Working paper No.3 Cyclically adjusting the public finances

Transcription

1 Working paper No.3 Cyclically adjusing he public finances Thora Helgadoir, Graeme Chamberlin, Pavandeep Dhami, Sephen Farringon and Joe Robins June 2012

2 Crown copyrigh 2012 You may re-use his informaion (no including logos) free of charge in any forma or medium, under he erms of he Open Governmen Licence. To view his licence, visi hp:// or wrie o he Informaion Policy Team, The Naional Archives, Kew, London TW9 4DU, or [email protected]. Any queries regarding his publicaion should be sen o us a: [email protected] ISBN PU1342

3 Cyclically adjusing he public finances Thora Helgadoir, Graeme Chamberlin, Pavandeep Dhami, Sephen Farringon and Joe Robins Office for Budge Responsibiliy Absrac The specificaion of he Governmen s fiscal mandae in cyclically-adjused erms requires he OBR o make an assessmen of he effec of he economic cycle on he public finances. These esimaes are generally produced for he main fiscal aggregaes using cyclical adjusmen coefficiens. In his paper we reassess he size of he cyclical adjusmen coefficiens boh by revisiing previous Treasury analysis and by considering a range of oher approaches. Our esimaes sugges a conemporaneous cyclical adjusmen coefficien o he oupu gap for ne borrowing and curren budge of 0.5 and a lagged coefficien of 0.2, which are he same as he coefficiens he OBR has used in is forecass o dae. We use hese coefficiens and he OBR's hisorical oupu gap series o produce an updaed hisorical series for srucural ne borrowing. We also analyse he effec ha flucuaions in asse prices and propery ransacions, which are no relaed o he economic cycle, could have on he public finances using wo differen approaches. We are graeful for commens from colleagues a he Office for Budge Responsibiliy, he OBR s Advisory Panel and colleagues a HMRC and DWP. JEL references: E62, E32 Keywords: Fiscal policy, Cycles

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5 Conens Chaper 1 Inroducion... 1 Chaper 2 Esimaing cyclical adjusmen coefficiens... 5 One-sep approach... 6 Two-sep approach Conclusion Chaper 3 Alernaive approaches o cyclical adjusmen SVAR model Componen mehod (ECB) Conclusion Chaper 4 Asse price adjusmens Adjusing for asse prices and propery ransacions Conclusion Chaper 5 Conclusion Chaper 6 References Annex A Sensiiviy and robusness Annex B The relaionship beween he one-sep and wo-sep approaches Annex C Simulaneous equaion bias and he problem of idenificaion Annex D Srucural VARs and idenificaion... 83

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7 Inroducion 1 Inroducion 1.1 The Office for Budge Responsibiliy (OBR) has been asked wih judging wheher he Governmen has a greaer han 50 per cen probabiliy of achieving he medium-erm fiscal arges ha i has se iself. The Governmen s fiscal mandae is currenly defined as he requiremen o balance he cyclically-adjused curren budge (CACB) by he end of a rolling, five-year period. 1.2 The specificaion of he fiscal mandae in cyclically-adjused erms requires he OBR o make an assessmen of he effecs of he economic cycle on he public finances. This is generally done by adjusing a given fiscal aggregae, such as ne borrowing or he curren budge, for he amoun of spare capaciy in he economy (he oupu gap) using cyclical adjusmen coefficiens. 1.3 To dae, he OBR has adoped he Treasury s approach o cyclical adjusmen as presened in he 2008 Treasury working paper: Public Finances and he cycle. In his paper we reassess he size of he cyclical adjusmen coefficiens. We do his by revisiing he previous Treasury analysis and by considering a range of alernaive approaches o cyclical adjusmen. Esimaing cyclically-adjused fiscal aggregaes 1.4 The cyclical posiion of he economy is likely o have an impac on public secor receips and expendiure. If he economy is operaing below is poenial (i.e., here is a negaive oupu gap ) hen, oher hings equal, here is likely o be higher expendiure on iems such as jobseekers allowance. Similarly, here are likely o be lower receips from sources such as income ax, corporaion ax and VAT, due o lower labour income, corporae profis and consumer spending, respecively. 1.5 This implies ha governmen borrowing will ypically end o be higher when oupu is below is poenial level, and lower when oupu is above is poenial. Adjusing for he impac of he cycle on he public finances provides an esimae of he srucural posiion of he public finances, once he emporary effecs of he economic cycle have been removed. 1.6 The cyclical adjusmen coefficiens used o make his adjusmen are derived by analysing he pas relaionship beween he oupu gap and he fiscal posiion. As explained in he OBR s Economic and fiscal oulooks (EFO), he esimaes of hese coefficiens are highly uncerain for a number of reasons: 1 Cyclically adjusing he public finances

8 Inroducion he oupu gap is no direcly observable, so here is no hisorical fac from which o esimae he coefficiens; he number of observaions on which o base coefficien esimaes is limied; he fiscal posiion is affeced by evens ha do no necessarily move in line wih he cycle, such as one-off fiscal policy adjusmens and movemens in commodiy and asse prices; and insofar as he curren economic cycle differs from he average cycle, he relaionship beween he public finances and he oupu gap over he course of ha cycle will no be capured in he coefficiens. 1.7 In his paper we aemp o address hese uncerainies as far as possible. We compare he resuls from several approaches o esimaing he cyclical adjusmen coefficiens. In our cenral esimaes we make use of he hisorical oupu gap series published in he OBR s Working paper No. 1: Esimaing he UK s hisorical oupu gap, bu we es he sensiiviy of hese resuls o alernaive oupu gap series. We exend our analysis by using he srucural VAR approach o consider he poenial feedback from fiscal policy o he oupu gap. We also analyse he poenial impac on he fiscal posiion from emporary facors ha may no be correlaed wih he economic cycle, in paricular asse prices and ransacions. Main conclusions 1.8 Our esimaes sugges a conemporaneous cyclical adjusmen coefficien of 0.5 and a lagged coefficien on he previous year of 0.2. These are he same coefficiens ha have been used in EFOs o dae. We have used hese coefficiens and he OBR s hisorical oupu gap series o produce an updaed hisorical series for srucural ne borrowing. The change in he oupu gap series means ha srucural borrowing appears somewha higher in he 1990s and in he run up o he 2008 financial crisis han previous Treasury esimaes have implied. Srucure of he paper 1.9 The analysis in his paper is srucured as follows: in Chaper 2 we esimae cyclical adjusmen coefficiens using he previous Treasury approach and he approach used by he Organisaion for Economic Cooperaion and Developmen (OECD). Boh approaches are based on economeric esimaion of he pas relaionship beween he oupu gap and he fiscal posiion; Cyclically adjusing he public finances 2

9 Inroducion Chaper 3 considers some exensions o hese approaches. We esimae a srucural vecor auoregressive model (SVAR) which aemps o address he endogeneiy of he oupu gap and fiscal policy. We also look a he approach used by he European Cenral Bank (ECB) which aemps o correc for he impac of changes in he composiion of GDP; Chaper 4 analyses he poenial emporary effecs on he fiscal posiion of flucuaions in asse marke prices and ransacions, which may no be correlaed wih he economic cycle; and Chaper 5 summarises and ses ou our conclusions. 3 Cyclically adjusing he public finances

10 Inroducion Cyclically adjusing he public finances 4

11 Esimaing cyclical adjusmen coefficiens 2 Esimaing cyclical adjusmen coefficiens 2.1 This chaper explains and presens he resuls from wo economeric approaches used o cyclically adjus he public finances. To dae in he OBR s forecass of he public finances i has adoped he approach firs se ou in deail in a Treasury Occasional paper published in 1995, Public finances and he cycle. The resuls have since been updaed by he Treasury on regular occasions mos recenly in 2008 bu he underlying mehodology has remained broadly unchanged. 1 We call his he one-sep approach as i involves regressing public expendiure and receips direcly on he oupu gap. 2.2 We hen consider a more widely-used mehodology developed by he OECD. We label his he wo-sep approach as i involves firs regressing he ax/expendiure economic base (for example, oal labour income as he base for income ax receips) on he oupu gap, and hen esimaing he responsiveness of he ax/expendiure sream o is base. The OECD applies his approach across a number of counries and herefore makes a number of simplifying assumpions o do so. We are able o ailor he approach o he UK using counry-specific models and daa. 2.3 We use boh approaches o esimae cyclical adjusmen coefficiens for he UK using he laes available daases. We hen assess he robusness and he relaive meris of he wo approaches. For our cenral esimaes we have used he oupu gap series published in he OBR s Working paper No. 1: Esimaing he UK s hisorical oupu gap, bu we also consider he sensiiviy of he resuls o alernaive hisorical oupu gap series. 2.4 The approaches produce cyclical adjusmen coefficiens consisen wih adjusing public secor ne borrowing (PSNB) figures. However, since he difference beween PSNB and he curren budge balance is mainly public invesmen, which is small as a share of GDP, he coefficiens can also be used o cyclically adjus he curren budge. 1 HM Treasury (1995), (1999), (2003) and Farringon e al, (2008). 5 Cyclically adjusing he public finances

12 Esimaing cyclical adjusmen coefficiens One-sep approach Overview of mehod 2.5 The underlying mehodology of he one-sep approach is relaively simple. Expendiure and revenue expressed as raios o GDP over he pas 30 years are regressed agains esimaes of conemporaneous and lagged oupu gaps. The coefficiens in he equaions indicae he average responsiveness of he public finances o he economic cycle. 2.6 In is analysis, HM Treasury adjused he resuls of he regression analysis o allow for prior expecaions based on srucural changes in ax and expendiure sysems ha migh no be picked up fully in he regression analysis. The adjused coefficiens were used by HM Treasury, and subsequenly by he OBR, o adjus nominal fiscal aggregaes (expressed as raios o nominal GDP) for he impac of he economy s posiion in he cycle. 2.7 There are a number of heoreical and pracical difficulies wih implemening his sraighforward approach. For example, he use of hisorical daa means ha he esimaes reflec he average effec of changes in he oupu gap on he public finances over previous cycles. If he curren economic cycle differs from he average cycle, he relaionship beween he public finances and he oupu gap over he course of ha cycle will no be capured in he coefficiens. We herefore conduc some sensiiviy analysis of he resuls o he choice of ime period by looking a he resuls for individual cycles and recursive esimaion of he equaions. The resuls are discussed in Annex A. 2.8 Anoher problem wih his approach is ha ideally i is necessary o remove he effecs of discreionary fiscal policy changes on he daa series of governmen expendiure and receips used in he regressions. Oherwise he regression may capure changes in receips and expendiure driven by policy choices. In pracice, as discussed below, adjusing daa for policy effecs is very difficul and is only really feasible for receips, alhough some aemp is made o model policy effecs in he expendiure regressions The following secions discuss, in urn, he approach o modelling he aggregae and individual ax receips effecs, he expendiure effec and how o combine he 2 Noe ha his approach is similar o wha has come o be ermed he narraive approach o he idenificaion of fiscal policy (see for example Romer & Romer (2010)). Indeed he daase of discreionary policy decisions ha we have made available on our websie alongside his paper should prove o be a useful ool for furher research in his area. Cyclically adjusing he public finances 6

13 Esimaing cyclical adjusmen coefficiens resuls ino a single esimae of cyclical adjusmen coefficiens ha can be applied o ne borrowing and he curren budge. Receips and he cycle 2.10 To esimae he effecs of he economic cycle on ax receips we begin by consrucing a policy-adjused daase for he bulk of ax receips using published cosings of ax policy measures since 1970 (see Box 2.1). In heory, removing he esimaed policy cosings from he individual (and aggregae) receips series leaves us wih a ax series ha should be predominanly driven by movemens in he economic cycle. Char 2.1 shows he resuls of his exercise. 3 Char 2.1: Indexed ax o GDP raios Index 100 = Source: OBR Unadjused Adjused 2.11 The adjused series follows our esimae of he economic cycle a lile more closely, hough he correlaion is no very srong. The difference beween he wo series also appears o be largely relaed o he cyclical posiion of he economy: from o : a gap opens up as he unadjused series falls, while he adjused series increases. This paern is consisen wih a cyclical increase in ax receips ha is more han offse by procyclial discreionary policy loosening; 3 The char sars in 1973 due o he unavailabiliy of more deailed informaion on ax receips prior o his year, which resrics he effecive size of our sample period. 7 Cyclically adjusing he public finances

14 Esimaing cyclical adjusmen coefficiens from o : boh series fall a approximaely he same rae, due o a cyclical fall in ax receips; and from o : he gap closes as (milder) procyclial discreionary policy ighening booss he unadjused series Noe ha his series only encompasses an average of around 85 per cen of oal ax receips and covers he major ax heads: income ax & NICs, VAT, corporaion ax, fuel duy (plus VED), capial axes and excise duies. 4 This is because Budge cosings for he oher principal elemens (e.g. local auhoriy axes) are no available on a consisen basis. We herefore exclude local auhoriy axes and oher receips (mainly ineres dividends, rading surpluses and ren) from his analysis. However, his is a slighly larger wider ax aggregae han used in previous Treasury analyses, which also excluded capial axes. Box 2.1 provides more deail of he mehod we use o produce he policy-adjused series and he uncerainies involved Once he daase has been policy-adjused i is also necessary o adjus for large, one-off, fiscal operaions ha can affec he calculaion of he cyclicallyadjused fiscal balances even hough hey have no, or very lile, implicaions for he fiscal sance. The only example in he UK ha requires a specific adjusmen is he aucioning of hird generaion mobile elephone licenses. The new classificaion reamen of hese receips as a ne capial ransfer will reduce PSNB (bu no ax receips) by a one-off amoun of 22.5bn in an effec which should be removed from he calculaion of cyclically-adjused borrowing. 5 4 The proporion of oal ax receips accouned for by hese ax heads rises hrough he 1980s from 75 per cen o over 90 per cen a he sar of he 1990s. 5 See Treamen of he sale of UK 3G Mobile Phone Licenses in he Naional Accouns - Augus 2011, available a for more deails. Cyclically adjusing he public finances 8

15 Esimaing cyclical adjusmen coefficiens Box 2.1: Consrucing he policy-adjused ax receips daase To compile our policy-adjused ax receips series we have consruced a daabase of all of he larger ax policy measures of he las 42 years. a These policy measures are lised in he ables which se ou he coss of new measures published by he Treasury a Budges and oher fiscal evens since Budge This approach herefore assumes ha hese iniial policy cosings were accurae, alhough here are significan uncerainies around many policy cosings, and heir accuracy is ofen very difficul o assess ex-pos. In he ineress of efficiency, we have ypically only included policy measures ha were cosed in excess of plus or minus 50 million in a leas one year. In some cases, smaller measures were grouped ogeher where i was easy o do so and in laer years smaller measures for he smaller ax heads have also been included. The Budge ables ypically only show cosings for he nex wo years, alhough more recen Budges have shown up o five years. So hese cosings were hen exrapolaed for he whole daa period using he growh rae of nominal GDP. This is anoher weakness of his approach bu here is no obvious beer alernaive. The policy-adjused receips series is hen consruced simply by subracing hese cosings from he relevan daa series of acual receips. Wih he very significan cavea of he uncerainies se ou above, he policy-adjused series is herefore heoreically showing he level of receips ha would have been recorded if no ax policy changes had been made afer Despie he inheren difficulies wih his approach, he headline resuls are reasonably inuiive. Taking he period as a whole, he fac ha he wo lines mee a he end as well as he beginning suggess ha discreionary ax increases and decreases have broadly offse each oher over he period. Discreionary income ax measures have reduced ax receips o couner he effecs of fiscal drag, while indirec ax measures, especially for VAT and fuel duies, have boosed receips. In he case of VAT, his reflecs a general shif in he burden of axaion from direc o indirec axes, while he fuel duy measures have parially offse he effecs of a declining ax base as fuel efficiency has improved. The increase in he ax-o-gdp raio across he sample period largely reflecs he choice of saring poin in , as he raio was a is cyclical low a his poin, following a year of very rapid growh in GDP. a The daabase is available on he OBR s websie a 9 Cyclically adjusing he public finances

