NBER WORKING PAPER SERIES INFLATION IMPLICATIONS OF RISING GOVERNMENT DEBT. Chryssi Giannitsarou Andrew Scott

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1 NBER WORKING PAPER SERIES INFLATION IMPLICATIONS OF RISING GOVERNMENT DEBT Cryssi Giannitsarou Andrew Scott Working Paper 2654 ttp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 050 Massacusetts Avenue Camridge, MA 0238 Octoer 2006 We tank Boris Glass for extensive researc assistance and support. We are also grateful to participants at ISOM 2006 and EEA-ESEM We are particularly grateful to Domenico Giannone, Eric Leeper and Lucrezia Reiclin for teir comments and suggestions for improving tis paper. Te views expressed erein are tose of te autor(s) and do not necessarily reflect te views of te National Bureau of Economic Researc y Cryssi Giannitsarou and Andrew Scott. All rigts reserved. Sort sections of text, not to exceed two paragraps, may e quoted witout explicit permission provided tat full credit, including notice, is given to te source.

2 Inflation Implications of Rising Government Det Cryssi Giannitsarou and Andrew Scott NBER Working Paper No Octoer 2006 JEL No. E3,E62 ABSTRACT Te intertemporal udget constraint of te government implies a relationsip etween a ratio of current liailities to te primary deficit wit future values of inflation, interest rates, GDP and narrow money growt and canges in te primary deficit. Tis relationsip defines a natural measure of fiscal alance and can e used as an accounting identity to examine te cannels troug wic governments acieve fiscal sustainaility. We evaluate te aility of tis framework to account for te fiscal eaviour of six industrialised nations since 960. We sow ow fiscal imalances are mainly removed troug adjustments in te primary deficit (80-00%), wit less sustantial roles eing played y inflation (0-0%) and GDP growt (0-20%). Focusing on te relation etween fiscal imalances and inflation suggests extremely modest interactions. Tis post WWII evidence suggests tat te widely anticipated future increases in fiscal deficits, need not necessarily ave a sustantial impact on inflation. Cryssi Giannitsarou Faculty of Economics University of Camridge Austin Roinson Building Sidgwick Avenue Camridge CB3 9DD, UK cg349@cam.ac.uk Andrew Scott Department of Economics London Business Scool Sussex Place, London NW 4SA, UK ascott@london.edu

3 INFLATION IMPLICATIONS OF RISING GOVERNMENT DEBT C. Giannitsarou y A. Scott z Octoer 2, 2006 Astract. Te intertemporal udget constraint of te government implies a relationsip etween a ratio of current liailities to te primary de cit wit future values of in ation, interest rates, GDP and narrow money growt and canges in te primary de cit. Tis relationsip de nes a natural measure of scal alance and can e used as an accounting identity to examine te cannels troug wic governments acieve scal sustainaility. We evaluate te aility of tis framework to account for te scal eaviour of six industrialised nations since 960. We sow ow scal imalances are mainly removed troug adjustments in te primary de cit (80-00%), wit less sustantial roles eing played y in ation (0-0%) and GDP growt (0-20%). Focusing on te relation etween scal imalances and in ation suggests extremely modest interactions. Tis post WWII evidence suggests tat te widely anticipated future increases in scal de cits, need not necessarily ave a sustantial impact on in ation. JEL classification: E3, E62 Keywords: Fiscal de cit, scal sustainaility, government det, in ation, intertemporal udget constraint.. Introduction Figures and 2 sow recent scal trends for six large industrialised nations. Levels of government det increased markedly during te 970s, ten stailised and improved during te 980s and 990s, ut ave recently sown signs of furter deterioration. Wit OECD countries experiencing an ageing population, it is widely expected tat scal positions will worsen yet furter in coming decades (see inter alia Roseveare, Leifritz, Fore and Wurzel, 998, for projections). Tese considerations raise tree important issues: (a) Is current scal policy sustainale? () How ave OECD governments acieved scal sustainaility in past decades? (c) Wat are te implications for in ation of tese projected rising scal de cits? Tis paper seeks to provide insigts to eac of tese tree questions. Key to our analysis is te intertemporal udget constraint of te government. To answer te rst question (on sustainaility), we use te metodology of Giannitsarou and Scott (2006) and derive a log linear approximation to te intertemporal udget constraint. Using tis framework, we sow ow det sustainaility requires an equilirium relationsip etween te market value of government det, te stock of narrow money and te levels of government revenue and expenditure. We sow ow to estimate We tank Boris Glass for extensive researc assistance and support. We are also grateful to seminar participants at ISOM 2006, and EEA 2006 Vienna. We would like to tank in particular Domenico Giannone, Eric Leeper and Lucrezia Reiclin for teir comments and suggestions for improving tis paper. y Faculty of Economics, University of Camridge and CEPR. cg349@cam.ac.uk. z Economics Department, London Business Scool and CEPR. ascott@london.edu.

4 Inflation and Rising Det 2 tis relationsip and derive a measure of sustainaility for six OECD countries and use our estimates to caracterise te dynamics of scal adjustment for our six countries. In order to answer te second question (ow do governments acieve scal adjustment) we sow analytically ow deviations from te equilirium relationsip etween det, money and te primary de cit ave to e met troug future canges in eiter primary de cits, monetary liailities, real interest rates, in ation or GDP growt. Using te VAR metodology proposed y Campell and Siller (988), we assess te relative contriution of eac cannel to nancing scal activity, for te period Our tird and nal focus is to use tis framework to assess statistically weter te sustantial expected increase in scal de cits treatens te current low levels of in ation. Our ndings can e summarised as follows. For te period under consideration and for US, Japan, Germany, UK, Italy and Canada, scal imalances are mostly removed troug adjustments in te primary de cit (80-00%), wit less important adjustments troug in ation (0-0%) and GDP growt (0-20%). In particular, te relation etween scal imalances and in ation suggests extremely modest statistical interactions etween te two; suggesting tat widely anticipated increases in scal de cits, due to demograpic factors, are not necessarily predictors of iger future in ation. It is important to stress tat tis conclusion is ased around an analysis wic is in essence a purely accounting exercise. Tere exists a large and varied teoretical literature examining te economic linkages etween scal de cits and in ation (see inter alia Sargent and Wallace, 98, McCallum, 984, Leeper, 99, Sims, 994 and Woodford, 995) ut, y contrast, our analysis pursues a di erent pat. Using te accounting framework of te intertemporal udget constraint to empirically document te relative statistical role of di erent factors in acieving scal alance. Te plan of te paper is as follows. In Section 2 we examine te properties of our data set and argue tat our sample period is appropriate for reviewing ow scal adjustment is acieved in te face of large variations in government det in response to sarp increases in social transfers. Using te period-y-period udget constraint we examine evidence for scal sustainaility and te drivers of te det/gdp ratio. A simple accounting exercise sows tat nominal GDP growt, and especially in ation, played an important role in acieving det staility. In Section 3 we extend our analysis and introduce our log linearised version of te intertemporal udget constraint and derive our key measure of scal imalances, namely a relationsip etween levels of government liailities and te primary de cit. We sow ow variations in tis relationsip are related to expected canges in future de cits, money creation and canges in in ation, real interest rates and real GDP growt. In Section 4 we sow ow to estimate tis long run relationsip etween liailities and te de cit and we ten construct estimates of scal imalances across te countries in our sample and draw conclusions aout te dynamics of scal adjustment. Section 5 uilds on tis long run relationsip and te restrictions imposed y te intertemporal udget constraint to perform a variance decomposition for ow scal sustainaility is acieved. We extend our framework to assess te separate importance of government expenditure and tax revenue in acieving scal alance and examine te predictive role of scal imalances in predicting future in ation. A nal section concludes.

