Estimating fiscal policy reaction functions: The role of model specification

Journal of Macroeconomics 46 (2015) 113–128

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Estimating fiscal policy reaction functions: The role of model specificationR Martin Plödt∗, Claire A. Reicher Kiel Institute for the World Economy, Kiellinie 66, Kiel 24105, Germany

a r t i c l e

i n f o

Article history: Received 15 April 2015 Accepted 20 August 2015 Available online 5 September 2015 JEL Classification: E62 H61 H62 Keywords: Fiscal reaction function Fiscal policy Autocorrelation Euro area Primary surplus One-off operations

a b s t r a c t The literature has not yet come to a consensus on the actual responses of fiscal policy to output and to past public debt levels within industrialized countries. While the cyclical adjustment literature has suggested a strong response of the primary surplus to the output gap, the time-series literature has tended to report a far smaller response. However, recent theoretical findings suggest that some of this difference may be due to the way in which the time-series literature has typically handled the issue of autocorrelation, in a way which is incompatible with the timing of automatic stabilizers. In order to find a way around this problem, we formulate and estimate a set of fiscal policy reaction functions for the euro area, which allow for the primary surplus to feature three components: a fast-moving (stabilizing) response to the output gap, a consolidating response to the debt-GDP ratio, and an exogenous, persistent fiscal policy shifter. When we formulate a fiscal reaction function in this way, our estimates are compatible in magnitude with previous estimates from the cyclical adjustment literature. Furthermore, based on a set of model comparison exercises in line with what has been done in the monetary policy literature, we argue that our specification explains the data better than does the more commonly used specification. © 2015 Elsevier Inc. All rights reserved.

1. Introduction The crisis in the euro area, the desire for macroeconomic stability, and the need to consolidate public finances have provoked a renewed discussion about the positive systematic conduct of fiscal policy as well as the design of normative fiscal policy rules. Despite this interest in fiscal policy, however, not much consensus exists in the literature on the actual degree of counter-cyclical stabilization policy or consolidation in response to the debt ratio that euro area governments have historically pursued. While the cyclical adjustment literature implies a strong stabilizing response of the primary surplus to the business cycle, the timeseries literature on fiscal reaction functions has come to conflicting conclusions. Time-series studies that employ first differences have usually found results broadly in line with the cyclical adjustment literature, while studies that estimate a fiscal reaction function in levels with a lagged dependent variable on the right hand side have usually found an acyclical primary surplus.1 Somewhat puzzlingly, these results seem to hold both for cyclically-unadjusted and cyclically-adjusted data. These results are puzzling because one would expect the differences of these responses to be on the order of 0.5. These discrepancies with the cyclical adjustment literature, as argued by Golinelli and Momigliano (2009), may occur because a specification with a lagged R ∗

1

We would like to thank Maik Wolters, Tim Schwarzmüller, and the participants of the 2013 EUROFRAME conference for their helpful comments. Corresponding author. Tel.: +49 431 8814 604. E-mail addresses: [email protected] (M. Plödt), [email protected] (C.A. Reicher). See Golinelli and Momigliano (2009) and Reicher (2014b) for a review of this literature.

http://dx.doi.org/10.1016/j.jmacro.2015.08.005 0164-0704/© 2015 Elsevier Inc. All rights reserved.

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dependent variable implies a different model of automatic stabilizers than the fast-moving automatic stabilizers implied by the cyclical adjustment literature. If this were the case, then a specification with a lagged dependent variable would be misspecified, and any resulting coefficient estimates would be inconsistent and biased toward an arbitrary number. This is likely to be a serious problem in practice, resulting in extremely low estimates of the degree of stabilization policy even when there is a large degree of stabilization policy in reality. With the results of Golinelli and Momigliano (2009) in mind, we develop a way around this problem, which results in a workable, parsimonious way to estimate a fiscal reaction function in the presence of autocorrelation. We show that our approach, when applied to data from the euro area, delivers estimates that are consistent with the cyclical adjustment literature. To do this, first, we specify a fiscal reaction function that allows for the primary surplus to respond to deviations of actual GDP from potential GDP (the output gap) and to the public debt. Then we assume that the error to this equation, which represents any omitted drivers of fiscal policy, follows an AR(1) process, in line with Mendoza and Ostry (2008) but not in line with most of the remaining literature. This assumption gives us a nonlinear estimation equation, which we then go on to estimate numerically. We estimate this equation under different assumptions about the panel structure of our dataset, under different assumptions about the endogeneity of output, and for different orders of integration (assuming an AR(1) coefficient below or at one). In all of these cases, we find a strong and positive response of the primary surplus to the output gap (on the order of 0.4 to 0.7) and we find a positive response of the primary surplus to the debt-GDP ratio (on the order of 0.05 to 0.08). We then show, based on a model comparison exercise, that this specification outperforms a specification that controls for autocorrelation by using a lagged dependent variable, as in most of the literature, and that our specification also behaves well in comparison with a more general model specification (see Section 4). Our baseline fiscal reaction function features an automatic adjustment of the primary surplus to the current output gap and the lagged debt-GDP ratio, alongside a slow-moving, exogenous fiscal policy shifter which may exhibit autocorrelation or unit-root behavior. As Taylor (2000) points out, a fiscal reaction function along these lines would be analogous in its form to a monetary policy reaction function. There is a parallel between these two ideas, in that the specification of the fiscal reaction function reflects the goal of fiscal policymakers to jointly stabilize output and the public debt, just as monetary policymakers seek to stabilize output and inflation. Furthermore, both kinds of reaction functions face the issue of model specification in the presence of autocorrelation. In the context of monetary policy reaction functions this issue has already been discussed by Rudebusch (2002) and empirically investigated by English et al. (2003).2 In fact, we follow a similar approach to that taken by English et al. (2003) to show that our specification of a fiscal reaction function is more in line with a general model than is the lagged dependent variable specification. Based on our baseline fiscal reaction function, we then go on to revisit further issues that have been discussed so far in the literature on fiscal reaction functions. First, we revisit the issue on how the systematic conduct of fiscal policy has changed over time (Section 5). On this issue, our results differ somewhat from previous results on how European fiscal policy has changed in response to the Maastricht Treaty and EMU.3 Moreover, our results indicate that the period before the 2008 financial crisis may have been characterized by a lack of attention to fiscal consolidation in response to the past debt, while the period after the crisis has seen a renewed interest in fiscal consolidation. This result is particularly interesting insofar as it coincides with the onset of the crisis in the euro area. Next, we estimate our reaction function using data on the cyclically-adjusted primary surplus, which allows for a closer look at the discretionary reaction of fiscal policy (Section 6). We find evidence for a slightly counter-cyclical discretionary reaction, i.e. one that increases with output. Most importantly, in line with the cyclical adjustment literature, we find that the difference between the counter-cyclical discretionary reaction and the counter-cyclical overall reaction of fiscal policy is around 0.5 for those subperiods for which we have data. Based on this result, we argue that our specification helps to reconcile the time-series literature with the cyclical adjustment literature. Then, we go on to investigate the role of high debt levels and asymmetric reactions to the output gap (Section 7). Our results suggest that euro area governments have pursued economically and statistically significant consolidation policies only if their debt-GDP ratios have exceeded the 60% (Maastricht) threshold. Our results also suggest a stronger response of the primary balance to a positive output gap than to a negative output gap. Both of these results are in line with previous literature on these issues, which suggests that these results are not sensitive to model specification. After looking at nonlinearities, we go on to investigate the role of data revisions and news about the future business cycle (Section 8). We find that fiscal authorities respond substantially to both the real-time and ex-post output gaps, which suggests that both measures of the output gap deliver important information as to the conduct of fiscal policy. In contrast, fiscal authorities do not seem to significantly respond to forecasts. Our estimates of the overall cyclical response of the primary surplus, however, are robust to the inclusion of output gap revisions or forecasts. Finally, we present further robustness checks (trend GDP as a cyclical indicator, and the role of political variables) as well as country-specific estimates for our fiscal reaction function. We present these in the Appendix. We find that our results are robust

2 Rudebusch (2002, p.1161) argues that “the illusion of monetary policy inertia evident in the estimated policy rules likely reflects the persistent shocks that central banks face”, rather than an inherent motive for interest-rate smoothing. 3 Galí and Perotti (2003), García et al. (2009), Bénétrix and Lane (2013), and others mention the choice of time period – particularly the 1993–1998 period – as exhibiting a particularly strong degree of cyclical stabilization policies. Our results on cyclicality, by contrast, show fewer changes over time; we find that this difference is mainly due to the treatment of one-off operations.

