Does the Fiscal Theory of the Price Level hold for
the Euro Area?
∗†Nikki Panjer University of Groningen
January 11, 2016
Abstract
This paper examines whether there is evidence in favor of the Fis-cal Theory of the Price Level (FTPL) in the euro area. The FTPL states that if a fiscal authority follows a non-Ricardian regime, sur-pluses move in an arbitrary way and the price level adjusts in order to fulfill the government’s budget constraint. At the contrary, if a fis-cal authority follows a Ricardian regime, surpluses adjust in order to preserve government solvency. In order to determine whether a Ricar-dian or a non-RicarRicar-dian regime is more plausible for the euro area, the empirical strategy by Canzoneri, Cumby, and Diba (2001) is followed. A bivariate Vector Autoregressive (VAR) model is estimated including the variables primary surplus and government debt, both proportional to GDP. The impulse response functions show that a Ricardian regime is more plausible for the euro area in the period 1980q2-2013q4. The analysis is extended in two ways. First, I evaluate whether the GFC has a significant impact on the outcomes. This is done by estimating the VAR for different subsamples and by estimating a VAR including a dummy interaction term. Second, the initial bivariate VAR is esti-mated for several individual euro area countries. All extensions of the model suggest that Ricardian fiscal regimes are more plausible in the euro area.
Keywords: Fiscal Theory of the Price Level, Fiscal Policy, Monetary Policy, VAR
JEL Classifications: E63, H62, H63
∗
A thesis presented for the degree of Master of Science.
†
1
Introduction
In 1999, the European Monetary Union (EMU) was formed while there were still many economic differences among member countries. At the establish-ment of the monetary union it was assumed that convergence among the involved countries would accelerate if they shared a common currency. Yet, more than a decade later, euro area countries still differ. For example, labor mobility is still low (CEPS, 2014) and there is no clear evidence that business cycles converge (De Haan, Inklaar and Jong-a-Pin, 2007). These differences between euro area countries are also reflected in their fiscal policies as can be seen from their debt-to-GDP ratios.
Monetary policy is now conducted by the European Central Bank (ECB) at the union level. With a common monetary policy and one common cur-rency, fiscal policy is now the only instrument left at the national level to react promptly to asymmetric shocks. According to De Grauwe (2003), na-tional governments should therefore be permitted fiscal flexibility and should be able to run temporary budgetary deficits in order to insure against these shocks. For example, if due to a recession aggregate demand in a certain economy suddenly falls, this economy should be permitted to run a deficit and should not be forced to cut government spending.
Yet, flexibility in the use of national fiscal policies might have negative effects for price and financial stability in the euro area as a whole. For ex-ample, the ECB (2011) points out that if a government pushes aggregate demand when the economy is already producing at maximum capacity this may generate inflationary pressure. In addition, a government that borrows excessively from the capital market may push up the interest rate. As a con-sequence of the latter effect, investment is crowded out, aggregate demand decreases and prices decrease. These examples illustrate that national fiscal policies may affect price and financial stability in the euro area as a whole. Recent literature on fiscal dominance shows the importance of the in-teraction between monetary and fiscal policy for the determination of the equilibrium price level. Sims (2012) argues that the effectiveness of monetary policy actions is impaired if fiscal authorities do not respond in an appro-priate way. If so, monetary contractions might in fact lead to inflationary pressures and fiscal policies are dominant in the determination of the price level. Much evidence exists in favor of fiscal dominance in Brazil around the turn of the century (Blanchard, 2004; Tanner and Ramos, 2002) which shows that fiscal policies can be an important factor in the determination of the price level.
of price determination. Traditional ‘monetarists’ theories state that only monetary policy is able to determine the equilibrium price level. The price level is determined as the unique value that equates money demand and money supply. On the other hand, the Fiscal Theory of the Price Level (hereafter: FTPL) states that it is fiscal policy that determines the equilib-rium price level. Important contributions by Woodford (1994, 1995), Leeper (1991), and Sims (1994) show that price determination depends on the way in which the government’s present value budget constraint is satisfied.
According to Woodford (1995), if the fiscal authority follows a ‘Ricar-dian regime’, surpluses are determined in such a way that the government budget constraint holds. In this case the price level is determined by mone-tary policy in the same way as the traditional monetarist theories describe. However, if the fiscal authority follows a ‘non-Ricardian’ regime, surpluses can follow an arbitrary process and the price level adjusts in order to satisfy government solvency. In this case, the equilibrium price level is determined as the unique value that equates the real value of government debt to the expected present value of future surpluses.
Determining the plausibility of Ricardian and non-Ricardian regimes is particularly important for the euro area as it reveals the ability of the ECB to achieve price stability by means of monetary policy. According to the FTPL, evidence in favor of a non-Ricardian regime would mean that national fiscal policies drive national price levels. Under such circumstances, monetary policy would play a minor role in the determination of prices. Since euro area countries set their national fiscal policies in different ways, price differences might occur among euro area countries which would hamper a common monetary policy. If fiscal price determination holds, fiscal policy would have to play a larger role in achieving the price stability objective. Fiscal policy may have to play an even greater role in achieving the price stability objective if monetary policy is at the zero lower bound, as it is since the recent financial crisis.
In this paper, I follow the methodology of Canzoneri, Cumby and Diba (2001) and estimate a bivariate Vector Autoregressive (VAR) model in order to find out whether fiscal authorities in the euro area follow a Ricardian or a non-Ricardian regime. The model includes the variables primary govern-ment surplus and governgovern-ment debt, both proportional to GDP. An (unex-pected) shock to the surplus is imposed and the plausibility of Ricardian and non-Ricardian regimes is evaluated by means of impulse response functions of both endogenous variables.
I find that the debt-to-GDP ratio responds negatively to an increase in the surplus. This finding can be interpreted in both a Ricardian and a non-Ricardian fiscal regime. However, in a non-Ricardian regime, the negative response can only be explained if there exists negative correlation between current and future surpluses. Since evidence for this cannot be found, a Ricardian regime is more plausible for the euro area. The analysis is extended in two ways. First, I evaluate whether the GFC has a significant impact on the outcomes. This is done by estimating the VAR for different subsamples and by estimating a VAR including a dummy interaction term. Second, the initial bivariate VAR is estimated for several individual euro area countries. All extensions of the model suggest that Ricardian fiscal regimes are more plausible in the euro area.
The paper proceeds as follows. Section 2 explains the FTPL and dis-cusses the relevant literature. Section 3 presents the methodology that is used in order to test for the plausibility of Ricardian and non-Ricardian regimes. Section 4 discusses the data that is used. Section 5 reports the results that are obtained. Section 6 extends the analysis in several ways and Section 7 concludes.