5 Inflation and Rising Det 3 2. Fiscal Sustainaility: A ackward looking approac Our focus is on assessing te sustainaility of scal policy in six industrial nations - US, Japan, Germany, UK, Italy and Canada - over te period Our interest is not just to assess scal sustainaility, ut also to identify te means troug wic tis sustainaility is acieved. We coose tese nations ecause we are interested in te implications of demograpic induced de cits tat are expected to a ect tese countries in te coming decades. We coose tis time period ecause, in contrast to te majority of te literature, we are interested in ow governments acieve scal alance in te face of rising non-war related expenditures. Wit demograpic cange expected to lead to increasing social transfers, tis sample is a natural environment wit wic to consider te likely impact of rising det. For example, over tis period, Canada increased social transfers y 4.7% of GDP, Germany y 6.6%, Italy 7.8%, Japan 9.2%, UK 5.9% and US 6.7%. wic accounted for 04%, 57%, 5%, 49%, 88% and 46% respectively of te oserved increase in total government expenditure during tis period. In oter words our period is one were increases in government expenditure were eavily linked to rises in social transfers. A furter reason for focusing on tis post WWII period is tat it is te most recent and most relevant: our results in Giannitsarou and Scott (2006), using istorical UK and US data, suggest tat te means troug wic scal adjustment is acieved ave canged signi cantly across centuries and in particular war induced increases in det are nanced troug di erent cannels tan general increases in det. We leave undiscussed te political economy features tat migt explain wy military expenditure is nanced troug di erent means to social transfers ut te implication is tat focusing on modern times of peace is critical if we are to gauge te impact of demograpic induced future scal de cits. For tis period to e informative regarding te means werey governments acieve scal sustainaility it is important tat det and de cits sow signi cant variation. Anoter reason wy so many previous researcers ave focused on war related expenditure is it leads to dramatic swings in pulic det and de cits and so is a natural period wit wic to examine scal sustainaility. Tale documents some stylised facts for key scal variales over our post war period. Det relative to GDP sows large volatility, wit a standard deviation ranging from to Wit te exception of te US, all countries see an increase in det/gdp over te sample period and in two of our six cases, det/gdp rises aove 00% GDP. Tis is far from eing a period of tranquil pulic nances or modest variation in det, suggesting once more its relevance as a case study for coming decades. Performing various unit root tests (see Tales 2-5) to te market value of government det, government expenditure (excluding interest payments) and revenue, all expressed as a ratio to GDP, provides furter evidence of te variaility of government nances. Te strong consensus tat emerges from tese results is tat all variales appear to e non-stationary and contain unit roots. Te fact tat government expenditure/gdp and tax revenue/gdp are non-stationary over tis period is testimony to te rise of social transfers commented on in previous paragraps. Te suggestion tat det/gdp is also non-stationary furter implies tat acieving scal sustainaility in tis post war period as een A detailed description of our data and its sources is provided in appendix A.

6 Inflation and Rising Det 4 a callenge. Te nding tat te det/gdp ratio is non-stationary also con icts wit te ndings of Giannitsarou and Scott (2006) tat use longer runs of istorical data. It tus seems tat te sample in tis paper is one of unusual scal prolems. Te nding tat det/gdp is non-stationary may appear to e inconsistent wit scal sustainaility, ut as stressed y Bon (2006), tis is not necessarily te case. Critical for sustainaility, according to tis analysis, is te existence of a feedack from te level of det to te current primary de cit. In oter words, wen estimating a regression of PrimarySurplus t = A(L)X t + Det t + t ; were X t denotes a set of relevant explanatory variales, it is necessary tat is positive and larger tan te interest rate paid on government det. Te nal column in Tale reports estimates of (and associated p values) for eac of our countries were X t consisted of lagged values of te primary surplus. Only in te cases of Japan and Germany is te det term not signi cant at te 5% level or less (altoug including additional variales suc as GDP, interest rates, etc. remedied tis prolem for Germany), suggesting tat most countries sow evidence of scal sustainaility over our period. Interestingly, Japan and Germany are te only countries were te maximum value for det/gdp is oserved in te nal oservation in te sample period. We include all six countries in our estimation elow, ut tese results suggest some care sould e taken in interpreting te Japanese and German ndings. To etter understand te movements in te det/gdp ratio and its relationsip wit oter scal variales it is useful to consider te period-y-period udget constraint. Let + { t denote te growt in nominal GDP and + i t te one year olding return on nominal government onds. Let B t, G t and T t e te ratios of nominal det, government spending and tax revenues to nominal GDP. 2 Ten we ave B t = (G t T t ) + i t + { t B t { t + { t B t : () In oter words, te det to GDP ratio increases troug te ratio of te primary de cit to GDP and interest payments on det (using te growt adjusted real interest rate), and reduces troug a nominal growt dividend { t B t = ( + { t ). To investigate te role of variations in ond prices as a way of ensuring tat te intertemporal udget constraint of te government olds (te focus of Marcet and Scott, 2005a), we evaluate () y considering i t as te one year olding return on government onds. In oter words, we include ot coupon payments and capital gains, so tat our udget constraint is speci ed in terms of te market value of government det, rater tan te stock of outstanding det. Following Bon (2005), to gain some understanding of wat drives canges in te det/gdp ratio, we can evaluate () using sample averages for our period. Te results are sown in Tale 6. As noted in Tale, Japan and Germany sow te most dramatic increases in det, wit only te US and UK sowing road det staility. Tese sustantial di erences in det dynamics are despite te fact tat, wit te exception of Italy, te total de cit/gdp ratio is reasonaly similar across countries. Te main 2 For easy reference, te notation we use trougout te paper is summarised in Appendix B.

7 Inflation and Rising Det 5 reason eind Germany and Japan s di erent det dynamics is teir low value of te growt dividend; tis is particularly noticeale for te in ation component (te nominal growt dividend consists of a real growt and an in ation component). Reviewing Tale 6, it is seems tat in ation as een a signi cant in uence in acieving scal sustainaility. At rst glance, tis would seem to generate te serious concern tat rising de cits induced y demograpic cange may lead to rising in ation. Tale 6 is a useful accounting exercise, ut in focusing on ex post realisations only provides a ackward looking analysis. Equation () olds for all scal policies, regardless of weter tey are sustainale or not, and as a consequence cannot e used to assess te sustainaility of scal policy. Moreover, it does not provide information on ow governments expect to acieve scal sustainaility or ow scal policy responds to socks to key economic variales. In order to gain insigts into tese issues we next turn to a forward looking perspective y introducing te intertemporal udget constraint. 3. Fiscal Sustainaility: A Forward Looking Approac In tis section we use te intertermporal udget constraint to derive an alternative accounting framework for studying scal sustainaility. Tis alternative approac produces a relationsip etween te level of government liailities relative to te primary de cit and projections of future values of key scal variales. We will argue tat tis relationsip is a natural way to caracterise imalances in scal policy. Furtermore, using tis expression we can examine ow adjustments to te government s scal position are made in order to restore scal sustainaility. In oter words, wile te ackward looking accounting equation () elps quantify ow te average value of scal variales are related tis forward looking approac elps quantify ow key variales cange in order to ensure scal sustainaility. In deriving te government s intertemporal udget constraint we use te same log-linearisation approac as in Giannitsarou and Scott (2006). Log-linearising te intertemporal udget constraint as een used in a wide variety of applications; e.g. Campell and Siller (987) and (988) apply tis approac to equity prices and dividends, Campell and Siller (99) use it to analyse te yield curve, Lettau and Ludvigson (200) examine te consumption-wealt ratio and its aility to predict capital gains, and Bergin and Se rin (2000) and Gourincas and Rey (2005) apply te framework to te alance of payments. Altoug te overall metodology is similar to tese oter studies we sare wit Gourincas and Rey (2005) a signi cant prolem. Log linearisation requires approximating around stationary variales ut in our case te trending nature of government expenditures and revenues prevents a straigtforward approac. Te non-stationarity of scal variales creates a numer of signi cant di culties tat need to e overcome if we are to utilise a long linearisation approac. Since we focus on te implications of scal de cits for in ation, we start wit a version of te government s udget constraint () augmented wit monetary liailities i.e. G t T t = B t t t Q t B t + H t t Q t H t ; (2) were H t denotes te ratio of monetary liailities to GDP, t te in ation rate ( + t ), and Q t is te growt in real GDP ( + t ).

