Growth effects of fiscal policy and debt sustainability in the EU

Empirica 28: 3–19, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands. 3 Growth Effects of Fiscal Policy and Debt Sustainability in the EU ⋆ GANG GONG1, ALFRED GREINER1 and WILLI SEMMLER1,2 1 University of Bielefeld, Department of Economics, P.O. Box 100131, 33501 Bielefeld, Germany; 2 New School University, 65 Fifth Avenue, New York City, NY 10003, USA Abstract. In this paper we study the relationship of fiscal policy and economic performance of some core countries in the EU. Our aim is to find out whether public deficit and public debt have consequences for real variables in the economies we consider. The background of our empirical study is a growth model that provides us with some predictions on the relationship between fiscal policy and economic growth. In a first step we then use Granger causality tests to analyze empirically whether some of the implications of our model are compatible with the data. In a second step, we investigate whether the fiscal policies of the member states have been sustainable. Given this information, we then pursue the question of whether differences in the fiscal positions of countries have consequences as concerns the outcome of our empirical tests of step one. Finally, we study whether the impact of the public deficit ratio depends on the magnitude of the debt ratio. Key words: European integration, fiscal policy, sustainability. JEL codes: H62, O52 I. Introduction In recent times empirical studies have emerged which try to analyze the question of whether a rise in public spending shows positive effects on the growth rate of an economy. Perotti (1999), for example, demonstrates that low levels of debt or deficit are likely to generate positive effects of public expenditure shocks, while high levels of public debt lead to negative effects. Giavazzi and Pagano (1990) studied the fiscal consolidations in Denmark and Ireland in the 1980s and showed that in these countries a drastic cut in public deficits led to a sharp increase in private consumption. Alesina and Perotti (1995) reach a similar result. In addition to the two countries mentioned above, those authors consider Belgium, Canada, Italy, Portugal and Sweden over the time period form the mid 1980s to the beginning of the 1990s. In each of these countries the primary deficit was strongly reduced while the growth rate of private consumption was positive and larger than in the years prior to the adjustment. ⋆ We are grateful to Bas van Aarle for providing us with the data we used in our empirical estimations. We thank two referees for comments. 4 GANG GONG ET AL. The question of whether fiscal consolidation shows positive or negative effects is also of great relevance for European countries which joined the Economic and Monetary Union (EMU). Since the transition to EMU has been characterized by considerable monetary and fiscal consolidation efforts it is interesting to analyze the effects of that fiscal policy on the economic performance. Moreover, one may want to know the growth effects of the strict fiscal rules that were introduced at the start of the Euro. van Aarle et al. (1999) for example study the economic impact of fiscal retrenchment on economic activity during the transition towards EMU. They analyze whether countries under fiscal stress show different reactions to public policy measures compared to other countries. In their paper, an economy is supposed to be under fiscal stress if its primary budget gap is larger than −0.05 (in absolute terms). They find strong effects of adjustments in government spending on private consumption and investment for countries under fiscal stress. For countries which are not under fiscal stress fiscal consolidation shows negative effects as to private consumption and investment. In this paper, we will pursue a similar line of research. Our goal is to study the impact of public deficit and public debt on real variables, such as investment and GDP, for some countries of the EU. Further, we intend to clarify whether countries which seem to have unsustainable policies experience different effects of fiscal policies compared to countries with sustainable policies. We will address these topics in the context of an endogenous growth model. The theoretical model we use is in the tradition of endogenous growth models where public investment is allowed for, as in Barro (1990). Unlike in Barro, the government budget in our model is not balanced but deficit is admissible. Moreover, what the deficit is used for depends on fiscal rules that we will