2
Literature review
2.1 Traditional ‘monetarist’ theories
For a long time, the leading theory on price level determinacy has been the Quantity Theory of Money (hereafter: QTM). It has been built upon the principle of Ricardian equivalence (Barro, 1979), which states that fiscal policies do not have an effect on the real economy. In order to illustrate this, consider the case where a government runs a deficit and the level of government debt increases. Intuitively, Ricardian equivalence implies that in such a situation, consumers believe that higher government debt has to result in increased taxes in the future in order for the government to remain solvent. Consumers incorporate this in their current consumption decision, decide to save more and, consequently, aggregate demand decreases. According to Ricardian equivalence, the government is not able to steer the economy by fiscal policy.
is able to affect the price (Fisher, 1911). It is often characterized by the well-known equation of exchange:
MtVt= PtTt, (1)
where Mt is the nominal value of the money supply, Vt is the velocity at
which money circulates, Pt is the price level, and Tt is an index of the real
value of aggregate transactions. In quantity theoretic models, the price level is determined as the unique price level that equates the purchasing power of the money supply (the left-hand side of Eq. (1)) to the desired level of real balances (the right-hand side of Eq. (1)). This principle forms the basis for many macroeconomic models and analyses such as the IS-LM framework. According to these models, the government is able to determine the price level by varying money supply. Yet, the price level might be indeterminate in some cases. This is most obvious in an endogenous money supply regime, in which, the money supply depends on the price level in the economy. However, this price level again depends on the money supply, and as a result both the money supply and the price level are indeterminate (Sargent and Wallace, 1975). Therefore, there are certain situations where the QTM is not able to determine the price level.
2.2 The Fiscal Theory of the Price Level
The FTPL aims at providing more insight into the situation where the price level is indeterminate. The theory – put forward mainly by Woodford (1994, 1995), Leeper (1991), and Sims (1994) – states that it is not monetary policy but fiscal policy that determines the price level. As a result, the price level is determined even if the money supply is determined endogenously. Moreover, Woodford (1995) shows that fiscal policy is the factor that determines the price level in the case of exogenous monetary policy or an interest-rate peg. Woodford (1995) explains that the price level affects aggregate demand through a wealth effect. The intuition is as follows. An increase in the price level decreases the real value of the government’s liabilities. Since this can also be seen as a reduction of the value of the net assets of the private sector, demand for goods and services is reduced through a wealth effect. As a result, the price level needs to adjust in order to restore equilibrium. A similar wealth effect arises if households have expectations regarding future government deficits. Thus, the effects of the price level on aggregate demand depends upon the nominal level of government debt and the wealth effects of expected future government budgets. To see this, we take a closer look at Woodford’s model.
the government’s budget constraint is satisfied. In equilibrium, the following present value government budget constraint must hold:
dt= st+ Et +∞ X j=t+1 j−1 Y k=t αk ! sj, (2)
where dt is the ratio of government debt to nominal GDP at the beginning
of period t, st is the ratio of government primary surplus to nominal GDP
in period t, and αt is the discount factor for period t. More details on the
derivation can be found in Appendix A. The definition of the present value budget constraint used here differs slightly from the one used by Woodford (1995) since we scale all variables by nominal GDP instead of by the price level. Doing so facilitates the empirical analysis and allows for sticky prices as will be explained below. Simplified, Eq. (2) states the following:
Dt
Ptyt
= Expected present value of primary surpluses at time t, (3)
where Dt is the nominal government debt level at the beginning of period
t, Pt is the price level in period t, and yt is nominal GDP in period t.
Even though quantity theoretic models also acknowledge such an equality, the difference between the quantity theoretic view and the FTPL lies in its interpretation. Let us analyze both views in turn.
In the monetarist view, Eq. (2) is a constraint and should hold in order for the government to be solvent. Primary surpluses are set in such a way that the equality holds no matter the price level. According to Woodford (1995), the fiscal authority follows a ‘Ricardian regime’ in this case. Equa-tion (2) does not matter for price determinacy. Instead, the price level is determined in the money market.
The FTPL reinterprets Eq. (2), and states that the price level will jump in such a way that the equality holds. In the latter view, the government can choose any arbitrary path for its surpluses, and the price level will adjust in such a way that the equality holds and the government is solvent. Woodford calls this a ‘non-Ricardian regime’. How then is the price level determined? Suppose st unexpectedly falls. For example, the fiscal authority decides to
run larger deficits. According to the FTPL, consumer wealth increases which leads to higher demand and a higher price level. Since Dtis predetermined,
the price level adjusts so that Eq. (2) is satisfied. Vice versa, if st rises
unexpectedly, the price level will fall. In the case of a Ricardian regime, a change in st would never affect the price level as the changes in st in
with a lag while real GDP adjusts immediately in order to keep Eq. (2) satisfied. Scaling the present value government budget constraint by nominal GDP instead of by the price level allows for a scenario with sticky prices. The amount of price rigidity determines whether fiscal adjustments affect nominal GDP via (possibly slow) price changes or real GDP changes.
Another important contribution to the FTPL is done by Leeper (1991), who studies monetary and fiscal policy interactions in a theoretical model incorporating stochastic monetary and fiscal shocks. With the aid of the characteristic roots of his model he shows that there are four possible sta-bility outcomes. The outcomes depend on whether the monetary policy authority or the fiscal policy authority is ‘active’. An active authority is defined as paying “no attention to the state of government debt and is free to set its control variable as it sees fit” (Leeper (1991), p. 130). A passive authority responds to the active authority’s action. In order for the model to yield a stable equilibrium outcome, one policy authority needs to be active and the other needs to be passive. Therefore, there are two possibilities for a stable outcome. One corresponds to the ‘Ricardian regime’ put forward by Woodford. This is the case if fiscal policy is passive and monetary pol-icy is active. If in such a case a debt shock occurs, monetary polpol-icy is set independently and fiscal policy has to be set in such a way that it satisfies the government’s budget constraint. The second corresponds to Woodford’s ‘non-Ricardian regime’. Here, monetary policy is passive and fiscal policy is active. Now, if a debt shock occurs, fiscal policy does not react in order to satisfy the budget constraint. In this case, the price level needs to adjust and monetary policy becomes passive. Therefore, if fiscal policy is active, the FTPL holds and fiscal policy determines the price level.
Bergin (2000) develops a theoretical model that includes two distinct countries and a common central bank in order to study the FTPL in a mon-etary union. In his model, the two national governments have no control over the creation of money. Instead, money is created by a common central bank through open market purchases of central bank bonds. The govern-ments of the distinct economies are also able to issue nominal government bonds. Households of both countries face their own intertemporal budget constraints and their wealth consists of government bonds and money bal-ances. Equilibrium solutions of the model show that the aggregate price level is determined jointly by the budget constraints of member govern-ments. Bergin provides evidence for the FTPL in a monetary union since a deficit in one member country can raise the price level throughout the monetary union.
2.3 Empirical studies on the FTPL
first sight, one might wish to estimate a regression equation such as:
Pt= α1st+ α2dt+ ρ0Xt+ t, (4)
where Pt is the price level, st is the primary surplus proportional to GDP,
dt is the government debt level proportional to GDP at the beginning of
period t, Xt is a vector consisting of a set of other possible determinants of
the price level, and tis an error term. Estimates of α1 and α2 will tell how
much the price level depends on the measures of fiscal policy, i.e. st and
dt. Nevertheless, estimating such a regression does not provide convincing
evidence for or against the FTPL for three reasons. First, as Creel and Le Bihan (2006) point out, estimating an equation such as Eq. (4) “relies on the joint hypothesis of the FTPL and fully flexible prices”(p. 342). As explained above, Woodford (1996) proves that the FTPL holds for the case of sticky prices. In this case, adjustments work via changes in real GDP. Estimating an equation as Eq. (4) does not prove helpful as it is not able to distinguish between flexible or sticky prices. Second, a positive relationship between the surplus and the price level may exist even in a Ricardian regime. For example, it is plausible that fiscal policy is dependent on the price level. In this case, regressing Eq. (4) would also result in a positive relationship while causality actually runs the other way.
