labour servces) wth "best guess" elastctes of substtuton of 0.3 (Harrs, 1989). There are four major components of fnal demand: consumpton, nvestment, exports and government expendture. Of these, consumpton s a lnear homogeneous functon of real dsposable ncome. Exports (and mports) are generally determned va an Armngton lnk (Armngton, 1969) and are therefore relatve-prce senstve wth trade substtuton elastctes of 2.0 (Gbson, 1990). Nomnal government expendture n Scotland s taken to be exogenous and the polcy shocks nvolve changes to ths varable. Of course when we have full updatng of the Barnett formula there s a degree of endogenety n that we lnk DEL government nomnal expendture to the populaton level. Investment s ntally set equal to deprecaton although, as explaned later n ths secton, n some closures captal stock s endogenous. In all of the smulatons reported n ths paper we mpose a sngle Scottsh labour market charactersed by perfect sectoral moblty. In general we explore the consequences of wages beng subject to a barganng functon n whch the regonal real consumpton wage s drectly related to workers barganng power, and therefore nversely to the regonal unemployment rate (Mnford et al, 1994). Ths hypothess has receved consderable support n the recent past from a number of authors. Here, however, we take the barganng functon from the regonal econometrc work reported by Layard et al. (1991): w, = a u, w, 1 (10) st st st where w s and u s are the natural logarthms of the Scottsh real consumpton wage and the unemployment rate respectvely, t s the tme subscrpt and a s a calbrated parameter. 10 Emprcal support for ths wage curve specfcaton s now wdespread, even n a regonal context (Blanchflower and Oswald 1994). 10 The calbraton s made so that the model, together wth the set of exogenous varables, wll recreate the base year data set. Ths calbrated parameter does not nfluence smulaton outputs, but the assumpton of ntal equlbrum s, of course, mportant. 16

18 The only excepton to ths treatment of the labour market occurs n the senstvty analyss reported n Secton 6. Here we explore the consequences of a natonal barganng system under whch small open regons face a natonally determned wage. Essentally ths mples that the regon s charactersed by a fxed nomnal wage rate, a labour-market closure that has been very wdely appled n tradtonal regonal macroeconomc modellng. We report the results of smulatons under three conceptual tme ntervals: the short, medum and long runs. In the short run, populaton and all sectoral captal stocks are fxed. In the medum run, all sectoral captal stocks reman constant, but populaton s allowed to adjust fully. In the long run, adjustments of both captal and populaton stocks are complete. The populaton adjustment s drven by a relatonshp whereby Scottsh net mgraton s postvely related to the real wage dfferental, and negatvely to the unemployment rate dfferental, wth the rest of the UK (RUK). Ths varant of the Harrs and Todaro (1970) model s commonly employed n studes of US mgraton (e.g. Greenwood et al, 1991; Treyz et al, 1993). It s parametersed here from the econometrcally estmated model reported n Layard et al. (1991): m= b 008. ( u u ) ( w w ) (11) s r s r where: m s the net n-mgraton rate (as a proporton of the ndgenous populaton); w r and u r are the natural logarthms of the RUK real consumpton wage and unemployment rates and b s a calbrated parameter. 11 Full populaton adjustment mples a change n the populaton, wth the attendant changes n the unemployment rate and consequently the real wage rate, to the pont where net mgraton falls to zero. Therefore settng m = 0 n equaton (11) generates the followng zero-net-mgraton relatonshp between the wage and unemployment rate: 17

19 b ws = wr ( us ur) (12) The Scottsh populaton s ntally assumed to be n equlbrum. Combnng equatons (10) and (12) means that wth unchanged values for the RUK real wage and unemployment rate, populaton equlbrum wll renstate the Scottsh ntal real wage and unemployment rate (McGregor et al, 1995). In the long run, both populaton and captal stocks are optmally adjusted. In the case of captal, ths means that the actual and desred captal stocks are equated, so that the rsk-adjusted captal rental rate n each sector equals the user cost of captal. Agan we assume the Scottsh economy to be ntally n long-run equlbrum. Wth all the labour market closures adopted n ths paper, renstatng long-run equlbrum n the face a demand dsturbance produces no change n prces, the real wage or the unemployment rate. The economy acts as a populaton-endogenous Input-Output system (McGregor et al, 1996). Therefore the equlbrum populaton relatonshp - dentfed n the prevous secton - between nomnal government expendture and the populaton level s represented, n ths case, by a straght lne. 6. Smulatng Barnett equlbra Smulaton strategy Both our theoretcal analyss and emprcal model focus on the mpacts on the economy of Scotland of the mposton of a Barnett equlbrum n the determnaton of Scottsh publc expendture. As dscussed n the Secton 4, the smulatons are performed whlst holdng all other exogenous varables constant, so that the economc mpacts are measured relatve to the status quo. Aganst ths background we perform a number of numercal smulatons. 11 Agan, the calbrated parameter s to ensure populaton equlbrum (zero net mgraton) n the base year. 18