8 Inflation and Rising Det 6 In seeking to derive a log linear version of te government s udget constraint Giannitsarou and Scott (2006) stress two di culties: (a) G t ; T t and B t sow evidence of non-stationarity and () it is not possile to take logs and linearise te primary de cit D t = G t T t due to its possile negative values; terefore te log linearisation needs to e done separately for G t and T t. To overcome tese di culties and arrive at a useful version of te intertemporal udget constraint, we need to make te following assumptions : Assumption : Tere exists a variale W t suc tat G t =W t ; T t =W t ; B t =W t and H t =W t are stationary. Assumption 2: Te real and nominal interest rate, te growt rate of GDP, in ation and te growt rate of W t are all stationary, wit steady states i, r,, and! respectively. Assumption 3: Te No-Ponzi condition olds i.e. N lim (B t+n + H t+n ) = 0; N! were denotes te growt adjusted real interest rate less growt in W t. Tis condition olds if ( + ) ( +!) < + r: Assumptions and 2 are required to pursue our log linear approac. Assumption 3 is a version of te standard transversality condition tat ensures scal sustainaility olds and enales us to express current scal policy in terms of nite valued in nite orizon present value expressions. Given te importance tese assumptions it is wortwile discussing eac of tem more extensively. Assumption invokes te existence of a variale W t, tat transforms te ratios of government spending, revenues and det to GDP to stationary variales. As explained in Campell and Siller (988), in order to e ale to consider a rst order approximation to te udget constraint, te variales tat are approximated need to e stationary. Te standard practice is to assume tat de ating variales y GDP is su cient to induce stationarity. However, Tales 2-5 suggest tat apart from det/gdp, expenditure, revenue and money over GDP also seem to e non-stationary. We terefore need to invoke te assumption of a common trend W t across all four variales wic is capale of inducing stationarity. An ovious issue is te identity of W t : wat variale would induce stationarity in te pulic nances? One possile interpretation is tat W t is a purely statistical term representing a common trend amongst tese variales. Alternatively, W t could ave an economic interpretation, for instance, te value of te stock of pulic assets. However, ecause our focus lies in deriving a log-linearised version of te udget constraint, we need only assume tat suc a variale exists; we do not need to empirically oserve tis variale. Tis is ecause ultimately terms in W t cancel out after te linearisation leaving us wit just log-linear expressions for G t ; T t, B t.and H t : Altoug W t does not gure in our later empirical exercise, Assumption does ave testale implications: if tese variales sare a common trend W t, we sould nd cointegrating relations etween te variales in te pairs fg t ; T t g ; and fg t; B t g and fb t ; H t g. Indeed,

9 Inflation and Rising Det 7 evidence for suc cointegrating relations is given in Tale 7, wic o ers general support for Assumption. Assumption 2 requires tat certain key variales ave stationary growt rates. We performed various unit root tests tat provide evidence in support of Assumption 2. Tese tests are omitted ere, ut are availale from te autors upon request. Assumption 3 is more controversial and is critical in order for us to derive te intertemporal udget constraint. Te form of tis assumption is standard across many applications, ut in our case we require tat te average real interest rate e greater tan te sum of real GDP growt and te growt in W t. Clearly, testing tis assumption is impossile since W t is unoserved. Neverteless, if we assume tat W t as positive mean growt, ten a weak test of Assumption 2 is weter r > or not. For our sample period tis condition olds only for Canada, Germany and te US. Te majority of te literature simply invokes tis assumption and rarely tests weter it is true (see Ball, Mankiw and Elmendorf (998) for an extended discussion on te validity of tis assumption and te options it provides scal autorities if te condition fails to old). Presumaly te fact tat so many studies do not test te assumption is ecause implicitly it is assumed tat even if over te sample period r and do not satisfy te restriction future values will ensure it olds and so te intertemporal udget constraint is well de ned. For instance, Giannitsarou and Scott (2006) sow tat over te sample period tis restriction olds for te UK, so altoug it is violated etween , looking forward over an in nite orizon te assumption is justi ed. An alternative approac is tat suggested y Bon (2006), wo sows ow it is possile to derive an intertemporal udget constraint, even wen ( + ) ( +!) > + r, if one treats tis as a merely tecnical ostacle. Te trick is to use an alternative "interest" rate, r > r, wic satis es ( + r ) > ( + ) ( +!) and ten amend te udget constraint for te di erence etween r and r and ten linearise tis transformed udget constraint. Appendix C sows ow to apply tis metod to our model and uses a particular example for r wic ensures te validity of our main expressions even wen r < : Fundamental to our analysis is a relationsip etween te level of liailities and government expenditures and revenues. De ne were l t t + t + g g t + t (3) = (4) = (5) g = ( + ) g (6) = ( + ) (7) ten Giannitsarou and Scott (2006) sow tat te log-linear version of te government s present value constraint is

10 Inflation and Rising Det 8 l t ' + + X E t T X j E t j=0 j= r t+j j d t+j + ( )E t X j t+j j=0 + t+j + + t+j : (8) Note tat y Assumption 3, it must e tat > and < : Te variale d t g g t + t ; were g and are of opposite signs, is essentially a transformed version of te primary de cit. Te critical variale for our analysis is l t, wic is a measure of te imalances in scal policy. If g > 0 and < 0, ten l t de nes a relationsip etween government liailities and te primary de cit; if g < 0 and > 0, ten instead te relationsip is etween government liailities and te primary surplus. Since > and <, te coe cient on det is positive and te coe cient on money is negative, regardless of te signs of g and : Equation (8) pins down a long run equilirium relationsip etween te market value of government det, monetary liailities and a version of te current primary de cit, d t. We interpret tis expression as follows. For given values of mean interest rates, real GDP growt and money oldings, tere as to e a steady state relationsip etween det and te primary de cit, if det is to e sustainale and for te intertemporal udget constraint to old. Under our Assumption 2 and given our empirical evidence on unit roots, te rigt and side of (8) is stationary, so tat E t l t+j =, as j! ; suggesting l t as a natural measure of required scal adjustment. Wen l t = 0, ten tis equilirium relationsip olds, ut for l t > 0 det is too ig relative to current scal de cits. Adjustment is acieved troug variations in te rigt and side of (8). Furter insigts into (8) and l t can e gained from considering te results of Trean and Wals (988) and (99), and Bon (2006). Te former sow tat te intertemporal udget constraint requires tat te primary de cit and det satisfy a cointegrating relationsip. Given Assumption 2 and te fact tat E t l t+j =, te same is true for our approximation to te intertemporal udget constraint. 3 Bon (2006) focuses on an alternative insigt, namely tat det sustainaility requires a feedack rule from det to de cits. Given Assumption 2, we know tat l t must e stationary, wic can e acieved troug a feedack rule from det to te de cit, altoug in tis case te feedack is from a weigted average of marketale det and monetary liailities. If te left and side of (8) measures te degree of scal adjustment required, ten te rigt and side of (8) tells us ow tis scal adjustment (l t ) is acieved troug eiter: (a) future improvements in te primary de cit d t+j, () issuing more monetary liailities, t+j or (c) variations in te growt 3 Strictly speaking (8) states tat if te components of l t are of order of integration N, ten te rigt and side of (8) is order N.