Third, both the FTPL and the QTM only establish whether fiscal or monetary policy determines the equilibrium price level, i.e. whether it is fiscal or monetary policy that provides the nominal anchor for price stability. In the case of the FTPL, there is still a role for monetary policy to play in the determination of the price level. However, the channel is indirect and works via the effect it has on the interest payments of the government. In the case of the QTM, fiscal policy also has an effect on the price level. For example, high government expenditure, while an economy is already producing at maximum capacity, leads to inflationary pressures. The point is that even though fiscal policy might still affect the price level, the QTM tells that monetary policy provides the nominal anchor for price level determination. On the other hand, in the case of the FTPL, fiscal policy provides the nominal anchor while monetary policy might still have an affect. Performing a regression as in Eq. (4) and finding positive estimates for α1 and α2 does
not provide conclusive evidence in favor of the FTPL since fiscal policy can also influence the price level in the QTM.
since the price level adjusts in order to satisfy the present value government budget constraint. Therefore, investigating whether surpluses are set in such a way that they guarantee government solvency may provide evidence in favor of a Ricardian or a non-Ricardian regime. As D’Erasmo, Mendoza, and Zhang (2015) state, a large literature analyzes whether debt is sustainable by analyzing whether the present value government budget constraint is satisfied. In other words, whether expected discounted future surpluses match the current debt level.
Many papers attempt to estimate an equation as Eq. (2) directly, yet this approach is heavily criticized by Bohn (1995) as they require strong assumptions on the discount factor. Instead, Bohn (1998) presents an inno-vative approach that estimates a fiscal policy rule such as:
st= αdt+ ρ0Xt+ t, (5)
where st, dt, and t are defined as above, and Xt is a vector consisting of
a set of control variables. He finds that the surplus responds positively to beginning-of-the-period debt in the U.S. for the period 1948-1989. Proposi-tion 1 in Bohn (2005) demonstrates that a positive α is sufficient to satisfy the present value government budget constraint. Therefore, the author con-cludes that U.S. government debt is sustainable for his sample. Bohn’s approach has been applied widely. Greiner, K¨oller and Semmler (2007) es-timate a fiscal policy rule for four euro area countries and find evidence in favor of debt sustainability in all cases. This result has often been inter-preted as empirical evidence in favor of a Ricardian regime: the surplus responds to the debt level in order for the government to be solvent.
Cochrane (1998) criticizes this interpretation with the argument that an observational equivalence exists between Ricardian and non-Ricardian regimes. Both regimes accept Eq. (2) as an equilibrium condition; therefore, the positive relation that Bohn finds is inconclusive evidence for a Ricardian regime. However, causality runs in opposite ways for both regimes. In a Ricardian regime, the surplus responds positively to beginning-of-the-period debt in order for the government to be solvent. In this case, the price level is not affected, and stresponds to dt in order for Eq. (2) to hold. In a
non-Ricardian regime, if an increase in st causes the right-hand side of Eq. (2)
to rise, the price level will decrease because of the wealth effect which makes sure the left-hand side of Eq. (2) increases as well (Dt is predetermined
according to the FTPL). Therefore, a positive relation between st and dt
can also be found in the case of a non-Ricardian regime.
post-war period for the U.S. by estimating a Vector Autoregression (VAR) model. More details on VAR modeling will follow in Section 3. Their model includes two variables: primary surplus and government liabilities, both proportional to nominal GDP. Government liabilities are defined as government debt plus the monetary base.
CCD show the responses of both variables after a shock to the surplus. Since out-of-equilibrium properties of the variables are analyzed, the obser-vational equivalence problem is circumvented. Impulse response functions show that the liabilities-to-GDP ratio decreases for several periods after a positive shock to the surplus. Ricardian regimes provide an intuitive in-terpretation of this: if there is a positive shock to the surplus, liabilities are paid off. A non-Ricardian interpretation for this outcomes exists as well; however, the authors regard this as less plausible for the following rea-son. For a non-Ricardian regime to hold in this case, the decrease in the liabilities-to-GDP ratio has to result from a decrease in the present value of expected future liabilities (the right hand side of Eq. (2)). This would mean that there is a negative correlation between current and future sur-pluses. The increase in the current surplus triggers a decrease in expected future surpluses which in turn lowers the debt-to-GDP ratio in the case of a non-Ricardian regime. Since the authors are not able to find this negative correlation, they conclude that a Ricardian regime is more plausible for their data.
Semmler and Zhang (2004) perform a similar analysis for France for the period 1967 until 1998 and for Germany for the period 1970 until 1998. The authors exclude the monetary base; therefore, the endogenous variables are primary surplus and government debt, both proportional to GDP. The impulse responses indicate that the debt-to-GDP ratio decreases for several periods after an increase in the surplus. As explained above, this can occur in both a Ricardian and a non-Ricardian regime. In order to differentiate between a Ricardian and a non-Ricardian regime, Semmler and Zhang also analyze a debt shock. The impulse responses indicate that the surplus-to-GDP ratio decreases after such a shock; consequently, the authors conclude that a non-Ricardian regime is most plausible for France and Germany. However, the theoretical reasons for this conclusion remain unclear. Most likely, this is because in a Ricardian regime a positive response of the surplus is expected after a debt shock. Nevertheless, to my knowledge, in a non-Ricardian regime, no predictions can be made about the response of the surplus after a debt shock either.
3
Method
analyze the sustainability of government debt by estimating a straightfor-ward fiscal policy rule. Second, I adopt a forstraightfor-ward-looking approach following CCD. This approach estimates a bivariate Vector Autoregressive model and looks at the dynamics between government debt and the surplus.
3.1 Backward-looking approach: debt sustainability
Estimating a fiscal policy rule provides a first step in analyzing whether a Ricardian or a non-Ricardian regime is more plausible. If government debt is unsustainable, a non-Ricardian regime is more likely since in such a regime the surplus can follow an arbitrary process. In order to investigate the matter, the following fiscal policy rule is estimated:
st= α0+ α1dt+ α2BCt+ α3Dt+ t, (6)
where st, dt, and t are defined as above, BCt is an indicator term for the
business cycle and Dt is an indicator term for the recent financial crisis. A
description of the data will follow in Section 4. Both indicator terms are included in order to account for the systematic components of the debt-to-GDP ratio. If α1 is estimated to be larger than zero, government debt is
sustainable since expected future surpluses respond sufficiently to a change in the debt level. Bohn (2005) shows that if t goes to infinity in the present value government budget constraint, the right-hand side becomes finite for any positive α1. Some studies compare the coefficient for debt to the ratio of
the real interest rate and the growth rate of output. For dtto remain stable
at a certain level, α1 needs to be larger than the aforementioned ratio. Yet,
as D’Erasmo, Mendoza and Zhang (2015) state, a positive α1 is sufficient
for debt sustainability even though debt is still rising. This means that expected future surpluses match the debt level today and the present value government budget constraint is satisfied.
Even though a positive estimated coefficient for debt in Eq. (6) provides evidence of sustainable debt, an observational equivalence problem exists as pointed out by Cochrane (1998). Since both the QTM and the FTPL accept the present value government budget constraint, i.e. Eq. (2), as an equilibrium condition, a positive α1 need not be conclusive evidence in
favor of a Ricardian regime. In a non-Ricardian regime, a change in the surplus causes a change in the price level such that the debt-to-GDP ratio still satisfies the present value government budget constraint. If prices react immediately, a positive relation between the surplus and debt is also found in a non-Ricardian regime.