20 Frst we undertake core smulatons where economc mpacts are determned over alternatve tme perods. In these smulatons, all parameter values are set to ther best-guess values, wages are determned through the real-wage barganng mechansm and where mgraton s allowed t has a flow equlbrum form, drven by nterregonal varatons n the unemployment rate and the real wage. We calculate the effects of the Barnett formula beng appled wth both fxed (base-perod) or varable (constantly updated) populaton weghts. At present the Barnett formula operates n nomnal terms. In the AMOS model, Scottsh prces can dverge from RUK prces and they wll, n general, vary across dfferent tme perods. These prce changes are ncorporated nto the Scottsh government real-expendture adjustments mpled by the Barnett equlbra. As we note n Secton 3, some contrbutors to the debate have argued that the Barnett mechansm should be replaced by a needs-based allocatve system. We therefore have carred out a set of smulatons where Scottsh DEL expendture s determned by the last avalable offcal needs assessment for Scotland. Fnally, we perform a lmted amount of senstvty analyss. In partcular we consder the effect of replacng the regonal wth a natonal wage barganng mechansm and the mpact allowng full captal adjustment but no populaton adjustment. Core smulatons We consder the fxed- and varable-populaton-weght cases n turn. Barnett equlbra wth fxed populaton weghts Imposng the Barnett equlbrum mples for Scotland a reducton n DEL expendture. We begn wth the Barnett equlbrum wth fxed weghts. In ths case the new nomnal DEL expendture would be the Scottsh ntal populaton tmes the Englsh per capta nomnal DEL. Ths gves a new Scottsh nomnal DEL expendture that s entrely ndependent of subsequent changes n populaton. Recall from Fgure 2 n Secton 4 that n the short run ths produces a Barnett equlbrum at B: populaton s fxed at P 0 and the nomnal DEL expendture falls to G F. The smulaton results 19

21 reported n the frst column of Table 1 gve the accompanyng changes n GDP, employment, the unemployment rate, cp and real and nomnal wage. The smulaton results report the real-resource squeeze that accompanes the expendture squeeze. For each smulaton, our frst step s to dentfy the approprate real government expendture contracton that corresponds to the requred change n nomnal Scottsh DEL. For ths, two calculatons must be made. Frst, changes n the Scottsh consumer prce ndex (cp) need to be ncorporated, so as to convert the nomnal DEL expendture changes nto real terms. The adjustments take full account of the endogenety of the cp changes. Second, the real change n DEL expendture must be expressed as a proporton of total publc sector expendture n Scotland. Ths s the way the model accepts a shock to government expendture and the way n whch the publc expendture shocks are reported n ths secton. Note that ths means that any margnal changes to government DEL expendture are assumed to have the sectoral composton of average publc expendture. The short-run fxed-populaton-weghts smulaton results are gven n the frst column of Table 1. Note frst that the 17% reducton n nomnal DEL translates to a 10.65% reducton n real Scottsh government expendture. Ths contracton n government expendtures, mpled by contnued rgorous applcaton of the Barnett formula, would have sgnfcant negatve effects on the relatve prosperty of Scotland. Scottsh GDP falls by 1.27% and employment by 1.49%. There s an accompanyng large fall n the real wage as the unemployment rate rses. Fgure 3 llustrates the correspondng sectoral employment, value added and output mpacts. Note that n ths case, the overall contracton n actvty s focussed on the sectors n whch government expendture s concentrated Publc Admnstraton, Educaton Health and Socal Work, and Sewage and Refuse Dsposal. In all other sectors the reducton n the nomnal wage mproves Scottsh compettveness and crowds n actvty thereby stmulatng actvty and employment. For all sectors the proportonate change n employment, ether postvely or negatvely, s greater than the change n value added reflectng the short-run captal fxty. 20