16 Esimaing cyclical adjusmen coefficiens 2.14 The policy adjused series is hen included in he following simple regression: ( TR / Y ) ygap ygap Y (1) * Where ( TR / Y ) is policy adjused ax receips as a share of nominal GDP, Y, α * is a consan, ygap is he oupu gap, Y is he level of poenial oupu (in logs) and is an error erm. The regression is esimaed using ordinary leas squares (OLS) over he sample period, financial years, The coefficiens on he oupu gap and he lagged oupu gap are he coefficiens of ineres and indicae he responsiveness of ax receips o he cycle. The lagged oupu gap is included in he specificaion on he basis of prior expecaions ha here are likely o be lags from changes in he oupu gap o changes in receips. This may be due o lags in he economy - for example changes in he labour marke may lag changes in oupu. There are also lags in he ax sysem. For example selfassessmen ax is paid some period afer earnings are received, and hese receips are no accrued back o he earlier period as happens for income ax receips. The poenial oupu variable can be hough of as a proxy for he effecs of real fiscal drag The use of a policy-adjused series ackles one possible source of endogeneiy, bu anoher remains: here migh also be a simulaneous relaionship beween expendiure, receips and he oupu gap. The oupu gap can be affeced by fiscal policy working hrough he level of receips and expendiure. The level of governmen expendiure (he consumpion elemen of which is scored in GDP) is also likely o depend in par on he level of ax receips, and vice versa One possible mehod for addressing his issue is o esimae he equaion using insrumenal variables. Bu in pracice i can ofen be difficul o idenify srong insrumens. This was he approach used in he Treasury s 2008 working paper, using he world oupu gap and world ineres raes as insrumens. This deeced no significan evidence of bias, in line wih he conclusions of Darby and Meliz (2008). An alernaive mehod, discussed in Chaper 3, is o adop a more formal srucural modelling approach and esimae a srucural vecor auoregressive model (SVAR). 6 Fiscal drag is he name given o he endency for ax receips as a percenage of GDP o increase over ime. This is due o he progressive naure of he ax sysem, whereby he average ax rae increases he more income is earned. Nominal fiscal drag occurs when inflaion pushes incomes up; real fiscal drag occurs when wages rise faser han inflaion due o produciviy growh. Cyclically adjusing he public finances 10

17 Esimaing cyclical adjusmen coefficiens Resuls for ax receips and he cycle Aggregae axes 2.18 The resuls of esimaing he aggregae ax receips equaion are shown in Table 2.1, and presened alongside hose of he previous Treasury analysis o faciliae comparison. The updaed esimaes migh be expeced o differ from he Treasury resuls due o he use of a longer sample period, which now includes movemens in he oupu gap caused by he recen recession, and he use of he OBR esimae of he oupu gap, as opposed o he Treasury s consrucion of his variable. 7 Table 2.1: Aggregae ax receips (per cen of GDP) Consan Oupu gap Oupu gap Sandard Trend GDP R squared (-1) error (0.6) (2.9) (-0.0) OBR (-1.9) (1.0) (4.5) T-saisics in brackes 2.19 However, while he resuls differ in a few respecs from he previous Treasury esimae, he coefficiens on he key variable he oupu gap are of a similar magniude. The resuls coninue o indicae no significan relaionship wih he curren oupu gap wih a slighly smaller coefficien on he lagged oupu gap. The divergen esimaes of he coefficien on poenial oupu appear o be due o an anomalous resul in he Treasury s 2008 analysis, as he previous analyses published in 1999 and 2003 boh repored coefficiens closer in magniude o our updaed esimaes. The size of he coefficien implies ha real fiscal drag increases he ax o GDP raio by around 0.1 per cen a year The fall in he R-squared saisic a measure of he explanaory power of he regression is likely o be due o he exension of he end of he sample period from 2006 o Tha he equaion does no fi very well over he recen recession suggess ha he responsiveness indicaed by he regression coefficiens may no be a good guide o he curren responsiveness of ax receips o he economic cycle In is 2008 paper he Treasury judged ha, despie he resuls of he regression analysis, i is reasonable o allow for some conemporaneous effec beween he cycle and ax receips. For example, he Treasury suggesed ha he inroducion 7 Se ou in Pybus (2011), Esimaing he UK s hisorical oupu gap, OBR Working paper No Cyclically adjusing he public finances

18 Esimaing cyclical adjusmen coefficiens of quarerly insalmen paymens (QIPs) of corporaion ax for large companies from 1999 migh have led o more imely responsiveness of receips o he cycle. The Treasury herefore adjused he regression resuls and placed a coefficien of 0.1 on he conemporaneous oupu gap, and a coefficien of 0.1 on he lagged oupu gap. This is broadly equivalen o bringing forward half he impac associaed wih he esimaed regression coefficien on he lagged oupu gap This is a conclusion shared by oher analyses of cyclical adjusmen. For example, he OECD s implemenaion of he wo-sep approach (Girouard and Andre (2005)) commens ha exac lag srucures for UK corporae and personal income ax are no known, and hey may vary significanly over ime. On he basis of judgemen, however, he OECD also assumes a wo year adjusmen period, wih equal weigh on he conemporaneous and lagged effec. Individual axes 2.23 To complemen he op-down regression analysis, and o gain furher insigh ino he cyclicaliy of ax receips, we carry ou similar regression analysis for each of he individual componens of he aggregae ax receips series. The responsiveness o he oupu gap could differ across he ax base, and individual componen regressions (as are also used in he wo-sep approach), can provide useful addiional informaion on he relaionship beween he cycle and aggregae receips. The resuls are shown in Tables 2.2 o 2.8. Table 2.2: Income ax and NICs receips (per cen of GDP) Consan Oupu gap Oupu gap Sandard Trend GDP R squared (-1) error (-7.5) (-2.7) (2.9) (8.5) OBR (-9.2) (-2.4) (11.0) Table 2.3: Non-oil corporaion ax receips (per cen of GDP) Consan Oupu gap Oupu gap Sandard Trend GDP R squared (-1) error (1.1) (2.0) (3.9) (-0.9) OBR (31.0) (3.7) Cyclically adjusing he public finances 12

19 Esimaing cyclical adjusmen coefficiens Table 2.4: VAT receips (per cen of GDP) Consan Oupu gap Oupu gap Sandard Trend GDP R squared (-1) error (3.8) (3.3) OBR (34.4) (-0.89) Table 2.5: Excise moor 8 ax receips (per cen of GDP) Consan Oupu gap Oupu gap Sandard Trend GDP R squared (-1) error (2.5) (-0.3) (-2.4) OBR (11.1) (3.4) (-11.0) Table 2.6: Oher excise 9 ax receips (per cen of GDP) Consan Oupu gap Oupu gap Sandard Trend GDP R squared (-1) error (19.3) (-18.7) OBR (16.4) (2.7) (-16.3) Table 2.7: Capial axes (per cen of GDP) Consan Oupu gap Oupu gap Sandard Trend GDP R squared (-1) error OBR (-10.0) (3.0) (10.8) Table 2.8: Sum of oupu gap coefficiens 10 (per cen of GDP) Oupu gap Oupu gap (-1) OBR Fuel duy and vehicle excise duy. 9 Tobacco, alcohol and being duies. 10 Where saisically significan i.e. excluding he VAT coefficien in he OBR equaion. 13 Cyclically adjusing he public finances

20 Esimaing cyclical adjusmen coefficiens 2.24 Our resuls are again broadly similar o hose of he 2008 Treasury paper. A negaive sign on he conemporaneous oupu gap in he income ax equaion is no immediaely inuiive, bu probably reflecs cyclicaliy in he labour share of income, alhough here is no longer a parial counerbalance by he finding of a saisically significan posiive relaionship for he lagged oupu gap. The coefficien on rend GDP is consisen wih fiscal drag of around 0.2 per cen a year The corporae ax equaion now shows a bigger conemporaneous effec han previously, which lends some suppor o he adjusmen made by he Treasury for he inroducion of QIPs, discussed in paragraph The excise equaions poin o a larger effec from he lagged oupu gap, which offse he loss of significance in he income ax equaion. The negaive coefficiens on rend GDP reflec he downward rend in he share of GDP of hese axes. The VAT equaion performs exremely poorly, wih a complee absence of saisical significance and explanaory power. Overall, he resul is ha he sum of he individual esimaes shown in Table 2.8 is now smaller han in he 2008 analysis, bu consisen wih he resuls of he aggregae equaion On he basis of hese updaed regression resuls, here seems o be lile evidence poining srongly o a differen conclusion from he Treasury s 2008 analysis of he cyclicaliy of receips. However, he insabiliy of he individual equaion esimaes raises quesions abou he robusness of he one-sep approach. Expendiure and he cycle 2.27 Frequen changes in he coverage and srucure of expendiure programmes mean ha i is no possible o adjus he public expendiure series for policy effecs in he same way as we did for receips. For example, aside from rae changes, he basic srucures of income ax and VAT have remained largely unchanged, whereas i is no possible o rack a consisen series hrough ime for programmes such as ax credis, which are responsible for a large share of expendiure, bu are a relaive recen innovaion in heir curren form. I is herefore necessary o ry o capure some of he possible expendiure policy effecs in he modelling approach. The Treasury s choice of expendiure regression herefore has a slighly differen specificaion o he receips regression: TME Y 1 TME Y TME Y ygap T T 02 (2) ( / ) ( / ) 1 2 ( / ) Where ( TME / Y ) is Toal Managed Expendiure (TME) as a share of nominal GDP, Y, α is a consan, ygap is he oupu gap, T75 and T02 are ime rends saring in and respecively, and is an error erm. The Cyclically adjusing he public finances 14

21 Esimaing cyclical adjusmen coefficiens regression is esimaed using ordinary leas squares (OLS) over he sample period, financial years, The inclusion of lagged dependen variables is designed o capure endogenous policy responses. For example, policymakers may decide o increase social securiy expendiure, over and above he auomaic increase in unemploymen relaed benefis, once i becomes clear he economy is in a downurn. Bu noe ha under hese assumpions (i.e. ha he policy response is counercyclical and responds wih a lag) he long-run response of spending o he economic cycle implied by he regression is likely o be an overesimae The inclusion of a number of ime rends again follows he previous Treasury approach and is designed o capure poenially more long-lasing srucural policy effecs. For example, he inclusion of a rend from 2002 is inended o accoun for a discreionary decision o increase he level of expendiure over subsequen years, announced in Budge The choice of dependen variable in he expendiure regression is oal spending, also known as Toal Managed Expendiure (TME), which he Treasury spli ou ino Annually Managed Expendiure (AME) and Deparmenal Expendiure Limis (DEL). DEL is mainly composed of expendiure on he provision of public services such as educaion and healh, which has ypically been fixed in cash erms in muli-year plans and is herefore no direcly linked o he economic cycle. AME will ypically follow he economic cycle more closely as i conains elemens such as social securiy expendiure which are direcly linked o he level of unemploymen and earnings. However, hese elemens are generally quie small relaive o he res of public expendiure Therefore, wih much of expendiure broadly fixed in nominal erms we migh expec ha, when measured as a raio o GDP, expendiure will be sensiive o he cycle principally hrough a denominaor effec. In oher words, movemens in GDP will be he main driver of he conemporaneous effec of he cycle on he public finances. For example, a fall in GDP will auomaically increase he share of TME o GDP if he level of TME is broadly sable in nominal erms The raio of TME o GDP has averaged 43 per cen across he sample period, which implies ha a one per cen increase in oupu relaive o rend would reduce he share of TME as a percenage of GDP by around 0.4 percenage 11 Calculaed as 1 ). 1 /( In paricular, Budge 2002 announced significan increases in healh spending o an average annual growh rae of 7.5 per cen over he five years o 2007/ Cyclically adjusing he public finances

22 Esimaing cyclical adjusmen coefficiens poins in he firs year. The regression resuls repored in Table 2.9 provide empirical suppor for his conclusion. Table 2.9: Toal managed expendiure (per cen of GDP) Consan TME(-1) TME(-2) Oupu gap T75 T02 R-squared Sandard error (9.0) (6.3) (-4.3) (-4.7) (-7.9) (1.8) OBR (5.8) (3.9) (-2.1) (-3.0) (-5.0) (4.8) Table 2.10: Dynamic response of he TME o GDP raio o a 1 per cen increase in he oupu gap T T+1 Long run OBR The relaionship beween he oupu gap and TME appears o be relaively sable as he esimaed coefficiens are similar o previous Treasury analysis. The increase in he coefficien on he oupu gap is likely o be due o he exension of he sample period o cover he recen recession. This would be he case if he increase in spending in response o recen cyclical weakness has been larger han he hisorical average, perhaps due o counercyclical discreionary policy decisions for which we are unable o adjus. The resuls imply ha a one per cen rise in GDP, relaive o poenial oupu, reduces he TME o GDP raio by 0.44 percenage poins in he firs year. This is in-line wih he prior expecaion of a coefficien of around 0.4 due o he denominaor effec However, he equaion also includes dynamic effecs and he esimaed lagged and long-run responses are shown in Table The expendiure response rises o 0.7 per cen in he second year and remains around ha level over he longer erm. This is above he 0.5 adjusmen for expendiure in he Treasury s 2008 paper, alhough as discussed earlier, he coefficien may be subjec o some upward bias if he endogenous policy response capured by he lagged erms is counercyclical (i.e. spending is increased when GDP falls). Cyclical social securiy 2.36 As discussed above some elemens of AME expendiure in paricular Jobseeker s Allowance and oher income relaed elemens of he social securiy sysem are likely o be closely linked o movemens in he cycle. A separae regression is herefore esimaed o es for he effec of cyclical social securiy expendiure, which we define as all DWP income-relaed benefis and ax credis Cyclically adjusing he public finances 16

23 Esimaing cyclical adjusmen coefficiens adminisered by HMRC. 13 Cosings for some policy measures relaed o hese benefis are available, bu we have no aemped o adjus he series for he subse of measures ha are available as he oupu would only be a pariallyadjused series. The resuls are shown in Table Table 2.11: Cyclical social securiy (per cen of GDP) Consan Oupu gap (-1) Time R squared Sandard error (4.8) (-3.0) OBR (14.3) (-4.9) (9.7) 2.37 The resuls indicae a sronger relaionship han in he previous Treasury analysis, or a coefficien of 0.18, which is likely o be due o he wider definiion of cyclical social securiy used in our analysis. 14 If we use he narrower measure of unemploymen relaed benefis as he dependen variable, hen we find ha he coefficien on he oupu gap drops back o 0.1. The slighly larger coefficien is also consisen wih he rise in he cyclical response of oal expendiure in he +1 period, given by he dynamic erms in he TME regression. The inclusion of a ime rend, which accouns for he seady increase in his measure of he level of social securiy expendiure hrough he sample period, improves he fi of he regression Unlike he individual ax receips exercise, simply adding he coefficiens from he TME and cyclical social securiy regressions would likely lead o some doublecouning, as his social securiy expendiure is already included in he TME measure. This was confirmed by repeaing he TME regression in Table 2.9, bu subsiuing a TME excluding cyclical social securiy measure as he dependen variable. In his case he coefficien on he oupu gap drops from 0.43 o 0.40, as shown in Table Table 2.12: TME excluding cyclical social securiy (per cen of GDP) Consan TMEx (-1) TMEx (-2) Oupu gap T75 T02 R-squared Sandard error OBR (5.7) (3.2) (-2.1) (-2.8) (-5.3) (5.3) 13 We also include conribuory jobseekers and employmen and suppor allowances. The relevan hisorical series can be found here: hp://research.dwp.gov.uk/asd/asd4/index.php?page=medium_erm. We scale hese figures up o produce UK aggregaes. 14 Due o a ypographical error, he resuls in he 2008 working paper show a relaionship wih he curren oupu gap in fac, his should be he lagged oupu gap. 17 Cyclically adjusing he public finances

24 Esimaing cyclical adjusmen coefficiens 2.39 The Treasury analysis also invesigaed he possibiliy of deb ineres paymens being cyclical. However, he coefficien on he oupu gap in he deb ineres regression was no saisically significan in eiher he Treasury s 2003 or 2008 analysis. We found he same resul so we have chosen no o repor he deail here. This may be because if economic growh is above rend hen ineres raes will end o rise (increasing deb ineres paymens) bu borrowing will end o fall (reducing deb ineres paymens). A large proporion of deb ineres coss will also reflec paymens on he hisorical sock of deb. Any cyclical influence would only affec he deb ha is being refinanced a he ime. Therefore, cyclical effecs on deb ineres paymens are likely o be small bu persisen. Updaed esimaes of he cyclical adjusmen coefficiens 2.40 The main resuls of all he regression equaions are summarised in Tables 2.13 o Table 2.13 shows he unadjused resuls of he economeric esimaes in he Treasury s 2008 analysis, and he adjusmens made by he Treasury o produce he cyclical adjusmen coefficiens is given in Table Finally Table 2.15 shows he resuls of our updaed analysis The resuls of our regressions are broadly similar o hose in he Treasury s 2008 paper. Our esimaes produce slighly higher coefficiens on boh he conemporaneous oupu gap and he lagged oupu gap. However, if he same ses of adjusmens are made o our resuls as were made in he Treasury paper hen a very similar se of cyclical adjusmen coefficiens would be produced. As we have discussed above, he argumens ha he Treasury cied o jusify hese adjusmens on he expeced size of he expendiure denominaor effec and he expeced conemporaneous effec of he oupu gap on ax coninue o have some suppor in he empirical resuls However here are a number of limiaions wih his approach. Policy adjusmen is only feasible on he revenue side and relies on a number of srong assumpions (see Box 2.1). The resuls of he regression analysis are no very robus in a number of cases, and our sensiiviy ess in Annex A indicae ha he resuls are also no very robus o he choice of sample period. In paricular, his means ha we may only be capuring (imprecisely) he average effec of he cycle on he public finances when we are really ineresed in he marginal effec a he curren juncure. The OECD or wo-sep approach discussed in he nex secion seems beer suied o capure his effec. Cyclically adjusing he public finances 18

