Pushing the Limit? Fiscal Policy in the European Monetary Union

Transcription

1 Pushing the Limit? Fiscal Policy in the Euopean Monetay Union Betty C. Daniel Depatment of Economics Univesity at Albany Albany, NY Chistos Shiamptanis Depatment of Economics Ryeson Univesity Toonto, ON M5B 2K3 Octobe 2011 Abstact Govenments ae facing inceasing scutiny ove debt and de cits following the woldwide ecession and nancial cisis which ended in Additionally, policy makes ae confonted with the gowing ealization that they face scal limits on the size of debt and de cits elative to GDP. These scal limits invalidate Bohn s citeion fo scal sustainability since it allows explosive debt elative to GDP, eventually violating any scal limit. The pupose of this pape is to deive estictions on scal policy, necessay fo the govenment to be expected to satisfy scal limits in the long-un. We show that the estictions equie that the pimay suplus espond lage enough to debt. Additionally, since scal limits ule out explosive behavio, they imply cointegation between debt and the pimay suplus and between the pimay suplus and output. We test these two equivalent empiical implications fo a panel of ten EMU counties, and nd that in the yeas peceeding the nancial cisis, scal policy was esponsible, in the sense that govenments did not expect to violate scal limits in the long un. Key Wods: Euopean Monetay Union, monetay policy, scal policy, scal limits, panel cointegation, eo coection JEL codes: C32, C33, E42, E62, F33 The authos would like to thank Pete Pedoni fo numeous consultations on empiical techniques, as well as Dale Hendeson, John Jones and Mauice Roche fo helpful discussions. Additionally, thanks ae due to semina paticipants at the Cental Bank of Cypus, Union College, Univesity of Massachusetts Datmouth, and NewYok Camp Econometics.

2 Pushing the Limit? Fiscal Policy in the Euopean Monetay Union 1 Intoduction Fiscal authoities ae facing enewed scutiny ove govenment debt and de cits following the woldwide ecession and nancial cisis that began in The scutiny has been especially intense in Euopean Monetay Union (EMU) counties, whee scal poblems have theatened the value of the Euo, and aised the spectes of both soveeign default and a beakup of the monetay union. What is "esponsible" scal policy, and have counties in the EMU been following such a policy? Stated anothe way, ae ecent scal di culties due to bad policy o bad luck? The design of esponsible monetay policy has eceived much moe attention than that of esponsible scal policy. If the objective of monetay policy is in ation stabilization, then consensus is that a monetay authoity should follow a ule in which the nominal inteest ate is inceased moe than one-fo-one in esponse to an incease in in ation: the Taylo Rule with the Taylo Pinciple. Numeous papes estimate Taylo Rules ove di eent peiods of time and in di eent counties, testing whethe the inteest ate esponse to in ation is lage enough fo monetay policies to have been esponsible. Leepe (2010) agues that we need to place scal policy unde the same scutiny. Speci cally, we need to detemine citeia fo esponsible scal policy, and then test whethe counties meet those citeia. Responsible scal policy must imply sustainability. Ealy tests of scal sustainability (Hamilton and Flavin 1986; Tehan and Walsh 1991) focused on cointegation between gov- 1

3 enment debt and pimay supluses as an indication that cuent scal policy satis ed the intetempoal budget constaint, and hence was sustainable. Howeve, Bohn (2007) agued that sustainability tests based on cointegation wee unnecessaily estictive. This is because a scal policy could be sustainable with a gowing gap between govenment debt and the pimay suplus, in violation of cointegation. He demonstated that the govenment s intetempoal budget constaint is expected to hold unde cuent scal policy if pimay supluses adjust by any positive amount to lagged debt. Theefoe, a test fo scal sustainability is whethe the pimay suplus esponds positively to lagged debt (Bohn 1998, 2008). Howeve, Bohn s (1998, 2008) de nition of scal sustainability clashes with the new and gowing liteatue on scal limits (Davig, Leepe, and Walke (2010a,b), Davig and Leepe (2010), Cochane (2010), Daniel (2010), Sims (1997, 1999), Daniel and Shiamptanis (2011)). This liteatue ecognizes that thee is an uppe bound on the value of the pimay suplus that a county can aise. A scal limit is in pat due to the La e Cuve; since taxes ae distotionay, thee is an uppe bound on the level of taxes a county can aise. It also aises due to political will. Thee is an uppe bound on a county s willingness to tax itself and a lowe bound on expenditues on public goods. In the pesence of these scal limits, explosive debt and pimay supluses, which satisfy the intetempoal budget constaint, do not epesent equilibium paths because they will eventually violate any uppe bound. Theefoe, a esponsible scal policy must not only satisfy the intetempoal budget constaint, but also espect scal limits, theeby uling out explosive debt and supluses. 2

4 Bohn (2007) acknowledges that his analysis abstacts fom scal limits. Theefoe, ou pape can be viewed as an extension of Bohn, necessay when counties face scal limits. We specify a simple scal policy ule, analogous to the Taylo Rule fo monetay policy, and deive the estictions on paametes necessay fo scal policy to be esponsible, de ned as satisfying both the govenment s intetempoal budget constaint and scal limits. Satisfaction of the intetempoal budget constaint equies that the pimay suplus espond positively to lagged debt, as in Bohn (1998, 2008). Howeve, a positive esponse does not assue that the county satis es its scal limits. Satisfaction of scal limits adds the equiement that the debt and pimay suplus eventually stabilize elative to output. Theefoe, the govenment ow budget constaint, combined with the scal ule, must yield a globally stable model. That is, the system is expected to each a long-un equilibium, uling out explosive behavio of the debt and pimay suplus elative to output. The theoy implies that thee ae two equivalent empiically testable citeia to detemine whethe scal policy is esponsible. The st is the magnitude of the esponsiveness of the pimay suplus to lagged debt. We demonstate that, fo the system to be expected to each the long-un equilibium in a globally stable model, this esponsiveness must be lage enough. The second is cointegation. Since the pimay suplus and debt ae expected to each a long-un equilibium in a globally stable model that ules out explosive behavio, consideation of scal limits estoes cointegation between the pimay suplus and debt as a necessay equiement fo esponsible scal policy. When scal policy must satisfy scal limits in addition to the intetempoal budget constaint, the equiement fo cointegation 3