11 Inflation and Rising Det 9 adjusted real interest rate (r t+j t+j t+j ). Te coe cients on eac of te components of te growt adjusted real interest rate di er, as te nominal dividend e ect ( t+j t+j ) operates on ot onds and money, wile r t+j a ects only onds. As a result, equation (8) tells us tat, if te intertemporal udget constraint olds, any deviations in te long run relationsip etween det and de cits must elp predict movements in eiter future primary de cits, money creation, nominal interest rates, in ation or GDP growt. We stress once more tat our intertemporal udget constraint is an accounting framework and te predictive role of l t is a purely statistical rater tan necessarily causal penomenon. 4. Estimating Fiscal Imalances Crucial to implementing our approac to te intertemporal udget constraint is construction of an estimate for l t and so estimates of ; ; g and :A common approac to estimating (3) and its analogues in te literature is to use Stock and Watson s (993) Dynamic OLS estimator. In our case tis would involve estimating te regression: kx g t = t + 2 t + 3 t + (c i t i + c i t i + c i t i ): (9) i= k Using (3), (4)-(7) and te fact tat g + =, we get te implied restrictions = = ; (0) : () Tale 8 sows te results from estimating tis equation and te implied estimated coe cients for te parameters of interest,,, g and. Tese estimated coe cients are calculated as follows. First, we ceck tat in eac case, we cannot reject restriction (0), at eiter te 5% or 0% level. Next, equation (9) contains tree key estimated parameters, namely ; 2 and 3. From tese reduced form estimates we wis to estimate te structural parameters ; ; ;, using relations (4)-(7). However, due to (0), we ave in e ect only two independently estimated parameters. Terefore identifying our structural parameters requires using additional information. In particular, we can estimate as te sample average of narrow money to government det ratio (H=B) and y de nition we ave = = ( + ) ( + r). Using tese additional restrictions we can ten just identify te key structural parameters of interest and construct our estimate of l t : ^lt = t + t + d t : Te variale ^l t is a measure of te deviation of a weigted average of government liailities from a transformed measure of te primary de cit d t. Te larger l t is, te larger det is relative to te steady state level of de cits and te greater te required degree of scal adjustment. Note tat given te estimates of Tale 8, te weigts on government expenditure and tax revenue ( g and ) are of opposite

12 Inflation and Rising Det 0 sign and approximately equal in asolute value, so tat d t is only mildly di erent from te primary de cit (and in te case of Japan and te UK tere is very little di erence). Te coe cients g and, re ecting te relative importance of te primary de cit relative to liailities, clearly sow signi cant variations across countries. Tese variations re ect te fact tat te size of te primary de cit needed to ensure sustainaility depends on te level of interest rates, GDP growt and det and small variations in tese numers can produce large variations in g and. Wile tis approac is standard in te literature our use of Assumption creates additional prolems wic make te aove analysis prolematic. Assumption implies tat G t ; T t ; B t and H t all sare a common stocastic trend, W t. As a result tere exist tree (linearly independent) cointegrating vectors. Evidence for tis was sown in Tale 7, wic we used earlier as support for Assumption. In oter words, in our data we ave te following cointegrating relationsips: 4 g t = ' t t + u t t = ' 2 t + u 2t g t = ' 3 t + u 3t were u it ; i = ; 2; 3 are stationary error terms, since te variales cointegrate. Given tat eac of tese pairs is stationary, it also must e te case tat any linear comination of tese cointegrating relations must also e stationary. In oter words, Assumption implies tat for any ; 2 and 3 te following olds : (g t ' t t ) + 2 ( t ' 2 t ) + 3 (g t ' 3 t ) = w t were w t is a stationary error term wic is a linear comination of te u 0 its. Rearranging tis expression yields g t = ' + 3 t t 2 3 ' t + 2' t + w t Assumption implies tat tis equation must old for aritrary, 2 and 3 wile te intertemporal udget constraint implies, troug (3), (4)-(7), tat only one speci c cointegrating vector is useful in predicting future scal eaviour e.g te rigt and side of (8). Assumption means tat wen we estimate (3) using DOLS we are in e ect estimating some weigted average of te tree cointegrating vectors, were te weigts are aritrary and not uniquely determined. Wile (3) and (4)-(7) imply some cross parameter restrictions, tey are not enoug to uniquely pin down ; 2 and 3 and overcome tis indeterminacy. In oter words, it is not ovious tat te estimates in Tale 8 truly uncover te structural parameters tat we are interested in. 4 Here we follow Gourincas and Rey (2005) and allow te coe cients in tese cointegrating relationsips to di er from. Measurement important wen dealing wit scal data; in particular ecause of o -alance seet items, o cial det data does not accumulate purely as a consequence of te total de cit.

13 Inflation and Rising Det In order to validate te estimates of Tale 8 as reliale measures of scal imalance, we use two independent arguments. Te rst and most powerful is tat te intertemporal udget constraint implies more tan just a linear cointegrating vector of te form (3) exists. In particular te intertemporal udget constraint implies tat te "true" l t, i.e. expression (3), equals te rigt and side of (8). Assumption entails tat tere exist many cointegrating vectors etween t ; t ; g t and t t ut te intertemporal udget constraint implies tat only one particular cointegrating vector sould e useful in predicting te present value of future scal variales. Tis in turn implies tat innovations in l t sould e equal to te innovations in te present value of tese future scal variales. We sow in a later section ow to exploit tis to test for te validity of our estimated (3) as a measure of scal imalances. For te cases were tis test is not rejected we can e con dent tat DOLS does not estimate an aritrary cointegrating relationsip ut te speci c one implied y te intertemporal udget constraint. Te second means of verifying our DOLS estimates of (3) as a valid measure of scal imalances is to provide alternative estimates of te key structural parameters ; g ; ; ; and use tese to construct an estimate of fl t g wic can ten e compared wit tose otained from DOLS. Sample estimates of real interest rates, real GDP growt, government expenditure, tax revenues and money oldings as sares of GDP were constructed and an estimate of! (te growt of te common trend W t ) formed y averaging te trend growt rates of t ; t ; g t and t t. Estimating l t in tis way is prolematic for several statistical reasons and is not our preferred approac. Te rst prolem is tat g t and t t are non-stationary and so do not ave a well de ned unconditional mean. Te second is tat wen we use DOLS we can exploit te order of integration of te variales and arrive at superconsistent estimates. However, tis approac does o er, owever awed, a furter means of assessing our measure of scal imalances. Tale 9 sows te results for our key parameters from tis alternative estimation metod and also o ers some information on ow tis measure of l t compares wit tat from using DOLS. For Canada, UK and US te results are astoundingly similar, ot in terms of te structural parameters and te correlation etween te estimates of l t and l t. In all tree cases we can reject strongly te null of non-stationarity for tis alternative estimate of l t. For Italy te coe cient estimates are roadly similar except tat tose on det and money are around twice as large ut te two estimates roadly track one anoter and sow similar eaviour in teir rate of cange. Te only countries were tere are important di erences are for Japan and especially Germany, note tat tese are te two countries for wic our earlier analysis questioned te degree to wic scal policy ad een sustainale over our sample period. For Japan te main di erence is tat te coe cients on government expenditure and taxation are muc smaller tan from DOLS and so tis estimate of l t places muc greater weigt on te det and monetary liailities term. Tis leads to a weaker correlation etween te two estimates altoug te uctuations in l t are roadly similar. Te two estimates for Germany are owever very di erent, wit a near perfect negative correlation arising from te fact tat g and t ave opposite signs to tat from DOLS. Note also tat tere is only weak evidence tat tis alternative measure of l t is stationary, wic our assumptions require. Tese independent validations of our DOLS estimates of