3.2 Forward-looking approach: a bivariate VAR
Since the backward-looking approach is subject to an observational equiv-alence problem, the focus of this paper is on the forward-looking approach which estimates a bivariate Vector Autoregressive (VAR) model following CCD. Adopting a VAR approach has several advantages. Most importantly, it provides insight into the causality between variables by analyzing (un-expected) shocks. Since out-of-equilibrium dynamics are analyzed, the ob-servational equivalence issue is circumvented. Furthermore, since a VAR includes all structural variables in a symmetrical way, there is no need to impose ad-hoc identification restrictions as needs to be done in a simulta-neous equations model (Sims, 1980).
The estimated bivariate VAR model includes two endogenous variables: st, the government’s primary surplus in period t , and dt, government debt
at the beginning of period t, both proportional to GDP. More details on the construction of the respective variables and the data that is used will follow in Section 4. The structural model, including p lags, is as follows:
st= αs,0+ γsdt+ Ass(L)st−1+ Asd(L)dt−1+ st (7)
dt= αd,0+ γdst+ Ads(L)st−1+ Add(L)dt−1+ dt, (8)
where Aii(L) = A1,ii+ A2,iiL + ... + Ap,iiLp−1 for i = s, d. In words, both
endogenous variables are explained by a constant term, the contemporaneous value of the other variable, lagged values of the variable under consideration and the other variable, and an error term. The error terms are assumed to be serially and mutually uncorrelated. Using matrix notation, the structural model becomes: 1 −γs −γd 1 st dt =αs,0 αd,0 +Ass(L) Asd(L) Ads(L) Add(L) st dt + s t dt , (9)
which can also be written short-hand as:
ΓZt= D + A(L)Zt−1+ t. (10)
The variance-covariance matrix of the structural errors is Σ = E(t0t). It is
assumed that Γ is invertible as a result of which the reduced form can be given as:
Zt= Π + C(L)Zt−1+ et, (11)
where Π = Γ−1D, C(L) = Γ−1A(L), and et are the estimated shocks. The
derivation makes use of the fact that et = Γ−1t. As a result, the
variance-covariance matrix of the estimated shocks is Ω = E(ete0t) = E(Γ−1t0tΓ−10) =
Γ−1ΣΓ−10.
the VAR analysis is to show the response of the endogenous variables to a structural shock. However, the estimated parameters in C(L) only give information on the reduced-form model and do not yet reflect the structural model. In order to identify the structural model, one identifying restriction is needed. There are many possible identifying restrictions that can be used. For example, restrictions can be placed on the contemporaneous parameters in Γ, short-run or long-run restrictions can be imposed to the parameters in C(L), or the signs of some parameters can be restricted in a Bayesian approach.
In the analysis that follows, a restriction is placed on the contempora-neous parameters in Γ which imposes an ordering between the endogenous variables. Specifically, γs is restricted to be zero which imposes an ordering
where st comes first. In other words, st is not affected contemporaneously
by dt, as can be seen from equations (7) and (8). As soon as Γ is identified
the structural shocks of the model can be retrieved. As CCD explain, an ordering where stcomes first is more consistent with a non-Ricardian regime
since it enables dtto react contemporaneously to a shock in stand this is not
possible in a Ricardian regime. As a robustness check, the same analysis is also repeated with dtordered first. However, since the results are essentially
the same, these are not presented.
3.3 VAR modelling and the FTPL
The VAR model estimated by CCD includes the variables surplus and liabil-ities, both scaled by GDP. Liabilities is defined as general government debt plus the monetary base. Here, the monetary base is disregarded. Creel and Le Bihan (2006) give two reasons why disregarding the monetary base is appropriate. First, disregarding the monetary base in the measure of public liabilities avoids mixing up the testing of the FTPL with the testing of the QTM. For, if the monetary base is included, there is still scope for price determination to be a monetary phenomenon. By excluding the monetary base, fiscal price determination is solely analyzed1. Second, inclusion of the monetary base implicitly assumes that the central bank is not independent from the fiscal authority. In this case, it is assumed that seigniorage can be used in order to finance part of the public deficit. Yet, as Cochrane (1998) states: “Seigniorage [...] is an insignificant fraction of government revenue” (p. 361). This especially holds true for the euro area where the money supply is decided by a central institution instead of at the national level.
In order to find whether a Ricardian regime or a non-Ricardian regime is more plausible, I analyze the effects of a positive shock in st. Impulse
Response Functions (IRFs) show how the surplus-to-GDP ratio and the debt-to-GDP ratio respond in current and future periods. In a Ricardian
1
regime, a negative response of dt+1should always follow a positive shock in
st since in this case the higher surplus is used to pay off government debt.
A non-Ricardian regime is slightly more difficult to identify. The re-sponse of the debt-to-GDP ratio in a non-Ricardian regime depends on the possible correlation between the surplus in the current period and future surpluses. First, consider the case where there is no correlation. In such a case, an innovation in st will lead to zero change in dt+1 for the following
reasons. In period t, the increase in st leads to a one-by-one increase in dt
through a change in nominal income as a result of the wealth effect. In the next period, the increase in stpays off debt by the same amount. Therefore,
dt+1 is unaffected by an increase in st. Next, consider the case where there
is a positive correlation between the current surplus and future surpluses. In this case, a positive response of dt+1 will be found after a shock in st. The
innovation in stleads to a higher expected present value of future surpluses
as a result of the positive correlation. Even though the shock in st pays off
part of the debt in period dt+1, the revaluation through the wealth effect
and a decrease in the price level result in a higher dt. The shock to the
surplus leads to a higher present value of future surpluses.
So far, it is possible to differentiate between a Ricardian and a non-Ricardian regime by looking at the response of dt+1. If dt+1 responds
neg-atively to a shock in st, a Ricardian regime is more plausible. In any other
case, a non-Ricardian regime is more plausible. However, if there exists a negative correlation between the current surplus and future surpluses, it be-comes more difficult to distinguish between a Ricardian and a non-Ricardian regime on the basis of the response of dt+1 . In this case, a shock in st will
lead to a lower present value of expected future surpluses. In a non-Ricardian regime, this will lower dt through an immediate increase in nominal GDP.
In addition, the increased surplus pays off part of the debt which leads to a lower dt+1 as well. Thus, an observed negative response of dt+1 may be
evidence in favor of both a Ricardian and a non-Ricardian regime.
In order to identify whether a Ricardian or a non-Ricardian regime is more plausible in the latter case, the response of st+1 to a shock in st is
analyzed. The response of the surplus-to-GDP ratio indicates how future surpluses react after a shock and whether the shock is persistent in the estimated model. In a non-Ricardian regime, a negative response of dt+1
4
Data
The analysis detailed in the previous section includes the following vari-ables: primary surplus proportional to nominal GDP (hereafter referred to as surplus/GDP), debt proportional to nominal GDP (hereafter referred to as debt/GDP) and an indicator term for the business cycle (BC ). The primary surplus consists of net borrowing/lending by the general govern-ment plus net interest payable (interest payable minus interest receivable). Debt consists of the level of general government debt at the beginning of the period. The main part of this paper applies the backward-looking and the forward-looking approach to a euro area aggregate sample. Section 6 presents extensions to the forward-looking approach one of which entails an individual country analysis. Therefore, this section describes the datasets for both the euro area aggregate and for individual countries.