5 is not unnecessaily stong. We conduct tests to assess both citeia using annual data on eal debt, eal pimay supluses, and eal GDP fo a panel of ten EMU counties ove the peiod , a sample that ends befoe the woldwide nancial cisis and ecession. 1 We nd that, pio to the woldwide ecession and nancial cisis, scal policy was adequately esponsive to inceases in debt and that the data exhibits the equied cointegation to imply scal esponsibility in ou panel of ten EMU counties. Howeve, in a stochastic wold, esponsible scal policy is not su cient to assue the absence of a nancial cisis because any county can expeience bad luck. Ou esults imply that ecent scal poblems ae pimaily due to negative shocks, inclusive of the policy esponse to those shocks, ceated by the woldwide nancial cisis and ecession. The pape is oganized as follows. Section 2 deives the estictions on the paametes of the scal ule necessay fo a esponsible scal policy. Section 3 contains the empiical analysis, and Section 4 povides conclusions. 2 Deivation of Model Restictions In this section, we conside how scal limits a ect the citeia fo designing a esponsible scal policy that satis es both the intetempoal budget constaint and scal limits. 1 We choose to end the sample befoe the nancial cisis because thee wee likely to have been substantial changes in scal policy ove that peiod. 4

6 2.1 Fiscal Limits Wold-wide inceases in govenment debt/gdp atios have spaked inteest in a new liteatue on scal limits, whee these limits ae endogenous to a county s economic and political system and have no elation to the limits imposed in the Euopean Monetay Union o any othe limits imposed exogenously on a govenment. These intenal scal limits ecognize that thee is an uppe bound to the tax evenue that can be aised because taxes ae distotionay; explicitly, thee is a top to the La e Cuve. And the political limit on taxation could be eached pio to eaching the top of the La e Cuve. Additionally, thee is a minimum below which tansfes o govenment spending on public goods cannot be educed. Togethe these scal limits imply an uppe bound on the value of pimay supluses, elative to GDP, that a govenment can geneate. The uppe bound on pimay supluses in tun implies an uppe bound on debt/gdp since agents will not lend if they do not expect pimay supluses to pay the debt. Davig, Leepe, and Walke (2010a,b), Davig and Leepe (2010), and Cochane (2010) have exploed the implications of scal limits fo in ation, and Daniel (2010) exploes thei implications fo an exchange ate cisis. Sims (1997, 1999) and Daniel and Shiamptanis (2011) conside thei implications fo pice stability in a monetay union. Bohn s citeia fo scal sustainability is deived in the absence of these limits. To illustate, if we ignoe stochastic behavio, and take the simplest model in which the pimay suplus elative to GDP esponds to only lagged debt elative to GDP (d t 1 ) with coe cient, then we can solve the govenment s budget constaint fowad to show that the value of 5

7 debt elative to GDP N peiods into the futue is given by d t+n = (1 + i ) N d t ; whee i is the gowth-adjusted inteest ate. The citeia fo satisfaction of the govenment s intetempoal budget constaint is that the pesent value of debt must be zeo in the limit, explicitly lim N!1 d t+n 1 + i (1 + i) = lim N N!1 N d t = 0: 1 + i Clealy, > 0 is su cient to assue intetempoal budget balance. As long as debt/gdp gows moe slowly than the gowth-adjusted inteest ate, its pesent value is zeo in the limit. Howeve, when i > 0; debt/gdp gows foeve, eventually violating any scal limit, without violating the govenment s intetempoal budget constaint. In the following section, we detemine estictions on the paametes of a simple scal ule necessay fo policy to satisfy both scal limits and intetempoal budget balance. Leepe (2010) de nes the scal limit as the point at which the govenment can no longe aise taxes o educe spending and tansfes. In models without gowth and with an exogenous path fo govenment spending and tansfes, he models the scal limit as a xed value fo taxes. We genealize Leepe and do not assume exogenous govenment spending and tansfes. This leads us to expess the scal limit in tems of the pimay suplus. We assume that thee is a limit on the taxes that can be aised and a limit on the amount by which govenment spending and tansfes can be educed. In a model with output gowth 6

8 this limit should be inceasing with income. 2 We model the limit as s t ' max y t : (1) whee s t is the eal pimay suplus, y t is eal GDP, and ' max epesents the limit on the pimay suplus elative to output. 2.2 Fiscal Policy We deive citeia fo scal policy such that the govenment s intetempoal budget constaint holds and scal limits ae espected. We label this policy esponsible scal policy. We use a simple speci cation fo scal policy, analogous to the Taylo Rule fo monetay policy. All vaiables ae expessed in eal tems. Ou scal ule genealizes those oiginally intoduced by Leepe (1991) by allowing the pimay suplus (s t ) to espond to its own lag, to lagged output (y t 1 ) and to lagged debt (b t 1 ). The scal ule is given by s t = 1 s t y t b t 1 + t ; (2) whee t is a mean-zeo distubance epesenting scal shocks. Fiscal shocks e ect both politically-detemined shocks to taxes o govenment spending, and the esponses of the scal authoity to othe shocks that a ect the economy. The lagged value of the pimay suplus is necessay to t the data. It allows pesistence and e ects the desie to smooth the e ect of shocks ove time. Bohn (1998, 2008) shows that the pimay must espond positively to lagged debt fo scal policy to satisfy the intetempoal budget constaint. In a model with all vaiables gowing, the esponse to lagged output eplaces the constant in Leepe s scal 2 Bi s (2010) model implies that ' max is stochastic. Ou esults would not be a ected by this altenative assumption. 7