define. In this context, the composition of public spending matters as concerns its impacts on economic growth. The rest of the paper is organized as follows. In the next section we present an endogenous growth model which analyzes the relation between public debt, deficit and the growth rate of an economy. In Section III, we conduct Granger causality tests in order to test empirically whether the theoretically derived results are compatible with empirical observations. Then, we construct sustainability indicators and study whether countries which seem to have unsustainable policies experience different effects of public debt and deficits compared to countries with sustainable policies. Finally, we test whether the effect of public deficit on GDP depends on whether the debt ratio is high or low. The last section gives a short summary and concludes the paper. II. A Model on Fiscal Policy and Economic Growth The endogenous growth model we want to introduce here allows to study the impact of public deficit and public debt on the balanced growth path (BGP) of an economy. The model is described in detail in Greiner and Semmler (1999). We confine our exposition to the basic structure of the model as well as to its empirical GROWTH EFFECTS OF FISCAL POLICY 5 predictions that we use as a guide for our subsequent empirical work. The economy consists of three sectors, a household sector, a productive sector and the government, where the first two sectors are modelled by a representative individual and by a representative firm respectively. The individual solves the following optimization problem, max C(t )
∞ exp[−(ρ − n)t]L0 (C(t)1−σ − 1) = (1 − σ ) dt 0 subject to C(t) + K̇(t) + (δ1 + n)K(t) + Ḃ(t) + nB(t) = (w(t) + r1 (t)K(t) +r2 (t)B(t))(1 − τ ) + Tp (t). with C(t) consumption at time t and 1/σ the elasticity of substitution between consumption at two points in time. For σ = 1 the utility function can be replaced by the logarithmic function ln C(t). The assets accumulated by the household are physical per capita capital K(t); which depreciates at the rate δ1 , and government bonds or public debt B(t).1 Tp (t) is the lump-sum transfer payment to the household which the household takes as given in solving its optimization problem. The term τ is the income tax rate and w(t), r1 (t), and r2 (t) denote the wage rate, the return to physical capital and the return to government bonds respectively. The noarbitrage condition requires the after tax equalization of the two rates of returns. Moreover, ρ is the constant rate of time preference. The labor supply which equals L0 at t = 0 is assumed to grow at the constant rate n. The representative firm behaves competitively and has a per capita production function of the form,2 f (K, G) = K 1−α (Ḡ/L)α . where Ḡ is the aggregate stock of public capital which is subject to congestion. As to the congestion effect we assume that the per capita stock of public capital G = Ḡ/L affects per capita output. That specification implies that a rise in the labour input leads to a decline in the contribution of public capital to total ooutput. (1 − α) and α ∈ (0, 1), denote the elasticities of output with respect to private and public per capita capital. Since K denotes per capita capital the wage rate and the return to private capital are determined as w = αK 1−α Gα and r1 = (1−α)K −α Gα . The budget constraint of the government in per capita terms is given by Ḃ = r2 B + Cp + Tp + Ip − T − nB. where r2 B is the debt service, Cp stands for public consumption, Tp for transfers, Ip for public investment and T for the tax revenue, given by T = τ (w+r1 K +r2 B). 6 GANG GONG ET AL. In addition as to the sustainability of public debt we posit that the government is not allowed to play a Ponzi game. We thus state that the government has to set its expenditures and revenues in a way such that the usual transversality condition  
t (1) lim B(t) exp − (r2 (s) − n) ds = 0, t →∞ 0 holds. It should be noted that economies which have unsustainable policies in the medium run may nevertheless be sustainable for t → ∞. In the next section we will show how implementable indicators can be derived from this condition. As concerns the behaviour of the government we suppose that the government does not follow optimizing rules but sticks to budgetary regimes or rules. In strict budgetary rules the deficit is used for public investment while in less strict budgetary regimes it can be used for debt service and public investment. We define the rules of the government in terms of ratios. This allows us to undertake a comparative static study and to explore