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On the impact of public debt on economic growth: does country risk matter?

This study examines the nonlinear impacts of four country risk indices on the debt-growth nexus for 61 countries in a panel data framework. Our results show evidence of the different debt-growth nexus under the different degrees of country risk. Under a high-risk environment, a country's economic growth is harmed by raising its public debt. The negative effects public debt has on economic growth become weak under low political and financial-risk environments, while an increase in public debt could help to stimulate economic growth under low composite and economic risk environments. In addition, the differences of countries' income and debt levels also lead country risks to have different effects on the debt-growth nexus, suggesting that a country should borrow appropriately based on its current risk environments while improving economic performance. (JEL C33, E02, H63, O43)

I. INTRODUCTION

Public debt has a crucial impact on economic growth for many countries. It can promote a country's economic growth; however, higher debt could instead be a burden on economic growth. In the developing countries, the domestic savings cannot provide the demand for investment goods and export earning is not enough to finance imports. The lack in terms of domestic savings and export earnings is quite harmful to economic development (Ramzan and Ahmad 2014). They thus tend to borrow from external economies to accumulate their capital and develop their infrastructure, etc. for raising economic growth. Besides, in the periods of economic and financial crises, the build-up of government debt is undertaken to raise economic growth (Reinhart and Rogoff 2010; Spilioti and Vamvoukas 2015). However, using plentiful public debt to financial economic growth will increase the government deficit ratio rapidly and thus harm long-run fiscal sustainability.

As the economic impacts of public debt exist and the problems of high public debt emerge, the relationship between public debt and economic growth is of concern to many economists and academic researchers. In theory, the debt Laffer curve and debt overhang hypothesis suggest that if a country borrows too much, where public debt is larger than its repayment ability, then the debt service costs will restrain investments and thus harm economic growth. Based on the theory, most of the existing empirical studies have found evidence of a nonlinear effect of the debt-to-gross domestic product (GDP) ratio on the debt-growth nexus, indicating that higher public debt results in lower economic growth (after Reinhart and Rogoff 2010; Checherita-Westphal and Rother 2012). However, there is less literature investigating the impacts of public debt on economic growth under different institutions (the composite risk index in Abbas and Christensen 2010; the democracy and executive constraints in Kourtellos, Stengos, and Tan 2013; the financial stress index in Proano, Schoder, and Semmler 2014). This paper attempts to fill the gap by exploring whether the impact of public debt on economic growth varies across countries with different degrees of country risk. The multidimensional risk measures could provide a more comprehensive evaluation than the single indicator of external environmental factors.

When a country is under unstable economic, political, or financial conditions, debt financing becomes difficult and can thereby harm economic growth (i.e., Abbas and Christensen 2010; Kourtellos, Stengos, and Tan 2013). As noted by Abbas and Christensen (2010), a better institution can substitute for the collateral and risk-underwriting functions, which is the performance of public debt on the banks' balance sheets. And, it can help to optimally use the fiscal resources for providing public services, developing infrastructure, protecting property rights, and then leading to higher economic effects of public debt. Proano, Schoder, and Semmler (2014) state that by way of the impact on risk premiums (especially for bond spreads), the financial stress can affect the debt-growth nexus. Additionally, in the environments of stable macroeconomy and fewer distortions, the efficiency of capital investment will increase, leading to economic growth (Ramzan and Ahmad 2014). This implies that if we examine the debt-growth nexus without considering the country risk environments, the results may not be correct. Thus, it is worthwhile examining the impacts of a country's various risks on the relationship between public debt and economic growth.

This study contributes to the existing relative studies by exploring the nonlinear debt-growth nexus as the country risk environments change employing multifaceted indicators and the panel smooth transition regression (PSTR) model with instrumental variables. The PSTR model used in this study can consider the effects of country risks on the debt-growth nexus across countries and over time, and it allows for a continuous and smooth switch from a high-risk regime to a low-risk regime. Indeed, if the country risk environments mainly affect the relationship between public debt and economic growth, then it can be expected that we can obtain the estimated results of the debt-growth nexus for countries with the same economic conditions.

The purpose of this study is firstly to examine if a country's risk environments can affect the debt-growth nexus. To this end, we adopted the International Country Risk Guide (ICRG) data, that is, the composite, economic, political, and financial-risk indices, and the advanced PSTR model to examine the relationship between public debt and economic growth under different country risk environments. Second, countries with different income levels are in different economic situations and have different debt-paying ability, and thus the debt-growth nexus could be different between these countries. Besides, many existing studies have found evidence of an inverted U-shaped relationship between public debt and economic growth (for example, Reinhart and Rogoff 2010; Checherita-Westphal and Rother 2012). Ghosh et al. (2013) define "debt limit" and "fiscal space". (1) When the level of debt is higher than the debt limit, the interest rate will shoot up, and then a country will not have enough primary balance to bear a high interest bill. It implies that a country with a high level of debt has a low debt-paying ability. Thus, in order to discuss the nonlinear effects of the country risks on the debt-growth nexus, we classified our sample data into two income groups and two debt groups based on countries' income and debt levels, respectively.