25 Esimaing cyclical adjusmen coefficiens Table 2.13: Previous HM Treasury 2008 economeric resuls Fiscal aggregae Oupu gap Lagged oupu gap CA expendiure = TME CA receips = PSCR CAPSNB = PSNB Table 2.14: HM Treasury 2008 cyclical-adjusmen coefficiens afer adjusmen Fiscal aggregae Oupu gap Lagged oupu gap CA expendiure = TME CA receips = PSCR CAPSNB = PSNB Table 2.15: Updaed OBR economeric resuls and adjusmens Fiscal aggregae Oupu gap Lagged oupu gap CA expendiure = TME CA receips = PSCR Unadjused CAPSNB = PSNB Adjused CAPSNB a = PSNB a Same adjusmens as in Table 2.14 are applied Two-sep approach 2.43 This secion looks a he approach developed and used by he OECD o cyclically adjus he fiscal aggregaes of is member counries. 15 The mehod esimaes cyclical adjusmen parameers for individual revenue and expendiure caegories in wo seps. The firs sep is o esimae how he economic base (e.g. consumpion and profis) of he ax/expendiure iem responds o he oupu gap and he second sep is o esimae how ax receips and expendiure move wih he relevan base. Those esimaes are hen combined o produce a single elasiciy which ells us how much ax receips and expendiure move wih he oupu gap. These ax and expendiure esimaes are aggregaed o produce a 15 See Van den Noord (2000) and Girouard and Andre (2005). 19 Cyclically adjusing he public finances

26 Esimaing cyclical adjusmen coefficiens single se of cyclical adjusmen coefficien for he fiscal aggregaes, which are comparable o he coefficiens derived in he one-sep approach see Figure 2.1. Figure 2.1: Flow diagram of he OECD mehod Elasiciy of ax/spending base o he oupu gap Elasiciy of ax receips and spending o relevan ax/spending base Aggregaed elasiciy of ax receips and spending o he oupu gap The raio of ax and spending o GDP Semi-elasiciy of ne borrowing 2.44 We make use of HMRC and DWP forecas models o esimae he elasiciies of ax and expendiure o heir relevan bases. They represen he marginal change in ax and expendiure consisen wih curren fiscal policy and are herefore invarian o he effecs of hisorical discreionary policy measures. This is a major benefi compared o he one-sep approach, given he difficulies of adjusing he revenue and expendiure series for he effecs of policy However, hese elasiciies may hemselves be cyclical. For example, effecive ax raes may differ over he economic cycle due o movemens in ax evasion, he composiion of consumer spending, he use of losses in corporaion ax and he greaer use of par-ime workers. These issues are discussed in Box This approach can also only be used where we can clearly idenify boh a base and he sensiiviy of he paricular ax or expendiure caegory o i. For example, his is he reason he OECD only akes accoun of unemploymen relaed expendiure. The mehod could herefore underesimae cyclicaliy if oher areas of social securiy expendiure ha are no included in he analysis are also relaed o he cycle. In similar fashion o he one-sep approach, he wo-sep approach is also vulnerable o he possibiliy ha he endogeneiy of fiscal policy may be biasing he resuls. This issue is addressed in Chaper 3. Cyclically adjusing he public finances 20

27 Esimaing cyclical adjusmen coefficiens Box 2.2: Effecive ax raes and he cycle A poenial disadvanage wih he wo-sep approach is ha, unlike he one-sep approach, i does no ake ino accoun oher cyclical facors ha migh affec receips bu no he ax base. Possible examples would be cyclical movemens in ax evasion (or speed of compliance), consumpion paerns and he use of losses in corporaion ax which could amplify he responsiveness of axes o he cycle. A recen IMF sudy suggess ha ax revenue efficiency does indeed move wih he business cycle. a In paricular a worsening of VAT efficiency is found o be driven by shifs in consumpion paerns, a decrease in he share of sandard rae consumpion, and changes in ax evasion during conracions. b The sudy also finds a correlaion beween personal income ax and social securiy ax efficiency and he oupu gap. There is some evidence o sugges ha oher cyclical facors have affeced receips in he UK in he recen downurn. In paricular: he VAT gap, he difference beween he heoreical oal VAT liabiliy and acual cash receips, increased in as he economy moved ino recession. The VAT gap can indicae he degree of ax compliance. The VAT gap increased primarily because of a rise in unauhorised VAT deb and he use of he governmen s ime-o-pay scheme o spread ax paymens over a longer ime period. However, he VAT gap fell back o pre-recession levels in and There was also a fall in he share of sandard raed consumpion in and ; he effecive ax rae on corporae profis was lowered by firms being able o carry back losses agains recenly paid ax relaed o previous years liabiliies and carrying forward losses o be used when he firm reurns o profiabiliy. The carrying back of losses boosed repaymens in , while rading losses carried forward are expeced o be remain higher han prior o he downurn for a prolonged period, paricularly in he financial secor; and he effecive ax rae on labour income was affeced by he shif owards par-ime work. Par-ime workers generally face a lower marginal ax rae. In addiion, high-paying secors such as he financial secor end o be more cyclical han oher secors, reducing he ax ake from workers wih high marginal ax raes. a Sancak, C. e al. (2010). b Tax efficiency: he share of ax revenues in he ax base, normalised by he sandard ax rae. 21 Cyclically adjusing he public finances

28 Esimaing cyclical adjusmen coefficiens Overview of mehod 2.47 Cyclically-adjused ne borrowing b*, as a share of poenial oupu 16, can be defined as cyclically adjused governmen expendiure (G*) minus cyclically adjused receips (T*) minus. 17 b * n * * * [ G ( T i )]/ Y (3) i The cyclically-adjused receips and expendiure erms in equaion (3) can be esimaed using he elasiciies of ax receips ) and expendiure ) wih respec o he oupu gap: (, ygap ( g, ygap T * i, ygap i ( Y * / Y ) T i (4) G ( Y / Y ) * * g, ygap G (5) 2.49 The elasiciies are calculaed using a wo-sep approach. On he revenue side he firs sep is o calculae he elasiciy of revenue wih respec o he relevan ax base ( b ) and hen o calculae he elasiciy of he ax base o he oupu gap. The produc of hose elasiciies gives he oupu elasiciy of each ax caegory (i): (6) i, ygap i, b i bi, ygap 2.50 Similarly on he expendiure side he elasiciy of expendiure can be spli ino wo componens: he elasiciy of expendiure wih respec o is base (unemploymen) and ha of he base wih respec o he oupu gap: (7) g, ygap g, UU, ygap 16 Noe ha his definiion uses poenial oupu as he denominaor for he cyclically-adjused budge balance; whereas he one-sep approach uses acual oupu as he denominaor. To compare he resuls of he wo approaches herefore requires a lile algebraic manipulaion. The relaionship beween he wo mehods is discussed in more deail in Annex B. 17 Here G* is cyclically-adjused governmen expendiure (he cyclical elemen is assumed o be dependen on unemploymen); Ti* is cyclical adjused ax caegory i; and Y* is he level of poenial oupu. Cyclically adjusing he public finances 22

29 Esimaing cyclical adjusmen coefficiens The relevan ax and expendiure caegories 2.51 The saring poin for his approach is o idenify which ax and expendiure caegories are likely o have a cyclical elemen. The OECD idenifies corporae ax, personal income ax, indirec ax and social securiy conribuions on he receips side, and unemploymen benefis on he spending side. The economic bases ha correspond o hese ax caegories are wages and salaries, corporae profis and consumer expendiure and he main economic base for unemploymen benefis is he level of unemploymen To provide a comparable and consisen esimae of cyclically-adjused fiscal aggregaes he OECD uses he same ax and spending caegories and bases across all he counries ha i covers. We are able o develop his approach by allowing for he paricular srucure of he UK ax and expendiure sysem We herefore idenify income ax, naional insurance conribuions, non-oil and non-financial corporaion ax, financial secor corporaion ax, business raes, VAT, fuel duy, excise duies and capial axes as poenially cyclical elemens of receips in he UK. On he expendiure side we idenify Jobseeker s Allowance and oher DWP income-relaed benefis paid o jobseekers (such as housing and council ax benefis) as direcly relaed o unemploymen and herefore cyclical. The relevan economic bases for hese iems are se ou in Table Table 2.16: Tax and expendiure caegories and bases Tax /expendiure caegory Income ax Naional insurance conribuions Non-oil, non-financial corporaion ax Financial corporaion ax Business raes VAT Fuel duies Excise duies Capial axes Unemploymen relaed expendiure Tax /expendiure base Wages and salaries Wages and salaries Non-oil, non-financial corporae profis Financial corporae profis Oupu Consumer expendiure Consumer expendiure Consumer expendiure Equiy and house prices and propery ransacions Unemploymen Elasiciies of ax and expendiure bases wih respec o he cycle 2.54 The sensiiviy of each of he bases wih respec o he oupu gap is esimaed economerically using he funcional form in equaion (8). This equaion relaes changes in a ax base, X, (e.g. wages and salaries) o changes in he conemporaneous and lagged oupu gap. 23 Cyclically adjusing he public finances

30 Esimaing cyclical adjusmen coefficiens 2.55 The variables wages and salaries, consumpion and profis are expressed in erms of heir raio o poenial oupu. The level of unemploymen is expressed as he rae of unemploymen consisen wih poenial oupu. 18 For equiy prices, house prices and propery ransacions we use esimaes of heir gap from equilibrium discussed in more deail in Chaper The series are inended o represen a deviaion from an esimaed long run rend As before he oupu gap series used in his paper is aken from he OBR Working paper No. 1: Esimaing he UK s hisorical oupu gap as se ou in Box 2.3. All he esimaes are based on robus sandard errors. log( X ) n * 1log( Y i / Y i ) i0 (8) 2.57 This regression is esimaed for each of he nine differen bases idenified in Table The resuls are collaed in Table The coefficiens on he oupu gap can be inerpreed direcly as he shor-run elasiciies of each ax and expendiure economic base wih respec o he oupu gap. A coefficien greaer han 1 (in absolue value) implies ha swings in he economic cycle lead o he base moving by more han acual oupu. 18 The variable is he log(1-u/1-u*), where U* is he rae of unemploymen consisen wih poenial oupu or NAIRU. For our esimaes we use he OECD esimae of he NAIRU. 19 We use he so-called benchmark series for equiy prices and he OECD house price gap series. 20 We use fiscal year daa from o for he variables wages and salaries, consumpion and non- oil, non-financial corporae profi. For financial company profis daa is only available from 1982 and for he propery ransacions gap from The equiy and house price gaps daa is available from Cyclically adjusing he public finances 24

31 Esimaing cyclical adjusmen coefficiens Table 2.17: Elasiciies of ax and expendiure bases wih respec o he cycle Tax base Oupu gap Oupu gap (-1) R Squared MSE Wages and salaries 0.73*** (0.20) 1 Consumer expendiure 1.14*** (0.12) Non-oil, non-financial profis 4.16*** (0.60) Financial profis 1.18* (0.64) Equiy prices (gap) (2.60) House prices (gap) 3.48* (1.77) Propery ransacions (gap) 5.40* (3.00) Unemploymen -3.77*** -3.34*** (0.74) (0.62) 1 Robus sandard errors in brackes *** Significan a 1 per cen, ** Significan a 5 per cen, *Significan a 10 per cen. The equiy price gap equaion is significan a 20 per cen, if we exclude he las wo years from he sample he variable becomes significan a 5 per cen, see Annex A The resuls in he able show he average response of each base o he cycle using he whole daa sample. To check he robusness of he resuls we have also produced rolling window esimaes which can be found in Annex A. The esimaes indicae some variaion in coefficiens over ime, especially during he economic cycle Profi elasiciy 2.59 The elasiciy of profis o he cycle in Table 2.17 looks high compared o he coefficien on wages and salaries, alhough i is no inconsisen wih wha we would expec considering he curren composiion of profis and wages and salaries in oupu. 21 However he resuling semi-elasiciy of CT o he oupu gap, which is comparable o he one-sep approach, is 0.1 slighly lower han he 21 A 1 per cen increase in nominal GDP in is higher, equivalen, han he combined increase in profis and wages and salaries suggesed by he coefficien in Table This is because he variables used in he economeric esimaes, wages and salaries and profis, only accoun for around 65 per cen of GDP. 25 Cyclically adjusing he public finances

32 Esimaing cyclical adjusmen coefficiens coefficien obained from he one-sep approach individual regression (Table 2.3) Anoher way o esimae he elasiciy of profis o he oupu gap is o make use of he Naional Accouning ideniy ha naional income is he sum of labour compensaion (roughly speaking wages and salaries) and capial compensaion (roughly profis). This implies ha he elasiciy of profis wih respec o oupu mus be proporional o he elasiciy of wages and salaries wih respec o oupu, as, loosely pu, he wo series sum o oal oupu The esimae produced using his approach will depend on he assumpion made of he share of profis in naional income. If we assume ha he profi share is around 24 per cen, which is consisen wih Naional Accouns daa in 2010, he elasiciy is 1.9. If we however assume i is smaller or around 20 per cen of GDP, which is consisen wih he variables used in his economeric esimae, he elasiciy is 2.1. Using a simple meric of profis as share of profis and wages and salaries (around 29 per cen) gives us an elasiciy of A lower profi elasiciy such as he ones derived using his mehod migh be preferred because he rolling window regression resuls, shown in Annex A, sugges ha he sensiiviy of profis o he cycle has diminished over ime, while ha of wages and salaries has increased. In Table 2.20 and Table 2.21 we show he sensiiviy of he semi-elasiciy o ne borrowing using a profi elasiciy of 1.6 and 2.1. Overall we would assume profis o be more sensiive o he business cycle han wages and salaries for example due o he sickiness of nominal wages. Elasiciies of ax receips and expendiure wih respec o he base 2.63 The sensiiviy of each ax and expendiure caegory wih respec o is base is esimaed by he OECD using ax legislaion and relaed fiscal daa. The elasiciy of personal income ax and social securiy conribuions is, for example, esimaed on he basis of sauory ax raes and he income disribuion o which 22 Firsly we calculae he elasiciy of CT wih respec o he oupu gap, a combinaion of he elasiciy of non-financial, non-oil profis wih respec o he oupu gap (4.16) and he elasiciy of CT receips wih respec o profis (1.5). This gives us 6.2. As non-oil non-financial CT is only around 2 per cen of GDP, his implies non-oil non-financial CT o GDP moves by around 0.1 per cen of GDP. See Annex B equaion B2. Z 23 (1 (1 ) ws, y ) Z Y ( Y W & S) Y Z W & S Y Y * * (1 (1 )( * ) Y here Z is profis. Y Z Y Z Y Y W & S Z Z / Y Cyclically adjusing he public finances 26

33 Esimaing cyclical adjusmen coefficiens hey are applied. 24 For corporae ax, indirec ax and unemploymen benefis he OECD assumes an elasiciy of uniy We make use of ready reckoners produced by HMRC and DWP forecas models consisen wih fiscal forecass published in he OBR s Economic and fiscal oulook (EFO) documens, when available and appropriae. Furher informaion on he models can be found in he OBR s Briefing paper No. 1: Forecasing he public finances and he ready reckoners are discussed in he OBR s Briefing paper No. 4: How we presen uncerainy, published alongside his paper. The resuls are shown in Table 2.18 and represen he impac of a 1 per cen increase in he relevan base. Table 2.18: Elasiciies of ax and expendiure caegories o heir bases Tax/expendiure caegory Tax/expendiure base Elasiciy Income ax and NICs Wages & salaries 1.2 VAT Consumer expendiure 1.0 Non-oil, non-fin corporaion ax Non-oil, non-fin corporaion profi 1.5 Financial corporaion ax Fin corporae profi 1.5 Fuel duy Consumer expendiure 1.0 Excise duies Consumer expendiure 1.0 Business raes Oupu 1.0 Capial gains ax Housing 0.3 Inheriance ax Housing 0.8 Samp duy land ax Housing 1.2 Samp duy land ax Transacions 1.0 Capial gains ax Equiy 1.8 Inheriance ax Equiy 0.5 Samp duy shares Equiy 1.0 Unemploymen relaed benefis Unemploymen 1.0 Esimaing he overall elasiciy of he fiscal posiion o he cycle 2.65 The sensiiviy of each ax receips and expendiure iem o he economic cycle can now be calculaed by combining he esimaes in he wo previous secions. We presen hem in Table 2.19 boh showing he elasiciy in levels, or as a share of poenial oupu, and as a share of GDP consisen wih he one-sep approach (see Annex B). For unemploymen we combine he impac in year 1 and 2 for illusraive purposes. 24 For an individual worker he elasiciy of income ax (social securiy conribuions) wih respec o income is n n calculaed using he following equaion axperwor ker, w imai / i AV Here γi is he weigh of earnings i i1 group i of oal earnings MAi is he marginal income ax rae a poin i (earnings group i) on he earnings disribuion and AVi is he average income ax rae a poin i (earnings group i) on he earnings disribuion. i1 27 Cyclically adjusing he public finances