14 Inflation and Rising Det 2 l t suggest tat, wit te exception of Germany, tey are valid measures of te degree of scal imalance as suggested y te intertemporal udget constraint. We now move to consider in more detail wat tese estimates imply aout te dynamics of scal adjustment. In order to make comparisons across countries it is necessary to standardise our measures of l t, due to te fact tat te estimated coe cients in Tale 8 di er so muc across countries. As previously descried, ^l t is te deviation in te relationsip etween liailities and te primary de cit. Consider te case were scal equilirium, i.e. l t = 0, is acieved purely troug adjustments in tax rates. Given our de nition of l t tis would require an increase in taxes of ^l t = i[^l t m l ]: + were m l is te sample mean for l t and ^l t is a normalised measure of scal imalances wic can e used to make comparisons across countries: it is te required increase in te tax revenue/gdp needed to restore scal equilirium and can e tougt of as an alternative measure of scal sustainaility to tose proposed y Blancard et al (989) and Polito and Wickens (2006). Estimates of ^l t are sown in Figure 3, for our sample period. Tese suggest tat te discrepancy etween det and de cit in te US is currently on a par wit te Reagan years, altoug it as sown some signs of improvement over te last year. After a protracted correction during te 980s and 990s, te estimates suggest tat Canadian pulic nances are now in roug alance as is German policy. Not surprisingly Japan s scal situation as sown a dramatic recent deterioration, as as te scal position of UK. Finally, after many consecutive years of scal improvements, our estimates suggest tat from a long term perspective, Italian pulic nances ave deteriorated signi cantly in recent times. Tale 0 reports some summary statistics regarding scal adjustment for our countries during tis period. Te degree of imalance varies etween around plus and minus 5% for all economies, except for te US were te range is narrower (plus or minus 3%). In all cases scal adjustment is igly persistent altoug not a unit root process; as discussed aove, it is critical for our analysis tat l t is stationary. Fiscal adjustment is a protracted process, wit a alf life of etween 2 and 4 years. Given tat our sample period contains 46 years of data for most countries we ave several completed cycles of scal adjustment. However, te case of Japan sows weakest evidence of adjustment in scal policy, peraps re ecting our earlier comments tat te continual rise in Japanese government det may re ect an uncompleted scal adjustment. 5. Financing te Budget Te previous section constructed estimates of our measure of scal imalance and statistically caracterised its variaility. Equation (8) states tat tese uctuations in l t are associated wit uctuations in future de cits, money creation, real interest rates, in ation and real GDP growt in a manner tat ensures te government s intertemporal udget constraint olds. If te left and side of 8) sows a measure of scal imalance ten te rigt and side sows wic variales account for variations in scal

15 Inflation and Rising Det 3 imalances. We now turn our attention to using tis equation to perform a variance decomposition on l t. De ne z t = (l t ; d t ; t ; r t ; t ; t ) and assume z t follows a VAR(p) process, i.e. z t = A z t + A 2 z t 2 + ::: + A p z t p + " t ; were A k ; k = ; :::; p are 6 6 matrices. Denoting z t = zt; 0 zt 0 ; :::; z0 t p+ and "t = (" 0 t; 0; :::; 0) we can rewrite tis VAR(p) as a VAR() so tat z t = Az t + " t ; were 0 A = A A 2 A p A p C A : Noting tat conditional expectations satisfy E t z t+j = A j z t and de ning appropriate indicator vectors e suc tat e 0 l z t = l t ; e 0 d z t = d t ; e 0 rz t = r t ; e 0 z t = t ; e 0 z t = t ; e 0 z t = t ; we can ten, following Campell and Siller (988) rewrite (8) as e 0 l z t = + + X (= ) j e 0 d Aj z t + j= X (= ) j e 0 ra j z t + j=0 + X (= ) j e 0 A j z t ; j=0 X (= ) j e 0 A j z t j=0 X (= ) j e 0 Aj z t j=0 or equivalently e 0 l z t = ( e 0 r + e 0 e 0d A I + e 0 I A + ) A e 0 I A z t : (2)

16 Inflation and Rising Det 4 Tis is simply a restatement of our key equation (8), ut were we ave replaced te expectation terms wit conditional forecasts otained from our VAR representation for z t. If our log linearisation to te udget constraint is appropriate we ave e 0 l I A = e 0 r + e 0 e 0d A + + e 0 e 0 : (3) Tis expression sows te restriction our present value formula imposes on innovations to l t relative to innovations in de cits, money and growt adjusted real interest rates. It can terefore e used as a joint test for te adequacy of ot our approximation to te intertemporal udget constraint and te forecasting system used for our variales. It is tis test we referred to earlier as a means of validating our DOLS estimates of l t. implement formulation of tis restriction is: As sown in Giannitsarou and Scott (2006), an alternative and easier to 0 = E t ( t t ) + l t r t t ( t + t ) : Tis last expression can e easily tested y regressing te expression in te expectation on variales in te t- information set and testing for teir signi cance. If our log linear approximation to te intertemporal udget constraint is to old, ten tese lagged variales sould e insigni cant. were To proceed wit our variance decomposition we rewrite our system as l t = F d;t + F ;t + F r;t + F ;t + F ;t ; F d;t = F ;t = F r;t = F ;t = F ;t = + e 0 e 0 r I I I e 0 + A A z t ; z t ; A z t ; I e 0 e 0d A I A z t : A z t ; were F j;t denotes te projected contriution of component j towards maintaining te intertemporal