22 In the medum run, the new fxed-populaton-weght Barnett equlbrum s dentfed by pont C n Fgure 2 ndcatng a negatve populaton adjustment. The smulaton results are reported n the second column of Table 1. As noted n Secton 4, the medum-run equlbrum wth the regonal barganng labour-market closure leads to the renstatement of the orgnal unemployment rate and real wage (McGregor et al., 1995). The populaton adjustment lmts the fall n the nomnal wage so that the extent of crowdng n s reduced. Scottsh GDP now falls by 1.75% and employment by 2.27%. Fgure 4 presents the sectorally dsaggregated results for the medum-run Barnett equlbrum wth the fxed populaton weghts. In ths case the reducton n actvty s no longer lmted to sectors domnated by publc sector demand. The much smaller reducton n the nomnal wage n ths case leads to a much reduced postve compettveness effect. Therefore the fall n ntermedate and consumpton demand now generates small reductons n actvty n a number of servce and utlty sectors such as Energy and Water, Wholesale and Retal, and Hotels, Restaurants and Caterng. In long-run equlbrum - that s where there s full captal adjustment - the populaton change assocated wth achevng the fxed-populaton-weght Barnett equlbrum s even greater. Ths s shown as pont D n Fgure 2, and the smulaton results assocated wth ths equlbrum are summarsed n Column 4 of Table 1. The real contractonary mpact on the Scottsh economy generated by the reducton n government demand s now renforced by reduced capacty, wth Scottsh GDP and employment fallng by 3.56% and 3.88% respectvely. Note that there are no changes n commodty prces or the nomnal wage. We therefore obtan, as expected, extended Input-Output results. However, because populaton s fully endogenous, the unemployment rate returns to ts orgnal level (McGregor et al, 1995, 1996). The Input-Output character of the results s mmedately apparent from the sectorally dsaggregated results presented n Fgure 5. In the long run all sectors contract. The explanaton s that n ths case nether the nomnal wage nor the captal rental rates are ultmately affected by changes n exogenous demand, so nether are any value added 21

23 or commodty prces. Therefore the entre mpact of the government expendture fall s on quanttes and no ncentve from the relatve cost sde leads sectors to change producton technques. Ths mples that all nputs adjust equ-proportonately wthn ndvdual sectors so that employment, value added and output all change by the same proportonate amount. Barnett equlbra wth varable (constantly up-dated) populaton weghts Over tme perods wthn whch the populaton s allowed to vary, the contractonary mpact on Scotland of the mposton of the Barnett equlbra s ncreased f the populaton weghts are constantly updated. In Fgure 2, the adopton of varable populaton weghts leads to the medum-run Barnett equlbrum movng from ponts C to E and the long-run equlbrum from D to F. In columns 3 and 5 of Table 1, we report the results from the smulatons that replcate these equlbra. The correspondng sectorally dsaggregated results are gven n Fgures 6 and 7. In each case the declne n real government expendture n Scotland s hgher than for the correspondng fxed-weght equlbrum. Smlarly the GDP, employment and populaton declne s greater. However, for smulatons over comparable tme ntervals, the qualtatve mpacts are smlar. These smulatons serve to emphasse the mportance of populaton up-datng n the operaton of the Barnett formula. Where regons are relatve losers from Barnett, populaton, up-datng wll further renforce that loss. Wth populaton up-datng, the Scottsh long-run Barnett equlbrum mples a level of GDP 4.61% below what t otherwse would have been, as compared to 3.56% wth fxed populaton weghts. Potentally the Darlng amendment has an mportant mpact on the dstrbuton of demand among the regons of the UK. In our long-run model closure t produces a contractonary effect that s nearly 30% greater than n the fxed-populaton-weghts case. Needs Assessment 22