34 Esimaing cyclical adjusmen coefficiens Table 2.19: Elasiciies of ax and expendiure caegories o he oupu gap Tax/expendiure caegory Elasiciy level (sensiiviy) Elasiciy share of GDP (semielasiciy) Income ax NICs VAT Non-oil, non-fin corporaion ax Financial corporaion ax 1.8 >0.01 Fuel duy 1.1 negligible Excise duies 1.1 negligible Business raes Capial axes Spending (Unemploymen) To produce aggregaed ax elasiciy involves weighing he individual elasiciies for each ax caegory by heir share in oal receips. 25 On his basis he oal ax elasiciy, in levels, is esimaed o be 1.3 for year 1 and 0.0 for year 2. The oal expendiure elasiciy is esimaed o be for year 1 and for year 2. This represens a change in ax and expendiure in response o movemens in he oupu gap. This can be compared o he resuls from he one-sep approach wih minor adjusmens (see more deail in Annex B). We show he resuls in Table The sensiiviy of ne borrowing o he cycle can hen be measured by combining hese wo esimaes as shown in equaion (9). This is done by muliplying he elasiciies wih he raios of ax and expendiure o GDP. The resul ells us how much he level of ne borrowing, or ne borrowing as a share of poenial GDP, changes wih he cycle: b, y G T g, y ( ), y ( ) (9) Y Y 2.68 To compare his o he resuls from he one-sep approach we need o derive a semi-elasiciy, which esimaes how much ne borrowing as a share of acual GDP responds o he cycle. This can be calculaed using he following equaion. ~ G T b, y ( g, y 1)( ) (, y 1)( ) (10) Y Y 25 Average share from o , fiscal years Cyclically adjusing he public finances 28

35 Esimaing cyclical adjusmen coefficiens 2.69 The difference beween he wo esimaes is explained in more deail in Annex B. The semi-elasiciy includes a erm for borrowing as a share of GDP aking ino accoun he denominaor effec. Therefore if boh he level of borrowing and he size of he oupu gap are small, he difference beween he wo esimaes is small. Table 2.20: Toal ne borrowing elasiciy (negaives as for borrowing) Year 1 Year 2 Toal ax (sensiiviy) Toal expendiure (sensiiviy) Toal ax (semi elasiciy) Toal expendiure (semi-elasiciy) Ne borrowing (sensiiviy - equaion 9) Ne borrowing (semi-elasiciy - equaion 10) Ne borrowing (semi-elasiciy) profi elasiciy (2.1) Ne borrowing (semi-elasiciy) profi elasiciy (1.6) Overall, a one per cen change in he oupu gap is esimaed o change ne borrowing as a share of GDP by beween 0.47 and 0.54 in he firs year. This is consisen wih our one-sep esimae of 0.5 for he conemporaneous oupu gap se ou in he firs secion of his chaper. However, he wo-sep economeric resuls alone sugges a small coefficien on he lagged oupu gap, compared o he 0.2 coefficien found in he one-sep approach. This is parly due o he srucure of he wo-sep approach which essenially imposes a non-lagged srucure on he elasiciy beween he ax or expendiure iem and is base. We consider his issue furher in he nex secion The resuls from he one-sep and wo sep approaches have limied sensiiviy o differen measures of he oupu gap (Box 2.3) and he alernaive regression resuls repored in Annex A. For he wo-sep resuls, we have also invesigaed he effec of using differen assumpions for he elasiciy of profis wih he respec o he oupu gap. Table 2.20 shows ha i did no have a maerial impac on he resuls. 29 Cyclically adjusing he public finances

36 Esimaing cyclical adjusmen coefficiens Box 2.3: The oupu gap To cyclically adjus he public finances we generally need a prior esimae of he oupu gap. Such esimaes will always remain highly uncerain since he level of poenial oupu is never observed. The esimaes also remain sensiive o he assumpions, daa and mehodology used. The OBR s approach is o combine a range of indicaors of he cyclical posiion of he economy. Char A: Esimaes of he oupu gap 10 8 Per cen of poenial oupu Source: OECD, HMT, OBR OECD OBR HMT - March Budge 2010 Differen esimaes of he oupu gap can produce differen esimaes of he elasiciies of he budge balance wih respec o he oupu gap. Previous Treasury esimaes were produced using an alernaive oupu gap series which was consruced using an onrend poin mehod. The OECD also produces heir own esimaes of he oupu gap o calculae heir esimaes of he UK s cyclically adjused budge balance. To check he sensiiviy of our esimaes o differen oupu gap measures we have reesimaed our resuls using he Treasury and OECD measures. The resuls for he wo sep approach are shown in Table A and indicae ha he difference is relaively small overall. We also es he resul from he one-sep resul using he old HMT series, which give similar resuls (see Annex A). Table A: Cyclical adjusmen coefficiens Oupu gap Year 1 Year 2 OBR basic model OECD HMT Cyclically adjusing he public finances 30

37 Esimaing cyclical adjusmen coefficiens Incorporaing he effec of lags and a wider definiion of spending 2.72 There are wo ypes of lags in he way in which receips and expendiure can respond o he cycle. Firs, he lag from movemens in he oupu gap o movemens in he relevan economic base, and second he lags from changes in he base o changes in receips and expendiure The wo-sep approach esimaes he firs of hese direcly. The resuls sugges ha he only base showing a lag o he oupu gap is unemploymen, alhough his effec is found o be diminishing over ime as shown in Annex A. The wosep approach does no direcly ake ino accoun he second ype of lag from he economic base o receips and expendiure. Therefore o esimae his we have considered informaion on he srucure of he UK ax and benefi sysem and correced for he following: corporaion ax (CT) has a one year collecion lag for small businesses; and he final paymen of self assessmen (SA) and capial gains ax (CGT) liabiliies is in he nex financial year, i.e. a one year lag Adjusing for hose suggess ha around 0.1 of he esimaed conemporaneous receips elasiciy would acually be lagged by one year. This gives us an overall elasiciy of ne borrowing o he oupu gap of 0.5 in he conemporaneous year and 0.1 in he lagged year As menioned earlier he wo-sep approach only capures unemploymen relaed spending and could herefore be underesimaing he cyclicaliy of oal spending. In paricular, he resuls from he one-sep approach show ha looking a a wider measure of cyclical social securiy spending (including all DWP income relaed benefis and ax credis) raher han jus unemploymen, increases he coefficien on he lagged oupu gap by 0.1. Taking his ino accoun suggess ha we should add 0.1 o he lagged coefficien of he wo-sep resul. The final resul is herefore a conemporaneous coefficien of 0.5 and a lagged coefficien of 0.2. Table 2.21: Toal elasiciy wih lags and wider definiion of spending Year 1 Year 2 Toal ax Toal expendiure Ne borrowing (semi-elasiciy) Ne borrowing (semi-elasiciy) profi elasiciy Ne borrowing (semi-elasiciy) profi elasiciy Ne borrowing (semi-elasiciy) + cyclical social securiy Cyclically adjusing he public finances

38 Esimaing cyclical adjusmen coefficiens Conclusion 2.76 The pros and cons of each approach are summarised in Table Overall we believe ha he wo-sep approach has a number of advanages over he onesep approach Making use of HMRC and DWP s deailed forecas models means he relaionship beween ax and expendiure iems and heir economic bases should be beer esimaed han in he one-sep approach. Using he elasiciies embedded in he models ha he OBR uses o produce is fiscal forecas o calculae he cyclically-adjused fiscal aggregaes ensures here is an inernal consisency o he calculaions. These esimaes should also represen he marginal impac consisen wih he curren ax and expendiure sysem. By conras he one-sep approach is essenially esimaing he average relaionship over he enire sample period By esimaing he individual elasiciies of a number of ax and expendiure iems he wo-sep approach should also provide greaer undersanding of he conribuions of individual iems o he overall cyclical adjusmen coefficiens. The wo-sep approach also avoids he need o creae a policy-adjused ax series, which is difficul o consruc and prone o measuremen errors, making he economeric resuls more robus A poenial drawback of he wo-sep approach is ha i only capures unemploymen-relaed spending. However, i is possible o correc for his by drawing on resuls from he one-sep approach, as discussed above. Addiionally, i doesn ake ino accoun wider cyclical facors ha migh affec receips bu no he relevan economic base. This is discussed furher in Box 2.2. Cyclically adjusing he public finances 32

39 Esimaing cyclical adjusmen coefficiens Table 2.22: Comparing he approaches One-sep Pros - Poenially capures oher cyclical facors, like movemen in ax evasion - Looks a a broader measure of spending - Mehod is simple and ransparen Cons - Has o rely on adjused series ha are difficul o esimae - The economeric esimaes are herefore less robus - Esimaes he average impac no he marginal impac Two-sep - Avoids using adjused ax series - Provides greaer insigh ino which iems are driving he cyclical balance - Produces more robus economeric esimaes - Esimaes he marginal impac of movemen in base o receips/spending using HMRC and DWP models - Only akes ino accoun unemploymen relaed spending - Doesn capure oher cyclical facors ha could impac on he effecive ax rae, like movemens in ax evasion 2.80 Table 2.23 summarises he resuls produced by he wo approaches on a comparable basis (he ransformaions required o do his are explained in Annex B). Table 2.23: Cyclical adjusmen coefficiens Approach Year 1 Year 2 One-sep Two-sep basic model Two-sep wih lags Two-seps wih lags and adjusmen o spending The approaches produce broadly similar resuls. The adjused resuls of he onesep approach produce cyclical adjusmen coefficiens of 0.5 in he firs year and 0.2 in he second year. The wo-sep resuls produce 0.5 in he firs year and 0.1 in he second year once he lags in he srucure of he ax sysem are aken ino accoun. Incorporaing a wider measure of expendiure ino he wo-sep approach produces coefficiens of 0.5 and 0.2. We consider hese coefficiens o be appropriae for use in he OBR s EFO forecass, given our expecaions ha here are lags in he ax sysem and ha cyclical expendiure exends beyond jus unemploymen relaed benefis Our resuls differ slighly from hose of oher insiuions, discussed in Box 2.4, bu he differences are relaively small. In pracice, he esimae of he oupu gap used in he calculaion of cyclically-adjused deficis is more variable. 33 Cyclically adjusing he public finances

40 Esimaing cyclical adjusmen coefficiens Box 2.4: Alernaive cyclical adjusmen esimaes The OECD regularly produces esimaes of he elasiciy of he curren budge o he cycle for all is member counries, including he UK, using he wo-sep approach. The mos recen UK esimae, from 2005, poins o an overall elasiciy of a This is slighly smaller han our cenral wo sep esimae of 0.5 in year 1 and 0.2 in year 2, which akes ino accoun he lagged effec of a wider measure of cyclical social securiy. The difference is probably due o he fac ha he OECD uses a consisen mehod for all is member counries and ha limis is abiliy o ake ino accoun specific feaures of ax and expendiure sysems. We are able o allow for more disaggregaion of ax receips in our calculaions, use informaion from HMRC and DWP forecas models, ake ino accoun lagged responses inheren in he UK ax sysem and use more economeric esimaes insead of imposing uni elasiciies. For example, he OECD assumes a uni elasiciy of corporaion ax receips o profis for all counries. Using HMRC s forecas model we assume an elasiciy of 1.5. The ECB produces a comparable esimae for EU counries, including he UK, se ou in Bouhevillain e al (2001), bu wih a slighly differen approach discussed in more deail in Chaper 3. The approach aemps o correc for changes in he composiion of demand. The resuls poin o a semi-elasiciy of 0.65 in he firs year, close o our esimae over wo years. As wih he OECD esimae, having o produce consisen esimaes across he EU member saes limis he abiliy o fi he calculaions o each sysem. The main difference beween he OECD and ECB resuls is he esimaed response from income ax and unemploymen, which he ECB finds o be larger. a see Giouard and Andre (2005) 2.83 We can use he cyclical adjusmen coefficiens of 0.5 and 0.2 and he OBR hisorical oupu gap series o go back and esimae hisorical series of cyclical and srucural ne borrowing Char 2.2. For example, in he run up o he financial crisis in and srucural ne borrowing, adjused for he cycle, is esimaed o have been 2.7 and 3.5 per cen of GDP respecively. This is larger han previous HMT esimaes of 2.3 and 2.6 per cen, see Char 2.3, because of differences in oupu gap esimaes. The srucural posiion is also esimaed o have been slighly higher in mos of he 1990s. Given unchanged cyclical adjusmen coefficiens he OBR s forecas for srucural ne borrowing would remain unchanged. Cyclically adjusing he public finances 34

41 Esimaing cyclical adjusmen coefficiens Char 2.2: Srucural and cyclical PSNB Per cen of GDP Source: OBR CA PSNB (srucural) Cyclical PSNB Toal Char 2.3: Cyclical adjused PSNB, previous and updaed esimaes Per cen of GDP Source: HMT, OBR CA PSNB - OBR updaed oupu gap CA PSNB - HMT oupu gap 35 Cyclically adjusing he public finances

42 Esimaing cyclical adjusmen coefficiens Cyclically adjusing he public finances 36

43 Alernaive approaches o cyclical adjusmen 3 Alernaive approaches o cyclical adjusmen 3.1 This chaper looks a wo alernaive approaches o he cyclical adjusmen of he public finances. The firs approach uses a more srucural modelling approach, specifically a Srucural Vecor Auoregressive (SVAR) model, o allow for he influence of he fiscal posiion on he oupu gap. The second augmens he wosep approach o allow for he effecs of changes in he composiion of demand on he cyclically-adjused defici. SVAR model 3.2 The convenional approaches o cyclical adjusmen, discussed in Chaper 2, require a prior esimae of he oupu gap. Bu his suffers from wo main drawbacks (discussed in more deail in Annex C): firs, i reas he esimaion of he oupu gap and he cyclically-adjused curren balance as wo separae evens. I herefore ignores he possible feedback of fiscal policy o he oupu gap or reverse causaliy. If his feedback is presen i can bias downward he esimaed cyclical adjusmen coefficiens; and second, as Blanchard (1989) saes, measures based on he oupu gap are unnecessarily conroversial. There are many ways ha he oupu gap can be calculaed and he esimaed cyclically-adjused curren budge can be sensiive o he choice of mehod adoped. This is discussed in more deail in Box This secion explores an alernaive approach o cyclical adjusmen using a SVAR model. In his approach cyclical adjusmen and esimaion are ackled a he same ime and no prior esimae of he oupu gap is required. This direc approach herefore avoids some of he problems menioned above. 3.4 For furher deail on SVAR models see Annex D. In brief a vecor auo-regressive (VAR) model is a sysem where each variable is regressed on is own lags and he lags of oher variables in he sysem. A SVAR model is a form of VAR model where a cerain srucure has been imposed so ha all he variables in he model are deermined by he hisory of: 37 Cyclically adjusing he public finances

44 Alernaive approaches o cyclical adjusmen srucural shocks (also known as impulses) - he rick is o give hese economic meaning such as demand (business cycle) and supply (produciviy) shocks; and he impac of hese shocks on differen variables in he model. This is characerised by he impulse response funcion which shows how each srucural shock is propagaed ono each variable. Esimaing he cyclically-adjused curren balance wih an SVAR 3.5 In his secion we presen resuls for our esimaes of he cyclically-adjused curren budge in he UK following an idenificaion procedure similar o Blanchard and Quah (1989) using a wo variable VAR. 3.6 As all variables in he unresriced VAR are required o be saionary we esimae a wo variable VAR consising of: he growh rae of real GDP y; and he curren budge balance as a percenage of nominal GDP b / gdp so ha Y y b / gdp 3.7 We sipulae wo ypes of srucural shocks: produciviy shocks: hese are supply shocks ha only affec he rend growh rae of oupu; and business cycle shocks: hese can be inerpreed as emporary demand shocks and by definiion have no long-run impac on GDP growh. 3.8 Specifying hese wo shocks and heir long-run impac on he endogenous variables is sufficien o idenify he SVAR model. 3.9 The basic model has he form: Y C K e prod e e cycle (11) e y Where C*(K) is a marix of lag operaors which describes he impulse response funcions, i.e. how each of he srucural shocks affecs each of he model Cyclically adjusing he public finances 38