9 policy ule. We test fo empiical signi cance of the coe cients of ou scal ule, genealized to include the lagged suplus and lagged output. The govenment s ow budget constaint can be expessed as b t = (1 + ) b t 1 s t + t ; whee b t includes publicly held govenment bonds and the money supply backed by the county s bonds, and t epesents mean-zeo shocks to the eal value of debt. 3 We also assume that the eal inteest ate,, is exogenously detemined in the est of the wold, and as a simpli cation, assume that it is constant. Substituting fo the suplus fom equation (2) yields b t = (1 + 3 ) b t 1 1 s t 1 2 y t 1 t + t : (3) Togethe, equations (2) and (3) constitute a dynamic system in the pimay suplus and debt as a function of output and stochastic distubances. 2.3 Dynamics To complete the model, we specify output dynamics. Consistent with ou empiical evidence, we specify output to be integated of ode one, giving the system a unit oot. Output is detemined by y t (1 + g) y t 1 = [y t 1 (1 + g) y t 2 ] + t ; (4) 3 Ou focus is on the govenment s ow and intetempoal budget constaint, since that is the focus of scal policy. Howeve, the equiement that the govenment s intetempoal budget constaint be satis ed in equilibium in a mico-founded model is deived fom the combination of the agent s tansvesality condition on debt (agent s intetempoal budget constaint) togethe with goods maket equilibium. 8

10 whee is the autocoelation in output gowth, g is the aveage gowth of output and t is a well behaved output shock. Ou assumption, that output is an independent integated stochastic pocess, is consistent with a model in which output is diven by integated exogenous technology shocks. Theefoe, we ae assuming that the pimay suplus has no impact on output. In the maco liteatue, the sign of this e ect is contovesial and model speci c. Ou speci cation should be viewed as a simpli cation, which is standad in the liteatue on scal sustainability, 4 and consistent with at least one mainsteam macoeconomic model. The system has a long-un equilibium in which all vaiables gow on aveage at the ate of aveage gowth of output (g). To solve fo this equilibium, quasi-di eence equations (2) and (3), to yield s t (1 + g) s t 1 = ( 1 1 g) s t y t b t 1 + t ; (5) b t (1 + g) b t 1 = 1 s t 1 2 y t 1 + ( g 3 ) b t 1 + t t : (6) Setting these equations to zeo and solving, with shocks taking on thei expected values of zeo, yields long-un equilibium elationships whee s t = 'y t and s t = g 1 + g b t (7) ' = 2 h i < ' max ; (8) (1 + g) g g and whee ' has the intepetation of the long-un value of the pimay suplus. In a long-un equilibium, the pimay suplus and debt both gow at the ate of gowth of output, and 4 Leepe (2010), Bohn (1998, 2007, 2008). 9

11 the pimay suplus is popotional to output and to debt, with the facto of popotionality expessed as the gowth-adjusted eal inteest ate. Using equation (7), then equations (5) and (6) can be eaanged and witten in eo coection fom as s t (1 + g) s t 1 = 3 (1 + g) g 1 + g b t (1 + g) b t 1 = 3 (1 + g) g s t 1 g 1 + g b t 1 g s t g b t 1 2 ' [s t 1 'y t 1 ] + t (9) + 2 ' [s t 1 'y t 1 ] + t t The expessions in squae backets ae the cointegating vectos, equivalently the long-un equilibium elationships, given by equations (7). The eo coection fom implies that when the system deviates fom its long-un equilibium, the pimay suplus and debt both adjust to these deviations. If the adjustment is in the coect diection and lage enough, then the system is globally stable. A globally stable system is expected to etun to its longun equilibium, uling out explosive behavio. Theefoe, a system, which etuns to these long-un equilibium elationships, does not allow the pimay suplus to explode elative to output, especting scal limits, and does not allow debt to explode elative to the pimay suplus, implying intetempoal budget balance. To detemine the estictions necessay fo global stability, we need to solve the dynamic system, expessed in tems of the cointegating vectos and the long-un elationship fo (10) output. De ne Y t and B t as deviations fom cointegating vectos and t as the deviation of output fom its long-un gowth elation accoding to Y t = s t 'y t 10

12 B t = s t g 1 + g b t t = y t (1 + g) y t 1 : and Rewite the dynamic system, compised of equations (4), (9), and (10) in tems of Y t, B t t B t = 2 ' Y t = 1 + g 2 ' 1 + Y t g 1 + g Y (1 + g) 3 t 1 B t 1 ' t 1 ' g t + t 3 (1 + g) 1 + B t 1 + g 1 + g t = t 1 + t : 1 + g t t 1 + g 1 + g Letting denote the oots of the system above, the chaacteistic equation is ( ) 1 + g 2 ' 1 + g 3 (1 + g) g g 3 (1 + g) 2 g ' 1 + = g Using equation (8) to substitute fo '; the chaacteistic equation simpli es to ( ) 2 ( ) + (1 + ) 1 = 0: Given that is less than one 5, the system is globally stable if the emaining oots ae also less than one in absolute value. This equies 3 > (1 1 ) and (1 + ) 1 < 1: (11) In a globally stable system, the values of Y t, B t and t ae expected to appoach zeo in the limit. Equivalently, deviations fom the cointegating vectos vanish, and the system eaches its long-un elationships, given by equation (7). Equation (11) implies that the 5 The goup-mean estimate of is

13 esponsiveness of the pimay suplus to lagged debt, given by 3 ; must be lage than the eal inteest ate times one minus the pesistence in pimay suplus. A positive, but weak esponse, implies that any initial deviations fom cointegating elationships will explode ove time, violating scal limits. Conside the implications of the model solution fo the intetempoal govenment budget constaint and scal limits. If the estictions in equation (11) ae satis ed, then the system is expected to each long-un equilibium elationships, given by equations (7). These estictions ae su cient to assue intetempoal budget balance and satisfaction of scal limits as long as ' < ' max, whee ' is given by equation (8). Altenatively, if the estictions in equation (11) ae not satis ed, then initial deviations fom the cointegating elationships ae expected to gow foeve. Gowth of the pimay suplus elative to output violates the scal limit, no matte what its value, while gowth of deviations of the pimay suplus fom debt sevice might o might not violate Bohn s (1998, 2008) citeion fo scal sustainability. Since esponsible scal policy must satisfy both scal limits and Bohn s sustainability citeion, necessay citeia fo esponsible scal policy equie satisfaction of the estictions in equation (11). Ou solution demonstates that the cointegating elationships, equivalently the long-un elationships in equations (7), exist when the estictions in equation (11) ae satis ed. Theefoe, we can test ou hypothesis of scal esponsibility using eithe. The intoduction of scal limits bings the liteatue on scal sustainability full cicle. Ealie wok on scal sustainability, summaized by Tehan and Walsh (1991), de ned sustainability as satisfaction of the govenment s intetempoal budget constaint and agued 12