24 There has been much nterest n the dea that the DEL devolved expendtures should be determned through some needs-based formula (Chrste, 2002). It s therefore of value to compare the real mpact of such a scheme as aganst the Barnett equlbrum. However, one problem s n determnng the precse form that a needs assessment would have. Here we take the last offcal needs assessment, made for 1977 (HM Treasury, 1979) that estmated the requred Scottsh DEL per capta expendture to be 16% hgher than the Englsh level. We have therefore adjusted the real Scottsh DEL per capta expendture to ths level and n Table 2 present the correspondng smulaton results for the short-, medum- and long-run closures as descrbed for Table 1. The key result here s that the 1999 Scottsh per capta DEL expendture s only slghtly hgher than the estmated needs-assessment level. Ths means that whlst the qualtatve characterstcs of the adjustments n Table 2 are smlar to those n Table 1, the absolute scale s much lower. Therefore even n the long run, wth full captal and populaton adjustment the reducton n GDP s only 0.29% and n employment and populaton 0.32%. Senstvty analyses Assumptons about the nature of both the wage barganng and mgraton behavour can have a sgnfcant mpact on the nature of the response to a Barnett-nduced contracton. We have seen n the results presented n Table 1 that the fall n the nomnal wage that accompanes the short- and medum-run Barnett equlbra ncreases compettveness and has, n tself, a stmulatng mpact on the regonal economy. But wth alternatve wage closures, where there s a degree of wage rgdty, such flexblty would be curtaled or non-exstent. In Table 3 we therefore explore the mpact of mposng Barnett fxed- and varableweght equlbra, but n ths case assumng natonal, rather than regonal, barganng whch as dscussed n Secton 5 mples a fxed (exogenously determned) nomnal wage. Ths alternatve assumpton about wage barganng has a major mpact n the short-run, causng GDP to contract by 1.99% as compared wth 1.27% n the regonal 23

25 barganng case. Ths dfferental mpact s less marked n the medum-run results. Ths s because regonal barganng combned wth full populaton adjustment mples that the real wage returns to ts orgnal level, mplyng a much smaller (0.87%) fall n the nomnal wage. Over the long run, for the Barnett equlbra, the structure of barganng makes no dfference. In both regonal and natonal barganng regmes Input-Output results preval over ths nterval and there are no prce, wage or unemployment rate changes. The regonal and natonal barganng smulaton results therefore converge. Populaton change, generated n the AMOS model through mgraton, has two man effects on the Barnett equlbra mpacts. The frst s that the populaton level drectly affects the change n DEL expendture snce the Darlng amendment and the subsequent contnuous updatng of the populaton weghts. Second, populaton change affects the unemployment rate that s assocated wth any change n DEL expendture. Where there s regonal barganng ths affects the real and nomnal wage and therefore compettveness. Where there s natonal barganng, the unemployment level has an mpact on beneft-funded consumpton. In the smulatons reported n Table 1, comparng the short- and medum-run results dentfes the addtonal mpact of allowng mgraton but holdng captal fxed for the regonal barganng closure. Table 3 presents the same results for the natonal barganng closure. Wth the results from the smulatons reported n Table 4, we can dentfy the mpact of allowng mgraton n both the regonal and natonal barganng closures where captal s allowed to adjust fully. The frst column n Table 4 gves the proportonate mpacts on key varables n the Scottsh economy of the Barnett equlbrum where there s regonal barganng, full adjustment to the captal stock but no populaton change. Frst, because populaton has not changed there s no possble updatng of the populaton weghts. Second, comparng these changes wth those reported n column 1 of Table 1 solates the mpact of the captal stock adjustment. The adjustment to the captal stock n tself produces a very small addtonal fall n GDP and employment over those reported n the short-run smulaton. 24

26 Agan, comparng the fgures n column 1 of Table 4 wth those n column 4 of Table 1 gves the addtonal mpact of allowng a full populaton adjustment once we have allowed for a full captal stock adjustment. In ths case the addtonal fall n actvty s large. The change n GDP and employment are both reduced by over two percentage ponts. As observed already, the loss of compettveness n the economy as the real wage s reganed has a large negatve mpact on local economc actvty. Smlar comparsons can be made for the results n column 2 of Table 4, whch are for the natonal barganng smulatons wth full captal adjustment, and those n columns 1 and 4 of Table 3. Note that n these smulatons the assumpton of natonal barganng removes the lnk between Scottsh populaton and the nomnal wage. The ntal short-run adjustment here shows a much bgger reducton n actvty and the addtonal effect of allowng a full captal adjustment s rather large. For example, wth natonal barganng GDP falls by 1.99% n the short run and by 3.30% f full captal adjustment s ncorporated. In fact ths result s very smlar to the long-run Barnett equlbrum wth fxed populaton weghts, where the GDP change fall s 3.56%. The only dfference between these two smulatons s that n long-run equlbrum the unemployment rate returns to ts ntal level so that consumpton funded by benefts s lower. Fgure 8 summarses ths nformaton for GDP. It shows the full range of alternatve decompostons of the long-run varable-populaton-weght Barnett equlbra adjustments to Scottsh GDP that can be made usng the nformaton n Tables 1, 3 and Conclusons Whle prevous analyses of the operaton of the Barnett formula have been nstructve, the system-wde economc consequences of ts strct mposton have been neglected, despte the fact that the Barnett formula drves the regonal dstrbuton of an mportant element of aggregate demand. The present paper attempts to fll ths gap. We use a mult-sectoral general equlbrum regonal Layard et al. (1991) model to quantfy the real-resource Barnett squeeze on the Scottsh economy. Ths s the lkely 25