45 Alernaive approaches o cyclical adjusmen variables; and e is he vecor of shocks. The resricions give he following long run represenaion: y b / gdp b / y gdp c k 0 11 c k 0 21 k k 0 c k 0 22 k e e prod cycle (12) 3.10 Using lag selecion crieria we esimae a wo period lag for he SVAR model. The srucural produciviy and business cycle shocks are presened in Char 3.1 and he impulse response funcions are shown in Char 3.2. The cyclically adjused curren budge can be produced by using he business cycle shocks and he impulse response of he curren budge wih respec o hese shocks o deduce wha he curren budge would look like in he absence of hese shocks. The resuls are presened in Char Char 3.1: Srucural produciviy and business cycle shocks Percenage poins Source: OBR Produciviy Business cycle 1 In heory we could also consruc an esimae of he rend produciviy growh rae (and herefore he oupu gap) bu his is no he focus of his exercise. In his SVAR approach produciviy is really a cach all ype of supply side variable so populaion and capial may be included. 39 Cyclically adjusing he public finances

46 Alernaive approaches o cyclical adjusmen Char 3.2: Impulse response of he curren budge wih respec o each srucural shock Percenage poins Quarers Source: OBR Alernaive specificaions Produciviy Business cycle 3.11 The modeller has a high degree of freedom o impose various forms of srucure in he SVAR. In his secion we consider wo alernaives The firs alernaive (SVAR 2) replaces real GDP growh wih he unemploymen rae u. The srucural shocks in his model have he same inerpreaion as before bu now demand shocks are idenified by having no long run impac on he unemploymen rae. 2 Therefore he SVAR specificaion akes he following form: u u b / gdp b / gdp c k 0 11 c k 0 21 k k 0 c k 0 22 k e e prod cycle (13) 2 Boh variables are saionary according o uni roo ess and lag selecion crieria also sugges a second order VAR. We also considered a model using he change in he unemploymen rae bu his produced similar resuls. The SVAR could in principal be used o esimae he NAIRU by removing he effecs of business cycle shocks from he unemploymen rae. Cyclically adjusing he public finances 40

47 Alernaive approaches o cyclical adjusmen 3.13 As he unemploymen rae and he real GDP growh rae end o move ogeher, a priori, we migh expec here o be lile differences beween he wo models. 3 However his SVAR 2 model idenifies larger business cycle and smaller produciviy shocks han he previous specificaion The second alernaive specificaion (SVAR 3) follows Hjelm (2003) in choosing a hree variable model consising of: he unemploymen rae; he growh rae of real GDP; and he curren budge balance as a percenage of GDP. so ha Y u y b / gdp 3.15 The SVAR represenaion is herefore driven by hree shocks which we assume are: labour marke shocks: hese relae o facors like changes in social securiy sysems, demography, hyseresis ec. ha generae shifs in he verical longrun Phillips curve (and hence long run aggregae supply). There are no resricions imposed on his shock so i is allowed o affec he unemploymen rae, real GDP growh and he curren budge balance in he long run; produciviy shocks: as before hese are viewed as supply shocks, bu while we assume ha hese can have a long run impac on real GDP growh and he curren budge, we assume ha here is no long-run impac on he unemploymen rae. Following he raionale of he long-run Phillips curve he unemploymen rae is deermined only by he srucure of he labour marke; and business cycle shocks: as before hese can be inerpreed as emporary demand shocks ha by definiion have no long-run impac on he growh rae of real GDP (aggregae supply) or he unemploymen rae (he long-run Phillips curve). 3 Rule of humb esimaes of he Okun s Law for he UK sugges ha he unemploymen rae decreases by 0.5 o 0.75 pp for a 1 per cen increase in he real GDP relaive o poenial GDP. 41 Cyclically adjusing he public finances

48 Alernaive approaches o cyclical adjusmen 3.16 Specifying hese hree shocks and heir long-run impac on he endogenous variables is sufficien o idenify he SVAR model. Y C K e LM e prod e e (14) cycle e y The resricions give he following long run represenaion u u y y b / gdp b / gdp c k 0 11 c k 0 21 c k 0 31 LM k 0 0 e prod k c k k e cycle k c k c k e k 0 32 k Here he business cycle shock is idenified by having no long run impac on he unemploymen rae and real GDP growh rae, and he produciviy shock is idenified by having no long run effec on he unemploymen rae Comparisons of he hree cyclically-adjused curren budge esimaes are presened in Char 3.3. The differences highligh he relaive size and impac of he esimaed demand shocks in each se up. In he firs alernaive model (SVAR 2) hese demand shocks are esimaed o have a greaer impac on he curren budge resuling in a larger cyclical adjusmen. In he second alernaive (SVAR 3), here are wo sources of supply shocks labour marke and produciviy which likely reduces he conribuion of business cycle shocks o he dynamics of he curren budge and leads o a smaller cyclical adjusmen. (15) 4 All variables in he VAR are saionary and lag selecion crieria sugges a second order VAR. The model was also esimaed using he change in he unemploymen rae and produced similar resuls. Cyclically adjusing he public finances 42

49 Alernaive approaches o cyclical adjusmen Char 3.3: Cyclically-adjused curren budge 2 1 Forecas 0 Per cen of GDP Source: OBR CACB (EFO March 2012) CACB SVAR 1 CACB SVAR 2 CACB SVAR 3 Issues wih SVAR models 3.19 SVAR models have wo main advanages. Firs hey do no require a prior esimae of he oupu gap. Second, hey address he endogeneiy beween oupu (gap) and he curren budge ha migh oherwise lead o simulaneous equaions bias. However, here are also a number of objecions o he SVAR mehodology The relaively small number of variables in VAR models means ha he enire sysem ypically ends up being driven by a small group of fundamenal shocks such as demand and supply. 5 The effecs of oher relevan shocks are no fully capured in he model because hey don fi well ino hese classificaions. Furhermore, defining shocks as eiher demand or supply can be perilous As judgemens are required o idenify he SVAR sysem, Uhlig (1999) poins ou he possible degree of circulariy in SVAR conclusions. Assumpions imposed in previous work, which have no been empirically esed, may be used o jusify 5 Because a VAR model is esimaed as a sysem raher han a number of individual equaions, he number of coefficiens ha need o be esimaed grows quickly as he number of variables in he model increases. As a resul he number of degrees of freedom available in he esimaion run ou much faser- which usually means VAR models are resriced o low dimensions (i.e. a small number of variables). Here he problem is compounded by he daa being low frequency (fiscal year) which reduces he number of possible observaions/degrees of freedom available. 43 Cyclically adjusing he public finances

50 Alernaive approaches o cyclical adjusmen imposing a paricular se of resricions. The dynamics of he model can herefore reflec he prejudice of he modeller as much as he daa and informal resricions in he role of idenifying shocks lead o undisciplined daa mining. These issues make i difficul in pracice o use his mehod for forecas purposes. Componen mehod (ECB) 3.22 The fiscal posiion is likely o be sensiive o changes in he composiion of demand. Domesic demand led growh is, for example, likely o affec ax revenue more han growh led by he expor indusry. The ECB approach aemps o correc for such oupu composiion effecs by using separae esimaes of cyclical componens of individual ax and expendiure bases As wih he wo-sep approach discussed in Chaper 2, he ECB approach is disaggregaed - ax revenue is broken down ino individual ax caegories and he relevan ax bases are idenified. On he expendiure side unemploymen relaed benefis are considered o be cyclical and move wih changes in he unemploymen gap. Overview of mehod 3.24 Cyclically-adjused ne borrowing, b *, can be defined as he difference beween ne borrowing (b) and he cyclical componen of borrowing (b c ): b * b b n i c b b c i1 (16) i 3.25 Furhermore, b c can be defined as he cyclical componen of each budge caegory i. To compue b i c, in line wih he ECB approach, a rend series for each of he ax and expendiure bases is consruced. The rend series is used o esimae a gap series which represens he deviaion of he base (macroeconomic variable) from is equilibrium rend level. The gap series are analogues o he oupu gap, which is a gap series for oupu. In addiion o he gap series an esimae for he elasiciy of he ax receips and expendiure o he relevan base ) is esimaed. ( i i b, v b i c i i b iv b v c (17) i, 6 Bouhevillain e.al. (2001). Cyclically adjusing he public finances 44

51 Alernaive approaches o cyclical adjusmen i 3.26 Here V c is he gap of he corresponding macro-economic variable V in real erms from is rend level. Afer subsiuing equaion 17 in o equaion 16 he cyclical balance in year can be defined as. b * b n i1 b i i b V Vc, (18) i i 3.27 This mehod does no produce cyclical adjusmen coefficiens comparable o hose produced wih he approaches discussed in Chaper 2 and presened in Table This is because he correcion in relaion o he oupu gap varies over ime since he relaionship beween he various gap series and he oupu gap is no consan over ime. Elasiciies of ax and expendiure wih respec o heir base 3.28 In he ECB approach he sensiiviy of he ax receips and expendiure o heir bases are calculaed by using an economeric regression or derived from ax or expendiure regulaion similar o he OECD approach described in Chaper 2. In his paper we make use of he exising forecas ools used in he OBR s economic and fiscal forecas o assess he relaionship beween individual ax and expendiure caegories and heir relevan bases (see Table 2.18). The gap esimaes 3.29 In line wih Bouhevillain e al. (2001) we use Hodrick-Presco (HP) filers wih a smoohing parameer of 30 o esimae he gap measures for each of he following ax and expendiure bases: wages and salaries, non-oil, non-financial profis, financial profis, consumpion and unemploymen. The gap refers o he deviaion of he variable from is equilibrium growh pah. To correc for he end poin problem we exend he series using he OBR s laes forecas and an AR(4) model. The gap esimaes for wages and salaries and consumer expendiure are shown in Char 3.4. To deflae he series we use he consumpion and GDP deflaors. 45 Cyclically adjusing he public finances

52 Alernaive approaches o cyclical adjusmen Char 3.4: Wages & salaries, consumer spending and oupu gaps 8 Forecas 6 4 Per cen Source: OBR Real wage and salaries Oupu gap Real consumer spending 3.30 To undersand he relaionship beween he gap measures i is useful o look a correlaions over ime. If he gap measures differ markedly from movemens in he oupu gap i suggess an oupu composiion effec. The correlaion resuls in Table 3.1 indicae ha a composiion effec could be presen. Table 3.1: Correlaion wih he oupu gap Wages & Consumpion Non-oil, nonfin. Financial profis Unemploymen salaries gap gap profis gap gap gap Oupu gap Re-esimaing he srucural defici 3.31 Combining he gap esimaes and he elasiciies from Chaper 2 we can reesimae he srucural defici aking ino accoun composiion effecs by using equaion (18). The difference beween he resuls and he laes cyclicallyadjused curren budge (CACB) esimae is quie large, especially in The main reason is ha wages and salaries, an imporan variable for ax receips, has a low correlaion wih he oupu gap in recen years reflecing he relaively srong performance of he labour marke compared o he size of he fall in oupu. Cyclically adjusing he public finances 46

53 Alernaive approaches o cyclical adjusmen Table 3.2: Re-esimaed cyclically adjused curren budge Share of GDP Curren budge CACB (Composiion) CACB (Composiion wih adjusmen for capial axes) CACB (March 2012 EFO) Unlike he esimaes in Chaper 2 his approach does no provide a sraighforward way o incorporae cyclical adjusmen o capial ax receips since hey are no direcly relaed o movemens in oupu or oupu composiion. One way o incorporae heir effec would be o consruc cyclical asse price and ransacion gap series consisen wih he resuls from he economeric esimae in Chaper 2. Tha ells us how much hose gap series move wih he cycle. We do he opposie in Chaper 4 when we use cyclically adjused asse price and ransacion gap series, he residual, o adjus for flucuaions unrelaed o he cycle. The impac from capial axes using his mehod, shown in Table 3.2, is found o be relaively small The main benefi of he ECB approach is ha i aemps o correc for he composiion of demand which could give a beer picure of he srucural posiion. The main disadvanage is ha i relies on a simple esimae of a number of gap series which can be prone o measuremen error. This would be paricularly challenging for forecas purposes since he mehod applied a Hodrick Presco (HP) filer- implies an end poin problem where he esimaes are less reliable a he end of he daa series he area ofen of mos ineres. In addiion, unlike he mehods in Chaper 2, i does no produce a single cyclical adjusmen coefficien relaing borrowing o he oupu gap and herefore is less ransparen. I canno also easily ake ino accoun he cyclicaliy of capial axes The ECB approach looks a he effec of changes in composiion of demand, bu i does no explicily consider he effec of changes in he relaive prices of he demand componens. One furher possible refinemen of our cyclical adjusmen calculaions is o allow for he poenial effec of changes in he erms of rade. We consider his issue briefly in Box Cyclically adjusing he public finances

54 Alernaive approaches o cyclical adjusmen Box 3.1: Adjusing for he erms of rade If he fiscal balance depends heavily on revenue from commodiy expors or changes in he erms of rade, a correcion for movemens in relaive prices could give a beer idea of he underlying srucural balance. A simple way o do his is o look a movemens in he real income gap insead of he oupu gap (Turner (2006)). Real gross domesic income measures he purchasing power of oal income from domesic producion which includes gains from erms of rade changes. The difference beween gross domesic income and gross domesic produc is herefore equal o hose gains. The income gap (IG) is equal o he oupu gap (OG) plus he erms of rade gap imes he share of expors in GDP (EX). IG OG EX ( TT TT * ) The erms of rade gap can be esimaed using a Hodrick Presco (HP) filer similar o he calculaions in he ECB approach in Chaper 3. The gap for he UK is he difference beween he series in Char A. Char A: Income and oupu gap Per cen Source: OBR Oupu gap Income Gap Having esimaed he erms of rade gap we can calculae he income gap. High correlaion beween he income and oupu gap measures, as shown on Char A, indicaes lile need o correc for movemens in he erms of rade for he UK. To calculae he effec of changes in he erms of rade we re-esimaed he elasiciies of he ax and spending bases wih respec o he oupu gap by including he componen of he erms of rade gap. This should give us he response o he real Cyclically adjusing he public finances 48

55 Alernaive approaches o cyclical adjusmen income gap spli ino he oupu gap and he erms of rade gap. The following equaion was esimaed for each base (X). log( X / Y * ) n * n * ilog( Y i / Y i ) i ilog( EX ( T i T 0 / i i0 )) The erms of rade gap componen is shown o affec wages and salaries, consumpion and house prices in year 1. The elasiciy of he erms of rade gap componen o ax receips as a share of GDP is calculaed o be around However, since he erms of rade componen (he difference beween he wo series in Char A) has hisorically been very small his would amoun o an insignifican correcion o he fiscal posiion. Conclusion 3.35 Char 3.5 shows esimaes of he cyclically adjused curren budge using he preferred cyclical adjusmen coefficiens, he OBR s oupu gap series from Chaper 2 and he main resuls from he approaches presened in his Chaper. The main SVAR resul is smooher han he oher wo while he ECB resul, excluding capial ax adjusmen, indicaes a larger srucural defici in recen years and for he forecas period. Char 3.5: Esimaes of he CACB 2.0 Forecas 0.0 Per cen of GDP Source: OBR CACB (One-sep and wo-sep) CACB ECB mehod CACB SVAR 1 49 Cyclically adjusing he public finances

56 Alernaive approaches o cyclical adjusmen 3.36 The approaches are designed specifically o address some of he perceived weaknesses of he more sandard approaches discussed in Chaper The SVAR approach sideseps he requiremen o make an esimae of he oupu gap and can ake ino accoun any feedback from fiscal policy on he economic cycle. However, he idenifying procedure is subjecive and he accuracy of he esimaes largely depends on he resricions imposed The ECB mehod is designed o allow for he possibiliy ha shifs in he composiion of growh beween more or less ax-rich componens of aggregae demand can be imporan for he fiscal posiion. The resuls emphasise he imporance of he composiion of growh o he fiscal forecas. This is somehing he OBR will coninue o monior and analyse as a risk o he fiscal forecas in fuure EFOs. However he componen gap series require an esimae of he benchmark composiion of demand. Bu, unlike poenial oupu, here is no equivalen reference for he equilibrium srucure of aggregae demand. Furhermore he mehod is no as robus for forecas purposes since he simple gap esimaes are less reliable a he end of he daa series. Cyclically adjusing he public finances 50