the growth effects when we assume alternative fiscal regimes. We define public consumption and transfer payments to the household as a fraction of total tax revenue, i.e., Cp = ϕ2 T and Tp = ϕ1 T , ϕ1 , ϕ2 < 1. Moreover, we define (gross) investment in per capita public capital, Ip , as Ip = ϕ3 (1 − ϕ0 )T , with ϕ3 ≥ 0. The fraction ϕ0 The fraction ϕ0 depends on the budgetary regime under consideration. The per capita public capital stock then evolves according to Ġ = ϕ3 (1 − ϕ0 )T − (δ2 + n)G, with δ2 the depreciation rate of public capital. We consider three alternative rules which define the government spending and borrowing rules.3 For regime 1, we posit that government expenditures for public consumption, transfers and interest payment must be smaller than the tax revenue, Cp + Tp + r2 B = ϕ0 T , with ϕ0 < 1.4 It should be noted that the requirement Cp + Tp +r2 B = ϕ0 T makes ϕ0 an endogenous variable which must satisfy ϕ0 < 1. This, of course, also holds for the other regimes. A modification of this regime, regime 2, is obtained when allowing that only a certain part of the interest pay- ment on public debt must be financed out of the tax revenue and the remaining part may be paid by issuing new bonds. In this case, the budgetary regime is described by Cp + Tp + ϕ4 r2 B = ϕ0 T , with ϕ4 ∈ (0, 1). The third regime, regime 3, requires that public consumption plus transfers to individuals must not exceed the tax revenue, but the government borrows in order to finance interest payments and public investment, Cp + Tp = ϕ0 T , ϕ0 < 1. Table I gives a summary of the regimes. Solving the above optimization problem of the household, taking into account the marginal productivity rules and imposing budgetary regime 2, the dynamics of our economy is described by a four-dimensional system of differential equations which we will not write down explicitly (for details see Greiner and Semmler, 1999). A BGP for this model is defined, as usual in endogenous growth models, as a path on which all variables grow at the same and constant growth rates. 7 GROWTH EFFECTS OF FISCAL POLICY Table I. Budgetary regimes 1 2 3 Target Deficit due to Cp + Tp + r2 B < T Cp + Tp + ϕ4 r2 B < T Cp + Tp + Ip > T , Cp + Tp < T Public investment Public investment +(1 − ϕ4 )r2 B Cp + Tp + Ip + interest payment Analyzing that model on a BGP using numerical simulation it turns out that sustained per capita growth (with a positive government debt) is not feasible in regime 3 and in regime 2 if the parameter ϕ4 is lower than a certain threshold value. Note that this does not say anything about the sustainability of public debt. The economic reason for this outcome is that public debt is higher in soft regimes and that the introduction of budgetary regimes implies that public interest payments appear in the economy wide resource constraint and lead to an (external) crowding out of private investment. This implies that very soft budgetary regimes, i.e., regimes where the government deficit is used to finance a large portion of interest payments on public debt by issuing new debt, does not yield sustained per capita growth. It should also be noted that the transversality condition of the government, Equation (1), is not necessarily fulfilled on a BGP. This holds because on a BGP public debt grows at a constant rate. (1) is only fulfilled if the balanced growth rate is smaller than r2 − n where r2 is an endogenous variable. But this depends on the numerical values of the parameters in the model. Comparing regimes 1 and 2, with a ϕ4 such that sustained per capita growth is feasible in regime 2, shows that the less strict budgetary regime 2 is accompanied with a higher ratio of public debt to private capital, B/K, on the BGP and a lower balanced growth rate. This implies that countries with a higher debt ratio have lower growth rates. The first reason for that outcome is the external crowding out effect described above which is the higher the higher the debt ratio. Besides this external crowding out effect, there is an internal crowding out effect which acts as follows: If countries are characterized by a high debt ratio a large fraction of the tax revenue must be used for interest payments on public debt implying that less resources are left for public investment. This effect can be called the internal crowding out effect. With a given public debt this effect is higher in more strict budgetary regimes since in less strict budgetary regimes the government may finance a part of its interest payments by issuing new debt. However, less strict budgetary regimes are characterized by a higher public debt which can offset this effect. As concerns growth effects of public deficit it is of importance for what the deficit is used for. So, if the deficit is used for public investment it does not necessarily imply that countries with a higher deficit are characterized by a lower growth rate, because public investment stimulates economic growth. 