17 Inflation and Rising Det 5 udget constraint. Figure 4 sows te value of l t and our estimated series for F d;t +F ;t +F r;t +F ;t +F ;t in te case of te US and sows tat our forecasting model does an excellent jo capturing te restrictions implied y te intertemporal udget constraint. Tis is con rmed y te 2 test of te ortogonality condition (3), wic olds at te 5% level or less for te majority of cases, once more con rming te validity of our DOLS estimates.. Te ene ts of applying tis VAR forecasting framework to our intertemporal udget constraint is tat it can e used to perform a variance decomposition on l t. In oter words, it is possile to measure te relative importance of eac of our variales (canges in primary de cit, issuance of monetary liailities, canges in return on onds or in ation or GDP growt) in acieving scal alance. As sown y Cocrane (992), te relative importance of variale j can e measured y te estimated coe cient from a regression of F j;t on l t. Tale sows results from our sample period and demonstrates clearly te importance of de cit uctuations as te main source of adjustment in l t. Compared to te importance of te de cit, te role of te oter variales is minor, including tat of in ation. Te minor role for variations in rates of return on government det in acieving scal alance is consistent wit te ndings of Marcet and Scott (2005) regarding te lack of scal insurance o ered y existing det instruments. Because te F jt components are possily correlated amongst temselves our variance decomposition is not an ortogonal one and so our estimates of te relative contriution of eac variale are not ounded etween 0 and. Tis leads to te possiility tat if our in ation term is strongly correlated wit uctuations in te primary surplus ten our ig estimate of te role of uctuations in te primary de cit and our low estimate for in ation may re ect te non-ortogonality of our decomposition. However, te strongest correlations in our data are etween F ;t, F r;t and F ;t rater tan wit F d;t. For instance, for US, Italy, Canada, UK, Japan and Germany te correlations etween F ;t and F d;t are -0.26, 0.78, -0.5, -0.24, 0.42 and -0.6 compared to -0.78, 0.46, 0.25, -0.90, 0.97, 0.67 for te correlation etween F ;t and F ;t. Only if te correlation etween F ;t and F d;t is large and negative can an appeal to non-ortogonality e used to explain wy our estimates of te importance of in ation may e an underestimate. Te importance of te de cit in te variance decomposition is surprising given our previous ndings on te importance of te nominal growt dividend. However, as stressed earlier te growt dividend focuses on ow te average level of te det/gdp ratio is linked to average levels of te primary de cit, interest rates, GDP growt and in ation. By contrast our use of te intertemporal udget constraint focuses on ow canges in tese variales account for variations in te de cit to liailities ratio. Examination of te raw data also reveals te importance of sifts in te primary de cit. For instance, in Italy te primary de cit started at 0%, ut deteriorated to more tan 8% efore det started to improve as te primary de cit moved to -6%. Similar movements in det and primary de cits occur in te oter countries in our sample. Tis analysis suggests tat uctuations in te primary de cit are te main means werey scal alance is aceived. Tis raises te question weter uctuations in te primary de cit are driven more y government expenditure or y canges in tax revenue. We terefore extend our VAR using te

18 Inflation and Rising Det 6 decomposition l t = F g;t + F ;t + F ;t + F r;t + F ;t + F ;t ; were F g;t = F ;t = + + g e 0 ga I e 0 A I A z t ; A z t : Te results of tis extended VAR are also sown in Tale. As in Bon (99) ot expenditure and revenue variations play a sustantial role in scal uctuations wit a sligtly more important role for expenditure uctuations, altoug tis e ect is far more pronounced in te UK. Tese variance decomposition results suggest tat in ation movements play only a very minor role in accounting for sifts in te scal position of governments. However, tis does not necessarily mean tat scal movements are insigni cant in predicting future in ation. We now turn to anoter implication of equation (8), i.e. tat l t sould e useful in predicting future in ation. In particular, we look at te aility of l t to predict future in ation at orizons from to 20 years. We do tis y rst specifying an optimal forecasting equation for in ation. We use lag selection criteria in a model were in ation depends on lagged values of in ation, nominal interest rates and GDP growt, were we consider lags of up to 8 periods for eac variale. Having arrived at an optimal model, we ten add l t j to gauge te additional explanatory power from our measure of scal imalance. Te results are sown in Tale 2, were we quote te p-value for l t j ; j = ; ::; 20. Te results are consistent wit Tale : scal measures ave a very marginal impact on predicting in ation. Te vast majority of lags are insigni cant altoug in a few cases tere is evidence of predictive aility at orizons of around 3-4 years. However, te marginal statistical contriution of l t is fairly small. Te pitfalls of suc Granger causality tests are well known and teir inaility to successfully identify causal economic mecanisms well documented. We sould terefore take care in interpreting tese ndings and not necessarily interpret tem as implying tat scal policy does not in uence in ation. For instance, te scal teory of te price level would argue tat expectations aout future de cits, tat is P j E t j= dt+j would in uence te current level of prices and so a ect contemporaneous in ation. Tis is entirely consistent wit our nding tat l t as only a minor role in predicting future canges in P j in ation i.e E t j= t+j. However, wile we need to e careful in te economic conclusions we draw from tese ndings we can draw te statistical conclusion tat rising government det is not a good predictor of rising future in ation. Tat is, te increased indetedness originating from demograpic cange is not necessarily a statistical aringer of rising future in ation.

19 Inflation and Rising Det 7 6. Conclusion Tis paper sougt to apply a log linearised version of te intertemporal udget constraint to consider government s scal positions. It tried to answer tree key questions (a) is current scal policy sustainale? () ow ave OECD governments nanced teir scal de cits in recent decades and (c) wat are te implications for in ation of te expected rising de cits? Te contriution of te paper is purely empirical, using an accounting identity to quantify te statistical impact of certain key variales. In answer to te rst question, for eac country we estimated a measure of current scal imalance, de ned as te ratio etween current liailities and te primary de cit. For all countries, te current measure for tis imalance was witin te istorical range of variation suggesting tat current policies are sustainale, wit te possile exception of Japan. Using our version of te intertemporal udget constraint, we analysed ow in previous years governments ad acieved scal alance. We found an overwelming role for canges in te primary surplus wit only a minor role for in ation, growt and interest rate e ects. Furter we also found tat scal imalances ad only a very weak forecasting role for future in ation at nearly all orizons, wit some mild evidence tat scal imalances could elp predict in ation tree to four years aead. Oviously our results sould e interpreted wit care as tey are ased on a certain istorical period and an assumption tat governments cannot take a de cit gamle if r < ; inevitaly any attempt at an econometric approac to evaluating te intertemporal udget constraint is vulnerale to time dependence and non-stationarity. Our accounting framework also prevents us from attriuting any causal role to te statistical relationsips we discover. However, te statistical ndings are striking: variations in scal imalances and movements to scal sustainaility are acieved mainly troug variations in te primary de cit. Moreover, rising government det amongst tese countries is not a reliale predictor of iger future in ation. A. Data Notes on data sources for te UK and US can e found in Giannitsarou and Scott (2006). remaining countries details are as elow. Te following areviations are used: For te GFD: Gloal Financial Data IFS: International Financial Statistics (IMF) OECD-EO: OECD Economic Outlook Dataase OECD-CGD: OECD Central Government Det Statistics HSoC: Historical Statistics of Canada ( Statistics Canada ) DI: DataInsigt

20 Inflation and Rising Det 8 GDP, Prices and In ation Country variale sample period source ID/Speci cation CAN real GDP GFD GDPCCANM nom. GDP GDPCANM JAP nom. GDP IFS 5899B.CZF De ator 5899BIRZF JAP, ITA, GER nom. GDP OECD-EO De ator Te implicit GDP de ator is used as te price index. (Gross) in ation is ten otained as te annual rate of cange of te index. Base Money Country sample source ID/Speci cation CAN HSoC J69+J DI MBASENS@CN GER DI M@EURNS@GY ITA Fratianni (2005), p49 col BP Banca d Italia JAP DI MBASENS@JP For Canada, Italy, and Japan, ase money is used. For Germany, it is te national de nition of M (currency in circulation plus overnigt deposits). Government receipts and expenditure Country sample source ID/Spec. CAN Receipts, expenditure HSoC F09, F6 Receipts, expenditure DI REVG@CN, EXG@CN Interest EXGCDINS@CN GER, ITA, JAP Receipts, expenditure OECD-EO Interest All government expenditure data is net of interest service. Revenues are net of interest receipts for Germany, Italy and Japan, ut not for Canada. Te primary de cit is expressed as net expenditure minus (net) receipts. Government det and market values. Market values are approximated for central government marketale det, wic is from OECD-CGD. For te periods efore tese data are availale, te last availale sare of marketale in total det was used to otain marketale det. Te price of government det is approximated as