57 Asse price and ransacion adjusmens 4 Asse price and ransacion adjusmens 4.1 The approaches discussed in he preceding chapers aemp o adjus he fiscal posiion for he effecs of he economic cycle on governmen receips and expendiure in order o produce an esimae of he underlying or srucural fiscal posiion. However, he underlying fiscal posiion can also be affeced by oher emporary facors ha do no necessarily move in line wih he cycle, such as movemens in commodiy and asse prices. 4.2 This chaper herefore considers wheher i is possible o adjus he fiscal posiion o ake accoun of flucuaions in asse marke prices and ransacions. In paricular our focus is on he effec of prices and ransacions in he housing and equiy markes on receips from capial axes. We also exend he analysis o consider wheher asse marke movemens have driven he level of receips from a wider se of axes, including income ax, VAT and corporaion ax. 4.3 This issue is paricularly relevan in he UK given he size of he financial secor relaive o GDP and relaively high levels of owner-occupaion of housing compared o oher counries. One of he key facors driving he deerioraion in he UK public finances following he financial crisis in 2008 was a sharp fall in receips from he housing and financial secors. An undersanding of how he level of prices and ransacions in asse markes is affecing ax receips is herefore imporan o assessing he susainabiliy of he UK fiscal posiion. Adjusing for asse prices and propery ransacions Overview of mehod 4.4 To esimae he degree o which asse markes may emporarily affec he underlying fiscal posiion i is firs necessary o assess he posiion of prices and ransacions in asse markes compared o some concep of heir equilibrium level. We firs discuss approaches which have been used o make such an assessmen, and he uncerainies involved. 4.5 We hen assess he poenial impac on ax receips of he esimaed deviaion of asse markes from he equilibrium level using boh he one-sep and wo-sep approaches from Chaper Cyclically adjusing he public finances

58 Asse price and ransacion adjusmens Esimaing asse-price gaps 4.6 Esimaing he deviaion of asse prices from heir equilibrium level is he key aspec of his analysis. However, his is far from sraighforward. Indeed, he very concep of asse markes deviaing from equilibrium is iself conenious, paricularly in more liquid markes such as hose for equiies. The efficien marke hypohesis would imply ha asse prices in liquid markes adjus o publicly available informaion very rapidly, and herefore should always reflec he fundamenal value. Any deviaion from he equilibrium would lead o he asse being perceived as valued incorrecly. There would hen be an incenive for marke paricipans o rade unil perceived misalignmens and arbirage opporuniies were eliminaed. Under his heory asse price movemens will always be he resul of new informaion, for example abou financial innovaion, demographic change and he expeced growh in real incomes. 4.7 However, a more widely acceped view is ha deviaions from fundamenal values may persis for reasons relaing o informaion or behaviour of marke paricipans. For example, informaion asymmeries, cogniive bias, herd behaviour and financial marke fricions have all been cied as causes of such movemen. Alhough ulimaely emporary, hese deviaions may be susained for periods ha could be significan for he public finances. The effec on ax receips of movemens of longer-erm or fundamenal componens of asse prices would be srucural, while revenues aribuable o he deviaion of prices from hose fundamenals would be emporary. 4.8 The OBR s forecass for asse markes conained in he Economic and fiscal oulook are based on condiioning assumpions. The equiy marke is assumed o grow in line wih nominal GDP implying a consan equiy price o company earnings (P/E) raio. The housing marke forecas is iniially he median expecaion of he Treasury s Comparison of Independen Forecass, and hereafer rises in line wih he rae of earnings growh. These approaches are no based on conceps of an explici equilibrium asse price, which limis he scope for applying he analysis in his chaper o he EFO forecas. 4.9 There is no consensus in he wider lieraure on he bes mehod for measuring equilibrium asse prices and herefore esimaing deviaions from he equilibrium. For example, Jaeger and Schucknech (2004) use a echnique o locae asse price booms and buss ha deermines urning poins in his series. A more mechanical approach is aken by Girouard and Price (2004), who aemp o disinguish he cyclical elemen of asse price movemens by using a Hodrick- Presco filer In is 2008 working paper HM Treasury used an approach based on defining a hisorical benchmark level for asse prices. I defined he housing price Cyclically adjusing he public finances 52

59 Asse price and ransacion adjusmens benchmark as he observed median value of he raio of real house prices o real disposable income per capia, and used he median raio of share prices o nominal GDP o define he share price benchmark. I hen compared acual prices o hese benchmark levels o esimae deviaions from equilibrium. We have updaed and replicaed his approach in his paper. In more recen work for he OECD, Dang and Price (2011) aemp o adjus fiscal balances for asse price cycles according o a more fundamenals-based approach. We have also used his approach in his paper and he gap series we have derived are discussed in more deail below. Equiy price gaps 4.11 For equiies, Dang and Price (2011) use a form of he Gordon equiy pricing formula o esimae values for fundamenal equiy prices. The formula saes ha in he long run he dividend yield plus he fuure growh in earnings should correspond o he risk-free ineres rae plus a risk premium. By subsiuing corporae earnings growh for he growh rae in dividends he seady sae relaionship should be: ( P / E)* (1 g) /( r g) (19) where r is he risk-free ineres rae, is he risk premium, and g is he long-run growh of earnings. This leaves P/E* as he equilibrium or expeced measure of he price/earnings raio. Cerain proxies have o be used in he consrucion of his esimae. The risk-free ineres rae is based on he nominal 10 year governmen bond yield, plus he spread beween he US AAA corporae yield and he US Treasury 10-year bond yield. Long-run corporae earnings growh is consrained o equal he year-on-year growh rae of he economy Following he OECD approach, he risk premium is se a 4 per cen. However, as wih is wo-sep approach o cyclical adjusmen, he OECD s choice here is parly moivaed by simpliciy and comparabiliy across naions. In realiy he risk premium is unlikely o be consan, and will change over ime wih aendan economic facors. House price gaps 4.13 For house prices, Dang and Price (2011) use a housing valuaion model based on Poerba (1984) where long-erm equilibrium house prices are deermined by he influence of he user cos of housing on he price-o-ren raio. In equilibrium he model shows rens equal o he user cos: ( P / R)* 1/( ia f ) (20) 53 Cyclically adjusing he public finances

60 Asse price and ransacion adjusmens where i a is he afer-ax nominal morgage ineres rae, he propery ax rae on owner-occupied houses, f he recurring holding coss consising of depreciaion, mainenance and he risk premium on residenial propery and he expeced capial gain on houses. The morgage rae is proxied by using 10 year governmen bond yields. The expeced capial gain is approximaed by a five-year moving-average of consumer price inflaion. Depreciaion, mainenance coss and he risk premium are assumed o be 4 per cen. Esimaing residenial propery ransacions gap 4.14 Cycles in he housing marke are associaed no only wih movemens in house prices bu also wih movemens in he level of propery ransacions. A sharp fall in house prices, relaive o rend, could have a larger effec on ax receips if i is associaed wih a fall in ransacions To consruc a gap series for propery ransacions we firsly need o esimae an equilibrium rend level of ransacions. We make a simple assumpion ha he rend level is consisen wih he average level of owner occupied duraion over ime. We calculae he average implied duraion (Du) by dividing he housing sock (H) wih propery ransacions (PD) 1, equaion 21. We find he average duraion o be around 19 years. n H PD Du 0 (21) N 4.16 The rend level of ransacions is hen simply calculaed as he housing sock divided by average duraion: H PD (22) Du Resuls using he benchmark and gap approaches 4.17 Chars 4.1 and 4.2 show he resuls for hese series using boh he OECD gap approach and he benchmark approach. The benchmark for equiy prices is he observed median value of he raio of share prices, using he FTSE all share, o nominal GDP. The house price gap differs from he previous HMT mehod, by 1 Daa on housing sock is from he Deparmen for Communiies and Local Governmen and daa on propery ransacions from HMRC Cyclically adjusing he public finances 54

61 Asse price and ransacion adjusmens using he raio of real house prices o real rens, raher han he HM Treasury approach using he raio of real house prices o real disposable income per capia. As can be seen in Char 4.1, using his approach he benchmark series closely follows he OECD approach Boh chars show he esimaed percenage poin deviaion of he asse price from he esimaed equilibrium value. Under boh approaches he level of esimaed deviaion from equilibrium is very volaile, someimes reaching up o 50 per cen above or below he esimaed equilibrium The wo equiy price series evolve in very differen ways over his ime period. For example, he OECD approach suggess ha equiies were around 50 per cen undervalued in he run-up o he financial crisis in 2008 which does no seem paricularly plausible. By conras he benchmark approach suggess equiies were close o heir equilibrium value in and hen undervalued by around 16 per cen of GDP by The choice of equiy risk premium in he OECD approach can affec he series quie significanly, which is a poenial disadvanage of his approach Hisoric movemens in boh he OECD and benchmark mehods for esimaing house prices gaps are more similar, bu here is some divergence over recen periods. The OECD approach suggess house prices have fallen oward heir equilibrium value since he financial crisis, which seems reasonably plausible, while he benchmark approach suggess hey remain significanly overvalued. This may be explained by he hisorically low ineres raes following he financial crisis, which will no be picked up in he benchmark approach. This may sugges he OECD approach is beer suied for analysis of house prices. The analysis suggess ha ransacions fell significanly below heir equilibrium level afer he financial crisis which is in line wih expecaions In neiher approach is here an obviously srong correlaion beween he asse price series and he oupu gap. This suggess ha asse price flucuaions may no be capured by he cyclical adjusmen coefficiens esimaed in Chaper 2. However, he significan differences beween he series generaed using he wo approaches highlighs he difficulies involved in generaing a robus esimae of asse price gaps. 55 Cyclically adjusing he public finances

62 Asse price and ransacion adjusmens Char 4.1: House price and ransacions gaps Per cen Source: OBR, OECD Benchmark OECD Transacions Oupu gap (RHS) Char 4.2: Equiy price gaps Per cen Source: OBR, OECD Benchmark OECD Oupu gap (RHS) Cyclically adjusing he public finances 56

63 Asse price and ransacion adjusmens Measuring he effec on receips 4.22 Having derived measures of he deviaion from a normal or equilibrium level, we hen assess he poenial impac on ax receips of he esimaed deviaion of asse markes from heir equilibrium levels using he one-sep and wo-sep approaches from Chaper 2. For our cenral esimae we choose a hybrid combinaion of asse price gap series which we believe o be mos plausible by using he benchmark equiy price gap series and he OECD house price gap series. One-sep approach 4.23 If asse prices move in sep wih he oupu gap hen he one-sep approach discussed in Chaper 2, which we have exended o cover capial axes, should already fully capure heir effec on he public finances. Bu he divergence beween he asse price gaps and he oupu gap shown in Chars 4.1 and 4.2 suggess ha movemens in asse prices may be subjec o somewha longer cyclical swings han sandard measures of he business cycle. Some of heir effec may herefore be missed by sandard approaches. We can invesigae his proposiion more formally by regressing he cyclically-adjused ax receips series derived in Chaper 2 on hese asse price gap series. Once again replicaing he previous Treasury analysis, we esimae he following regression: CATR 1CATR 1 2Egap 3Hgap 4 Tgap (23) where CATR is cyclically-adjused ax receips, Egap is he equiy price gap, Hgap is he house price gap and Tgap is he ransacion gap. 2,3 The sample period begins in due o a lack of daa availabiliy and ends in for he Treasury resuls, and for our updaed esimaes. For he hybrid combinaion of he benchmark approach for equiy prices and he OECD house price gap series, we exend he analysis o include he effec of he ransacions gap shown in Char 4.1. The resuls are shown in Table Calculaed using he ax coefficiens derived in he one-sep approach (0.1 x conemporaneous oupu gap x lagged oupu gap) and he OBR s esimae of he oupu gap. Noe ha his calculaion is applied o oal ax receips, no jus he subse of receips included in he regression. 3 Noe ha as discussed in paragraph 4.19 our definiion of he benchmark house price gap differs from he previous Treasury definiion. 57 Cyclically adjusing he public finances

64 Asse price and ransacion adjusmens Table 4.1: Asse price and ransacion effecs Consan CATR (-1) Equiy price gap House price gap Transacions gap HMT 2008 (Benchmark) OBR (Benchmark) 11.7*** 0.68*** 0.034*** 0.014** OBR (OECD) 8.0** 0.78*** OBR (Hybrid) 9.5*** 0.74*** 0.030*** 0.011* OBR (Hybrid & ransacions) 15.4*** 0.59*** 0.024** 0.011* 0.021** *** Significan a 1 per cen level; ** Significan a 5 per cen level;*significan a 15 per cen level The Treasury s 2008 resuls implied ha a 10 per over-valuaion of boh equiy and house prices would boos cyclically-adjused ax receips by around 0.44 per cen of GDP. 4 We find similar resuls for he benchmark approach, which sugges a slighly larger adjusmen of 0.48 per cen of GDP, wih a lile more of he adjusmen aribuable o equiy price flucuaions. The resuls using he OECD based fundamenals approach show no economic or saisical significance. The resuls using our preferred hybrid approach yield similar resuls o he benchmark approach bu wih slighly more limied saisical significance. The addiion of he ransacions gap o he hybrid equaion marginally reduces he imporance of he equiy gap, bu booss he overall size of he asse adjusmen Char 4.3 shows he addiional adjusmens ha would need o be made o he cyclically-adjused receips o adjus for asse price effecs using his hybrid and ransacions approach. 4 The resuls shown here were he Treasury s preferred esimaes and are median values of he repored resuls across a range of sample periods. The resuls are also he same as he poin esimaes for he sample period saring in Cyclically adjusing he public finances 58

65 Asse price and ransacion adjusmens Char 4.3: Adjusmens o cyclically-adjused ax receips for asse price and ransacion effecs: one-sep approach Per cen of GDP Source: OBR Equiy House Transacions Aggregae 4.26 The resuls appear reasonably inuiive. On his analysis, emporary buoyancy in asse prices may have oversaed he srengh of he srucural fiscal posiion by 1 per cen of GDP in , around he ime of he do com boom. House price and ransacion effecs have a similar effec in he run-up o he financial crisis, also boosing he apparen srengh of he srucural balance by 1 per cen of GDP in (wih some help from equiy prices). This analysis suggess ha over 2 per cen of he deerioraion in he fiscal posiion beween and relaes o a sharp fall in asse prices and housing ransacions. Two-sep approach 4.27 The nex secion considers he issue of asse price adjusmen in he conex of he wo-sep approach. We use, as before, ready reckoners of he sensiiviy of receips o prices and housing ransacions produced by HMRC, as shown in Table 4.2. These ready reckoners can hen be applied o he esimaed deviaion in he asse price from he equilibrium level o esimae he size of he revenue gain or loss from he divergence. The ready reckoners sugges ha asse price and ransacions mainly influence capial axes The elasiciies shown are calculaed for he OBR s laes forecas, and in his sense do no show he hisoric relaionship ha may have exised in he pas. In effec, hey show he change in receips under curren policies. We correc he asse price and ransacion gap series for cyclicaliy using he resuls from Chaper 2 where we esimaed how much he series move wih he oupu gap. 59 Cyclically adjusing he public finances

66 Asse price and ransacion adjusmens We do his o make sure we are capuring oher flucuaions no relaed o he cycle. Table 4.2: Elasiciy of ax receips o asse prices and ransacions Tax/spending caegory Asse Elasiciy Capial gains ax Housing 0.3 Inheriance ax Housing 0.8 Samp duy land ax Housing 1.2 Capial gains ax Equiy 1.8 Inheriance ax Equiy 0.5 Samp duy shares Equiy 1.0 Samp duy land ax Transacions These resuls, using our preferred gap series, sugges ha flucuaions in asse markes have led o emporary deviaions in capial ax revenue of close o 0.4 per cen of GDP. For example, in he run up o he financial crisis capial ax receips were poenially above heir srucural level by around 0.3 per cen of GDP. The bulk of his is due o he esimae ha house prices were overvalued in his period. Equiy prices were esimaed o be close o equilibrium value a his ime using he benchmark approach The esimaed deviaion in revenue in he run-up o he financial crisis looks small in comparison o he deerioraion in oal ax receips seen afer he crisis. This is parly because he approaches we have used sugges equiy prices were no overvalued in his period. In addiion, however, capial axes only represen a small share of oal ax. Therefore in he nex secion we exend he wo-sep approach o consider he poenial effec of asse price and ransacions gaps on a wider se of axes. Two-sep exended o oher axes 4.31 Movemen in asse prices and ransacions could also affec oher ypes of axes. For example, higher asse prices migh drive higher wages in he financial secor, especially bonus paymens, which could in urn boos income ax receips. Higher asse prices and increased volumes of propery ransacions could also have creaed a wealh effec, causing an increase in consumpion and herefore VAT and excise duy receips. Higher asse prices could also boos corporae profis, especially in he financial secor, and increase corporaion ax receips To invesigae wheher asse price and ransacions gaps affec oher ax receips we re-esimae he equaions in Chaper 2. We modify he equaions by adding he addiional gap series as explanaory variables. We use he same preferred measures of equiy and house price gaps as before. Cyclically adjusing he public finances 60