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to these additional checks, while estimated country-specific fiscal reactions are subject to a significant amount of estimation error. Altogether, given our results, we argue that specifying a fiscal reaction function in our manner helps to resolve the problems identified by Golinelli and Momigliano (2009) and also helps to make sense of the differing results found in the literature on fiscal reaction functions. Furthermore, our specification helps to resolve discrepancies between the time-series literature and the cyclical-adjustment literature.

2. Data, specification, and estimation procedure 2.1. Data To conduct our baseline time-series analysis, we rely on the European Commission’s AMECO database for annual data on real GDP, nominal GDP, the nominal debt level, the primary budget balance, and potential GDP.4 Given that these are the variables on which euro area policy decisions are made, we believe it appropriate to base our sample on these variables. Our current sample, an unbalanced panel, covers all euro area countries excluding post-communist economies (i.e. the EA-15 except Slovenia). We exclude Slovenia and the newer euro area countries (Slovakia, Estonia, Latvia, and Lithuania) because these countries have experienced structural change to such a degree that it has been difficult to apportion movements in GDP to either movements in potential GDP or in the output gap. Additionally, into the 2000s, these countries engaged in massive privatizations and capital transfers, which do not reflect the normal operation of fiscal policy. As a result, we would need to control for these things if we were to include these countries in our sample. For the fourteen countries remaining in our panel, most series begin in the late 1960s or early 1970s, and all series end in 2014. Our sample therefore also covers fiscal policy during the Great Recession and the ensuing debt crisis. However, the AMECO dataset is based on the 2010 European System of National Accounts (ESA10), and we find that the historical ESA10 primary balance data have limited coverage. Therefore, to obtain a consistent series of historical primary balance data, we levelsplice the most recent vintage of the primary balance as a share of GDP using data from the most recent vintage of ESA95 data (which end in 2013). In addition, for historical primary balance data for Italy before 1980 and Spain before 1995, we expand our dataset using data on net lending and borrowing as well as interest payments as a share of GDP from the OECD Economic Outlook database. We level-splice the primary balance as a share of GDP at 1980 for Italy and 1995 for Spain, thus extending our series for those countries back to 1970. We also go through the same steps, using the same sources, to obtain a consistent series on the cyclically-adjusted primary balance as a share of potential GDP and net capital transfers as a share of GDP. While most of the literature takes the data on the primary balance and cyclically-adjusted primary balance as is, we find it useful to exclude large one-off operations from our data, in order to focus on the normal conduct of fiscal policy and to reduce the statistical influence of outliers. This is particularly an issue during the post-2008 period, since some of the rescue measures conducted during the crisis were extremely large in relation to the economies of the countries conducting these measures. It is, however, worth noticing that there were significant one-offs also before the 2008 financial crisis, for instance the assumption of debt related to the German reunification in 1995 as well as a large capital transaction in the Netherlands in 1995.5 While no series on one-offs exists throughout our whole sample, we follow the idea of Joumard et al. (2008) to infer one-offs from large transitory spikes in net capital transfers as a share of GDP. We identify these spikes algorithmically, by detecting episodes in which net capital transfers as a share of GDP deviate from the average from adjacent periods by more than a particular cutoff value.6 Where net capital transfers deviate in such a manner, we first check whether this deviation is reversed in subsequent periods.7 If so, we create a smoothed datapoint by taking an average from adjacent periods. Then, we repeat this process until there are no more large temporary deviations in our dataset. The difference between the original series on net capital transfers and the smoothed series then represents our estimate of large one-offs. There is also the issue of data revisions. In our baseline estimates, we focus on ex-post AMECO data since our main research question is concerned with the actual historical behavior of fiscal policy. However, since Golinelli and Momigliano (2009) and Cimadomo (2012) find important effects of data vintages on the measured cyclicality of fiscal policy, we consider this issue in Section 8. In order to address data revisions, we also include a series on output gap revisions based on annual projections contained in mid-year editions of the OECD Economic Outlook, compared with output gap estimates from the current vintage of the Economic Outlook. We also include a series on the expected change in the output gap between time t and t + 1, from the same editions of the OECD Economic Outlook. These series are available from 1995 through 2014.8

4

We investigate the sensitivity of our results to an alternative structural indicator (trend GDP instead of potential GDP) in A2. Correcting for one-offs has little effect on the main results of our paper. In fact, not excluding one-offs would cause fiscal policy to appear to respond somewhat more strongly to output, particularly for certain sub-periods. We return to this issue in Section 5. 6 We use 0.01 as a cutoff value; our results are not sensitive to the exact choice of the cutoff value. 7 There are a few situations, particularly in Greece, where this is not the case. 8 We do not use AMECO real-time data since the AMECO database was first set up in 2002. 5

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2.2. The main components of the fiscal reaction function Next, we derive our baseline fiscal reaction function. Our derivation follows the derivation of Reicher (2012, 2014a), which treats individual fiscal instruments (for example, government purchases or transfer payments) as having separate cyclical (stabilization), debt (consolidation), and exogenous components. Here, we treat the primary surplus in a similar manner. We focus on the primary surplus because, even though the behavior of specific fiscal policy instruments may be an important issue in practice, we wish to address the main technical issues regarding the estimation of a fiscal reaction function in a way that is compatible with the rest of the literature. In our analysis, the primary surplus as a share of GDP follows a fiscal reaction function which takes the general form:



Y¯t Pt =k+a 1− Yt Yt



+c

B

t−1

Yt−1



− b∗ + et ,

(1)

where the ‘sustainable primary surplus’ ratio k is given by:



k=

 (1 + i¯) − 1 b∗ , (1 + π¯ )(1 + g¯)

(2)

¯ and trend output growth is given by g. ¯ and where trend inflation is given by π¯ ; the trend nominal interest rate is given by i; These trends are all held constant. The quantity b∗ is some long-run debt ratio, which is also held constant. Meanwhile, the variable Yt represents real output; Y¯t represents a structural indicator such as potential GDP or trend GDP; Bt is the real end-ofperiod debt stock deflated by the GDP deflator; and et is some exogenous policy shifter. The model parameters are as follows: the coefficient a represents the total response of the primary budget balance to the output gap, which may result from some combination of discretionary fiscal actions and automatic stabilizers. The coefficient c represents the strength with which fiscal consolidation occurs in response to the past debt. As shown by Bohn (2007), in the absence of a multiplier, a value of c larger than the growth-adjusted interest rate ensures a nonexplosive path for the debt given any finite order of integration for et . We choose to work with a primary surplus reaction function (1) instead of a total surplus reaction function for several reasons. First of all, given a constant trend real interest rate and a constant trend growth rate, the value of k in (1) is likely to be more stable in response to fluctuations in trend inflation and the trend nominal interest rate than the value of k that would appear in a total surplus reaction function. Since we rely on a sample containing data from the 1970s and 1980s, the stability of k is of practical econometric concern. In fact, while we cannot identify k separately from b∗ , we revisit this issue in Section 5, where we find that a convolution of k and b∗ with the other model parameters appears to be stable over time. Additionally, we do not look at data on the total surplus since, in contrast with the primary surplus, interest payments in time t are predetermined and are hence not amenable to contemporaneous policy actions. 2.3. The estimation equation While it is tempting to estimate Eq. (1) directly, doing so would run into the problems of endogeneity and autocorrelation.9 Autocorrelation would occur because it is highly likely that the drivers of fiscal policy decisions which govern tax rates and spending are not independent across time. This lack of independence would result from persistence in political preferences, demographics, military expenditures, and any other omitted drivers of fiscal policy.10 In turn, this persistence would result in a driving process et that is correlated with the right-hand-side variables, particularly with debt, but also with output. To address this issue, we assume that et follows an AR(1) process with a persistence coefficient ρ . In this case, we can rewrite (1) as following the law of motion:



Y¯t Pt =k+a 1− Yt Yt



+c

B

t−1

Yt−1

∗

−b





+ρ



Y¯t−1 Pt−1 −k−a 1− Yt−1 Yt−1



−c

B

t−2

Yt−2

∗

−b



+ εt ,

(3)

where ε t is independent across time. Given this independence, we can use Eq. (3) as our baseline estimation equation. Alongside a fiscal reaction function estimated in levels, a number of studies such as those of Fatás and Mihov (2012) and Reicher (2014a) estimate a fiscal reaction function in first differences, since this is another way to correct for a high level of autocorrelation.11 In fact, we show that these studies should be expected to produce estimates similar to our baseline results. This is because a fiscal reaction function in first differences simply represents a special case of our baseline fiscal reaction function. In particular, if ρ were to equal one, then to a first-order approximation, (3) would collapse to:



Pt−1 Yt−1 Pt Y¯t−1 − =a − Yt Yt−1 Yt Y¯t



+c

B

t−1

Yt−1

−

Bt−2 Yt−2



+ εt .