14 that it equied a pimay suplus esponsiveness to debt at least as lage as the inteest ate. Bohn (1998, 2008) demonstated that any positive esponsiveness would su ce because the intetempoal budget constaint did not equie boundedness of the debt. Howeve, scal limits equie boundedness. When we add boundedness, we estoe oiginal citeia that the esponse of the pimay suplus to lagged debt must be lage enough. Ou magnitudes di e only because we have added additional tems to the scal ule. When 1 = 0; as assumed in ealie wok, ou estiction educes to ealie ones, whee pimay suplus must espond to lagged debt by moe than the eal inteest ate. 3 Empiical Results The pupose of the empiical wok is to test whethe scal policy in the EMU was esponsible pio to the nancial cisis. Ou analysis yields two equivalent testable citeia: 1) the existence of cointegating elationships between the pimay suplus and debt, and between the pimay suplus and output; and 2) a lage enough esponse of the pimay suplus to lagged debt to yield global stability fo the dynamic system. Eithe is su cient to detemine whethe scal policy was esponsible befoe the cisis. We test both, obtaining consistent esults. Additionally, estimation of the paametes of the scal ule povides paamete values which othe eseaches can use to calibate scal policy. We have annual data on the eal pimay suplus, s it, eal debt, b it, and eal GDP, y it, fo the peiod of thity-seven yeas ( ) fo a panel of ten EMU counties. 6 6 The counties wee chosen based on data availability. They include Austia, Belgium, Finland, Fance, Gemany, Geece, Ieland, Italy, the Nethelands and Spain. Fo moe details see the Data Appendix. 13

15 We use panel techniques to povide estimates of the paametes. Panels incease powe, an impotant featue in a elatively-shot time seies (37 yeas). Howeve, fo panels to be useful, counties must have some commonality. We assume that if these Euopean counties had enough in common to join a monetay union, then they have enough in common fo panel techniques to impove estimates. Mendoza and Osty (2008) estimate scal sustainability, using Bohn s (1998, 2008) citeia, fo a lage divese panel of industial and emeging makets, a panel which is much moe divese than ous. Additionally, to account fo the possible di eences acoss the EMU counties, we use techniques which allow fo heteogeneity acoss the membes in the panel. The model is compised of vaiables which can take on positive and negative values, but which also exhibit non-stationay geometic gowth. This equies decisions on estimation. The standad way of dealing with geometic tends using logaithms is not available to us since the pimay suplus does take on negative values. Bohn (1998, 2008) tansfoms the vaiables by dividing by output. We chose not to make this tansfomation fo seveal easons. Fist, such a tansfomation should eliminate the unit oot in the data, invalidating the use of cointegation tests between the pimay suplus and debt as a citeion fo esponsible scal policy. Second, the tansfomation makes the coe cients in the scal ule stochastic, depending on the ealization of the stochastic gowth ate. Thid, Bohn (1998, 2008) nds that estimates of the paametes of the scal ule, with vaiables expessed as factions of output, ae sensitive to measues of tansitoy vesus pemanent spending. We follow the ealie liteatue on sustainability and estimate the model in levels (Hamil- 14

16 ton and Flavin, 1986; Tehan and Walsh 1991). This allows us to exploit the time-seies chaacteistics of the data using cointegation methods to obtain supe-consistent estimates of the paametes of the cointegating vectos. Additionally, the eo coection speci cation makes a natual distinction between pemanent and tempoay changes without the need fo developing a sepaate methodology fo measuing tansitoy spending. Howeve, estimation in levels does have implications fo infeences on magnitudes of paamete values. Estimation in levels caies with it the implicit assumption that the data has a linea tend instead of a geometic tend. Replacing the geometic tend with a linea tend changes the coe cients on the cointegating elations and intoduces constants into the cointegating elationships and the eo coection speci cation. We deive the cointegating elationships and the eo coection speci cation with a linea tend in Appendix A, and denote the modi ed coe cients in the cointegating vectos with tildes (~). We show that the citeia fo global stability, equations (11), ae identical in the two speci cations. We also show that, at mean values, the cointegating elationships with the linea tend ae identical to those whee gowth has a geometic tend. 3.1 Time Seies Chaacteistics of Data Befoe we poceed with the estimation of cointegation and eo coection, we establish that the vaiables behave as unit oot pocesses, I (1). We use panel unit oot tests, which have moe powe than the time seies unit oot tests. Following Im, Pesaan and Shin (2003), we test the null hypothesis that all seies in the panel contain a unit oot, against the altenative hypothesis that some of the seies in the heteogeneous panel ae stationay. 15

17 The test is based on the aveage of N individual augmented Dickey-Fulle (1979) (ADF) t-statistics. The tests include an individual speci c constant and tend. They ae computed altenately using one lag, two lags, and heteogeneous numbes of lags acoss counties, with the lag ode estimated using consistent infomation citeia such as the Akaike and Schwaz citeia. Table 1 epots the esults with one lag. All the tests fail to eject the null hypothesis of a unit oot in s it, b it ; and y it at the 5 pecent level, implying that eal pimay suplus, eal debt and eal output ae I (1) Cointegation Given that the vaiables in the scal ule appea to behave as unit oot pocesses, we test fo the existence of long-un equilibium elationships, which ae explicitly deived in Appendix A, using panel cointegation techniques. We estimate the following cointegating model s it = a i + % i x it + e it whee e it = i e it 1 + it (12) and test fo the existence of cointegating elationships between the eal pimay suplus and eal debt, and between the eal pimay suplus and eal GDP. In equation (12), a i denotes the county speci c xed e ects, s it is the eal pimay suplus, x it is the egesso, b it o y it, and % i is the cointegating paamete, i o ~' i. 8 Since counties can have di eent scal ules, we model heteogeneity acoss counties by allowing each county s policy paametes 7 We also fail to eject the null of a unit oot when we use Beitung (2000), Maddala and Wu (1999), Choi (2001) tests, and we eject the null of no unit oot when we use Hadi (2000) test. Additionally, we con m the unit oot behavio of the seies using panel unit oot tests suggested by Beitung and Das (2005), Moon and Peon (2004) and Pesaan (2006), which account fo vaious foms of coss-sectional dependence. The tests ae computed using one lag and two lags. Fo Moon and Peon s (2004) pocedue we use one unobseved facto. All tests include an individual speci c constant and tend. 8 Since we estimate the model in levels, the cointegating elationships will contain constants, deived in Appendix A. 16