8 GANG GONG ET AL. As to the growth effect of a deficit financed increase in public investment the following results could be obtained. First, a rise in public investment raises the public capital stock and, thus, the balanced growth rate. However, second, an increase in public debt shows negative growth effects. Depending on which of those two effects prevails a deficit financed increase in public investment may raise or reduce economic growth. In particular, it turned out that less strict budgetary regimes are not more likely to yield positive growth effects of deficit financed increases in public spending compared to less strict budgetary regimes. The reason is that the higher public debt going along with a less strict budgetary regime compensates the lower internal crowding out effect of public debt, which results when a certain fraction of the interest payments need not be financed by the tax revenue. Overall we can state that our model predicts that countries with higher public debt will have lower growth rates. First, the reason is that there is a crowding out effect associated with high public debt which has a negative impact on public and private investment and, thus, on economic growth. Second, if public debt seems to be unsustainable then we would expect negative growth effects of deficit spending. As concerns the growth effects of public deficits no unambiguous result could be obtained. Here, it is of crucial importance whether the deficit is used for productive or non-productive spending. Thus, the composition effect of public spending (or retrenchment) is important. In the next section, we use Granger causality tests to check whether public debt and deficit have effects on detrended GDP and on private and public investment as predicted by our theoretical model. III. Granger Causality Tests First, we consider the impact of debt and deficits on real GDP. To do so we have to detrend real GDP. We do this by following the standard macroeconometric approach as suggested, e.g., in King et al. (1988) or Campbell (1994). That is we assume that the log of real GDP follows a linear time trend, i.e., ln(GDP) = a + bt, with t the time, and estimate that equation with OLS. The detrended variable then is given by ỹt ≡ ln(GDP) − (â + b̂t) â + b̂t , (2) with â and b̂ the OLS estimates for a and b. To perform this test the following equation is estimated yt = c + α1 yt −1 + · · · + αp yt −p + β1 xt −1 + · · · + βp xt −p + ut , with c a constant and ut a stochastic error term. If the hypothesis H0 : β1 = · · · = βp = 0 GROWTH EFFECTS OF FISCAL POLICY 9 Table II. Granger causality test of b and d on gdp B F G I Nl Sp Swe All ỹt caused by b ỹt caused by d Insig. Insig. Insig. −∗ (insig.) −∗∗ (−∗ ) +∗∗ Insig. −∗∗ Insig. Insig. Insig. Insig. (+∗∗ ) −∗ (insig.) Insig. (+∗∗ ) Insig. −∗∗ ∗ Significant at the 5% significance level. ∗∗ Significant at the 1% significance level. Insig.: not significant at the 1% and 5% level. can be rejected the variable x has a statistically significant effect on y: We tested whether public debt and public deficits have a negative impact on detrended real GDP (ỹt ). In all tests we have set p = 3 and p = 5. We have set p = 3 and p = 5 because we think that 3 and 5 years are a reasonable and large enough time lag over which public deficit and public debt can help to predict detrended GDP. Table II gives the results for p = 3 and p = 5 with the results for p = 5 in parenthesis if they differ from the ones obtained for p = 3. We consider the following core countries of the EU: Belgium, France, Germany, Italy, Netherlands, Spain and Sweden.5 ‘All’ in the table means that the countries in the sample have been pooled, i.e., put together in one sample. In order to get an idea of whether the effect of public debt and deficit is positive or negative we ran correlations between detrended GDP and current and lagged debt and deficit respectively which, however, we do not report here. The data we use are annual and from OECD (1999) and from European Commission (1998) and cover the time period from 1970–2000.6 Table II shows that the debt-GDP ratio has a negative impact on detrended real GDP in Italy (for p = 3) and the Netherlands, while this effect is significantly positive in Spain. In all