4.1 Euro area aggregate data
To analyze the plausibility of the FTPL at the euro area level, I use the Area Wide Model fiscal database of the ECB, which is compiled by Paredes, Pedregal and P´erez (2014). The dataset includes seasonally adjusted data on the levels of general government revenues, expenditures, and debt for the euro area-18 aggregate2. In order to aggregate the euro area data, an indicator-approach is adopted. As the authors point out themselves: “we use aggregated annual data as provided by the European commission (Eurostat) and (when available) quarterly euro area data from the same source, as anchors for the interpolation procedure, while at the same time we set up statistical models that incorporate ingredients that closely resemble those used to compile available quarterly government finance statistics data by Eurostat, for the biggest euro area economies, namely Germany, France, Italy, Spain and The Netherlands” (p. 804). This is different from an aggregation of individual euro area member state data. Paredes et al. (2014) state that an indicator-approach is used because of data availability and to avoid the controversial issues of weighting schemes. The time period that is available is 1980q2-2013q4.
As pointed out above, in order to construct the surplus/GDP variable, net interest payable is added to the total government surplus. However, the AWM fiscal database only includes data on interest payable and not on interest receivable. Data on interest receivable and interest payable can be obtained from the Eurostat Government Finance Statistics database, albeit for a shorter time span. The seasonally adjusted series (using Census X13) are exhibited in Figure 1. Net interest payable and interest payable follow
2The euro area-18 consists of: Austria, Belgium, Cyprus, Estonia, Finland, France,
Figure 1: Interest payable versus net interest payable, i.e. interest payable minus interest receivable, for the euro area aggregate
roughly the same pattern for the euro area-18. In addition, the fraction of interest receivable in the net interest calculation is considered to be fairly small. Therefore, interest receivable is considered to be zero and the in-terest payable from the AWM database is interpreted as being net inin-terest payable. Thus, primary surpluses are calculated as net borrowing/lending plus interest payable.
Nominal GDP is also obtained from the AWM database, that is from the non-fiscal counterpart compiled by the ECB. It is inferred from real GDP and the GDP deflator, since the AWM database does not give the nominal GDP as such.
After having obtained data on the primary surplus, government debt and nominal GDP, the surplus/GDP and debt/GDP ratios are derived. Figure 2 shows the time series for the euro area. Descriptive statistics for the two variables are given in table B.1 in Appendix B. From Figure 2 it becomes clear that the primary deficit and government debt rose sharply after the start of the Global Financial Crisis (GFC) at the end of 2008. A Chow structural break test points out that a structural break is present at 2008q3.3 One of the extensions of the model in Section 6 accounts for this break.
The indicator term for the business cycle (BC ) is obtained from the Centre for Economic Policy Research (CEPR) and is presented in Table B.2 in Appendix B. It equals 1 for recession periods and 0 otherwise. A recession is defined by the CEPR business cycle dating committee as “a significant decline in the level of economic activity, spread across the economy of the
3
Figure 2: Primary surplus (left y-axis) and debt (right y-axis), both propor-tional to nominal GDP, for the euro area aggregate
euro area, usually visible in two or more consecutive quarters of negative growth in GDP, employment and other measures of aggregate economic activity for the euro area as a whole”. The dummy variable for the recent financial crisis (D ) is constructed to equal 0 for periods before 2008q3 and to equal 1 for periods after 2008q3.
4.2 Individual country data
Data for individual euro area countries is obtained from the Government Finance Statistics database of Eurostat, and includes data on net interest payable, government net borrowing/lending, government debt and nominal GDP for the period 2000q2 until 2013q4. The individual countries analyzed are: Portugal, Greece, Germany and The Netherlands. In Section 6I will elaborate on the reasons why I select these countries in particular.
As for the euro area aggregate analysis, the primary surplus is calculated by adding net interest payable (interest payable minus interest receivable) to net borrowing/lending. Debt is the level of general government debt at the beginning of the period. All series are seasonally adjusted using the Census X13 additive approach since the surplus time series includes negative values. Figures for the individual country data on surplus/GDP and debt/GDP are presented in Figure C.1 in Appendix C.
5
Results
Both the backward-looking approach and the forward-looking approach are implemented for the euro area aggregate sample. This section discusses the results for both approaches.
5.1 Backward-looking approach
As explained in Section 3, the backward-looking approach entails, estimating Eq. (6). According to the QTM, the government’s surplus needs to respond positively to a change in debt in order to since prices do not adjust to satisfy the present value government budget constraint. Therefore, a positive estimate for α1 in Eq. (6) can be considered as evidence against the FTPL.
However, as explained in Section 2, a positive relation between the surplus and debt also exists according to the FTPL even though causality runs the other way. In the case of the FTPL, if the surplus increases, prices respond negatively which increases debt/GDP. Therefore, a positive α1 does not
enable us to distinguish between a Ricardian or a non-Ricardian regime. However, if a negative or zero estimate for α1 is found, this is evidence
in favor of unsustainable debt which is more plausible in a non-Ricardian regime.
An Augmented Dickey-Fuller (ADF) test for surplus/GDP indicates that this variable is stationary and does not have a unit root. The test statistic is -2.628 which is larger (in absolute terms) than its 1% critical value of -2.356. The unit root test for surplus/GDP includes three lags and a drift term. Considering debt/GDP, the null hypothesis of there being a unit root cannot be rejected in a ADF test. The test statistic is -2.117 which is smaller (in absolute terms) than the 1%, 5%, and 10% critical values which are -4.029, -3.446, and -3.146 respectively.
However, Bohn (1998) argues that standard unit root tests yield false conclusions regarding the stationarity of debt/GDP since they ignore the systematic components of debt/GDP. These systematic components obscure the underlying mean-reversion effect of debt/GDP. As long as one accounts for these systematic components, one can include debt/GDP in a regression analysis even though standard unit root tests indicate a unit root. In or-der to uncover the actual mean-reversion in debt/GDP, Bohn estimates the following equation:
∆dt+1= θ0+ θ1dt+ ρ0Xt+ t, (12)
where ∆dt+1 = dt+1 − dt is the change in debt between the beginning of
period t + 1 and the beginning of period t, and Xt includes the systematic
long as the coefficient for the lagged debt/GDP ratio is negative and the coefficients for the systematic components are positive, debt/GDP follows a mean-revertive process.
I implement the same approach to determine whether debt/GDP is mean-revertive. For the systematic components, I include the indicator terms (BC ) for the business cycle and for the recent financial crisis (D ). The latter indicator term is included in order to account for the structural break at the start of the GFC that was determined in the previous section. The equation that is estimated is:
∆dt+1= θ0+ θ1dt+ θ2BCt+ θ3Dt+ t. (13)
In order to support Bohn’s hypothesis considering the mean-revertive pro-cess of debt/GDP, θ1needs to be negative, and θ2and θ3 need to be positive.
In this case, the systematic components, BC and D, cause standard unit root tests to indicate a unit root in debt/GDP. Nevertheless, a negative θ1
indicates that the underlying debt/GDP process is mean-reverting.
Table 1: Determinants of changes in debt/GDP for the euro area aggregate (sample period: 1980q4-2013q4) ∆dt+1 constant 0.016∗∗∗ (0.004) dt −0.022∗∗∗ (0.006) BCt 0.003∗∗ (0.001) Dt 0.013∗∗∗ (0.002) F (3, 130) 26.730 P rob > F 0.000 R2 0.382 Observations 134 Note: White robust standard errors are in parantheses.