18 to di e andomly fom the EMU panel policy paametes. Letting i be the i th county s vecto of policy paametes, and the vecto of EMU policy paametes, we assume that i = + i, whee the i have zeo-means and constant vaiances fo all i. We begin with two goup-mean panel cointegation t tests suggested by Pedoni (1999, 2004). 9 Both tests ae esidual-based cointegation tests, which test the null hypothesis that the vaiables of inteest ae not cointegated fo all the counties in the panel against the altenative hypothesis that thee exists a heteogeneous cointegation vecto fo all the counties in the panel. Unde the null hypothesis of no cointegation, the esiduals fom (12), ^e it, ae I (1). Denoting the autoegessive coe cient of the i th county s esiduals by i, the goup-mean statistics test the null hypothesis of no cointegation, H o : i = 1 fo all i, vesus the heteogeneous altenative hypothesis, H A : i < 1 fo all i. The altenative does not pesume the same value fo i. The st goup-mean test uses semi-paametic coections, while the second is a paametic ADF test. 10 The tests ae extensions of the single time seies Phillips-Peon (1988) t-test and the ADF t-test. We account fo coss-sectional dependence and coss-membe cointegation by using common time e ects. 11 Fo the semi-paametic 9 The goup-mean statistics allow modeling an additional souce of potential heteogeneity acoss individual membes of the panel. Moeove, Gutieez (2003) nds that Pedoni s tests have highe powe than the system test poposed by Lasson, Lyhagen and Lothgen (2001). Additionally, Banajee, Macellino and Osbat (2004) show that fo small N the size distotions of Pedoni s tests ae lowe than those of Lasson and Lyhagen (1999) test. 10The speci cations ae given in Appendix C. 11Common time e ects allow us to model a limited fom of coss-sectional dependence and coss-membe cointegation (which is a fom of long-un coss-sectional dependence). Common time e ects assume that the coss-sectional dependence coelation between county i and j is identical fo all i; j. Thus, in the pesence of heteogeneous coss-sectional dependence, subtacting o the coss-sectional aveage does not completely eliminate coss-sectional dependence. The method by which coss-sectional dependence is modeled in panels is still an active aea of eseach. Bai and Ng (2002) and Moon and Peon (2004) conside models in which the eo tems have a facto stuctue in panel unit oot tests, howeve the implications fo such facto models have not been studied in the panel cointegation context. Notice though that time e ects ae a special case of a facto model whee thee is a single common facto and the esponse of each county is 17

19 test we use the Batlett kenel and the Newey-West bandwidth selection pocedue, and fo the paametic ADF-type test, we use the step-down pocedue to estimate the numbe of lags. The esults, epoted in Table 2, indicate that both tests eject the null hypothesis of no cointegation at the 5 pecent level. 12 Theefoe, Pedoni s tests povide stong evidence that s it and b it ae cointegated and that s it and y it ae also cointegated. We con m that thee ae two cointegating elations in the tivaiate model using the system panel cointegation test poposed by Lasson, Lyhagen and Lothgen (2001). Thei test is a panel vesion of Johansen s (1988, 1995) full infomation maximum likelihood method. The null hypothesis is that all of the N counties in the panel have at most q cointegating elationships among the 3 vaiables, H o : q cointegating elations fo all i; and the altenative is that all the counties have 3, H A : 3 cointegating elations fo all i: This is a sequential pocedue whee the st test is the null q = 0: If this hypothesis is ejected, then the null q = 1 is tested. The sequential pocedue continues until the null is not ejected o the hypothesis q = 2 is ejected. The test is computed using one-lag di eence tems and it includes individual speci c xed e ects. In Table 3 we veify that thee ae two cointegating elations in the model. The panel test statistic indicates that q = 2 in the model with thee vaiables s it, b it and y it. This implies that thee is a single stochastic tend in the data fo each county, implying that thee ae cointegating elations between s it and b it ; and between s it and y it ; consistent with pevious esults. simila. Theefoe, time e ects account fo both coss-sectional dependence and coss-membe cointegation when the souce of dependency is due to a single common time speci c shock. 12We also eject the null of no cointegation at the 5 pecent level when we use all seven panel statistics of Pedoni (1999, 2004). Additionally, we eject the null of no cointegation at the 5 pecent level when we do not use the common time e ects. 18

20 Theefoe, the data satisfy estictions necessay fo existence of a stationay long-un equilibium elationship between the pimay suplus and debt, and between the pimay suplus and output fo each county. Stationay long-un equilibium elationships ae consistent with a globally stable model, implying esponsible scal policy. 3.3 Fiscal Response to Debt Finally, we test whethe the magnitude of the esponse of the pimay suplus to lagged debt has been lage enough to satisfy estictions necessay fo global stability, given by equations (11). Appendix A povides a deivation of the eo coection model, unde the assumption in the estimation that the data has a linea tend, as s it s it 1 = ~' i g i 3i 2i ~' i i 1 + i s it 1 i b it 1 + ~' i g i s it 1 ~' i y it 1 + ~'2 i g i 2i 1 3i i i 1 + i + it i (13) whee g i is aveage linea gowth, and ~' i is a combination of the paametes in the scal ule and has the intepetation of the long-un value of pimay suplus. We estimate the paametes of the above eo coection model using a two-step pocedue, in which we initially estimate the cointegating paametes. In the second step, we estimate the coe cients on the eo coection tems. To estimate the cointegating paametes, we use Pedoni s (2000, 2001) goup-mean fully modi ed OLS (FMOLS) pocedue fo cointegated panels, which is based on equation (12). 13 The goup-mean FMOLS pocedue accommodates the heteogeneity that is typically 13Bohn (2008) consides a simila equation with x it given by debt, using ove two centuies of US data on the pimay suplus, output, and debt. His eal data seies have sevee heteoskedasticiy, due to two centuies of 19