(4)

9 Autocorrelation is a large problem; when we estimate an exploratory fiscal reaction function in the form of (1) using OLS, we obtain a Durbin–Watson statistic of 0.32, or an autocorrelation coefficient of 0.84, which is economically and statistically distinguishable from 2 or 0, respectively. 10 While political economy variables are not our main focus, we conduct yet additional robustness checks with political economy variables in Appendix A3. We find that our results are robust to the inclusion of these variables. 11 Another example is Afonso and Jalles (2011), in the context of a panel VAR specification.

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A specification in first differences can be motivated by noting that the existing evidence does not necessarily rule out a unit root or near-unit-root behavior in the debt ratio, and a unit root would be implied by (4). This is relevant because historical experience and some econometric estimates (e.g. Bohn (1991) and Reicher (2014a)) suggest that fiscal authorities in most countries stabilize either the deficit-GDP ratio or growth in the debt-GDP ratio, while the evidence on the stationarity of the level of the debt-GDP ratio is less secure.12 Additionally, a specification in first differences eliminates the need to estimate the additional free parameter ρ , which our estimates find to be large. This implies that there could be gains in precision to fixing ρ , particularly when estimating country-specific fiscal reactions. We will therefore additionally estimate the fiscal reaction function in first differences and check whether the order of integration makes an economically significant difference in the estimated coefficients. We find that it does not. 2.4. Estimation strategy We estimate our fiscal reaction functions using both nonlinear OLS (nOLS) and nonlinear two-stage least squares (n2SLS), the latter following Amemiya (1974) and Zellner et al. (1965). We do this because it is highly conceivable that the output gap may be endogenously related to the fiscal impulse, and the model is nonlinear in its parameters.13 To handle the issue of endogeneity, we use as instruments the lagged output gap and two lags of the output growth gap (Y¯t−1 /Y¯t − Yt−1 /Yt ), as well as two lags of the debt ratio. In addition, we include post-2008 one-off measures as an additional instrument, since these measures reflect the severity of the crisis in a given country. To examine the relevance of these instruments, we find that the first-stage F-statistics for the n2SLS regressions are just below 10, which indicates that our instruments are somewhere on the border between strong and weak. In order to address the possibility of weak instruments, therefore, we present results using both nOLS and n2SLS. We also note that our instrumental variables approach, though standard in the literature, cannot completely control for the possible endogeneity of past potential output or trend output in response to fiscal policy, given that future shocks will affect filtered values of past variables. While the robustness checks provided by Reicher (2014a) indicate that this is likely to be a minor issue in practice, we acknowledge this issue (and other issues related to filtering), and we leave the revision of the European Commission’s filtering methodology for future work. Using both nOLS and n2SLS, we produce two sets of estimates for our fiscal reaction function based on our estimation equation: a set of baseline pooled estimates and an additional set of fixed-effects estimates which include country-specific dummies on the right-hand side. In the latter we also include a dummy representing the period after the break in German data in 1991. Given the presence of a lagged dependent variable in our model, these sets of estimates are subject to a tradeoff between unmodeled heterogeneity and dynamic panel data (small-T) bias, which motivates producing both sets of results (see also Section 3.3).

3. Estimation results for the baseline fiscal reaction function 3.1. Main results The upper part of Table 1 contains the estimated coefficients of the baseline fiscal reaction function in levels, as given by Eq. (3). In order to discuss some main results we focus first on the pooled n2SLS estimates (the second line of the top panel of Table 1). We then compare nOLS and n2SLS estimates as well as pooled and fixed effects specifications. Finally, we discuss the results for the fiscal reaction function (4) in first differences, which are presented in the lower part of Table 1. Note that the constant is a catch-all constant put in front of the regression; this is a convolution of all of the constant terms in the estimation equation. First, the pooled n2SLS estimates arrive at an estimated value of a of about 0.6, and this estimate is both economically and statistically distinguishable from zero. On average, this means that the primary surplus is high when the output gap is high. Furthermore, a value of 0.6 is statistically indistinguishable from the values of about 0.5 implied by the proposed fiscal reaction function of Taylor (2000), the cyclical adjustment coefficients derived by Girouard and André (2005) and Mourre et al. (2013) based on a structural approach, and the estimates of Reicher (2014a) for the OECD. However, this value of a is noticeably lower than that of 0.9 proposed by Snower et al. (2011) and, most interestingly, it is far higher than that estimated by Afonso and Hauptmeier (2009), Fatás and Mihov (2010), and Bénétrix and Lane (2013) for the euro area based on a model in levels. Secondly, the estimated debt coefficient c equals about 0.06 under the pooled n2SLS estimates, which indicates that euro area countries on average have engaged in a relatively strong degree of consolidation policy over the sample period. The value of c is again statistically distinguishable from zero, and it sits in the middle regions of the results reported elsewhere in the literature. Interestingly, we also find that the residual governing the primary surplus is quite persistent, with the pooled estimates of ρ coming in at about 0.87 per year. The size of this coefficient indicates that autocorrelation is a major issue when estimating a fiscal reaction function. Further tests for residual autocorrelation reveal a small amount of additional autocorrelation, with an unconditional autocorrelation in ε t on the order of 0.105 for the nOLS estimates and 0.087 for the n2SLS estimates. A formal 12 Based on our dataset, a battery of panel unit root tests and panel stationarity tests confirms these impressions. We find that the output gap within our panel appears to be stationary, while the debt-GDP ratio seems to follow a unit root process, and the order of integration of the primary surplus-GDP ratio is ambiguous. Results from these tests are available from the authors upon request. 13 We do this using proc model in SAS.

118

M. Plödt, C.A. Reicher / Journal of Macroeconomics 46 (2015) 113–128 Table 1 Estimation results for the baseline fiscal reaction function. Specification Levels: nOLS, pooled n2SLS, pooled

const.

a

c

ρ

obs.

AICc

−0.004 (0.001) −0.004 (0.001)

0.411 (0.039) 0.632 (0.103) 0.425 (0.039) 0.741 (0.119)

0.049 (0.013) 0.056 (0.013) 0.061 (0.012) 0.074 (0.012)

0.872 (0.026) 0.870 (0.026) 0.797 (0.032) 0.775 (0.032)

475

−4009.8

0.426 (0.039) 0.562 (0.082)

0.078 (0.014) 0.082 (0.014)

nOLS, FE n2SLS, FE First differences: nOLS, pooled n2SLS, pooled

−0.001 (0.001) −0.001 (0.001)

p(χ 2 |H0 )

472 475

−3999.5

472

1

475

1

472

0.127 0.065

−3974.5

Notes: See Eq. (3) for the baseline fiscal reaction function in levels. See Eq. (4) for the fiscal reaction function in first differences. Robust standard errors are given in parentheses. AICc denotes the (smallsample) Akaike Information Criterion. The last column reports the p-value corresponding to a test of the null hypothesis of poolability.