other countries no significant effect of the debt-GDP ratio on detrended GDP could be found. For Spain there is a positive effect of the debtGDP ratio on detrended GDP. This could be due to cumulated past government expenditure exerting a positive effect on GDP. However, since this only holds for Spain this conclusion must be considered with care. As concerns the deficit-GDP ratio, a significant negative effect on detrended GDP could be detected only for the Netherlands and this also becomes insignificant setting p = 5. In all other countries, this effect is not significant except Italy and Spain (for p = 5), where this effect is positive. So our conjecture that public deficits may have a stimulating 10 GANG GONG ET AL. Table III. Granger causality test of b and d on i and of b on ip B F G I Nl Sp Swe All it caused by b it caused by d ipt caused by b −∗∗ Insig. Insig. Insig. +∗∗ (+∗ ) Insig. (+∗∗ ) Insig. (−∗ ) −∗∗ −∗∗ −∗ Insig. Insig. −∗ (insig.) Insig. Insig. −∗∗ Insig. (−∗ ) Insig. −∗ Insig. −∗ (−∗∗ ) Insig. Insig. Insig. ∗ Significant at the 5% significance level. ∗∗ Significant at the 1% significance level. Insig: not significant at the 1% and 5% level. effect on GDP must be considered with care since only for Italy and Spain and only with p = 5 a significantly positive result could be found. Pooling all countries one gets an unambiguous result. In this case, Table II shows that there is a statistically significant negative effect of both the debt-GDP ratio and the deficit-GDP ratio on detrended GDP. In our view this result is the most reliable due to the large data basis. Further, we think that the countries under consideration are relatively homogeneous so that pooling these countries does not pose too great a problem. Other implications of our theoretical model were that private investment is crowded out by public debt and public deficits. Further, our model also implies a crowding-out effect of public investment by public debt. The results of the empirical studies analyzing these questions are shown in Table III. There, we test whether the public debt-GDP ratio, b, and the public deficit-GDP ratio, d, have a statistically significant effect on detrended private investment, i, where private investment was detrended by applying (2). Further, we also tested whether detrended public investment, ip , is significantly affected by b. Again, Table III gives the results for p = 3 and p = 5 with the results for p = 5 in parenthesis if they differ from the ones obtained for p = 3.7 This table shows that only in Belgium and in Sweden (with p = 5) there is a significantly negative effect of public debt on detrended private investment. In all other countries this relation is insignificant, in the Netherlands, and in Spain for p = 5, it is even positive. As to the effect of public deficit on private investment, this effect is statistically significant and negative for Belgium, France and the Netherlands (for p = 3), while in all other countries it is not statistically significant. If we pool all data in one sample we again get a clear result. In this case, both the debt-GDP and the deficit-GDP ratio have a negative effect on private investment. GROWTH EFFECTS OF FISCAL POLICY 11 Further, from Table III it can be seen that the hypothesis of a high public debtGDP ratio crowding out public investment must be rejected for almost all countries. Only for Germany, for the Netherlands and for Belgium (with p = 5) we found a statistically significant negative effect of the public debt-GDP ratio on public investment. In all other countries this effect is not statistically significant. This also holds if we pool the data. In this case, public debt does not have a significant effect on public investment either. A similar outcome is obtained when testing whether the ratio of public debt to GDP and the ratio of public deficit to GDP affect detrended real private consumption. As concerns the public debt-GDP ratio we could find a significant effect of that ratio on consumption in Belgium (significantly negative) for p = 3 and p = 5, in France (significantly negative for p = 5) and in Spain (significantly positive) for p = 3 and p = 5. In all other countries as well as in our pooled data set this effect was not significant at the 5% or 1% level. The deficit-GDP ratio has a significantly negative effect on private consumption only in Spain (for p = 3 and p = 5) and in France (for p = 5). In all other countries as well as in the pooled data set there was no significant effect at the 5% or 1% significance level. An interesting question is whether countries with