67 Asse price and ransacion adjusmens log( X n i0 i / Y * ) log( Hgap i ) n i0 n i0 log( Y i i i log( rans / Y i * i ) ) n i0 log( Egap i i ) (24) 4.33 The resuls sugges ha he equiy price gap affecs wages and salaries, consumpion and financial secor profis while he ransacions gap is found o affec consumpion. The house price gap is no found o significanly influence any of he oher ax bases. Table 4.3: The elasiciy of he ax base wih respec o various gap measures Tax base Oupu gap Equiy price gap Wages and salaries 0.35* 0.03* (0.20) (0.02) Consumer expendiure 0.77*** 0.04*** (0.11) (0.01) Fin profis * (1.57) (0.15) *** Significan a 1 per cen *Significan a 15 per cen Transacion Gap 0.02* (0.01) R squared This implies ha he equiy price gap affecs IT and NICs receips hrough wages and salaries; he equiy price and ransacion gaps affec VAT and excise duy hrough heir effec on consumpion, and he equiy price gap moves financial secor corporae profis. Table 4.4: Asse price and ransacion gap elasiciies Tax Receips Equiy price gap House price gap Transacion gap Share of Toal receips Income ax and NICs % VAT % Excise duies % Financial corporaion ax % Inheriance ax % Capial gains ax % Samp duy land ax % Samp duy shares % Toal elasiciy of receips as share of GDP Cyclically adjusing he public finances

68 Asse price and ransacion adjusmens 4.35 Combining hese esimaes wih he capial ax adjusmens we find ha he oal ax elasiciy o he equiy price gap is around 0.02, o he house prices gap around 0.01 and o he ransacion gap around Despie using a very differen approach he resuls are similar o he one-sep approach using our preferred gap series, alhough he coefficien on ransacion gap is smaller These esimaes are consisen wih he hisorical relaionship beween asse prices and ransacions and relevan economic ax bases like financial secor profis. This could have changed in he wake of he crisis due o srucural changes in he financial secor, for example relaed o he paymens of financial secor bonuses Using he wo-sep approach asse marke flucuaions are shown o have led o deviaions of ax receips from heir srucural level of up o around 0.6 per cen of GDP when wider axes are included Char 4.4. In he run up o he financial crisis he gap is around 0.2 o 0.4 per cen of GDP largely driven by house prices. Again his is parly due o he fac ha he equiy price gap is esimaed o have been relaively small in and Our resuls sugges a correcion of around 0.4 per cen of GDP in , due o he negaive effec of he equiy prices and ransacions gaps on income ax and VAT receips. This is, unlike he one-sep resuls, somewha offse by a posiive house price gap boosing capial axes. When we esimae he impac on capial axes in he wosep approach we adjus he gap series for he cycle. The resul is a larger posiive house price gap following he financial crisis compared o he unadjused series used in he one-sep approach. Cyclically adjusing he public finances 62

69 Asse price and ransacion adjusmens Char 4.4: Adjusmens o cyclically-adjused ax receips for asse price and ransacion effecs: wo-sep approach Per cen of GDP Equiy House Transacions Aggregae Source: OBR 4.38 A comparison wih he resul from he one-sep approach is shown in Char 4.5. The effec is smaller, which is mainly due o a smaller coefficien on he ransacion gap in he wo-sep resuls. The difference is mos pronounced in recen years, when he ransacion gap is esimaed o have been paricularly large. This illusraes ha no only can esimaes of he asse price gap series differ considerably, leading o very differen adjusmens for ax receips, bu ha small differences in he esimaed relaionship beween asse price and propery ransacions and ax receips also maer. This highlighs he difficuly of using his approach for forecas purposes. 63 Cyclically adjusing he public finances

70 Asse price and ransacion adjusmens Char 4.5: Addiional ax revenue from asse price and ransacion disequilibrium: one-sep and wo-sep resuls Share of GDP Two-sep One-sep Source : OBR 4.39 Using he resuls from he wo-sep approach shown in Char 4.4 we can show public secor ne borrowing broken down by cyclical borrowing, borrowing linked o asse prices and ransacion gaps and he residual, srucural balance - Char 4.6. In order o do his we re-esimaed he cyclical adjused PSNB using he resuls from Table 4.3 o avoid double couning he impac from equiy prices and ransacions on oher axes. Cyclically adjusing he public finances 64

71 Asse price and ransacion adjusmens Char 4.6: Cyclical, asse price and ransacions gaps, and srucural PSNB Per cen of GDP Source: OBR Cyclical PSNB Residual srucural PSNB Asse price and ransacion gaps PSNB Toal 4.40 Comparing his cyclically and asse price and ransacion gap adjused PSNB in Char 4.6 o cyclically adjused PSNB from Chaper 2 we find he series o be relaively similar. Small asse price and ransacion adjusmens offse somewha from lower cyclical adjusmen. The deviaions range from -0.4 o 0.4 per cen of GDP. In we find srucural ne borrowing correced for asse price and ransacion gap o be higher by around 0.4 per cen of GDP bu around 0.3 per cen of GDP lower in We could produce a similar char using he resuls from he one-sep approach which would sugges a larger adjusmen for asse price and ransacion gaps. This would lead o a larger deviaion from he hisorical srucural posiion shown in Chaper 2. Conclusion 4.42 This analysis confirms ha ax receips are sensiive o changes in asse prices and ransacions, as would be expeced given he relaive imporance of he financial and housing secors for UK ax receips However here are concepual problems wih adjusing our cyclically-adjused esimaes for asse prices effecs. The concep of an asse price gap is iself conroversial, and his is refleced in he reamen of asse prices in he EFO forecas, which implicily assumes ha no such gap exiss. This limis he scope for applying he analysis in his chaper o he EFO forecas. 65 Cyclically adjusing he public finances

72 Asse price and ransacion adjusmens 4.44 In addiion o he heoreical objecions, he analysis has highlighed a number of pracical problems in deriving equilibrium levels of asse prices. The wo approaches we have used here can generae very differen asse price gap series, and a several poins neiher series looks paricularly plausible. In paricular he differen mehods for calculaing he equiy price gap series give (unlike alernaive esimaes of he oupu gap) significanly differen oucomes, which would sugges large differences in adjusmens o receips. This finding is common o oher similar work produced by he OECD and he ECB, and here remains no consensus around he suiabiliy and mehod of including asse prices in cyclical adjusmen calculaions For hese reasons we do no hink i suiable o aemp o adjus for asse price and ransacion gap cycles in addiion o he economic cycle when esimaing he srucural posiion of he public finances. However, he OBR could use his ype of approach o underake risk and sensiiviy analysis in fuure EFO s The gaps series can hough be of pracical use in undersanding he hisorical relaionship beween asse prices, ransacions and he oupu gap. This informaion was for example used o cyclically adjus capial axes, in he wosep approach, in Chaper 2. Cyclically adjusing he public finances 66

73 Asse price and ransacion adjusmens 5 Conclusion 5.1 The specificaion of he Governmen s fiscal mandae in cyclically adjused erms requires he OBR o make an assessmen of he effecs of he economic cycle on he public finances. To dae, he OBR has adoped he Treasury s approach o cyclical adjusmen as presened in he 2008 Treasury working paper: Public finances and he cycle. In his paper we revisi he Treasury analysis and consider oher approaches including ha used by he OECD. Esimaing such coefficiens involves a number of uncerainies so we have aemped o ake a wide-ranging approach and have underaken sensiiviy analysis where possible. 5.2 We re-esimae he cyclical adjusmen coefficiens using boh he Treasury s approach and he wo-sep approach developed by he OECD. We find he wosep approach o have a number of advanages: i can be ailored o capure specific feaures of he UK ax and benefi sysem; i makes use of deailed and up-o-dae UK ax and benefi forecas models; i does no require he consrucion of a policy adjused-ax series; and he resuls are generally more robus economerically. 5.3 Our cenral esimae from he wo-sep approach, afer correcing for known lags in he ax sysem and exending he approach o capure a wider measure of cyclical spending, is a conemporaneous response of ne borrowing as a share of GDP o he oupu gap of 0.5 and a one year lagged response of 0.2. This is he same resul as was found using he Treasury approach in We also obained he same resuls when we re-esimaed he coefficiens using he Treasury s approach wih he laes daa. 5.4 We performed various sensiiviy ess on our resuls for robusness. The resuls, for example, were no found o be very sensiive o differen oupu gap series and were relaively sable over differen economic cycles. The wo-sep resuls were also esed for differen profi elasiciies. These did no change he resuls significanly. 5.5 On his basis he OBR inends o coninue o use coefficiens of 0.5 and 0.2 o produce esimaes of cyclically-adjused ne borrowing and he curren budge in fuure ediions of he Economic and fiscal oulook (EFO). While he approaches used all suggesed similar sized coefficiens we neverheless recognise he significan uncerainies involved in he esimaion process. The OBR will coninue o show he sensiiviy of is forecass o alernaive cyclical adjusmen coefficiens in he EFO. 67 Cyclically adjusing he public finances

74 Conclusion 5.6 In his paper we also consider he use of a srucural VAR model o cyclicallyadjus he public finances. This poenially addresses he issue ha he oupu gap may be iself affeced by fiscal policy, which could bias he economeric resuls of he OECD and Treasury approaches. However, he resuls are heavily dependen on he choice of modelling srucure and assumpions and we do no believe i would be appropriae o use hem in he EFO forecass. 5.7 We esimaed he cyclically adjused curren budge using he ECB approach which aemps o correc for changes in composiion of demand. The resuls highligh he imporance of he composiion of GDP for he public finances. However he componen gap series require an esimae of he benchmark composiion of demand. Bu, unlike poenial oupu, here is no equivalen reference for he equilibrium srucure of aggregae demand. Furhermore he mehod is no as robus for forecas purposes since he simple gap esimaes are less reliable a he end of he daa series. 5.8 Flucuaions in asse prices and propery ransacions ha are uncorrelaed wih he cycle can also affec ax revenues and poenially mask he rue srucural posiion of he public finances. In he paper we analyse he effec on UK ax receips of deviaions in equiy, house prices and housing ransacions from esimaed equilibrium levels. The analysis suggess ha asse prices and ransacions may have affeced he UK s pas fiscal posiion by as much as 1.3 per cen of GDP. Bu esimaing an equilibrium pah for asse prices is even more fraugh wih difficuly han esimaing poenial oupu. For his reason he OBR does no inend o incorporae an asse price adjusmen direcly ino he cyclical adjusmen mehodology. However he broad approach in his paper could be used in fuure EFOs o show he sensiiviy of he public finances o asse marke movemens, if i is judged o be a paricular risk o he forecass. 5.9 We re-esimae hisorical series for srucural ne borrowing using our esimaed cyclical adjusmen coefficiens and oupu gap series. We found srucural ne borrowing o have been somewha higher in he 1990s and in he run up o he 2008 financial crisis han previously esimaed by HMT. Since he cyclical adjusmen coefficiens used are he same as used by he Treasury he difference is enirely explained by differen esimaes of he oupu gap We would welcome any commens or suggesions on he approach and resuls we se ou here. Please [email protected]. Cyclically adjusing he public finances 68

75 6 References Bernanke, B., 1986, Alernaive explanaions of he money-income correlaion, Naional Bureau of Economic Research Working Paper 1842 Blanchard, O., 1990, Suggesions for a new se of fiscal indicaors, OECD Economics Deparmen Working Paper 79 Blanchard, O. and Quah, D., 1989, Dynamic effecs of demand and supply disurbances, American Economic Review, vol. 79, pp Bouhevillain, C. e al., 2001, Cyclically adjused budge balance: An alernaive approach, European Cenral Bank Working Paper 77 Dang, T. and Price, R., 2011, Adjusing fiscal balances for asse price cycles, OECD Economic Deparmen Working Paper 868 Darby, J. and Meliz, J., 2008, Auomaic sabilisers, Economic Policy, Ocober Farringon, S. e al., 2008, Public finances and he cycle, HM Treasury Economic Working Paper No. 5 Girouard, N. and André, C., 2005, Measuring cyclically-adjused budge balances for OECD counries, OECD Economics Deparmen Working Paper 434 Girouard, N. and Price, R., 2004, Asse Prices, One-off Facors and Srucural Budge Balances, OECD Economics Deparmen Working Paper 391 Goschalk, J., 2001, An inroducion ino SVAR mehodology, idenificaion, inerpreaion and inenions of SVAR models, Kieler Arbeispapiere 1072 Hjelm, G., 2003, Simulaneous deerminaion of NAIRU, oupu gaps and srucural budge balances: Swedish evidence, Naional Insiue Economic Research Working Paper 81 HM Treasury, 1995, Public finances and he cycle, The Saionery Office HM Treasury, 1999, Public finances and he cycle, The Saionery Office HM Treasury, 2003, End of year fiscal repor, Annex A, The Saionery Office 69 Cyclically adjusing he public finances

76 References Jaeger, A., and Schucknech, L., 2004, Boom-bus phases in asse prices and fiscal policy behaviour, IMF Working Paper 04/05 Murchison, S. and Robbins, J., 2003, Fiscal policy and he business cycle: a new approach o idenifying he ineracion, Deparmen of Finance Canada Working Paper Poerba, J.M., 1984, Tax subsidies o owner-occupied housing: an asse marke approach, The quarerly journal of economics, nr 98, pp Pybus, T., 2011, Esimaing he UK s hisorical oupu gap, OBR Working paper No.1 Quine, A. and Bouhevillian, K., 1999, Indicaors of srucural budge balances, Essays presened a he Banca d Ialia workshop, Perugia November 1998 Romer, C. and Romer, P., 2010, The macroeconomic effecs of ax changes: esimaes based on a new measure of fiscal shocks, American Economic Review 100. Sims, C., 1980, Macroeconomics and realiy, Economerica, vol. 48, pp 1-48 Sancak, C. e al., 2010, Tax revenue and response o he business cycle, IMF Working Paper 10/71 Turner, D., 2006, Should measures of fiscal sance be adjused for erms of rade effecs?, OECD Working Paper 519 Uhlig, H., 1999, Wha are he effecs of moneary policy on oupu? Resuls from an agnosic idenificaion procedure, Cenre for Economic Policy Research Discussion Paper 2137 Van den Noord, P., 2000, The size and role of he auomaic fiscal sabilizers in he 990s and beyond, OECD Economics Deparmen Working Paper 230 Cyclically adjusing he public finances 70

77 Sensiiviy and robusness A Sensiiviy and robusness One-sep mehod A.1 For he one-sep mehod we have esed he robusness of he resuls o wo key sensiiviies: he measure of he oupu gap used in he economeric regressions; and he sensiiviy of he regression coefficiens o he choice of sample period. A.2 In our cenral esimaes we use he oupu gap series published in he OBR s Working paper No 1: Esimaing he UK s hisorical oupu gap. Bu he oupu gap is an unobserved variable and esimaes of is size are herefore necessarily subjecive and inherenly uncerain. I is for his reason ha he OBR subjecs is forecass for he fiscal mandae measure o sensiiviy ess in Chaper 5 of he OBR s Economic and fiscal oulook. Those calculaions aemp o quanify he size of he error in he OBR s assessmen of he size of he curren oupu gap ha would likely cause he fiscal mandae o be missed. A.3 However, while esimaes of he curren size of he oupu gap are conenious, here is ypically more agreemen abou he ime series profile of he oupu gap, as can be seen in Box 2.3. We migh herefore expec he ime series regression resuls o be relaively insensiive o he choice of oupu gap. To invesigae his proposiion we have repeaed he regression analysis for he main equaion in Chaper 2, bu subsiuing he Treasury s previous esimae of he oupu gap (which was las updaed in he March Budge 2010) in place of our curren esimae. Table A.1 compares he resuls for he coefficiens of ineres: hose on he oupu gap. 71 Cyclically adjusing he public finances

78 Sensiiviy and robusness Table A.1: Sensiiviy of he resuls o he choice of oupu gap OBR oupu gap HMT oupu gap Equaion Coefficien on oupu gap Coefficien on lagged oupu gap Aggregae ax 0.14 TME Cyclical social securiy TME excluding CSS Aggregae ax 0.23 TME Cyclical social securiy TME excluding CSS A.4 The resuls are very similar in mos cases, wih only he coefficien in he aggregae ax equaion showing much of a deparure from he esimaes repored in Chaper 2. In general he esimaes using he HMT oupu gap end o repor slighly larger coefficiens, which can be explained by he slighly larger ampliude of he esimaed cyclical variaion in his measure. A.5 The use of hisorical daa means ha he esimaes reflec he average effec of changes in he oupu gap on he public finances over previous cycles. This means ha if he curren economic cycle differs from he average cycle, he relaionship beween he public finances and he oupu gap over he course of ha cycle will no be capured in he coefficiens. For example, he response of he labour marke o he recen recession appears ou of line wih hisorical experience on he basis of he curren vinage of daa. The smaller rise in unemploymen may imply a reduced sensiiviy o he cycle of social securiy paymens o ha implied by he esimaes of he average effec. On he receips side, here is some suggesion ha he recen large fall may reflec an increase in cyclical sensiiviy (alhough i may be linked o he asse price effecs discussed in Chaper 4). A.6 We herefore use recursive and spli-sample esimaion o es he sensiiviy of he regressions o he choice of sample period. For he recursive esimaes we experimen wih exending he sample boh forwards (i.e. gradually expanding he sample period from 1972) and backwards (i.e. expanding he sample period backwards from 2010). The resuls for hree of he main equaions esimaed in Chaper 2 are shown in Chars A.1 o A.3. Cyclically adjusing he public finances 72