test for a lack of residual autocorrelation involves placing lags of the regression residuals εˆt on the right-hand side of (3) and then re-estimating (3), seeing the degree to which these coefficients differ from zero. We do this for a lag order of one; longer lag lengths give similar results. Doing this for the nOLS estimates yields a coefficient estimate of 0.151 with a standard error of 0.053, while doing this for the n2SLS estimates gives a coefficient estimate of 0.141 with a standard error of 0.057. From this, we conclude that residual autocorrelation appears to be of some statistical significance but of relatively little economic significance. 3.2. nOLS versus n2SLS Next, we explore the degree to which nOLS and n2SLS produce different estimates from each other. We find that for all specifications, the nOLS estimates of the coefficient a on average are considerably lower than the n2SLS estimates, which makes sense given that one might expect a positive shock to the primary surplus to exert a contractionary effect on output. If this were the case, two factors would drive the unconditional statistical relationship between output and the primary surplus which would be captured by a nOLS regression. On one hand, the fiscal reaction function would imply a strong positive relationship between output and the primary surplus. On the other hand, a multiplier relationship between the primary surplus and output would imply a negative relationship between the primary surplus and output. A nOLS regression would capture both of these effects, measuring a less-positive relationship between output and the primary surplus than that implied by the fiscal reaction function. However, a properly-specified 2SLS regression would control for the endogeneity of output and therefore would produce larger coefficient estimates in the fiscal reaction function than the nOLS regression. We find that this endogeneity is an economically and statistically significant issue. To see this, we construct a Hausman– Wu-style test for exogeneity, which uses the residual from the first-stage regression, which has the output gap on the left-hand y side. We denote this residual by ˆt . Then, we include an additional freestanding term on the right-hand side of Eq. (3), given y exog  ˆ by a ˆt . We then re-estimate that equation by nOLS. As Hausman (1978) shows, a t-test on the null hypothesis H0 : aˆ = 0 is asymptotically equivalent to testing the null hypothesis of no endogeneity. However, when we do this test, we arrive at a tstatistic of −2.46, which suggests a problem with endogeneity. As a result, we argue that, in the current setting, endogeneity is a significant economic and statistical problem. 3.3. Pooled versus fixed effects estimates While running nOLS is likely to result in biased estimates, it is also conceivable that omitted heterogeneity would result in biased estimates. To check for this possibility, we next compare the pooled panel results with the fixed effects results. We find that while the pooled and fixed effects estimates seem to give relatively similar estimates of a, they seem to give slightly different estimates of c and ρ , particularly of ρ . We argue that we have some reason to better trust the pooled estimates. This is because the differences in the estimated magnitude of ρ in particular are highly compatible with the idea that the fixed effects estimates are biased downward because of small-T dynamic panel bias, on the order of that which might be expected for an average sample length of 33.7 yr, for fourteen countries. In fact, Phillips and Sul (2007) give a formula for small-T bias. Using the pooled OLS estimate of ρ = 0.872 and a value of T = 33.9, their formula implies a bias for the fixed-effects estimates of ρ of about −0.064, which accounts for the majority of the observed −0.075 difference between estimates. While the estimates behave in such a way as to make us believe that the pooled estimates are less biased, we also base our decision to favor the pooled estimates on two more criteria. First, we compare the small-sample Akaike Information Criterion (AICc) between the nOLS pooled and fixed effects estimates (the first and third sets of estimates in Table 1). It turns out that the

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AICc significantly favors the pooled results. Moreover, based on a formal test, we do not find especially strong evidence against the null hypothesis of poolability, with χ 2 p-values against the null hypothesis of no fixed effects equal to 0.127 and 0.065 under the nOLS and n2SLS results. Therefore, given all of these considerations, and given that the estimates of a are also relatively similar across pooled and fixed effects specifications, we treat the pooled results as our baseline estimates.14 In principle, another way to mitigate dynamic panel bias would be to engage in a more sophisticated estimation strategy which requires first taking our estimation Eq. (3) in first differences, and then finding additional instruments for the lagged dependent variable, following Arellano and Bond (1991) or Blundell and Bond (1998). However, our attempts to implement a strategy along these lines have run into problems with the endogeneity of lagged output growth and particularly of lagged debt growth. This problem occurs because both of these things are related to the lagged fiscal impulse. Furthermore, our attempts to instrument debt growth (in particular) with deeper lags seem to run into problems with weak instruments. Therefore, we choose to stick with a pooled n2SLS estimation strategy, since this strategy is relatively simple, and it is more in line with estimation strategies used elsewhere in the literature. 3.4. Levels versus first differences We also present estimates for the fiscal reaction function (4) in first differences, which are presented in the lower part of Table 1. We present these estimates since we find a likely unit root in debt levels, and because some estimates in the literature are also in first differences. In general, these sets of coefficient estimates are broadly similar to those estimated using the specification in levels despite the estimated coefficient ρ under the specification in levels being statistically distinguishable from one. Furthermore, the estimated coefficients for a are also in line with the results in first differences given by Fatás and Mihov (2012) and Reicher (2014a). In general, this similarity implies that in practical terms, given our model setup, the order of integration makes little systematic difference in the estimated coefficients. 4. Comparing specifications of autocorrelation 4.1. A specification with a lagged dependent variable While our estimated fiscal reaction function is robust to a different order of integration, we argue that this is because we handle the issue of autocorrelation in a particular way, whereby the first difference specification is a special case of the levels specification. In fact, we argue that differences in results from the literature (particularly under levels specifications) stem from the different ways in which autocorrelation is handled. In particular, our specification of the estimation equation as given in (3) resembles the specification in Mendoza and Ostry (2008) but differs from specifications more typically found in the literature on fiscal reaction functions. A more typical specification from the literature would simply include a lagged endogenous variable on the right-hand side of the fiscal reaction function in order to control for autocorrelation. Such a specification would take the form:



Pt Y¯t =k+a 1− Yt Yt



+c

B

t−1

Yt−1



− b∗ + β

P

t−1

Yt−1



− k + υt .

(5)

Simply including a lagged dependent variable in this way would imply that the primary surplus adjusts only slowly in response to the output gap. As a result, such a specification would imply a different model of the cyclical component of primary surpluses from one where the cyclical component consists largely of fast-moving automatic stabilizers. As Golinelli and Momigliano (2009) argue, this difference in specifications may help to explain why much of the previous literature on fiscal reaction functions (e.g. Afonso and Hauptmeier (2009), Fatás and Mihov (2010), and Bénétrix and Lane (2013)) has produced consistently lower estimates of the cyclical coefficient a than our baseline model, to the point that many of these estimates are only slightly positive and not statistically distinguishable from zero. Furthermore, these estimates are at odds with the cyclical adjustment literature and with the economic intuition of policymakers. To see how these estimates differ in practice, the third and fourth lines of Table 2 contain nOLS and n2SLS coefficient estimates for a fiscal reaction function whose estimation equation takes the form (5). In contrast with our baseline estimates, the estimated cyclical coefficients a reported there are neither positive nor always statistically distinguishable from zero, particularly for the nOLS estimates. This difference implies that the estimation of a fiscal reaction function in levels appears to be highly sensitive to the manner in which autocorrelation is specified, and this occurs because of the problems discussed by Golinelli and Momigliano (2009), whereby including a lagged dependent variable is incompatible with the behavior of automatic stabilizers. On the other hand, our baseline estimation results are based on a specification that allows for fast-moving automatic stabilizers, and our estimates are in fact comparable to estimates of the degree of automatic stabilizers derived from other sources. In fact, we present some analytical results in Appendix A1, which indicate that a lagged dependent variable specification is likely to be highly inconsistent when the errors in fact follow an AR(1) process. Letting σ equal the degree of first-order autocorrelation in the output gap, setting c to zero, and assuming that (3) actually describes the dynamics of the primary surplus, 14 While we do not reject poolability in comparison with a fixed effects specification, we also test for country-specific values for the constant, a, c, and ρ . Here, we can reject the null hypothesis of constant coefficients. Given this concern, we present a set of country-specific estimates in A4.

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M. Plödt, C.A. Reicher / Journal of Macroeconomics 46 (2015) 113–128 Table 2 Comparison of different model specifications. Specification

const.

a

c

ρ

nOLS, pooled

−0.004 (0.001) −0.004 (0.001) 0.000 (0.002) −0.004 (0.002) −0.003 (0.001) −0.004 (0.002)

0.411 (0.039) 0.632 (0.103) −0.091 (0.042) −0.086 (0.042) 0.411 (0.039) 0.632 (0.104)

0.049 (0.013) 0.056 (0.013) 0.007 (0.003) 0.007 (0.003) 0.049 (0.013) 0.056 (0.013)

0.872 (0.026) 0.870 (0.026)

n2SLS, pooled nOLS, pooled n2SLS, pooled nOLS, pooled n2SLS, pooled

β

0.878 (0.046) 0.871 (0.037)

p(χ 2 |H II )

obs.