21 pesent both in the tansitional seial coelation dynamics and in the long-un cointegating elationships. It is a semi-paametic appoach that adjusts fo the e ects of endogenous egessos and shot-un dynamics of the eos. 14 We use the Batlett kenel and the Newey- West bandwidth selection pocedue as suggested by Pedoni (2000). The esults, in Table 4, indicate that the goup-mean panel estimate fo the eal inteest ate is 4.22 pecent ( = 0:0422) and the goup-mean panel estimate fo the long-un value of pimay suplus is 3.80 pecent (~' = 0:0380). 15 In the nal step we conside estimation of the goup-mean panel scal policy paametes 1 ; 2 ~' ; and 3. It is impotant to ecognize that the esiduals in equation (13) could be autocoelated in the data. If so, then the esiduals could be coelated with the ight-handside vaiables, biasing estimates of the coe cients on the eo coection tems. Theefoe, we use Sims (1980) likelihood atio test to detemine the appopiate numbe of lags to fully captue the dynamics fo each county. Fo some counties, the test implies that equation (13) is appopiately speci ed. Howeve, fo othes, an additional lag is chosen. Theefoe, to be sue that we ae not omitting elevant lags and theeby biasing estimates of coe cients, gowth in eal GDP. He educes, but does not eliminate, these poblems by dividing by eal GDP. Standad deviations fo eal vaiables ae 64 to 98 times as high in the second peiod as in the st. Fo vaiables expessed as a faction of GDP, this numbe falls to something a little lage than 2. We have a vey di eent data set fom Bohn s a elatively shot time dimension and ten counties. The shote time dimension implies that we do not have Bohn s heteoskedasticity poblem. Ratios of standad deviations in the second half of the sample elative to the st half aveage to something less than 2, simila to his adjusted data. 14Since FMOLS is designed to educe bias associated with shot-un dynamics and the estimates in the I (1) model ae supe-consistent, it is not necessay to add stationay vaiables, like HP- lteed measues of the data, as in Bohn s model with stationay data (2008). 15The FMOLS esults ae obust to the choice of kenel and bandwidth. We obtain almost identical estimates when we use the Pazen and quadatic spectal (QS) kenels and the Andews (1991) bandwidth selection pocedue. Additionally, we obtain simila estimates when we use the goup mean dynamic OLS (DOLS) pocedue of Pedoni (2004) and the two-step estimato of Beitung (2005). 20

22 we estimate the model with an additional lag. 16 s it s it 1 = ~' i g 3i ~Bit 2i ~Yit i + 1i (s it 1 s it 2 ~' i ~' i g i ) (14) i ~' + 2i b it 1 b i g i it 2 + 3i (y it 1 y it 2 g i ) + it : i whee ~ B it and ~ Y it ae the cointegating vectos given by thei linea countepats and g i is the aveage gowth ate, all deived in the Appendix A. A pesistent, but negative scal shock, pehaps ceated by a wa, would imply a negative eo in the st cointegating elationship and ising lagged debt, implying a negative coelation between the two tems. Theefoe, failue to include the lagged change in debt could bias the estimate on the coe cient on the eo coection tems. 17 Now, conside estimation of the coe cients on the eo coection tems in equation (14). Fist, we use the estimated cointegating paametes of the eal inteest ate and longun value of the pimay suplus to constuct the eo coection tems fo each county, yielding an equation in which all the vaiables ae stationay. Asymptotically, the fact that we use the estimated eo coection tems athe than the tue eo coection tems in (14) does not a ect the standad popeties of ou estimates due to the supe-consistency 16The additional dynamics do not change the st citeion fo stability, 3i i > 1 1i, but modify slightly the second one. This becomes 1i 1 + 2i+ i( 1i 1) i 2 2i+ i(2 1i 1) < 1. 17Using long US samples of one and two centuies that highlight the ole of was, Bohn (2008) expesses the scal ule in tems of the suplus and debt as a faction of output, and nds it necessay to add HP- lte measues of tansitoy values of the vaiables to distinguish between the esponse of the suplus to pemanent and tansitoy shocks and educe "omitted vaiables bias." Tansitoy, but pesistent govenment spending, as associated with a wa, would be accompanied by ising debt implying that the esidual would be low when debt is high elative to the suplus. The eo coection model deals with this by adding lagged changes of the model vaiables. In this example the lagged change in debt would be high in a wa and would play the ole of Bohn s tansitoy militay spending, and the lagged change in output would play the ole of Bohn s HP- lteed output. 21

23 popeties of the estimato of the cointegating elationships. 18 Afte constucting the eo coection tems, we estimate the coe cients of the eo coection model, augmented with lagged changes in vaiables, poviding estimates fo 1 ; 2 ~' ; and 3. We use the goup-mean pocedue ecommended by Pesaan and Smith (1995). 19 Table 5 indicates that the panel estimates ae: 1 = 0:4911, 2 ~' = 0:1188 and 3 = 0:6277. Each coe cient is statistically signi cant at the 5% level, and 3 is statistically signi cantly lage than We also pesent paamete estimates fo each individual county in Table 6. Ou infeence fo each county s scal policy is weake. We nd that each county s 3i i is lage than 1 1i, although standad eos ae geneally too lage to yield signi cance fo each membe in the panel. The lage individual-county standad eos illustate the easons fo using panel estimation instead of time seies estimation in a elatively shot sample. Although the individual county esults ae not signi cant, signs ae coect, poviding some individual county cooboation fo ou panel esults. 21 At st glance the estimated coe cient on output, o equivalently on the long-un pimay suplus, 2, might seem to have the wong sign. An altenative and equivalent expession of the eo coection model is moe intuitive. Using esults in Appendix A, the scal ule in 18See Engle and Gange (1987), Toda and Phillips (1993) and Ubain (1992) fo the popeties of estimatos in cointegated systems. 19They show that when the paametes of inteest ae heteogeneous, the goup-mean pocedue povides consistent estimates, wheeas the pool panel pocedues give inconsistent estimates. 20We obtain almost identical estimates when we use the hieachical Bayes estimato of Hsiao, Pesaan and Tahmiscioglu (1999) and the weighted estimato of Swamy (1980) (also efeed as the empiical Bayes estimato). 21Ou esults also satisfy the second condition necessay fo global stability, ( 1 1) 2 2+(2 1 1) = 0:5035 which is less than 1. 22