unsustainable policies experience different effects of public debt and deficits compared to sustainable countries. To answer this question we next look at the sustainability of fiscal policy in EU countries. IV. Testing Sustainability of Fiscal Policy For studying the sustainability of fiscal policy of EU countries we use the above introduced budget constraint of the government and employ the following differential equation Ḃ(t) = G(t) − T (t) + r(t)B(t), B(0) = B0 , (3) with B(t) government debt at time t, G(t) total public spending and r(t) the interest rate, all in real terms. For a constant real interest rate a given fiscal policy is sustainable if the equation lim B(t) exp[−rt] = 0 t →∞ (4) holds which is basically the same as Equation (1). This condition is equivalent to requiring that the discounted sum of future primary surpluses equals initial debt, i.e.,
t D(s) exp[−rt] ds (5) B0 = − 0 must hold, with D the primary deficit. 12 GANG GONG ET AL. (4) and (5) have often been used in testing whether a given fiscal policy is sustainable. Examples are the contributions by Hamilton and Flavin, 1986, who employed the generalized and restricted Flood-Garber test (cf. Flood and Garber, 1980) in order to test whether these conditions hold for the US. Additional tests which used cointegration techniques and other time series methods followed and partly reached different conclusions (see, e.g., Kremers, 1989; Wilcox, 1989; Trehan and Walsh, 1991). Bohn (1995) has cast some doubt on the validity of these tests because they do not take into consideration expectations across different states of nature in the future. Therefore, he proposes as an alternative a test where it is investigated whether the primary surplus is an increasing function of the debt-GDP ratio. A positive response of the primary surplus to changes in debt shows that a given fiscal policy is sustainable (cf. Bohn, 1998). Another approach to test whether fiscal policies are sustainable is proposed by Blanchard et al. (1990), which at least gives us some information in the medium run. Since we have only relatively short time series available for the EU countries we consider, time series analysis as undertaken in the studies mentioned in the last paragraph are not very reliable. Therefore we adopt in this paper the approach worked out by Blanchard et al. (1990) which provides implementable indicators. In that contribution it is argued that it is more useful to rewrite the budget constraint in terms of ratios to GDP, since economies grow over time. This gives8 ḃ = g − τ + (r − w)b, b(0) = b0 , (6) with w the growth rate of real GDP and b = B/GDP; g = G/GDP; τ = T /GDP. A given fiscal policy is sustainable if
t (g(s) − τ (s)) exp[−(r − w)s] ds (7) b0 = 0 holds for t → ∞. Solving for τ gives the (constant) sustainable tax ratio τs . The deviation of the actual tax ratio τ from the sustainable tax ratio τs then is an indicator for sustainability. If τs − τ is positive the sustainable tax ratio is larger than the actual, and the government has to raise taxes or reduce spending to achieve sustainability. If the reverse holds, i.e., if τs − τ is negative the actual tax ratio is larger than the one which guarantees sustainabilty and the fiscal policy is sustainable. To get implementable indicators within finite time Blanchard et al. (1990) impose the requirement that the debt-GDP ratio returns to its initial value. This yields the sustainable tax rate in finite time, τsf ; as (for details as to the derivation, see Blanchard et al., 1990, pp. 15–17)  
t −1 τsf = (r − w) b0 + (1 − exp[−(r − w)t]) (g + h) exp[(r − w)s] ds . (8) 0 Since we are interested in the question of whether the effects of fiscal policy on the private economy depend on the fiscal discipline in a country we are interested in GROWTH EFFECTS OF FISCAL POLICY 13 a medium term indicator of sustainability. We believe that the decisions of private individuals are affected by the fiscal position of a country in the medium term, rather than by its fiscal position in the short term or long term. An approximation to ((8) − τ ) in the medium term is ((5 years average of g) + (r − w)b0 ) − τ. (9) Next we compute (9) for the countries we also considered in the last section. Figure 1 shows the results for the time period from 1982–2000. With the exception of Spain and Sweden none of the countries under consideration have sustainable fiscal policies in the mid-nineties. This outcome is similar to the result obtained by Grilli (1989). He conducts unit root tests for 10 EU countries and concludes that up to 1987 all EU countries with the exception