79 Sensiiviy and robusness Char A.1: Recursive esimaion of he oupu gap coefficien: aggregae ax equaion Forward Backward Full sample Char A.2: Recursive esimaion of he oupu gap coefficien: TME excluding CSS equaion Forward Backward Full sample 73 Cyclically adjusing he public finances

80 Sensiiviy and robusness Char A.3: Recursive esimaion of he oupu gap coefficien: cyclical social securiy equaion Forward Backward Full sample A.7 The resuls are quie mixed and poin o some sensiiviy in he resuls o he choice of sample period. In paricular he resuls for he spending equaion show a large disconinuiy a he poin a which he second ime dummy is inroduced in 2002 o accoun for he discreionary spending increase. A.8 We also invesigae dividing up our sample period ino disinc economic cycles wih he periods idenified by fiscal years when he economy is hough o have been roughly a is poenial level (i.e. a zero oupu gap). This is an aemp o see if he cyclical sensiiviy of he public finances has evolved over ime, wihou he poenial bias inroduced by sample periods in which he oupu gap does no average close o zero. However i ineviably does so wih a considerable loss of sample size which severely limis he weigh ha can be placed on he resuls, which are summarised in Table A.2. Cyclically adjusing he public finances 74

81 Sensiiviy and robusness Table A.2: Sensiiviy of resuls o individual cycles Aggregae ax eqn TME equaion CSS equaion TME exc. CSS eqn All Sample OG OG (-1) OG OG (-1) OG OG (-1) OG OG (-1) OG OG (-1) *** 0.52*** 0.48* *** *** *** * * ** * ** *** -0.17** -0.31*** *** Significan a 1 per cen; **significan a 5 per cen; *significan a 10 per cen. A.9 In general he resuls are no robus o he reducion in sample size. The resuls for he period provide evidence ha he use of larger sample periods, which includes incomplee cycles, does no significanly bias he resul. Two-sep mehod A.10 We also esed he resuls from he wo-sep mehod by analysing how he elasiciy of ax and expendiure bases o he oupu gap varied over differen economic cycles. We also looked a he relaionship excluding he las wo years. 75 Cyclically adjusing he public finances

82 Sensiiviy and robusness Table A.3: Elasiciy of ax and expendiure base o he oupu gap, rolling cycles All Sample Tax base OG OG (-1) OG OG (-1) OG OG (-1) OG OG (-1) OG OG (-1) Wages and salaries 0.73*** (0.20) *** (0.20) 0.52 (0.45) 0.06 (0.25) 0.22 (0.21) 1.04* (0.17) Consumer expendiure 1.14*** (0.12) 1.17*** (0.13) 0.78* (0.37) 0.77** (0.25) 1.20*** (0.20) Non-oil, nonfin profis 4.16*** (0.60) 4.26*** (0.63) 7.06** (2.90) 4.11*** (0.67) 1.83** (0.69) 2.63** (0.84) Fin profis 1.18* (0.64) 1.46** (0.66) 2.92 (1.88) 2.86* (1.37) Equiy price Gap 3.79 (2.60) 4.75** (2.16) 0.58 (2.89) 8.15*** (1.60) House price Gap 3.48** (1.77) 2.77 (1.83) 3.09 (3.98) 2.89** (1.18) Transacion gap 5.40** (3.00) 6.85** (2.99) 2.95*** (0.93) 7.95*** (2.11) 8.36 (6.78) Unemploymen -3.77*** (0.74) -3.34*** (0.62) -3.40*** (0.83) -3.60*** (0.72) -4.33*** (0.89) -6.92*** (0.92) -9.43*** (1.69) -3.90*** (0.64) -1.91** (0.78) 1 Robus sandard errors *** Significan a 1 per cen; **significan a 5 per cen; *significan a 10 per cen. A.11 For wages and salaries he coefficiens are no significan in he cycle 1977 o 1986 and 1987 o 1997 bu here is a srong conemporaneous effec in he economic cycle 1998 o 2008 suggesing ha he relaionship has changed somewha over ime. For financial company profis, equiy prices and house prices he coefficien is also no significan in he economic cycle A.12 The effec on non-oil, non-financial profis diminishes over ime and he ime lag disappears. The relaionship beween he oupu gap, equiy prices and ransacions varies over ime and he effec of he lagged oupu gap on unemploymen is diminishing in he cycle A.13 Using he elasiciies from Table A.3 we can esimae he oal ne borrowing or budge balance semi-elasiciy, using hisorical averages for receips and expendiure as a share of GDP over o Table A.4: The budge balance semi-elasiciy Year 1 Year 2 Ne borrowing ( ) Ne borrowing ( ) Ne borrowing ( ) Ne borrowing ( ) Ne borrowing (All sample) Ne borrowing (All sample) wih lags Cyclically adjusing he public finances 76

83 The relaionship beween he one-sep and wo-sep approaches B The relaionship beween he one-sep and wo-sep approaches The relaionship beween he wo mehods B.1 The wo-sep approach produces ax and expendiure elasiciies ha represen percenage changes as a share of poenial oupu induced by a change in he oupu gap, equaion (B1). Those elasiciies are ofen referred o as sensiiviy elasiciies. The one-sep approach on he oher hand produces semi-elasiciies ha represen a change in he level of ax and expendiure as a share of acual GDP induced by a change in he oupu gap (equaion (B1)). T d Y semi elasiciy :, dy Y dt Y sensiivi y : *, (B1) dy T T Y, y B.2 Equaion (B2) shows how he sensiiviy elasiciy for ax receips can be ransformed o he semi-elasiciy using he chain rule. A similar ransformaion works for expendiure. Semi elasiciy T d dt Y T T T T, Y 1* y 1* (B2) dy dy Y Y Y Y :. B.3 The conemporaneous esimae of he ax sensiiviy o poenial GDP from he wo-sep approach was around 1.1 afer allowing for clear lags in he sysem, see paragraph 2.72; he corresponding semi-elasiciy would herefore be around 0.03, assuming ax receips are around 37 per cen of GDP. Similarly he expendiure sensiiviy o poenial GDP was esimaed o be around -0.04; he corresponding semi-elasiciy would be close o 0.4. B.4 The reason for he difference is ha he semi-elasiciy relaes o he raio of ax and expendiure o GDP while he sensiiviy elasiciy relaes o he level of ax and expendiure, or ax and expendiure as a share of poenial GDP. Any 77 Cyclically adjusing he public finances

84 The relaionship beween he one-sep and wo-sep approaches change in oupu is likely o be mached by a change in ax receips leaving he ax o GDP raio broadly unchanged, a semi-elasiciy of around zero bu suggesing a close o one-o-once change in he level of revenue o oupu a sensiiviy elasiciy of around one. B.5 On he expendiure side, only unemploymen relaed benefis are assumed o be cyclical and he oher 99 per cen of expendiure is no. As discussed elsewhere, his is a reasonable assumpion for much, bu no of all ousanding componens of expendiure. I does however sugges ha a change in oupu is likely o have only a limied effec on he level of governmen expendiure, suggesing a sensiiviy elasiciy of close o zero, bu some effec on he raio of expendiure o GDP relaed o changes in he denominaor. B.6 To perform he same ransformaion on he lagged response (year 2) on receips and expendiure he following formula applies: 1 T Semi elasiciy : T, Y 1. Y * (B3) Y B.7 This suggess ha he sensiiviy elasiciy from he wo-sep mehod is 0.1 in year 2 for ax and expendiure, afer allowing for lags in he ax sysem. Ne borrowing and he cycle B.8 Adjusing for he difference in definiions, he wo approaches show similar oucomes for boh ax and expendiure and herefore give broadly similar resuls when i comes o correcing ne borrowing or he budge balance. The sensiiviy elasiciy, using he resuls from he wo-sep approach, ells us how much ne borrowing would move in levels in response o changes in GDP - equaion (B4). I is consruced as he sum of he wo expendiure and ax sensiiviy parameers weighed by heir raio o GDP. This elasiciy should herefore be used when presening he cyclical adjused ne borrowing or curren budge as a share of poenial oupu. 1 The wo-sep mehod aemps o esimae he following relaionship (here X represens ax receips or * * * expendiure) log( X / Y ) 0 log( Y / Y ) 1 log( Y 1 / Y 1 ) (Y* is poenial oupu). If we * subrac log( Y / Y ) from boh sides we * * have log( X / Y ) ( 0 1) log( Y / Y ) 1 log( Y 1 / Y 1 ) which is he esimae produced by he one-sep mehod. This is a simple way o show how he wo mehods relaed when i comes o he lagged oupu gap impac, his is only consisen wih variables expressed as a share of poenial oupu. Cyclically adjusing he public finances 78

85 The relaionship beween he one-sep and wo-sep approaches 79 Cyclically adjusing he public finances Y G Y T Y G Y dy G dg Y T Y dy T dt dy dg dy dt Y g Y Y b,,, * * : (B4) B.9 The corresponding semi-elasiciy, from he one-sep approach, on he oher hand would ell us how much ne borrowing as a share of acual GDP would move in line wih changes in GDP or he oupu gap. Y G T Y G Y T Y G Y T Y dy Y G d Y dy Y T d Y g Y Y g Y Y b,,,,, 1 1 : ~ (B5) B.10 The main difference is ha a erm for ax receips minus expendiure as a share of GDP is included in equaion (B5), which capures he effec of any change in GDP on he denominaor of ne borrowing or he curren budge. B.11 I is analyically more rigorous o presen he fiscal aggregaes as a share of poenial oupu raher han acual oupu. This would correcly ell you wha he raio would be if he economy were a poenial. However since mos fiscal numbers are presened as a share of acual GDP he balance is rarely presened in ha way. B.12 Therefore i seems more appropriae o coninue o use a semi-elasiciy. The OECD, for example, uses he wo-sep approach o produce a sensiiviy adjusmen parameer before ransforming o a semi-elasiciy.

86 The relaionship beween he one-sep and wo-sep approaches Cyclically adjusing he public finances 80

87 C Simulaneous equaion bias and he problem of idenificaion C.1 The impac of he oupu (gap) on he curren budge can be esimaed using he following simple OLS regression: Lb Bby Ly eb b 1 y Bbb, C.2 where b is he curren budge, Lb (C1) y is oupu (or he oupu gap), B by Ly B bb are lags of oupu and he curren budge respecively, and b e, he residual. The coefficien 1 can hen be used o adjus he curren budge for he effec of oupu. C.3 Oupu eners equaion (C1) conemporaneously and is in effec reaed as an exogenous variable. However, his is unlikely o be he case in pracice as oupu will also be driven in par by he curren budge such ha: Lb B yy Ly e y y 2b B yb, (C2) C.4 If here is a significan feedback from he curren budge o oupu 2 0 simply esimaing (C1) by OLS will yield a biased esimae of he coefficien 1 ha is he effec of oupu on he budge balance. This is because oupu will now be correlaed wih he residual in (C1) which conradics he necessary condiion for unbiased esimaion 1. and 1 If Covy, e b 0 implying ha posiive shocks o he budge balance (higher axes or lower governmen expendiure) reduce oupu 2 0 hen 1 will be smaller han he rue srucural parameer and he effecs of he economic cycle underesimaed. The same issue would apply if we were esimaing a fiscal impac model such as equaion (C2) where 2 measures he impac of he curren budge balance on oupu. Any posiive feedback beween oupu and he budge balance 1 0 would lead o a biased coefficien if esimaed by OLS such ha he esimaed coefficien 2 would be closer o zero han he rue srucural parameer. 81 Cyclically adjusing he public finances

88 Simulaneous equaion bias and he problem of idenificaion C.5 One way of hinking abou his poenial bias is conneced wih he idea of idenificaion. Clearly (C1) could easily be rearranged so ha i has oupu on he lef hand side and he curren budge on he righ hand side of he equaion in which case i would have he same funcional form as (C2). Therefore, if (C1) is esimaed by OLS i is unclear wheher we are acually esimaing a model of he cyclically-adjused curren budge or a fiscal impac model which shows he effec of he curren budge on oupu. The coefficien of 1 is likely o be inconsisen reflecing an average of he underlying srucural parameers 1 and 2 where he weighs depend on he relaive sizes of he srucural disurbances e b, and e,. Because i is plausible ha 0 and 0 hen he average of coefficiens y 1 will be lower han he rue srucural parameer of 1. This is he essence of simulaneous equaions bias. C.6 Idenificaion could be achieved if we were able o find variables ha affeced oupu bu were uncorrelaed wih he residuals in (C1). These variables would essenially ac as insrumens for oupu in (C1), which could be esimaed using insrumenal variable echniques such as wo sage leas squares (2SLS) and he generalised mehods of momens (GMM) esimaors o derive unbiased esimaes of C.7 However, as Sims (1980) lays ou in his famous criique of dynamic simulaneous equaions models, i is difficul o find ruly exogenous variables in macroeconomics o use as insrumenal variables. For example, moneary policy variables may be considered o be a good insrumen for oupu, bu he curren budge balance iself is parly deermined by moneary policy variables such as ineres raes on governmen bonds and Treasury bills. 2 Murchison and Robbins (2003) use moneary policy variables, exchange raes and US GDP as insrumens in heir model of he Canadian cyclically adjused budge balance. Their resuls show he cyclical adjusmen coefficiens are around wice as large under GMM (2SLS) han OLS. Cyclically adjusing he public finances 82

89 Srucural VARs and idenificaion D Srucural VARs and idenificaion D.1 A vecor auo-regressive (VAR) model is a sysem where each variable is regressed on is own lags and he lags of oher variables in he sysem. An SVAR is a VAR model where a cerain srucure has been imposed so ha he variables in he sysem are deermined by he hisory of: srucural shocks known as impulses; and he impac of hese shocks on differen variables in he sysem, which is characerised by an impulse response funcion. D.2 One of he key elemens of SVAR modelling is imposing a srucure which gives hese srucural shocks economic meaning as well as impulse response funcions ha align wih economic heory or empirical work. 1 Because all variables in he sysem are reaed as endogenously deermined, an SVAR couners he Sims criique regarding he incredible idenifying resricions surrounding exogenous variables. D.3 The saring poin of he SVAR is o express he bivariae sysem in (C1) and (C2) in VAR form: where Y B L Y e (D1) Y b y, , BL B B bb yb L L B B by yy L L and e e e b, y, D.4 The reduced form of (3) can hen be esimaed by OLS as follows Y L B Y u (D2) 1 Goschalk (2001) provides a useful survey of SVAR models and heir inerpreaion. 83 Cyclically adjusing he public finances

90 Srucural VARs and idenificaion 1 D.5 where B B are he reduced form coefficiens and u 1 e are he reduced form residuals. D.6 The nex sep is o conver he VAR ino is moving average represenaion so he endogenous variables are expressed as a funcion of he reduced form innovaions. Y 1 I B L u (D3a) Lu Y C (D3b) b y u u b, y, C C bb,1 yb,1 C C by,1 yy,1 u u b, 1 y, 1 C C bb,2 yb,2 C C by,2 yy,2 u u b, 2 y, 2... (D3c) D.7 This is he firs represenaion of he impulse response funcion, showing how each variable is deermined by a hisory of shocks. The only problem is ha he sysem is no ye idenified. We can race hrough he impac of a shock on he economic variables in he sysem, bu he shocks hemselves have no economic meaning. The reduced form residuals are simply a linear combinaion of he underlying srucural innovaions. D.8 Therefore he sysem needs o be decomposed so ha he endogenous variables reflec he hisory of shocks o he srucural innovaions: Y C L 1 u (D4a) Y Le * C (D4b) C C L conains he impulse response o he srucural innovaions 1 D.9 where e e in u D.10 However, idenificaion will ypically require a number of resricions o be placed on he sysem. These generally ake he following forms: Orhogonaliy: srucural innovaions are orhogonal meaning ha hey are uncorrelaed cov( e b,, e y, ) 0. Bernanke (1986) describes srucural innovaions as primiive forces, no observed by economericians, which buffe he sysem. This, however, does no mean ha he endogenous variables in he sysem are no correlaed; in fac he opposie is likely because hey are driven by he same primary shocks; Cyclically adjusing he public finances 84

91 Srucural VARs and idenificaion Normalisaion: i is common pracice o sandardise he sysem so ha he impulse response funcions are expressed in erms of uni innovaions in he srucural shocks; and Idenifying resricions on : here are various oher ypes of resricions ha can be imposed on he sysem; hese normally place shor- or long-erm resricions on he response of endogenous variables in he sysem o he srucural innovaions. For example, Quine and Bouhevillain (1999) impose he shor-erm elasiciy of he budge balance o oupu in heir SVAR model of he French cyclically-adjused budge balance. Likewise, Blanchard and Quah (1989) impose long-run resricions on he impac of demand and supply shocks in he economy. 85 Cyclically adjusing he public finances

92