24 equation (13) can also be witten as s it s it 1 = (1 1i ) (~' i y it 1 s it 1 ) + 3i i ( i b it 1 ~'y it 1 ) + it which implies that pimay suplus inceases wheneve pimay suplus is below its long-un value and wheneve the debt sevice is above its long-un value. As shown in the Appendix A, the citeion 3i i > 1 1i is equivalent to 2i ~' i must be negative. < 0: Given that ~' i > 0; the value fo 2i We have not allowed estimates of the paametes of the eo coection model to change as the monetay union has evolved ove time. Howeve, if the coe cients in the cointegating elationships had changed and no account wee taken fo the change, then we should not have ejected the null of no cointegation. 22 The values fo the coe cients on the eo coection tems could have changed. To test fo a change in 1 ; 2 ~' ; and 3, we beak the sample into two sub-peiods, the pe-maasticht ea ( ) and the post-maasticht ea ( ). 23 Table 7 shows that 3 > 1 1 in both sub-samples, although standad eos ae too high to yield signi cance. 24 The split sample evidence suggest that the pimay suplus is su ciently esponsive to debt to imply that scal policy is esponsible in both subsamples. 25 In summay, ou goup-mean panel esults imply that pimay supluses in the EMU counties have been su ciently esponsive to lagged debt to satisfy the citeia fo esponsible 22Fo example, assume that thee is an unmodelled change in ~'. The esiduals in (12) will be non-stationay and cointegation would be ejected. 23The Maasticht Teaty began on Novembe 1, The sub-samples ae not long enough to allow eliable infeence. Most of ou panel techniques equie the time seies dimension to be substantially lage than the coss-section dimension, and we lose this when we split the sample. 25Afonso (2005) and Annett (2006), who use a simila EMU data set and othe empiical techniques, do not nd evidence fo a change in the scal policy afte the signing of the Maasticht Teaty. 23

25 scal policy. When we educe the size of the sample, eithe by estimating individual-county scal ules o by splitting the sample, we etain the magnitudes necessay fo esponsibility, but they ae not always sigi cant. 4 Conclusion The st contibution of the pape is theoetical. It establishes citeia fo esponsible scal policy, whee we de ne esponsible policy as a policy ule that is expected to satisfy both the govenment s intetempoal budget constaint and scal limits. Responsible scal policy must imply non-explosive debt elative to the pimay suplus and a non-explosive pimay suplus elative to GDP. We specify scal policy as a ule and detemine the estictions on paamete values necessay to assue non-explosive behavio. We nd that the esponse of the pimay suplus to debt must be lage enough to ende the system, expessed as long-un equilibium deviations (equivalently cointegating vectos), globally stable. This modi es Bohn s (1998, 2008) condition, in which he de nes a sustainable scal policy in the absence of scal limits as one which satis es the govenment s intetempoal budget constaint. Ou additional citeion that scal policy satisfy scal limits, equies a lage esponse of the pimay suplus to govenment debt. Moeove, consideation of scal limits estoes cointegation as a equiement fo esponsible scal policy, since debt, the pimay suplus, and GDP must each stable long-un equilibium elationships with each othe. These esults imply two equivalent empiically testable citeia fo esponsible scal policy. The st is cointegation, and the second is the magnitude of the esponsiveness of the 24

26 pimay suplus to lagged debt in the scal ule. Ou theoetical contibution bings the liteatue on scal sustainability full cicle. Tehan and Walsh (1991) summaized equiements fo scal policy to satisfy the govenment s intetempoal budget constaint as those which we pesent to satisfy both the intetempoal budget constaint and scal limits. Bohn (2007) agued that those equiements wee too stong to satisfy the govenment s intetempoal budget constaint alone. We show that adding scal limits estoes those oiginal citeia. The second contibution of the pape is empiical. We test fo cointegation, and we estimate the paametes of the scal ule fo a panel of ten EMU counties ove the peiod of , using panel techniques that allow fo heteogeneity acoss the counties. We nd that ove the sample peiod, the data exhibits the equied cointegation and the equied esponsiveness of the pimay suplus to lagged debt fo scal policy to have been esponsible. Howeve, even a county following a esponsible scal policy can expeience bad luck, when a sting of negative scal shocks, togethe with the policy esponse to those shocks, educes the pimay suplus. This analysis implies that the ecent nancial tumoil in seveal EMU counties is a consequence of seveely negative shocks athe than iesponsible scal policy ules. 25

27 Appendix A. Model with a Linea Tend The model consists of equations (2), and (3), but the equation fo output gowth is expessed as y t y t 1 g = [y t 1 y t 2 g] + t ; (15) whee g is the aveage change of output, such that y y = g: To solve fo long-un equilibium changes, st di eence equations (2) and (3) and dop time subscipts to yield s = b = ~'y = ~'g whee ~' = = 1 < 'max ; and whee ~' has the intepetation of the long-un value of the pimay suplus with linea tend. Since output changes on aveage by g, the pimay suplus changes on aveage by ~'g; and debt changes on aveage by ~'g : Di eencing and subtacting the linea tend in the suplus and debt fom equations (2) and (3), espectively, yields s t s t 1 g~' = ( 1 1) s t y t b t 1 g~' + t (16) b t b t 1 g~' = 1s t 1 2 y t 1 + ( 3 ) b t 1 g~' + t t (17) To solve fo long-un equilibium elationships, set the equations above equal to zeo, with distubances at thei expected values of zeo, to yield s t = b t 1 + ~'g = ~'y t ~' 2 g (18) 26