AICc

475

−4009.8

0

472 0.867 (0.027) 0.866 (0.027) 0.871 (0.027) 0.870 (0.027)

475

−3927.4

472 475

−4007.7

472

0.867 0.968

Notes: See Eq. (3) for the baseline fiscal reaction function in levels. See Eq. (5) for the specification with a lagged dependent variable. See Eq. (6) for the more general model specification that encompasses Eqs. (3) and (5). Robust standard errors are given in parentheses. AICc denotes the (small-sample) Akaike Information Criterion. The last column reports the p−value corresponding to a test of the null hypothesis H0II : ρ = β .

then the OLS estimate of a in (5) converges in probability toward a complicated function of a, ρ , σ , the variance of the de-meaned output gap given by Vy , and the variance of the fiscal impulse et given by Ve , rather than toward the true value of a. Additionally, as σ goes toward one (our estimate is approximately 0.74), then the OLS estimate of a converges to (1 − ρ)a; this is also a result obtained by Golinelli and Momigliano (2009). Furthermore, as ρ goes toward one (our estimate is approximately 0.87), then the OLS estimate of a converges toward zero. As a result of these exercises, we argue that the choice of an econometric specification may have important effects on the ability of the econometrician to recover a reasonable value for a. In addition to presenting these theoretical considerations, we also claim that our specification explains the data better than the lagged dependent variable specification. To support this claim, we compare the AICc from the third line of Table 2 (the lagged dependent variable specification) with the AICc from the first line of Table 2 (our baseline specification).15 The AICc from our baseline specification is considerably smaller in magnitude than the AICc from the lagged dependent variable specification. This difference indicates that our model explains the data considerably better than the lagged dependent variable model. Altogether, while model fit alone cannot serve as a model selection criterion, this model comparison exercise, combined with our theoretical motivation and our fit with the cyclical adjustment literature, suggests that our approach to estimating fiscal reaction functions provides a reasonable treatment of the cyclical behavior of the primary surplus. 4.2. Testing against a more general model specification We take our model comparison exercise one step further, by setting up a more general specification that encompasses Eqs. (3) and (5) as special cases. This approach mirrors the approach taken by English et al. (2003), who investigate the specification of a monetary policy reaction function with respect to the treatment of autocorrelation. In their investigation, English et al. (2003) set up a monetary policy reaction function that allows for some combination of interest-rate smoothing (as is common in the literature) and persistent monetary shocks following Rudebusch (2002). In line with our results, they find that the inclusion of persistent monetary shocks improves the fit of a monetary policy reaction function to the data. Following their setup, our more general fiscal reaction function takes the form:



Pt Y¯t =k+a 1− Yt Yt



+c

B

t−1

Yt−1



− b∗ + β

P

t−1

Yt−1



 

−k −ρ a 1−

Y¯t−1 Yt−1



+c

B

t−2

Yt−2

− b∗



+ νt .

(6)

Based on this formulation we separately evaluate the evidence against the null hypotheses H0I : ρ = 0 and H0II : ρ = β . Under the first null hypothesis H0I , the alternative fiscal reaction function (5) found elsewhere in the literature is consistent with the more general reaction function given by (6). Under the latter null hypothesis H0II , our specification of the fiscal reaction function (3) is consistent with the more general reaction function given by (6). In the bottom two lines of Table 2, we present estimation results for the general fiscal reaction function (6). These estimation results reveal strong evidence against the null hypothesis H0I : ρ = 0. A t-test of the null hypothesis H0I : ρ = 0 rejects that hypothesis for any reasonable critical value, with a t statistic over 20. This finding indicates that the fiscal reaction function (6) cannot be reduced to a specification like (5) with only a lagged dependent variable on the right-hand side. By contrast, a Wald test of the null hypothesis H0II : ρ = β delivers a p-value of about 0.97; an F-test gives similar results. Furthermore, the estimates values of β and ρ are extremely close to each other. We therefore conclude that the evidence against H0II is very weak, which supports collapsing β and ρ into a single parameter, as in our baseline specification. Altogether, our findings indicate that our 15

A comparison of the sum of squared residuals yields the same ranking, given that both models have the same number of parameters.

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Table 3 Comparison of results for different sample periods. const.

(1) n2SLS, pooled, to 1992

−0.003 (0.002) 0.001 (0.002) 0.001 (0.003) −0.013 (0.005)

0.345 (0.139) 0.503 (0.156) 0.839 (0.195) 0.693 (0.191)

0.040 (0.024) 0.063 (0.031) −0.008 (0.020) 0.088 (0.025)

0.880 (0.031) 0.932 (0.074) 0.811 (0.045) 0.815 (0.064)

0.004 (0.003) 0.004 (0.003) 0.000 (0.004) −0.014 (0.005)

0.158 (0.209) 0.494 (0.240) 0.336 (0.250) −0.145 (0.273)

0.023 (0.039) −0.048 (0.032) −0.071 (0.037) 0.096 (0.032)

0.051 (0.080) −0.069 (0.054) −0.120 (0.086) 0.003 (0.078)

(2) n2SLS, pooled, 1993–1998 (3) n2SLS, pooled, 1999–2007 (4) n2SLS, pooled, 2008–2014 Difference (2)−(1) Difference (3)−(1) Difference (3)−(2) Difference (4)−(3)

a

c

ρ

Specification

obs. 177 73 124 98

Notes: See Eq. (3) for the baseline fiscal reaction function in levels. Robust standard errors are given in parentheses.

specification of the fiscal reaction function as in (3) fits the general reaction function (6) better in certain ways than does the specification (5), which is more typically used in the literature. Additionally, we engage in a model comparison exercise using the AICc, based on the nOLS estimates. This exercise finds that our baseline model, correcting for model complexity, performs the best at explaining movements in the primary surplus. Our baseline model has an AICc value of −4009.8, while the more general model has an AICc value of −4007.7. Meanwhile, the model with a lagged dependent variable has an AICc value of −3927.4, which represents a significant deterioration in performance over the other two models. Therefore, based on these AICc values, we conclude that our baseline modeling approach provides significant improvements over both the lagged dependent variable approach and the more general approach.16 5. Temporal stability: Maastricht Treaty, EMU, and the 2008 financial crisis So far, our results have relied upon constant behavior over time. However, there is one strand of literature on fiscal reaction functions which has sought to estimate how the systematic conduct of fiscal policy has changed over time. This literature has in fact found some evidence of changes over time, with Galí and Perotti (2003) and Bénétrix and Lane (2013) finding a possible increase in a following the Maastricht treaty, and Bénétrix and Lane (2013) additionally finding an increase in c. To explore how these results change when one follows our baseline specification, Table 3 contains sets of pooled n2SLS estimates under our specification, for the pre-Maastricht period leading up until 1992, the 1993–98 transition period following the Maastricht treaty, the post-EMU period running from 1999 to 2007, and for the period following the 2008 financial crisis. Additionally, this table contains differences in estimated coefficients across periods, along with implied standard errors. These estimates are equivalent to estimates produced using dummy variables and interaction terms, allowing for the variance of residuals to change over time. A handful of results are worth noting. As noted by the previous literature, the measured reaction of the primary surplus to the output gap, captured by a, looks like it might be higher during the 1993–98 transition period than before. In addition, c looks like it might have risen during that period, which is not out of line with the idea that the Maastricht treaty promoted fiscal discipline during the 1990s. However, standard errors indicate that the initial rise in a and c during the transition period is not statistically distinguishable from zero. Moving on to the post-EMU period, a looks like it rose further, while c fell toward zero. During the post-crisis period, a remained high, while c bounced back to about 0.088. Taken together, these estimates are not out of line with the earlier literature with respect to c. These results indicate that the pre-crisis period may have been characterized by a lack of attention to fiscal consolidation in response to the past debt, while the post-crisis period has seen a renewed interest in fiscal consolidation. However, the results with respect to a and ρ indicate more temporal stability, particularly for the 1993–98 period, than previous estimates would indicate. Based on an alternative set of calculations (available upon request), we believe that this difference is driven by our exclusion of one-off outliers, which other studies do not exclude. We also find that this is an important consideration for the post-2008 period. In general, our estimates suggest that there appears to be more stability than instability in the systematic conduct of fiscal policy within Europe across time. Furthermore, the regression constant (a convolution of k, b∗ , and the model parameters, given by (k − cb∗ )(1 − ρ)), appears to be relatively stable over time, which further suggests that the degree of time-dependence in fiscal policy may be limited in this regard. 16 In a separate set of estimates, not published here, we find that this set of differences goes away when we use cyclically-adjusted data. This is because the true value of a for cyclically-adjusted data should be near zero, which would minimize the theoretical problems with inconsistency discussed here. Rather, the theoretical problem is with obtaining the correct degree of cyclicality using unadjusted data.