27 contractonary mpact of Barnett equlbra n Scotland. The mportance of the wage barganng and mgraton processes n governng the lkely scale of the effects s determned through senstvty analyss. Furthermore, we are able to show the even greater contractonary mpact of the recent change to regular up-datng of the populaton weghts n the Barnett formula, once the endogenety of populaton n a small regonal economy lke Scotland s accommodated through the mgraton process. Whle our analyss represents a sgnfcant generalsaton of past work, there reman four mportant areas for further research. Frst, whle we concentrate here on the mplcatons of Barnett (and other) equlbra, we know that these are only attaned after a substantal lag. In practce, the mpact of adherence to the Barnett formula over a perod of a few years s unlkely to be very sgnfcant, although ths s an ssue that clearly merts further nvestgaton. Second, our assumpton that the expendture changes analysed here consttute a pure demand dsturbance consderably smplfes our analyss. It allows us to focus on ths crtcal but, up to now, entrely neglected aspect of the formula. In realty, however, adverse supply-sde mpacts may well accompany the relatve expendture contractons, so that the estmates we present here cannot be regarded as provdng a worst case scenaro. Whle these supply mpacts wll undoubtedly prove dffcult to quantfy, they mert further nvestgaton. Thrd, our analyss explores the mpact of Barnett on economc actvty n Scotland alone. The extensve use of the small-regon assumpton means that nter-regonal spll-overs and natonal macro-economc constrants are gnored. However, future work wll relax these restrctons and provde an explctly nterregonal approach. A fourth area s nvestgaton of a wder range of alternatve schemes for dstrbutng publc expendtures among the regons of the UK. There are many forms and degrees of fscal federalsm and we am to explot the power of general equlbrum models to nvestgate the possble mpact of alternatve fscal systems n a UK context. 26

28 The neglected system-wde effects of the Barnett formula are mportant n practce. Yet alternatves to Barnett are often framed essentally n terms of mcroeconomc needs. If the macroeconomc consequences of Barnett really matter, as our analyss suggests, they should feature more heavly n decsons concernng the regonal dstrbuton of government expendtures. 27

29 REFERENCES Armngton, P. (1969), A Theory of Demand for Products Dstngushed by Place of Producton, IMF Staff Papers, Vol.16, pp Bell, D., Dow, S., Kng, D., and Masse. N. (1996), "Fnancng Devoluton." Hume Papers on Publc Polcy, Ednburgh Unversty Press, Vol. 4, No.2. Blanchflower, D., and Oswald, A. (1994), The Wage Curve, MIT Press: Cambrdge, MA. Chrste, A. (2002), "The 1979 Needs Assessment: Lessons from Australa and Canada", Fraser of Allander Quarterly Economc Commentary, July 2002, pp Cuthbert, J. (2001), "The Effect of Relatve Populaton Growth on the Barnett Squeeze", Fraser of Allander Quarterly Economc Commentary, May 2001, pp Gbson, H. (1990), Export Compettveness and UK Sales of Scottsh Manufacturers, Workng Paper, Scottsh Enterprse, Glasgow. Goude, A. (2003), "GERS and Fscal Autonomy", Scottsh Affars, No. 41, pp Greenaway, D., S.J. Leyborne, G.V. Reed and Whalley J. (1993), Appled General Equlbrum Modellng: Applcatons, Lmtatons and Future Developments, HMSO, London. Greenwood, M.J., Hunt, G., Rchman, D., and Treyz, G. (1991), "Mgraton, Regonal Equlbrum, and the Estmaton of Compensatng Dfferentals", Amercan Economc Revew, Vol. 81, pp Harrgan, F., McGregor, P., Perman, R., Swales, K. and Yn, Y.P. (1991), AMOS: A Macro-Mcro Model of Scotland, Economc Modellng, Vol. 8, pp