of Germany and Denmark have unsustainable policies.9 However, it can also be realized that in the nineties the fiscal positions have become better, i.e., convergence towards sustainable policies can be observed in all countries. This holds especially for France and the Netherlands. The reason for that outcome are the Maastricht criteria which required the deficit-GDP and the debt-GDP ratio not to exceed 3 and 60 percent respectively. Nevertheless, Belgium and Italy are characterized by highly unsustainable fiscal policies with a medium run gap of about 1.4 and 0.9 respectively. It should also be mentioned that the Netherlands were also characterized by highly unsustainable fiscal policies at the beginning of the eighties with a medium run gap which is almost as high as for Belgium and Italy. However, in the beginning of the nineties the Netherlands drastically changed their fiscal policy and succeeded to get an almost sustainable fiscal policy until the mid of the nineties. For Germany one realizes a sharp increase in the medium term gap at the beginning of the nineties due to the large increase in public deficits and public debt caused by German unification.10 There is again an increase in the medium term gap in 1993 which is due to the recession in this year. We should also like to point out that all of those countries had a negative medium term gap until the end of the seventies. This means that fiscal policies had been sustainable in the medium run in the countries we consider up to the seventies. Next we try to clarify whether countries which differ with respect to the sustainability of their fiscal policies also experience different effects of fiscal policies. Looking at Tables II and III we can try to establish a relation between the Results of the Granger causality tests of the last section and the sustainability tests of this section. However, it is difficult to come to a clear answer. On the one hand, in Table II we found a statistically significant Granger causality of public debt in Italy (with p = 3) and in the Netherlands, two countries which are or were unsustainable in the eighties and nineties, respectively. But, on the other hand, there is an insignificant effect of public debt in Belgium, which is also to be considered as unsustainable. A similar observation holds as concerns the effects of public deficits. GANG GONG ET AL. Figure 1a. 14 15 Figure 1b. GROWTH EFFECTS OF FISCAL POLICY 16 GANG GONG ET AL. The same holds when one looks at the effects of public debt and deficit on private and public investment. As one can see from Table III there is no unambiguous relationship between these effects and the sustainability of countries. For example, on the one hand, public deficits exert a negative effect on private investment in Belgium and the Netherlands (for p = 3), which can be considered as unsustainable. However, on the other hand, there is also a negative relation in France which must be considered as sustainable while in all other countries this effect is not significant including Italy which has an unsustainable policy. Similar conclusions hold when one looks at the other results of the Granger causality tests in this table. So, the overall conclusion is that there is no clear relation between the effects of public debt and of public deficits and the sustainability of fiscal policies. There are some hints that countries which appear to have unsustainable policies are more likely to have negative effects of public debt and deficits. However, there are also counter-examples so that this cannot be accepted as a fact. V. Testing a Nonlinear Relationship In Section III we have seen that public deficit has a negative impact on detrended GDP when the countries are pooled. In this section we want to study whether this relationship depends on the debt-GDP ratio or whether it is independent of this variable. That is we want to test whether the effects of public deficit on detrended real GDP differ according to whether the debt ratio in an economy is low or high. To get insight into the relation between public debt, public deficit and GDP we estimate a nonlinear equation which assumes that the effect of public deficit on detrended GDP depends on the debt-GDP ratio. This is done by assuming that the coefficient giving the impact of public deficit on detrended GDP is a function of the debt-GDP ratio. As to the latter function we assume a polynomial of degree 3. More concretely, we estimate the following equation, ỹt = α + β ỹt −1 + θ(bt )dt , (10) θ(bt ) = θ0 + θ1 bt + θ2 bt2 + θ3 bt3 . (11) with Equations (10) and (11) state that