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M. Plödt, C.A. Reicher / Journal of Macroeconomics 46 (2015) 113–128 Table 4 Results for the cyclically-adjusted primary surplus. aCA

ρ

Specification

const.

n2SLS, pooled, full sample

−0.004 (0.002) 0.000 (0.003) 0.001 (0.003) −0.012 (0.044)

0.197 (0.118) 0.090 (0.182) 0.303 (0.190) 0.223 (0.182)

0.056 (0.014) 0.061 (0.032) −0.006 (0.020) 0.093 (0.025)

0.849 (0.029) 0.892 (0.081) 0.815 (0.044) 0.834 (0.062)

0.001 (0.004) −0.013 (0.044)

0.213 (0.263) −0.080 (0.263)

−0.067 (0.037) 0.099 (0.032)

−0.077 (0.093) 0.019 (0.076)

(2) n2SLS, pooled, 1993–1998 (3) n2SLS, pooled, 1999–2007 (4) n2SLS, pooled, 2008–2014 Difference (3)−(2) Difference (4)−(3)

c

obs.

(a − aCA )

427 73

0.413

124

0.535

98

0.470

Notes: See Eq. (3) for the baseline fiscal reaction function in levels. Robust standard errors are given in parentheses. The last column reports the difference of estimates of a across subsamples when using noncyclically-adjusted data (cf. Table 3) and cyclically-adjusted data (this Table). Results for the sample period to 1992 are not reported due to an insufficient number of observations.

6. The discretionary reaction of fiscal policy: Results for the cyclically-adjusted primary surplus In the previous sections we have shown that our model specification consistently generates higher estimates of a compared to most other studies estimating a fiscal reaction function in levels. While we work with non-cyclically-adjusted data in our baseline analysis, several studies that estimate fiscal reaction functions look at cyclically-adjusted data (see Galí and Perotti (2003), Annett (2006), Turrini (2008), García et al. (2009), and Bénétrix and Lane (2013)).17 Studies using non-cyclically-adjusted data and studies using cyclically-adjusted data have tended to produce estimates of a that are relatively close to each other, and these estimates are usually not statistically distinguishable from zero. Seen from the lens of the cyclical adjustment literature, this represents a bit of a puzzle, since estimated values of a should actually differ by about 0.5. Here, we argue that our AR(1) specification does not generate this puzzle; our specification in fact produces values of a that differ by about 0.5. This difference is also remarkably constant across different sample periods. To see this, Table 4 shows estimates using the cyclically-adjusted primary surplus as a share of GDP for the full sample (subject to data availability) and for the same subsamples as discussed in Table 3. The final column of this table shows the differences between the values of a for unadjusted data (labeled as a) and adjusted data (labeled as aCA ), by subperiod. Three things become apparent. First of all, estimated values for aCA now appear to be weakly positive and statistically distinguishable from zero. Secondly, the estimated values for c and ρ do not appear to change by much. Thirdly, the difference between aCA and a hovers around 0.5 for all three subperiods. (The comparison for the full sample is not an apples-to-apples comparison because of missing data.) As a result of these findings, we argue that our results, taken together, are fully compatible with the cyclical adjustment literature. 7. The role of high debt levels and asymmetric reactions to the output gap 7.1. High debt levels Under the baseline specification of the fiscal reaction function, fiscal policy responds in the same way to the debt level no matter how high the debt level happens to be. However, recent work by Ghosh et al. (2013) has shown that fiscal authorities tend to respond in a nonlinear way to high debt levels. As a check on how robust our results are to nonlinear responses to high debt levels, we set up an alternate specification in order to see the degree to which the systematic marginal response of the primary surplus to the debt may be higher at high debt levels than at low debt levels. We set up our nonlinear model as follows: since the Maastricht criteria and the Stability and Growth Pact require a long-run debt-GDP ratio below 60% , we follow Snower et al. (2011) by adding an additional term cCR (Bt−1 /Yt−1 − bCR )+ to Eq. (3). When the debt ratio is below its 60% threshold, this term equals zero. When the debt ratio is above its 60% threshold, this term represents the degree to which the debt ratio exceeds that threshold. The term captures the additional consolidation that is required at high debt levels in order to push the debt-GDP ratio below bCR = 0.6 at a particular rate. The modified fiscal reaction function would now follow the form:



Pt Y¯t = k+a 1− Yt Yt



+ρ

17



+c

B



t−1

Yt−1



− b∗ + cCR

Pt−1 Y¯t−1 −k−a 1− Yt−1 Yt−1

 −c

B

B

t−1

Yt−1

t−2

Yt−2

− bCR ∗

−b



To understand how cyclical adjustment works, see Mourre et al. (2013).



+ CR

−c

B

t−2

Yt−2

CR

−b

  +

+ εt .

(7)

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Table 5 The role of high debt levels and asymmetric reactions to the output gap. const.

a

c

nOLS, pooled

−0.004 (0.001) −0.004 (0.001) −0.001 (0.002) −0.001 (0.002) −0.004 (0.001) −0.005 (0.001)

0.411 (0.039) 0.632 (0.103) 0.413 (0.039) 0.601 (0.101)

0.049 (0.013) 0.056 (0.013) 0.006 (0.022) 0.008 (0.022) 0.048 (0.013) 0.050 (0.013)

n2SLS, pooled nOLS, pooled n2SLS, pooled nOLS, pooled n2SLS, pooled

a+

cCR

Specification

a−

ρ

obs. 475

0.263 (0.055) 0.294 (0.182)

0.872 (0.026) 0.870 (0.026) 0.855 (0.028) 0.850 (0.028) 0.875 (0.026) 0.865 (0.027)

0.057 (0.026) 0.062 (0.026) 0.633 (0.070) 1.115 (0.203)

p(χ 2 |H III ) 0

472 475 472 475

0.000

472

0.013

Notes: See Eq. (7) for the baseline fiscal reaction function including bCR as additional explanatory variable. See Eq. (8) for the fiscal reaction function allowing for asymmetric reactions to the output gap. Robust standard errors are given in parentheses. The last column reports the p-value corresponding to a test of the null hypothesis H0III : a+ = a− .

Furthermore, in our estimation methodology, we include the lagged excess debt level in our list of instruments. To see what happens when we estimate a fiscal reaction function of this form, the middle of Table 5 presents the estimation results based on Eq. (7). As expected, the estimated c coefficients drop accordingly since now cCR captures most of the consolidation that c formerly captured. However, a and ρ are little changed. Interestingly, however, the point estimates of c are now neither economically nor statistically significant. This suggests that euro area governments have pursued consolidation policies mainly if their debt-GDP ratios have exceeded the 60% threshold. 7.2. Asymmetric reactions to the output gap Next, we look at what happens when we allow for an asymmetric reaction to the output gap. We do this by allowing for different a coefficients for positive and negative output gaps, given by a+ and a− . The fiscal reaction function now takes the form:



Pt Y¯t = k + a+ 1 − Yt Yt



+ρ





+ a− 1 − +

Pt−1 − k − a+ Yt−1



Y¯t Yt

Y¯t−1 1− Yt−1



+c −



B



t−1

Yt−1

− a− 1 − +

− b∗

Y¯t Yt



 −c −

B

t−2

Yt−2

− b∗



+ εt .

(8)

In our instrument set, we include lagged positive deviations and lagged negative deviations of the output gap, instead of the lagged output gap. To see what happens when we estimate a fiscal reaction function of this form, the bottom of Table 5 presents the estimation results based on Eq. (8). In line with Golinelli and Momigliano (2009), we find a stronger response of the primary balance to a positive output gap than to a negative output gap. From this, we conclude that this finding is robust to our method of handling autocorrelation using an AR(1) error term. 8. The role of output gap revisions and news 8.1. The role of data revisions Another strand in the literature has focused on the role of data revisions; for instance, Bernoth et al. (2013) argue that a positive response of the primary surplus to data revisions might help to disentangle the discretionary reaction of fiscal policy from the automatic reaction of fiscal policy. In fact, Cimadomo (2012) shows that forecasts of the output gap might play an important role for the ex post primary surplus. While we do not take a stand on exactly what such a statistical response might imply, this debate does imply that it might be important for estimates of the cyclicality of fiscal policy to take data revisions and forecasts into account. In order to investigate these issues, we first set up an augmented fiscal reaction of the form:



Y¯t Pt =k+a 1− Yt Yt



r

+ a Rt |T + c

B

t−1

Yt−1

∗

−b





+ρ



Y¯t−1 Pt−1 −k−a 1− Yt−1 Yt−1



r

− a Rt−1|T − c

B

t−2

Yt−2

∗

−b



+ εt ,

(9)

where Rt |T = ((1 − Y¯t /Yt ) − (1 − Y¯t |t /Yt |t )) indicates the revision to the output gap and where (1 − Y¯t |t /Yt |t ) indicates the realtime estimate for the output gap in t based on the OECD’s mid-year projections. A negative coefficient ar would indicate that fiscal authorities seem to respond to real-time measurements of the output gap rather than to the final measurements of the output gap. Furthermore, to maintain consistency, we use only the OECD’s measurements of the output gap, both in real time and as of this writing. We also take output gap revisions as exogenous.