*** p-value < 0.01 ** p-value < 0.05
Estimating Eq. (13) by the method of Ordinary Least Squares (OLS) yields the coefficients as presented in Table 1. The estimated coefficient for dt is negative and statistically significant, and the estimated coefficients for
at the 5% significance level). Therefore, these estimation outcomes are in line with Bohn’s hypothesis and debt/GDP is mean-reverting even though standard unit root tests indicate the presence of a unit root. Therefore, debt/GDP can be included in levels when applying the backward-looking approach, as long as the systematic components are also included in the regression equation.
As explained in Section 3, the backward-looking approach entails esti-mating the fiscal policy rule given in Eq. (6). OLS estimation results are presented in Table 2. Since the estimated coefficient for the business cycle indicator is non-significant, the estimation is also done without this variable. The results are similar.
Table 2: Estimated fiscal policy rule, with and without the business cycle indicator BC, for the euro area aggregate (sample period: 1980q4-2013q4)
st st constant −0.031∗∗∗ −0.032∗∗∗ (0.002) (0.003) dt 0.048∗∗∗ 0.049∗∗∗ (0.003) (0.003) Dt −0.013∗∗∗ −0.013∗∗∗ (0.001) (0.001) BCt 0.001 (0.001) F (2, 132) 354.710 259.780 P rob > F 0.000 0.000 R2 0.703 0.704 Observations 135 135 Note: White robust standard errors are in parantheses.
*** p-value < 0.01
The estimated coefficient for debt/GDP shows that surplus/GDP re-sponds positively to beginning-of-the-period debt for both specifications of the fiscal rule. This provides evidence in favor of debt sustainability. How-ever, as explained in Section 2, this result can be found both in a Ricardian and in a non-Ricardian regime as a result of the observational equivalence stressed by Cochrane. Therefore, more evidence is needed in order to eval-uate the plausibility of both regimes.
5.2 Forward-looking approach
into the dynamics between surplus/GDP and debt/GDP. Estimation with Maximum Likelihood gives the estimated parameters in Table 3. An eigen-value stability test shows that all eigeneigen-values lie within the unit circle which indicates that the estimated VAR is stable. Two lags are included in the model since this is suggested by several lag length criteria4.
In constructing the IRFs, surplus/GDP is ordered first. As explained in Section 3, this ordering is more consistent with a non-Ricardian regime as it allows for a contemporaneous effect of the surplus on debt/GDP which is not likely to occur in a Ricardian regime. In order to test the robustness of the results against a change in the ordering, the analysis has also been repeated with the reverse ordering between debt/GDP and surplus/GDP. Since the results are similar, only the results for the first ordering are presented. Table 3: VAR estimates for the euro area aggregate (sample period: 1980q4-2013q4 st dt constant −0.002∗∗∗ −0.004 (0.001) (0.003) st−1 1.251∗∗∗ −0.905∗ (0.083) (0.489) st−2 −0.344∗∗∗ 0.535 (0.077) (0.455) dt−1 −0.040∗∗∗ 1.503∗∗∗ (0.014) (0.082) dt−2 0.043∗∗∗ −0.496∗∗∗ (0.014) (0.084) χ2 4775.064 69526.850 P rob > χ2 0.000 0.000 R2 0.973 0.998 Model statistics Observations 133 Loglikelihood 1249.636 AIC −18.641
Note: asymptotic standard errors are in parentheses.
*** p-value < 0.01, * p-value<0.1
4In order to determine the appropriate lag length, the following information criteria are
Figure 3: Impulse response functions after a structural shock to sur-plus/GDP (sample period: 1980q2-2013q4)
(a) Debt/GDP (b) Surplus/GDP
Figure 3 gives the IRFs of surplus/GDP and debt/GDP after a positive shock to the surplus. The dotted lines indicate 95% confidence bands which are calculated using the estimated asymptotic standard errors. The IRF for debt/GDP shows that the shock leads to a decrease in debt/GDP. This neg-ative response can be consistent with both a Ricardian and a non-Ricardian regime. The Ricardian interpretation of the results is that an increase in the surplus is used to reduce government debt. Nevertheless, as explained in Section 3, a non-Ricardian interpretation might also be suitable for the negative response of debt/GDP. However, this is only the case when the shock to the current surplus causes a decrease in future surpluses. In such a case, the increase in surplus/GDP causes a lower expected present value of future surpluses. According to the FTPL, a lower expected present value of future surpluses results in a lower debt/GDP ratio since households see their wealth increase. Therefore, if the negative correlation between the current surplus and future surpluses is sufficiently strong, a negative response of debt/GDP might also be found in a non-Ricardian regime.
In order to see whether the non-Ricardian interpretation of the negative response of debt/GDP is plausible, I analyze the response of surplus/GDP to a shock to the surplus. The IRF shows that after a shock to surplus/GDP, future surpluses are expected to be positive up to 11 lags. Thereafter, the response becomes insignificant. Hence, I conclude that a non-Ricardian regime is implausible for the euro area since there is no evidence of a neg-ative correlation between current and future surpluses within 11 quarters. Therefore, at the aggregated level, fiscal authorities in the euro area followed a Ricardian regime for the period 1980q2-2013q4.
the economy is already producing at maximum capacity this may generate inflationary pressure. Nevertheless, these effects all work via the monetary channel. For example, a higher aggregate demand leads to a higher demand for money which pushes up the price level. As a consequence, the main channel through which the government is able to steer the price level is monetary policy.
Robustness of the results is tested by using different specifications of the bivariate VAR. As mentioned above, the results are robust to the reverse ordering of the variables. In addition, the VAR is estimated with 1, 3 and 4 lags, with a time trend and without a constant. These different specifications of the model all yield similar results. Furthermore, the VAR is estimated by specifying surplus/GDP and debt/GDP in logs and in first differences. The results are qualitatively the same; however, the confidence intervals are wider. In addition to these different VAR specifications, the analysis is extended in several other ways which is discussed in the following section.
6
Extensions
The analysis of the previous section is extended in two ways. First, I eval-uate whether the structural break at the start of the GFC has a significant impact on the outcomes of the bivariate VAR. This is done by estimating the VAR for different subsamples and by estimating a VAR including a dummy interaction term. Second, the bivariate VAR of the previous section is estimated for several individual euro area countries.
6.1 The effect of the Global Financial Crisis
6.1.1 Two subsamples
In Section 4 I showed that a structural break is present in 2008q3, at the start of the GFC. Since then, surplus levels have decreased and the debt level has risen sharply. The sharp increase in deficits and debt levels suggests that the euro area has shifted more towards non-Ricardian fiscal regimes. Nevertheless, if so, in the case of the FTPL, this shift towards non-Ricardian regimes should mean that prices have risen as well in the euro area for the period after the GFC. This has not been the case. Therefore, the evidence which I find in favor of Ricardian regimes together with the low inflation levels currently prevailing in the euro area speak against the FTPL for the euro area.
VAR analysis is repeated for a subsample excluding the GFC in order to see whether this yields different results. Figure 4 gives the IRFs of the estimated VAR. Again, lag length selection tests show that 2 lags are optimal.
Figure 4: Impulse response functions after a structural shock to sur-plus/GDP (sample period: 1980q2-2008q3)
(a) Debt/GDP (b) Surplus/GDP
The IRFs show that surplus/GDP and debt/GDP respond in a similar way as before: debt/GDP decreases after a shock to surplus/GDP. While the immediate response is not statistically significant, the negative response of debt/GDP is significant from the third period onwards. Surplus/GDP shows a positive response up until the eighth period. Thereafter, the response becomes insignificant. In other words, there is no evidence of negative future surpluses within a nine-year horizon after the shock. Therefore, I conclude that for the subsample up until the start of the GFC, a Ricardian regime is more plausible. Since the VAR analysis for the subsample excluding the GFC does not yield any different results from those of the whole sample, I conclude that the GFC does not have a determining impact on the outcomes.
