Moreover, most of these studies did not take into account possible discontinuities in the analysis of the linear relationships6. Agents fully expect the debt burden from the fiscal stimulus, and expect higher taxes in the future (wealth effect). Bertola and Drazen (1993), postulate that the sign of the fiscal multiplier depends on the debt-to-GDP ratio.
Bohn (1998) has suggested that the analysis of the soundness of fiscal policy should not be limited to the evaluation of the stationarity of the debt-to-GDP ratio. 13 See e.g. stability and growth pact for the euro area. These effects can be specified in the government's budget constraint in a continuous time frame.
Empirical evidence
However, Panizza and Presbitero (2014) find no evidence of an effect of public debt on medium-term growth. The evolution of real GDP growth and the series of public debt ratios are shown in Figures 2 to 5. The graphs suggest that the relationship between real GDP growth and the public debt ratio may have changed over time.
Second, we test the stability of the relationship between public debt and economic growth (and select the number of breaks) using the test proposed in Kejriwal and Perron.
Methodology
We test the instability of the parameters in the cointegration regression using the tests proposed by Kejriwal and Perron. They present issues related to structural changes in cointegrated models that allow for I(1) and I(0) regressors and multiple discontinuities. They also propose a sequential procedure that allows consistent estimation of the number of breaks, as in Bai and Perron (1998).
The model with k fractions is obtained by a global minimization of the sum of squared residuals, as in Bai and Perron (1998). Kejriwal and Perron show that the structural change tests may suffer from an important lack of power against spurious regression (i.e., no cointegration). This means that these tests can reject the null of stability when the regression is really a spurious one.
In this sense, tests for breaks in the long-run relationship are used together with tests for the presence or absence of cointegration, allowing for structural changes in the coefficients. First, we use the residual-based test of the null of cointegration with an unknown single break against the no-cointegration alternative proposed in Arai and Kurozumi (2007). They propose an aLM test based on partial sums of residuals, where the breakpoint is obtained by minimizing the sum of squared residuals and consider three models: i) Model 1, level shift; ii) Model 2, level shift with trend; iii) and model 3, regime change. The Arai and Kurozumi (2007) test is restrictive in the sense that only a single structural break is considered under the null hypothesis.
Therefore, the test may tend to reject the null of cointegration when the actual data generation process shows cointegration with multiple breaks. To avoid this problem, Kejriwal (2008) recently extended his test by including multiple breaks under the null hypothesis of cointegration.
Empirical results
We use the Model II proposed by Carrion-i Silvestre et al. 2009), which considers that the structural break can influence the slope of the time trend. As can be seen in Table 2, the null hypothesis of a unit root with multiple structural breaks cannot be rejected at the 5% significance level in any of the tests applied to all five series. 2013) show that the asymptotic theory of Carrion-i Silvestre et al. 2009) does not predict the finite sample power functions of M-tests well, and the power can be very low for the magnitude of trend breaks typically observed in practice. In response to this problem, Harvey et al. 2013) propose a unit root test that allows multiple trend breaks, both under the null and under the alternative hypotheses, obtained by taking the infimum of the series (over.
This estimation method provides a robust correction for the possible presence of endogeneity in the explanatory variables, as well as serial correlation in the error terms of the OLS estimation. To also overcome the problem of the low power of the classical cointegration tests in the presence of persistent roots in the residuals of the cointegration regression, Shin (1994) proposes a new test where the null hypothesis is that of cointegration. Consequently, the relationship between public debt and growth is likely to have changed due to variations in macroeconomic and market forces, such as changes in the structure of the economy and supply and demand shocks.
For three cases, the test results suggest instability and the sequential test of the null hypothesis of k fractions versus the alternative hypothesis of k+ 1 fractions (SP) selects one fraction and provides evidence against the stability of the long-term relationships and suggests a one-fraction model. fraction estimated at 1971 and 1971, respectively. We use the residuals-based test of the null of cointegration against the alternative of cointegration with unknown multiple fractions, proposed in Kejriwal (2008), ˜Vk(ˆλ). In this section we examine the issue of the possible non-linear relationship between public debt and growth.
At the empirical level, we estimate threshold time series models of the public debt–growth nexus associated with a threshold income level. Two main research issues in our study are to establish: firstly, the possibility of the presence of a threshold in the long-term relationship, and secondly, the asymmetric movements between the government debt-to-GDP ratio and the annual real GDP growth rate.
Methodology: A threshold cointegrated model
When testing for threshold cointegration, Balke and Fomby (1997) proposed applying several univariate tests previously developed in the literature to the known cointegration residual (i.e., the error correction term). Further contributions include Forbes et al. 1999), who developed a Bayesian estimation procedure; and Lo and Zivot (2001), who extended Balke and Fomby's approach to a multivariate threshold cointegration model with a known cointegrating vector, using Tsay (1998) and multivariate extensions of Hansen (1996) tests. More recently, Hansen and Seo (2002) further contributed to this literature by examining the case of an unknown cointegration vector.
In particular, these authors proposed a vector error correction model (VECM) with one cointegrating vector and a threshold effect based on the error correction term and developed a Lagrange multiplier (LM) test for the presence of a threshold effect. As can be seen, the threshold model (22) has two regimes depending on whether the deviations from equilibrium (defined by the value of the error correction term) are below or above the threshold, where A1 and A2 describe the dynamics in each regime. In one of the regimes, there would be no tendency for the variables xt to return to equilibrium (ie the variables would not be cointegrated); on.
Next, Hansen and Seo (2002) proposed two heteroskedasticity-consistent LM test statistics for the null hypothesis of linear cointegration (i.e., there is no threshold effect) against the alternative of threshold cointegration (i.e., model (22)). Finally, Hansen and Seo (2002) developed two bootstrap methods to calculate asymptotic critical values and p-values.
Empirical results
On the contrary, in the first or normal regime, the effects and dynamics of error correction are minimal, both in terms of significance and the size of the coefficients. In this figure, one can see the strong effect of error correction for both the annual real GDP growth rate and the public debt-to-GDP ratio to the left of the estimated threshold (when wt−1 < 1.93). In contrast, we can observe a minimal effect of error correction on the right side of the estimated threshold (when wt−1 > , 1.93).
On the contrary, in the other two equations shown in Table 8b, the error correction effects and dynamics are minimal, both in terms of significance and magnitude of the coefficients. This figure shows the strong error correction effect for both annual real GDP growth and government debt-to-GDP to the left of the estimated threshold (when pea −1 < 0.84). In contrast, we can observe the minimal error correction effect on the right side of the estimated threshold (when pea−1 >0.84).
This study contributes to the empirical literature on the analysis of the relationship between debt and growth. In this paper, we extend the existing empirical analysis of the linear model of the Debt Laffer curve in two ways. In particular, the nature of the long-run relationship between debt-to-GDP and GDP growth is analyzed using the residual-based test of the null hypothesis of cointegration with a single or multiple breaks.
Second, a common criticism of most debt curve tests is that the econometric procedures used require a large number of observations. After the war, the Bank of Spain began a process of monetizing the deficit and the public debt that caused a tax inflationary process, reducing the real value of the public debt. This monetization of the debt went in parallel with the rejection of the obligations issued by the Republican government during the Civil War.
Similarly, the results of Kejriwal-Perron and Arai-Kurozumi-Kejriwal cointegration tests for the second data set indicate a cointegrated model with one break estimated at 1971 and two regimes and 1972–2013. Marginal distribution of estimates in cointegrated regression models with multiple structural changes. The long-run variance of the cointegrating regression residual is estimated using a Bartlett window approximately equal to IN T T1/2.