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M. Plödt, C.A. Reicher / Journal of Macroeconomics 46 (2015) 113–128 Table 6 The role of output gap revisions and news. ar

Specification

const.

a

nOLS, pooled

−0.006 (0.002) −0.010 (0.003) −0.005 (0.002) −0.008 (0.003) −0.006 (0.002) −0.008 (0.003)

0.458 (0.058) 0.816 (0.166) 0.551 (0.062) 0.815 (0.138) 0.451 (0.058) 0.577 (0.117)

n2SLS, pooled nOLS, pooled n2SLS, pooled nOLS, pooled n2SLS, pooled

af

c

ρ

obs.

0.880 (0.042) 0.883 (0.040) 0.859 (0.044) 0.856 (0.044) 0.876 (0.043) 0.876 (0.043)

209

0.128 (0.139) 0.107 (0.150)

0.070 (0.020) 0.106 (0.025) 0.065 (0.018) 0.086 (0.020) 0.066 (0.021) 0.079 (0.023)

−0.326 (0.087) −0.490 (0.120)

p(χ 2 |H IV ) 0

187 209

0.007

187

0.002

209 187

Notes: See Eq. (9) for the fiscal reaction function including a data revision term. See Eq. (10) for the fiscal reaction function including the forecast of the change in the output gap. Results are based on a sample that comprises 11 euro area countries and starts in 1995. Robust standard errors are given in parentheses. The last column reports the p-value corresponding to a test of the null hypothesis H0IV : ar = −a.

To see the effects of data revisions, Table 6 reports an estimated fiscal reaction function for the OECD data, with and without an additional term for the output gap revision. From the coefficient estimates, it appears that the overall cyclical response a is robust to the inclusion of output gap revisions, and that the coefficient on the output gap revision is economically and statistically different from zero. Furthermore, these coefficient estimates imply that fiscal authorities respond substantially to both, the realtime and ex post output gaps. This suggests that both measures of the output gap deliver important information as to the conduct of fiscal policy. 8.2. The role of news about the output gap Next, we look at a specification that includes the (real-time) forecast of the change in the output gap as an additional righthand-side variable. This term captures any pre-emptive discretionary policies that might appear in the data. To do this, we now modify the fiscal reaction function to take the form:



Y¯t Pt = k+a 1− Yt Yt



+ρ

Pt−1 Yt−1



+ a f Ft+1|t + c



Y¯t−1 −k−a 1− Yt−1

B



t−1

Yt−1

− b∗



− a f Ft |t−1 − c

B

t−2

Yt−2

− b∗



+ εt ,

(10)

where Ft+1|t = ((1 − Y¯t+1|t /Yt+1|t ) − (1 − Y¯t |t /Yt |t )). We take this forecast of the change in the output gap as exogenously given. To see the effects of this additional variable, Table 6 also reports the results of a specification with the forecast of the change in the output gap. Here, we find similar results to the baseline specification. Furthermore, we find values of af that are statistically and economically close to zero, with positive point estimates. Therefore, we conclude that our estimated coefficient a mostly reflects responses to current conditions and not to news about expected fluctuations in the business cycle. 9. Conclusion In conclusion, the previous literature on fiscal reaction functions had not converged on known numbers for the cyclicality coefficient a and consolidation coefficient c, for the euro area or for elsewhere. In order to bring some order to these estimates, we take our lead from Golinelli and Momigliano (2009), who argue that this lack of convergence may stem from the ways in which different studies have treated autocorrelation in dependent variables. While most time-series studies have estimated a fiscal reaction function in levels with a lagged dependent variable on the right hand side, this approach does not allow for fast-moving automatic stabilizers. Furthermore, when this is the case, this approach can lead to inconsistent estimates. In order to arrive at consistent estimates, we estimate a fiscal reaction function in levels with an AR(1) error term, which allows for fast-moving automatic stabilizers. Our resulting estimates consistently point toward a cyclical response coefficient a on the order about 0.4 to 0.7, in line with the cyclical adjustment literature and in line with existing estimates in first differences. Furthermore, our estimates also point toward a debt response coefficient c of about 0.05 to 0.08. Furthermore, a set of statistical tests and model comparison exercises suggest that our specification better captures the behavior of the primary surplus than a specification which uses a lagged dependent variable. Based on these results, we argue that our specification of a fiscal reaction function may help to reconcile the various strands of the empirical literature with each other and with the cyclical adjustment literature. While we believe that our approach provides a workable way to deal with autocorrelation in fiscal policy within the current sample, there still exists a tradeoff between allowing for dynamic panel bias and unobserved heterogeneity. Given these issues we also believe that it is desirable to come up with an estimation strategy that can handle both of these things in an instrumental

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variables setting, without having to rely on weak instruments. One strategy not so far discussed might involve employing a sophisticated multilevel model that allows for endogeneity and random coefficients. Such a model might also help to deliver more precise country-level estimates. This approach would represent a substantial contribution to applied econometric practice, and given its sophistication, we leave this contribution for future work. Appendix A1. Additional analytical results In this appendix, we present some analytical results which indicate that a lagged dependent variable specification is likely to be highly inconsistent when the errors in fact follow an AR(1) process. Our results generalize those of Golinelli and Momigliano (2009). First, we assume that the true data-generating process is given by (3). For the sake of convenience, we also assume that k = 0 and c = 0, while a = 0 and ρ = 0. In addition, we let pt and yt denote the de-meaned primary surplus as a share of GDP and the de-meaned output gap, respectively. The true data-generating process therefore can be reduced to:

pt = ayt + et ,

(A.1)

where et has an autocorrelation coefficient ρ . Furthermore, we assume that the output gap is exogenous, with an autocorrelation coefficient σ . This represents a simplification of our actual setup; this simplification is meant to clarify a theoretical point. Now we assume that, instead of estimating (A.1), an analyst estimates a lagged dependent variable specification that takes the following form:

pt = ayt + β pt−1 + υt .

(A.2)

Assuming that the correct laws of large numbers hold, the probability limits for OLS estimates of a and β are then given by:

 

plim

aˆ

βˆ



=

Eyt2

Eyt pt−1

Eyt pt−1

E p2t−1

−1 

E pt yt E pt pt−1



.

(A.3)

Denoting the variance of the de-meaned output gap by Vy and the variance of the fiscal impulse et by Ve , (A.3) can be expressed as:



  plim

aˆ

βˆ

=

Vy

σ aVy

σ aVy a2Vy + Ve

−1 

aVy a2 σ Vy + ρVe

 .

(A.4)

From this it follows that:

plim aˆ =

(1 − σ 2 )a3Vy2 + (1 − σ ρ)aVyVe . (1 − σ 2 )a2Vy2 + VyVe

(A.5)

Hence, the OLS estimator aˆ in model (A.2) is a biased and inconsistent estimator of the true a in (A.1) if σ = 0. For σ → 1 the OLS estimator aˆ converges to (1 − ρ)a. More generally, aˆ converges toward a constant of doubtful economic meaning. A2. Trend GDP as alternative structural indicator So far we have used potential GDP as a structural indicator in all of our estimation equations. Potential GDP is calculated by the European Commission using a production function approach (see Havik et al. (2014)). A simpler but common alternative would be to use trend GDP as structural indicator. Trend GDP is obtained by applying the HP filter to the actual output series, and trend GDP is also readily available from the European Commission’s AMECO database. Here, we present estimates using trend GDP, since a different methodology behind the calculation of Y¯t might affect the degree of measured cyclicality in primary surpluses, which might in turn potentially lead to different policy conclusions. For this reason we estimate the baseline fiscal reaction function (3) using trend GDP instead of potential GDP. Estimation results are presented in Table A1. In general, these results seem to closely resemble the results for potential GDP. The similarity of these two sets of results suggests that the choice of a structural indictor does not have a major effect on the estimated cyclical and consolidation coefficients at the pooled level, though we find some differences for individual countries (results available upon request). A3. The role of political factors Our next robustness check involves including political economy variables as additional right-hand side variables to our baseline model. We do this in view of the vast literature on the political determinants of fiscal policy. In particular, we estimate the degree to which the primary surplus might potentially be affected by fiscal manipulations prior to elections (so-called ‘political budget cycles’ or ‘electoral cycles’ – see for instance Mink and de Haan (2006)). In addition, we analyze the effects of the political

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M. Plödt, C.A. Reicher / Journal of Macroeconomics 46 (2015) 113–128 Table A1 Trend GDP as alternative structural indicator. Specification

const.

a

c

ρ

obs.