6.1.2 Dummy VAR model
st=πs,0+ βs,0D + Css(L)st−1+ Csd(L)dt−1+ Bss(L)st−1D + Bsd(L)dt−1D + est (14) dt=πd,0+ βd,0D + Cds(L)st−1+ Cdd(L)dt−1+ Bds(L)st−1D + Bdd(L)dt−1D + edt, (15)
where Cii(L) = C1,ii+ C2,iiL + ... + Cp,iiLp−1 for i = s, d. In short-hand
matrix notation:
Zt= Π + ΦD + C(L)Zt−1+ B(L)Zt−1D + et. (16)
That is, both surplus/GDP and debt/GDP depend on a constant, a constant interacted with the dummy variable, lagged values for both endogenous vari-ables, lagged values interacted with the dummy variable, and an error term. The error term is assumed to be serially and mutually uncorrelated. Two lags are included in the VAR since this is suggested by several lag length criteria. The IRFs are found by imposing a recursive ordering as in the analysis above. Surplus/GDP is ordered before debt/GDP. In other words, surplus/GDP affects debt/GDP contemporaneously.
After estimating the above dummy VAR model, the estimated coeffi-cients are calculated for the two regimes, the first for which the dummy variable is zero (D=0), and the second for which it is one (D=1). If D=0, the VAR is equivalent to the one in Section 3. The interaction terms and their respective estimated coefficients are neglected in this case. If D=1, the coefficients of the VAR are found by summing up the estimated coefficients for surplus/GDP and debt/GDP with the coefficients of their respective in-teraction terms. For example, the constant in the estimated equation for st
is found by adding the estimates for πs,0 and βs,0.
Table 4 presents the estimated coefficients for the two separate VAR models. Figures 5 and 6 give the IRFs for surplus/GDP and debt/GDP after a shock to the surplus. In order to obtain standard errors for the estimated coefficients and confidence bands for the IRFs, a parametric bootstrap is performed with 1,000 repetitions. The bootstrap methodology that I use is explained in Appendix D.
Table 4 shows that while there are differences between the estimated coefficients for both states of the dummy variable, these differences are not extremely large. For example, the estimated coefficient for dt−1in the
equa-tion for dtis 0.818 when D=0, while it is 0.797 when D=1. For the majority
Table 4: Estimated dummy VAR model for the euro area aggregate (sample period: 1980q4-2013q4) Dummy=0 Dummy=1 st dt st dt constant −0.008∗∗∗−0.004 −0.011∗∗∗ 0.030∗∗∗ (0.001) (0.005) (0.001) (0.007) st−1 0.554∗∗∗−0.148 0.831∗∗∗−1.451 (0.073) (0.545) (0.147) (1.157) st−2 0.218∗∗∗−0.712 −0.098 1.866∗ (0.070) (0.499) (0.136) (1.106) dt−1 −0.013 0.818∗∗∗ −0.003 0.797∗∗∗ (0.011) (0.072) (0.011) (0.069) dt−2 0.014 0.189∗∗ 0.014 0.186∗∗ (0.012) (0.078) (0.012) (0.073) Model statistics Observations 133 Loglikelihood 1271.725 AIC −18.823
Note: the dummy variable equals 0 for periods before 2008q3 and equals 1 for periods after 2008q3. Bootstrapped standard errors are in parentheses.
estimated coefficient for st−2in the equation for st changes from being
pos-itive in the first regime, to being negative in the second regime. Therefore, the IRFs of the estimated models can result in different graphs for the two states of the dummy variable.
Comparing these estimated coefficients to the estimated coefficients of the bivariate VAR in Table 3 shows that the signs of the coefficients are the same in most cases. This holds for both the case where D=0 and when D=1. The signs of the estimated coefficients in Table 3 are mostly in ac-cordance with the estimated coefficients in Table 4 for the case where D=1. Nevertheless, the magnitudes of the coefficients differ.
The IRFs for the case where D=0 are presented in Figure 5. As before, debt/GDP decreases after a shock to the surplus. In order to find out whether this decrease is more consistent with a Ricardian or a non-Ricardian fiscal regime, the response of surplus/GDP is analyzed. Figure 5 shows that the estimated response of surplus/GDP after a shock to the surplus is positive and statistically significant for at least 8 periods. Therefore, if D=0, e.g. for periods before the start of the GFC, a Ricardian regime is more plausible.
Figure 5: Impulse response functions after a structural shock to sur-plus/GDP (Dummy=0)
(a) Debt/GDP (b) Surplus/GDP
Figure 6: Impulse response functions after a structural shock to sur-plus/GDP (Dummy=1)
Figure 6 gives the IRFs for the case where D=1. The immediate re-sponse of debt/GDP is negative and statistically significant. However, after 3 periods, the response becomes insignificant. Even though the immediate response in debt/GDP is both negative for the case when D=0 and when D=1, the response in later periods looks somewhat different. If D=1, i.e. for periods after the start of the GFC, the response in debt/GDP returns to zero relatively quickly after an unexpected increase in the surplus. If D=0, i.e. for periods before the start of the GFC, the negative response in debt/GDP is more persistent.
The response in surplus/GDP when D=1 is positive and statistically significant for at least 6 periods. Since the immediate response of debt/GDP is negative and there is no evidence for negative correlation between the current and future surpluses, a Ricardian regime is still more plausible for periods after the start of the GFC.
6.2 Individual country analyses
So far, all VAR models were estimated for a euro area aggregate. Since fiscal policy is managed at the national level and there exist differences in the way in which countries do so, it may seem inappropriate to analyze fiscal policies at a euro area aggregate level. In order to find out whether the results for individual countries differ, the bivariate VAR is also estimated for four individual euro area countries. The countries that are analyzed are: Greece, Portugal, Germany and The Netherlands. These countries belong to the first twelve countries that adopted the euro (euro area-12) and have therefore been in a monetary union for the major part of the sample period. Evidence in favor of a non-Ricardian regime for those countries would mean that for the major part of the sample, individual euro area countries were able to have an effect on the aggregate price level.
In particular, Greece and Portugal are selected since they have the high-est debt/GDP ratios and the greathigh-est fluctuations in surplus/GDP. On the other hand, Germany and The Netherlands show relatively low debt/GDP ratios and a rather stable surplus/GDP. In the analysis that follows, Greece and Portugal are referred to as ‘high-debt countries’ while Germany and The Netherlands are referred to as ‘low-debt countries’. The countries under consideration show the differences that exist between national fiscal policies within the euro area. For example, the reaction of their fiscal policies to the GFC has been different. Considering the high-debt countries, debt/GDP started increasing rapidly and surplus/GDP became more volatile. On the other hand, the surplus/GDP and debt/GDP of the low-debt countries re-mained relatively stable.
or-dered first. In other words, debt/GDP is affected contemporaneously by surplus/GDP.