detrended GDP depends on its own lagged value and on the deficit ratio dt , where the effect of the deficit ratio is assumed to be affected by the debt ratio bt . If θ(bt ) is positive the deficit ratio has a positive impact on detrended GDP if it is negative the reverse holds. Further, since θ(·) depends on the debt ratio the effect of the deficit ratio on detrended GDP also depends on the debt ratio. Estimating (10) for the pooled data set with nonlinear least squares gives the following result: 17 GROWTH EFFECTS OF FISCAL POLICY Figure 2. Estimated parameter Value Std. deviation α β θ0 θ1 θ2 θ3 0.00012 0.775 0.015 −0.112 0.169 −0.075 0.00012 0.044 0.026 0.129 0.189 0.084 Figure 2 gives the curve of θt and of bt , showing a negative relation for almost the whole range of bt . This implies that the public deficit-GDP ratio has almost everywhere a negative impact on detrended GDP. Only if the debt-GDP ratio is smaller than about 12 percent a marginal increase in the public deficit-GDP ratio has a positive impact on detrended GDP. We also estimated an equation assuming a linear relationship between the public deficit-GDP ratio and detrended output, i.e., we assumed θ to be a constant parameter to be determined by OLS. The estimated value for θ is θ = −0.006 and this value is also statistically significant. Comparing the linear and the nonlinear regression by looking at the residual sum of squares (2.66 × 10−4 in the nonlinear equation, 2.68 × 10−4 in the linear equation) as well as at the residual mean (0 in both estimates) and the residual variance (0 in both estimates) showed that the two estimations do not differ. VI. Conclusions In this paper we have studied the effects of public deficit and debt on economic variables of some EU countries. We could obtain the following main results. 1. The Granger causality tests showed no unambiguous results concerning the effects of public deficit and public debt on detrended GDP when studying single countries. Further, there are some hints that countries which seem to have a highly unsustainable fiscal policies are more likely to experience negative effects of public debt. However, this result is too vague to be accepted as a fact. Looking at the 18 GANG GONG ET AL. crowding-out effect of public debt and public deficit, again no unambiguous result could be obtained. The same holds if one looks at the effect of public debt on public investment. 2. When pooling the data in one sample we get mostly unambiguous results. In this case public debt and public deficit both exert a negative influence on detrended GDP. The same holds as concerns the crowding-out effect. When all countries are pooled there is a statistically significant negative effect of public debt and deficit on detrended private investment. However, we did not find a statistically significant effect of public debt on public investment. 3. Estimating a nonlinear equation for the pooled data set with detrended GDP as the dependent variable which is explained by its own lagged values and by the public deficit-GDP ratio multiplied by the public debt-GDP ratio showed that for small values of the debt-GDP ratio public deficits have a stimulating effect on detrended GDP. For higher debt-GDP levels an increase in public deficits goes along with a decrease in detrended GDP as predicted by our model. Evaluating our estimations we think that the results obtained for the pooled data are the most reliable ones because the data basis is the largest in this case. Performing the estimations for single countries may lead to doubtful outcomes due to the few observations available. Therefore we conclude that public debt and deficits have negative effects as to GDP and lead to crowding out once a certain threshold of debt is reached. We want to note that levels for which public deficits may have stimulating effects on GDP appear to be small. But this may be due to the time period we considered. Since our data started in the seventies where public policies have been characterized by chronic deficits it is probably not possible to find positive effects of public deficits, which may only occur in economies with relatively small debt and deficit ratios. Notes 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. The dot over a variable gives the derivative with respect to time. In the following we omit the time argument t. In Greiner and Semmler (1999) a fourth regime is considered which we will not consider here. This regime for example can be found in the German constitution and is binding for the government. 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