AICc

nOLS, pooled, trend GDP

−0.004 (0.001) −0.005 (0.001)

0.350 (0.037) 0.659 (0.085) 0.359 (0.037) 0.735 (0.102)

0.063 (0.015) 0.088 (0.016) 0.071 (0.014) 0.098 (0.015)

0.897 (0.026) 0.910 (0.023) 0.833 (0.031) 0.829 (0.030)

477

−4005.5

n2SLS, pooled, trend GDP nOLS, FE, trend GDP n2SLS, FE, trend GDP

p(χ 2 |H0 )

475 477

−3993.0

475

0.208 0.142

Notes: See Eq. (3) for the baseline fiscal reaction function in levels. Robust standard errors are given in parentheses. AICc denotes the (small-sample) Akaike Information Criterion. The last column reports the p-value corresponding to a test of the null hypothesis of poolability. Table A2 The role of political factors. Specification

const.

a

c

nOLS, pooled

−0.004 (0.001) −0.004 (0.001) −0.003 (0.001) −0.003 (0.001)

0.411 (0.039) 0.632 (0.103) 0.414 (0.038) 0.620 (0.098)

0.049 (0.013) 0.056 (0.013) 0.049 (0.012) 0.056 (0.013)

n2SLS, pooled nOLS, pooled n2SLS, pooled

elec

−0.004 (0.001) −0.004 (0.001)

left

−0.004 (0.004) −0.004 (0.004)

right

ρ

obs. 475

−0.001 (0.004) −0.002 (0.004)

0.872 (0.026) 0.870 (0.026) 0.875 (0.026) 0.873 (0.025)

472 475 472

Notes: See Eq. (3) for the baseline fiscal reaction function in levels. Robust standard errors are given in parentheses.

affiliation of the chief executive (right-wing or left-wing). We obtain an updated version of these data from Beck et al. (2001), via the World Bank’s website. For years prior to 1975 or after 2012, we hand-code the data. Additionally, we also include dummies for Spain until 1977 and Portugal until 1975, to represent the authoritarian regimes in those countries. Turning to parameter estimates (Table A2), we find some evidence for political budget cycles in euro area countries, though the effects of all of the political variables on primary surplus seem to be rather small. We find no economically or statistically significant effect of the political preferences of the chief executive on primary surplus, and based on a Wald test, we cannot reject the null hypothesis that left-wing and right-wing governments run a similar budget surplus (with a p-value of about 0.31). Most importantly, including these additional explanatory variables leaves the estimates for a, c and ρ almost unchanged in comparison with our baseline specification. A4. Country-specific estimates Finally, we present a set of country-specific estimates for our baseline fiscal reaction function (using potential GDP as structural indicator). We motivate this by noting that we were able to reject a null hypothesis that every country in our sample followed the same fiscal reaction function. In order to present country-specific results, Table A3 presents n2SLS estimates for the fiscal reaction function in both levels and first differences. We note that given smaller samples, country-specific estimates are generally not estimated with a high degree of precision, but some interesting findings emerge when we compare the results for some major European countries. We mainly focus on Germany, Italy, France, and Spain. For the fiscal reaction function in levels, the estimated value for c is positive and statistically distinguishable from zero for Germany, Italy, and Spain, which implies a tightening of these countries’ fiscal policy in response to the lagged debt ratio. Meanwhile, c appears to be positive but statistically indistinguishable from zero for France. By contrast, France significantly engages in a significant amount of stabilization policy, with an estimated a coefficient that is large, positive, and statistically distinguishable from zero, as is the case for Germany. Meanwhile, the estimate of a for Italy is large but statistically indistinguishable from zero. Looking at estimates in first differences, the estimated a coefficients for individual countries again indicate strong positive fiscal responses to cyclical developments in France, Spain, and Germany, and an imprecisely measured small, positive response in Italy. Turning to the estimated c coefficients, however, there seem to be larger differences between the specifications in levels and in first differences. For Germany, the estimated c coefficient falls from around 0.07 to 0.02 when taking data in first differences. In contrast, the estimated c coefficient for France markedly rises, even though it is again not statistically distinguishable from zero. The coefficients for Italy and Spain change by less. Altogether, country-specific estimates indicate a significant amount of imprecision, along with some possible heterogeneity. The imprecision of these estimates, in general, implies that it might make sense to take a weighted average of euro area-wide and country-specific estimates when making inferences. However, the possibility of heterogeneity indicates that future work might benefit from finding ways to treat the data as coming from a multilevel model, rather than as coming from country-specific

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Table A3 Country-specific estimates. Country

Austria Belgium Cyprus Finland France Germany Greece Ireland Italy Luxembourg Malta Netherlands Portugal Spain Pooled

Levels:

First differences:

const.

a

c

ρ

const.

a

c

−0.004 (0.006) −0.033 (0.017) −0.126 (0.058) 0.022 (0.011) −0.003 (0.004) −0.014 (0.006) −0.004 (0.011) −0.003 (0.004) −0.037 (0.015) 0.006 (0.008) −0.192 (0.042) −0.003 (0.009) −0.015 (0.009) −0.013 (0.006) −0.004 (0.001)

0.378 (0.259) 2.345 (0.665) 1.672 (0.498) 0.849 (0.200) 1.178 (0.357) 0.494 (0.181) −0.282 (0.327) 0.738 (0.228) 0.550 (0.498) 0.646 (0.307) 0.860 (1.184) 0.879 (0.242) 0.363 (0.361) 0.581 (0.203) 0.632 (0.103)

0.019 (0.019) 0.073 (0.023) 0.290 (0.069) −0.087 (0.038) 0.042 (0.051) 0.065 (0.021) 0.008 (0.050) 0.057 (0.064) 0.115 (0.018) 0.087 (0.127) 0.246 (0.039) 0.038 (0.044) 0.071 (0.051) 0.072 (0.031) 0.056 (0.013)

0.492 (0.139) 0.354 (0.142) 0.346 (0.302) 0.682 (0.125) 0.884 (0.096) 0.534 (0.127) 0.816 (0.153) 0.908 (0.204) 0.643 (0.127) 0.464 (0.179) −0.146 (0.222) 0.681 (0.124) 0.722 (0.127) 0.718 (0.143) 0.870 (0.026)

0.000 (0.002) −0.001 (0.002) 0.002 (0.006) 0.000 (0.003) −0.001 (0.002) 0.000 (0.002) −0.003 (0.005) −0.001 (0.003) −0.001 (0.003) −0.001 (0.003) 0.002 (0.003) 0.000 (0.002) −0.004 (0.004) −0.001 (0.002) −0.001 (0.001)

0.193 (0.183) 0.538 (0.190) 1.708 (0.966) 0.707 (0.152) 1.187 (0.291) 0.504 (0.158) −0.621 (0.349) 0.848 (0.206) 0.177 (0.310) 0.500 (0.226) 0.186 (0.280) 0.750 (0.235) 0.172 (0.275) 0.538 (0.224) 0.562 (0.082)

0.034 (0.065) 0.041 (0.037) 0.218 (0.061) −0.048 (0.056) 0.103 (0.066) 0.022 (0.070) 0.029 (0.056) 0.071 (0.032) 0.107 (0.071) 0.075 (0.217) 0.073 (0.077) 0.027 (0.065) 0.159 (0.067) 0.112 (0.049) 0.082 (0.014)

See Eq. (3) for the baseline fiscal reaction function in levels. See Eq. (4) for the fiscal reaction function in first differences. Estimates are derived using n2SLS. Robust standard errors are given in parentheses.

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