28 Theefoe, compaed with the theoetical model, which has a geometic tend, the empiical model, estimated with a linea tend ove the nite sample, yields cointegating vectos with constants and di eent coe cients. At mean values, the cointegating elationships ae identical to those in the model with a geometic tend. To pove this, expess the st equilibium elationship at the mean as s = b 1 + g~' = b s b Dividing both sides by b yields s b = s s s b b b Since s s = b b = g s = g 1 + g b: (19) The second cointegating vecto is obtained by setting equation (16) equal to zeo, with shocks at thei expected value of zeo. Evaluating at the mean yields ( 1 1) s + 2 y + 3 b g~' = 0: Substitute fo b fom equation (19) and use g~' = s to yield Dividing by y and eaanging yields 1 + g ( 1 1) s + 2 y + 3 s s = 0: g g s g y s s s = 0: y

29 Using s s = g yields 1 + g s 1 1 g + 3 g y + 2 = s g g A y = 'y: (1 + g) Using equations (16), (17), and (18), the eo coection model can be expessed as s t s t 1 = ~'g 3 s t 1 b t 1 + ~'g ~' s t 1 ~'y t 1 + ~'2 g (20) + t b t b t 1 = ~'g + 2 ~' 1 3 s t 1 ~'y t 1 + ~'2 g s t 1 b t 1 + ~'g t + t (21) De ning deviations fom cointegating vectos and long-un elationships as, ~Y t = s t ~'y t + ~'2 g ~B t = s t b t + ~'g ~ t = y t y t 1 g: we can ewite the dynamic system in tems of the cointegating vectos and the long-un elationship of output as ~Y t = 1 ~B t = (1 + ) 2 ~' ~ Y t ~Y 3 t 1 ~' 1 B ~ t 1 ~' ~ t 1 + t ~' t (1 + ) B ~ t 1 + (1 + ) t t 3 ~ t = ~ t 1 + t 28

30 Substituting fo ~'; the chaacteistic equation is identical to that fo the theoetical model with the geometic tend. Theefoe, the equiements fo global stability ae identical. The equiement that 3 > 1 1 is simply the equiement that 2 ~' = = 1 > 0: The loading on the second eo coection tem in equation (20) must be positive. B. Data Appendix Nominal pimay suplus, nominal GDP and GDP de ato ae fom the OECD database. The nominal debt is also fom OECD database and fo missing yeas data is obtained fom the ECB s AMECO database. The sample consists of annual data fom fo Austia, Belgium, Finland, Fance, Gemany, Geece, Ieland, Italy, the Nethelands and Spain. Fo Luxemboug and Potugal thee was not data available fo a lot of yeas. Fo Gemany we use the data fo West Gemany befoe uni cation and Gemany afte uni cation. The eal values of the vaiables fo each county ae obtained by dividing the nominal values by the GDP de ato. Fo the nominal pimay suplus we use the geneal govenment pimay balances (OECD Annex Table 29) and fo nominal debt we use the geneal govenment goss nancial liabilities (OECD Annex Table 33). C. Panel Cointegation Statistics (Pedoni (1999)) 1. Goup mean t statistic (semi-paametic): N 1=2 ~ ZtN;T N 1=2 N X i=1 ^ 2 i TX! 1=2 TX (^e i;t 1 ^e i;t ^! i ) ^e 2 i;t 1 t=1 t=1 29

31 2. Goup mean t statistic (paametic): N 1=2 ~ Z tn;t N 1=2 N X i=1 TX t=1 ^s 2 i ^e 2 i;t 1! 1=2 TX t=1 ^e i;t 1^e i;t whee ^! i = 1 T Xk i s=1 1 s k i + 1 TX t=s+1 ^ i;t^ i;t s ; ^s 2 i 1 T TX t=1 ^ 2 i;t; ^ 2 i = ^s 2 i + 2^! i ; ^s 2 i 1 T TX t=1 ^ 2 i;t and whee the esiduals ^ i;t and ^ i;t ae obtained fom the following egessions: ^e i;t = ^ i^e i;t 1 + ^ i;t ^e i;t = ^ XK i i^e i;t 1 + k=1 ^i;k ^e i;t k + ^ i;t and ^e i;t ae the esiduals fom equation (12). 30

32 Table 1: Panel Unit Root Tests Test statistic s it b it y it t IP S t BD ob t MP a t MP b t CIP S Note: t IP S is the goup mean t-statistic poposed by Im, Pesaan and Shin (2003), t BD ob is the OLS obust t-statistic poposed by Beitung and Das (2005), t MP a and t MP b ae the t-statistics based on the facto model poposed by Moon and Peon (2004) and t CIP S is the test poposed by Pesaan (2006). They all test the null of a unit oot against the altenative of stationaity. All tests ae computed using one lag and they include individual speci c constants and tends. The test statistics with ** eject the null of a unit oot at the 5 pecent level. Fo the t IP S, t BD ob, t MP a and t MP b tests, the null is ejected if t < 1:64 and fo the t CIP S test, the null is ejected if t CIP S < 2:85: 31

33 Table 2 : Residual Based Panel Cointegation Tests Test Statistics s it and b it s it and y it Goup mean t (semi-paametic) -4.22** -4.54** Goup mean t (paametic) -4.53** -4.83** Note: See Appendix C fo details. The statistics ae distibuted standad nomal. They test the null hypothesis of no cointegation against the altenative of cointegation. All the tests include individual speci c xed e ects and common time e ects. The test statistics with ** eject the null hypothesis at the 5 pecent level. The 5 pecent citical value is Table 3 : System Based Panel Cointegation Tests s it, b it, y it q = 0 q = 1 q = 2 Cointegating elations Panel test 14.26** 7.77** Note: The panel cointegation statistic tests the null hypothesis that thee ae q cointegating elationships against the altenative that thee ae 3 cointegating elationships. The test includes individual speci c xed e ects. The test statistics with ** eject the null at 5 pecent level. The panel test has a 5 pecent citical value of The moments used fo the panel test ae tabulated in Shiamptanis (2008). 32