First, consider the IRFs of the ‘high-debt countries’. It is unclear whether their immediate response in debt/GDP is positive or negative after a shock to the surplus since it is not statistically significant (using a 95% confidence interval). From period 2 onwards, the response of debt/GDP for both coun-tries is negative and significant. As explained in Section 3, this response can be consistent with both a Ricardian and a non-Ricardian regime. Thus, in order to distinguish between a Ricardian and a non-Ricardian regime, we need to analyze the estimated responses of surplus/GDP. For both Greece and Portugal, the response of surplus/GDP is positive after a shock to the surplus. However, from period 2 onwards, the response becomes insignifi-cant; therefore, the evidence for the longer term is inconclusive. The IRFs of Greece and Portugal do not give any evidence in favor of non-Ricardian regimes. Therefore, it is concluded that for these countries, a Ricardian regime is more plausible.
Second, consider the IRFs of the ‘low-debt countries’. For Germany, the response of debt/GDP is insignificant for all periods; therefore, the evidence is inconclusive. The response of surplus/GDP is positive and significant up until period 5. For The Netherlands, the immediate response of debt/GDP is negative and significant up until period 5. In addition, the response of surplus/GDP is positive and significant up until period 8. The responses of Germany do not give any conclusive evidence in favor of Ricardian regimes. However, a non-Ricardian regime is fairly unlikely since in such a case, persistent response of surplus/GDP to a shock to the surplus would not be found. Considering The Netherlands, there is conclusive evidence that a Ricardian regime is more plausible.
For both the high-debt and the low-debt countries, a Ricardian regime is more plausible. Nevertheless, some differences in the responses are found. Most importantly, the persistence of the shock largely differs. For the high-debt countries, the response of surplus/GDP returns to zero rather fast and becomes insignificant. Yet, for the low-debt countries, the response remains positive and significant for at least 5 periods. This indicates that surplus/GDP does not follow an arbitrary pattern but is rather persistent which is considered evidence in favor of a Ricardian regime.
Figure 7: Impulse response functions after a structural shock to sur-plus/GDP for individual countries (sample period: 2000q2-2013q4)
(a) Greece: debt/GDP (b) Greece: surplus/GDP
(c) Portugal: debt/GDP (d) Portugal: surplus/GDP
(e) Germany: debt/GDP (f) Germany: surplus/GDP
7
Conclusion
In this paper, the plausibility of the FTPL is investigated for the euro area. The FTPL states that it is fiscal policy that acts as a nominal anchor in determining the aggregate price level. If a government sets its surpluses in an arbitrary way, the price level adjusts in order to guarantee government solvency. Such a fiscal regime is called a non-Ricardian regime as in Wood-ford (1995). On the other hand, a fiscal regime where the government sets its surpluses in such a way as to guarantee government solvency, is called a Ricardian regime.
In order to find out whether a Ricardian or a non-Ricardian regime is more plausible for the euro area, I estimate a bivariate VAR, follow-ing Canzoneri, Cumby and Diba (2001). The model includes the variables surplus/GDP and debt/GDP. The analysis for the euro area as a whole yields evidence that debt/GDP responds negatively to a positive shock to surplus/GDP. In addition, the response of surplus/GDP is positive and sig-nificant up to 11 periods. These results suggest that a Ricardian regime is more plausible.
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A
Theoretical Model
The determination of the price level according to the FTPL evolves around the way in which the present value budget constraint is satisfied. Founders of the FTPL derive theoretical models including representative households and general equilibrium conditions (see Woodford (1994, 1995), Leeper (1991), and Sims (1994)). However, since the defining features of Ricardian and non-Ricardian regimes lie in the way the government’s budget constraint is satisfied, attention is focused on this part of the theoretical models here.
Consider the following government budget constraint in nominal terms at any period j:
Dj = (Tj− Gj) + Dj+1/(1 + rj), (A.1)
where Dj is the stock of government debt at the beginning of period j,
Tj− Gj is the primary surplus during period j, and ij is the nominal interest
rate for period j. Normally, a government’s budget constraint also includes the change in the monetary base on the right hand side, meaning that the existing level of government debt can be monetized. However, for reasons given in Section 4, the monetary base is neglected in the analysis of this paper.
Scaling the government’s budget constraint with nominal GDP, we ob-tain: Dj Pjyj = Tj− Gj Pjyj + Dj+1 (1 + rj)(Pjyj) = Tj− Gj Pjyj + yj+1/yj (1 + rj)(Pj/Pj+1) Dj+1 Pj+1yj+1 , (A.2)
where Pj and yj are the price level and the level of real GDP in period j,
respectively. Thus, the ratio of debt to nominal GDP in period j needs to be equal to the ratio of the surplus to nominal GDP in period j plus a discount factor times the ratio of debt to nominal GDP in the next period. The discount factor gives the ratio of growth in real GDP to the real interest rate. By defining dj as the debt-to-GDP ratio, sj as the surplus-to-GDP
ratio, and αj as the discount factor, Eq. (A.2) can be rewritten as:
dj = sj+ αjdj+1. (A.3)
Following Woodford (1995) and CCD, solving forward yields the present value budget constraint in the current period t:
dt= st+ Et +∞ X j=t+1 j−1 Y k=t αk ! sj. (A.4)
The derivation of Eq. (A.4) assumes that government solvency is ensured and the following holds in the limit:
lim T →+∞Et T +t−1 X k=1 αk ! dt+T = 0. (A.5)
B
Data
Table B.1: Descriptive statistics of surplus/GDP and debt/GDP for the euro area aggregate (sample period: 1980q2-2013q4
Surplus/GDP Debt/GDP Sample mean −0.002 0.644 Standard deviation 0.006 0.129 Minimum −0.013 0.384 Maximum 0.008 0.922 Observations 135 135
Table B.2: Business cycle indicator (BC ) from the Centre for Economic Policy Research (the indicator term equals 1 for recession periods)
C
Individual country analyses
Figure C.1: Primary surplus (left y-axis) and debt (right y-axis), both pro-portional to nominal GDP, for individual euro area countries
(a) Greece (b) Portugal
D
Bootstrap methodology
In order to obtain standard errors for the estimated coefficients and con-fidence intervals for the IRFs for the VAR model including the dummy interaction term, the bootstrap methodology explained by Runkle (2002) is used. The latter methodology is a parametric bootstrap method that is suitable for time-series data. The original bootstrap methodology of Efron (1982) cannot be used as this assumes that all observations in the sample are independently distributed. This is clearly too restrictive for time-series data. In order to preserve the temporal dependence of the data in generating bootstrap samples, the approach by Runkle proceeds as follows:
1. Estimate the reduced-form model in Eq. (16) using OLS. This gives the estimates: ˆΠ, ˆΦ, C(L),ˆ B(L), and ˆˆ et.
2. Using the estimated coefficients and residuals of the fitted model, es-timate the linear predictions for the endogenous variables. Using the reduced-form model specified above, the linear predictions are calcu-lated as: ˆZt= ˆΠ + ˆΦD +C(L)Zˆ t−1+B(L)Zˆ t−1D for t = (0 + p), ..., N ,
where p is the number of lags and N is the total number of observa-tions.
3. Using the linear predictions ˆZt, create bootstrapped time-series, Zt∗,
for t = (0 + p), ..., N as follows: Zt∗ = ˆZt+ e∗t, where e∗t is a random
draw from the empirical distribution of the residuals.
4. Estimate the reduced-form VAR as in Eq. (16) using the bootstrapped time-series in Zt∗ as dependent variables.
5. Compute impulse response functions for both endogenous variables using the coefficients given by the estimated VAR of the bootstrapped series.
6. Repeat steps 3-5 for a fixed number of times, e.g. 1,000.