21 Inflation and Rising Det 9 p t = + NC + NI ; were N is te average term to maturity of outstanding government securities, C is te average coupon rate, and I is te average market yield. Data on average terms to maturity and average yields is from OECD-CGD. If no average term to maturity was availale, average maturities were used. For earlier periods, te last average maturity availale was taken. If average yields were unavailale, yields are constant maturity encmark yields (from GFD). For a given year, te encmark yield closest to te average term to maturity of tat year was applied. Average coupon data is approximated as te ratio of gross interest service to gross government det, more precisely, C t = Interest t+ DEBT t :

22 Inflation and Rising Det 20 B. Variale Definitions and Notation variale de nition steady state G t T t B t H t W t P t Y t government spending over GDP tax revenues over GDP det over GDP seignorage over GDP aggregate wealt price index real GDP R t = + r t gross real interest rate R = + r t = + i t gross nominal interest rate = + i t = Wt W t = +! t = + t = Pt P t = + Q t = + t = Yt Y t Q = + G t = G t =W t G T t = T t =W t T B t = B t =W t B H t = H t =W y H w t = ln W t = ln G t = ln T t = ln B t = ln H t g t t t t d t = g g t + t = Q = Q g = G G = T T G T H = B m = ( ) B + ( ) H m l = samle mean of l t = summary of constants tat we can ignore

23 Inflation and Rising Det 2 C. Derivation of te Log-Linear Budget Constraint 5 Te udget constraint for te government, after aving adjusted wit GDP and prices, can e written as Dividing troug wit W t, we get G t T t = B t t t Q t B t + H t t Q t H t : G t W t T t = B t t B t + H t H t ; W t W t t Q t t W t W t t Q t t t i.e. G t Tt = B t t t Q t t Bt + H t t Q t t Ht : In tis last expression, all variales are y assumption stationary. Tus we can log-linearise te expression. To do tis, we rewrite it as We ten use te approximations and te steady state relationsip t Gt t Tt = t Bt t t Q t Bt + t Ht t Q t Ht ; exp(z) z + ; r t i t + t G T = ( ) B + ( ) H m or G T B + H = B + H ; to otain Sustituting forward we get T TX t = t+t + t = m t B d t + s t r t + t + + t : j=0 j m B d t+j + s t+j r t+j + t+j + + t+j Let l t = t + t + d t 5 See Tale?? for te notation of te variales and parameters we use.

24 Inflation and Rising Det 22 so tat wit some manipulations and under Assumption 3, we get tat in te limit, i.e. as T!, + l t = [( ) + ( ) ] + X j j=0 r t+j X j d t+j j= X j t+j j=0 + t+j + + t+j More details aout te steps of te derivations can e found in Giannitsarou and Scott (2006). C.. Violation of Assumption 3. We next consider te case were Assumption 3 is violated. As aove, te udget constraint G t Tt = B t t t Q t t Bt + H t t Q t t Ht Assume te existence of a nominal interest rate t, wit an associated real interest rate rt ( + r ) > ( + )( +!). We can ten rewrite our udget constraint as for wic G t Tt = B t t t Q t t Bt + t t t Q t t Bt + H t t Q t t Ht Bon s (2006) suggestion is to de ne and ten use te udget constraint G t G t = G t t t t Q t t Bt T t = B t t t Q t t Bt + H t t Q t t Ht However for our purposes, tis would require constructing a syntetic government expenditure series wose interpretation would e more di cult. assumption tat Instead we use te following approac and make te t t = & H t = B t Given te sign of H and B and in order for r > r, we need & < 0. Under tis assumption we ave or G t Tt = B t t t Q t t Bt + & H t = B t t Q t t Bt + H t t Q t t Ht G t Tt = B t t t Q t t Bt + H t & t Q t t Ht (4)

25 Inflation and Rising Det 23 Tis last equation is exactly te same as (2), except tat te coe cient on H t is di erent. All te aove steps for deriving a log-linear present value constraint can now e replicated y sustituting and wit = = + r ( + ) ( +!) and & ( + ) ( +!) respectively.

26 Inflation and Rising Det 24 References [] Ball, Mankiw and Elmendorf, 998, "Te De cit Gamle", Journal of Money, Credit, and Banking 30, [2] Bergin and Se rin, "Interest Rates, Excange Rates and Present Value Models of te Current Account", Economic Journal 0, [3] Blancard, Couraqui, Hagemann, and Sartor, 990. "Te Sustainaility of Fiscal Policy: New Answers to Old Questions", OECD Economic Studies, 5. [4] Bon, 99. "Budget Balance Troug Revenue or Spending Adjustments? Some Historical Evidence for te United States", Journal of Monetary Economics 27, [5] Bon, "Te Sustainaility of Fiscal Policy in te United States", CESifo Working Paper 446. [6] Bon, "Are stationarity and cointegration restrictions really necessary for te intertemporal udget constraint?", Mimeograp. [7] Campell and Siller, 987. "Cointegration and Tests of Present Value Models", Journal of Political Economy 95, [8] Campell and Siller, 988. "Te Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors", Review of Financial Studies, [9] Campell and Siller, 99. "Yield Spreads and Interest Rate Movements: A Bird s Eye View", Review of Economic Studies 58, [0] Cocrane, 992. "Explaining te Variance of Price-Dividend Ratios", Review of Financial Studies 5, [] Giannitsarou and Scott, "Pats to Fiscal Sustainaility", mimeograp. [2] Gourincas and Rey, "International Financial Adjustment", NBER working paper 55. [3] Hansen, Roerds and Sargent, 99. "Time-Series Implications of Present Value Budget Balance and Martingale Models of Consumption and Taxes", in Rational Expectations Econometrics, edited y Hansen and Sargent, Westview Press. [4] Lettau and Ludvigson, 200. "Consumption, Aggregate Wealt and Expected Stock Returns", Journal of Finance 56, [5] Leeper, 99. "Equiliria under active and passive monetary and scal policies", Journal of Monetary Economics 27, [6] Marcet and Scott, 2005a. "Det and De cit Fluctuations and te Structure of Bond Markets, Mimeograp.

27 Inflation and Rising Det 25 [7] Marcet and Scott, "Fiscal Insurance and OECD Det Management", Mimeograp. [8] McCallum, 984. "Are ond- nanced de cits in ationary? A Ricardian analysis", Journal of Political Economy 92, [9] Polito and Wickens, "Fiscal Policy Sustainaility", Mimeograp. [20] Roseveare, Leifritz, Fore and Wurzel, 998. "Ageing Populations, Pension Systems and Government Budgets", OECD Economics Department Working Paper 68. [2] Sargent and Wallace, 98. "Some Unpleasant Monetarist Aritmetic", Federal Reserve Bank of Minneapolis Quarterly Review. [22] Sims, 994. "A Simple Model for study of te determination of te price level and te interaction of monetary and scal policy", Economic Teory 4, [23] Stock and Watson, 993. "A Simple Estimator of Cointegrating Vectors in Higer Order Integrated Systems", Econometrica 6, [24] Trean and Wals, 988. "Common Trends, te Government Budget Constraint and Revenue Smooting", Journal of Economic Dynamics and Control 2, [25] Trean and Wals, 99. "Testing Intertemporal Budget Constraints: Teory and Application to US Federal Budget and Current Account De cits", Journal of Money, Banking and Credit 23, [26] Woodford, 995. "Price level determinacy witout control of a monetary aggregate", Carnegie Rocester Conference Series on Pulic Policy 43, -46. [27] Wickens and Uctum, 993. "Te Sustainaility of Current Account De cits: A Test of te US Intertemporal Budget Constraint", Journal of Economic Dynamics and Control 7,

28 Inflation and Rising Det 26 Country Mean Min Max Initial Final St. Dev Feed Coef P-Value Canada Germany Italy Japan UK US Tale : Det Variaility and Sustainaility. First 5 columns report te average, minimum, maximum, initial and nal period values of te market value of government det to GDP ratio. Te next column reports te standard deviation of te det/gdp ratio. Te penultimate column sows estimates of in a regression of a country s primary surplus on four lags of its own value and te lagged value of te det/gdp ratio wit te nal column reporting te p value (to two decimal places) of te feedack coe cient.

29 Inflation and Rising Det 27 Det/GDP Country Test Statistic statistic 5% CV verdict CAN ADF(8) C stationary ADF(8) C T trend stationary KPSS(4) unit root KPSS(4) T unit root GER ADF() stationary ADF() C T unit root KPSS(4) unit root KPSS(4) T unit root ITA ADF() stationary KPSS(4) unit root KPSS(4) T unit root JAP ADF() stationary ADF(3) C T unit root KPSS(4) unit root KPSS(4) T unit root UK ADF(2) C unit root KPSS(4) unit root KPSS(4) T unit root US ADF() C unit root ADF() C T unit root KPSS(4) stationary KPSS(4) T unit root C means constant included. T means trend included. Tale 2: Unit Root Tests, Gov Det/GDP. ADF denotes Augmented Dickey Fuller Test and KPSS te Kwiatowski, Pillips, Scmidt and Sin test. C denotes a constant also included in te test and T a trend. Numer in paranteses indicates numer of lags wit wic test was augmented. Te nal column sows te inference from evaluating null of test statistic at 95 per cent con dence intervals.

30 Inflation and Rising Det 28 Money Country test statistic 5% CV verdict CAN ADF() C unit root KPSS(4) unit root KPSS(4) T trend stationary GER ADF() C unit root ADF() C T unit root KPSS(4) unit root KPSS(4) T unit root ITA ADF(0) unit root ADF(4) C T trend stationary KPSS(4) unit root KPSS(4) T trend stationary JAP ADF() unit root KPSS(4) unit root KPSS(4) T unit root UK ADF(5) C unit root KPSS(4) unit root KPSS(4) T unit root US ADF() C unit root ADF(0) C T unit root KPSS(4) unit root KPSS(4) T unit root C means constant included. T means trend included. Tale 3: Unit Root Tests, H/GDP. Te tale reads as in tale 2.

31 Inflation and Rising Det 29 Expenditure/GDP Country test statistic 5% CV verdict CAN ADF(), C unit root KPSS(4) unit root KPSS(4) T unit root GER ADF(0) unit root KPSS(4) unit root KPSS(4) T unit root ITA ADF(2) C unit root ADF(2) C T unit root KPSS(4) unit root KPSS(4) T unit root JAP ADF(3) unit root ADF(3) C T unit root KPSS(4) unit root KPSS(4) trend stationary UK ADF(9) C unit root ADF(0) C T trend stationary KPSS(4) stationary KPSS(4) T unit root US ADF(7) C unit root ADF(6) C T trend stationary KPSS(4) stationary KPSS(4) T unit root C means constant included. T means trend included. Tale 4: Unit Root Tests, G/GDP. Te tale reads as in tale 2.

32 Inflation and Rising Det 30 Revenue/GDP Country test statistic 5% CV verdict CAN ADF(0) unit root KPSS(4) unit root KPSS(4) T unit root GER ADF() C unit root KPSS(4) unit root KPSS(4) T unit root ITA ADF(0) stationary KPSS(4) unit root KPSS(4) T unit root JAP ADF(0) stationary KPSS(4) unit root KPSS(4) unit root UK ADF() C stationary KPSS(4) stationary KPSS(4) T unit root US ADF() C stationary KPSS(4) stationary KPSS(4) T trend stationary C means constant included. T means trend included. Tale 5: Unit Root Tests, T/GDP. Te tale reads as in tale 2. Country Total Def. Prim. Def. Int. Paym. Nom. Gr. Div. Real Gr.Term In. Term % Det GDP US UK GER JAP ITA CAN Tale 6: Det Dynamics. Te rst column sows te average total de cit/gdp for eac country over te sample period. Te next colums sow average primary de cit/gdp and average interest payments/gdp. Te fourt column sows te average nominal growt dividend B t t =( + t )) and te next two columns decompose tis into a real growt term and an in ation term. Te nal column sows te average percentage cange in te Det/GDP ratio over te period.

33 Inflation and Rising Det 3 G t ; T t G t ; B t B t ; H t Lags Canada % 0% 5% 5% 0% % 0% 0% 5% 5% 5% 0% 0% Germany % 0% 0% 0% 5% % 0% 0% 5% 5% 5% 0% 0% 0% Italy 0% 5% 5% 5% % % % % % % % % % 5% Japan 5% 0% 0% % % % % % 5% 5% 5% 0% 0% UK 0% 0% 5% 5% 5% 5% 5% % % 5% % 5% 0% 5% 5% US 5% 5% 5% % % % 5% 5% 5% 5% % 5% % 5% 5% Tale 7: Cointegration tests. Te Tale sows te p-value of test for level of rejection of te null of no ypotesis etween variales listed in top row using Joansen (99). A indicates te lag augmentation selected y te AIC criteria. US Canada Germany Japan UK Italy g g H 0 : = Tale 8: Estimates of Equilirium Relationsip Det and De cits. Te rst row reports te sample average of H=B and te second row reports te sample average of nominal GDP growt. Te parameters and are estimated, as are g and (suject to te restriction tat g + = ). Te next four rows sow te implied estimated coe cients for de ning l t = t + t + g g t + t. Te last row sows p-values for te ypotesis tat = =( ).

34 Inflation and Rising Det 32 US Japan Germany UK Italy Canada g t g t Corr(l t ) Corr(l t ) ADF Tale 9: Alternative Estimates of Fiscal Imalances. Te rst row for eac country sows estimates of structural parameters and coe cients to form l t using sample averages and te second row sows estimates from DOLS. Te row laelled Corr(l t ) sows te correlation coe cient etween te two estimates of l t and te row laelled Corr(l t ) sows te correlation etween te rst di erences of te two estimates. Te nal row sows te p-value from an Augmented Dickey Fuller test for stationarity. US Canada Germany Japan UK Italy Max Min Std Dev Sum AR Unit Root % % % Tale 0: Dynamics of Fiscal Adjustment. Te rst row sows minimum value of l t over sample period, wile te second row sows te maximum value. Te tird row is te standard deviation of l t and te fourt row sows te sum of te AR coe cients wen l t is modelled as an AR(P) process were P is cosen optimally using AIC criteria. Te next row is te p-value from an ADF test tat l t is a unit root process. Te last tree rows sow te numer of periods it takes l t to adjust y 25%, 50% and 75% respectively to a sock to its value.

35 Inflation and Rising Det 33 F d F g F F F r F F Ort. Test US Canada Germany Japan UK Italy Tale : Variance Decomposition of Fiscal Adjustments. For eac country te rst row sows te asic variance decomposition and te second row sows te extended variance decomposition. US Canada Germany Japan UK Italy Tale 2: Predicting In ation. Te Tale sows p-values of signi cance of l t j (were j is listed in te rst column) in a forecasting equation for in ation, containing lagged values of in ation, interest rates and GDP growt.

36 Inflation and Rising Det 34 Figure : Det over GDP, for six industrialised countries, Figure 2: Total de cit over GDP, for six industrialised countries,