Contrary to Abbas and Christensen (2010), who only use the composite risk of the ICRG data, we further adopted the disaggregate data of the risk environments--economic, political and financial risks--in addition to the composite risk index. We thus could analyze the nonlinear debt-growth nexus under the different kinds of the country risks. Besides, the empirical models with the quartile dummy interaction variables used in Abbas and Christensen (2010) cannot consider the time-invariant and country-specific heterogeneity. However, the PSTR model used in our study allows for this heterogeneity.

Three aspects of country risk environments, that is, economic, political, and financial risks, affect the debt and economic growth in different ways. In the aspect of economic risk, under the unstable macroeconomic environment and more distortions, the capital inflows will be ineffective (Ramzan and Ahmad 2014), and this then leads to the negative effect of the debt-growth nexus. Besides, De Grauwe and Ji (2013) indicate that in the period of economic distress the debt-to-GDP ratio has a larger impact on bond spreads than in the period of economic stability. For the impacts of political risk on the debt-growth nexus, the poorly developed laws and institutions will make banks not lend much, or important segments of an economy will be unable to borrow (Kumhof and Tanner 2008), thus leading to an influence on economic development. And, if of legal origin, colonial conditions and related institutions cannot function well under unstable political environments, and political instability hinders financial and economic developments (Roe and Siegel 2011). As to the association of financial risk, debt, and economic growth, an unsustainable debt leads to the risks of long-run growth (Kourtellos, Stengos, and Tan 2013), and the volatility of the exchange rate can influence the cost of external debt. Brunnermeier and Oehmke (2012) bring up the "diabolic loop" where financial institutions suffer from sovereign risk as the riskiness of government debt increases, leading to an unstable banking system. Banks will decrease their lending and then reduce economic growth. Besides, in shallow financial markets and poor debt management capacity, an increase in domestic debt will have a negative impact on private investment and fiscal sustainability and further reduce economic growth (Abbas and Christensen 2010). Thus, we need to estimate the nonlinear relationship between public debt and economic growth based on economic, political, and financial-risk environments, respectively, since the different risk aspects have different ways of influencing the debt-growth nexus.

The remainder of this study is organized as follows. Section II reviews recent empirical studies on the debt-growth nexus. Section III introduces the empirical models and methodology. The data source, variables definition, and empirical results are presented in Section IV, and Section V presents the conclusions.

II. LITERATURE REVIEW

This study reviews the empirical studies of the debt-growth nexus based on the following three aspects. First, some studies applied a linear model to examine the relationship between economic growth and public debt. Jayaraman and Lau (2009) apply the panel cointegration test, fully modified ordinary least squares (FMOLS), and Granger causality test to investigate the economic growth-external debt nexus over the Pacific island countries. They find evidence of the positive impact of external debt on economic growth in the long run, and there is a bidirectional causality between economic growth and external debt. Using the autoregressive distributed lag (ARDL) model, Bal and Rath (2014) find that in the short run an increase in public debt can stimulate economic growth but harm economic growth in the long run for India. Ramzan and Ahmad (2014) argue that there are negative and positive impacts of bilateral and multilateral external debt on economic growth in Pakistan. By studying 74 countries, Teles and Mussolini (2014) show that the debt has an insignificant impact on economic growth, but a significant relationship is found between economic growth and the interaction of debt with productive expenditures. Their results suggest that an increase in public debt for productive expenditures can stimulate economic growth. Lof and Malinen (2014) use a panel vector autoregressions (VAR) model to estimate the relationship between sovereign debt and economic growth in 20 developed countries. They find no significant evidence for the impact of sovereign debt on economic growth, but the negative impact of economic growth on sovereign debt is present. For Greece, Spilioti and Vamvoukas (2015) indicate that there is a positive relationship between government debt and economic growth. Applying the panel Granger causality test, Puente-Ajovin and Sanso-Navarro (2015) show that government debt Granger causes economic growth for 14 of 16 Organization for Economic Co-operation and Development (OECD) countries. (2)

Second, since an influential empirical study of Reinhart and Rogoff (2010) shows evidence of an inverted U-shaped relationship between public debt and economic growth, many studies have started to investigate the nonlinear relationship between public debt and economic growth and attempt to estimate the value of a turning point. Reinhart and Rogoff (2010) analyze the relationship between public debt and economic growth for advanced and emerging market countries. They indicate that an increase in public debt can be beneficial to economic growth when debt is under 90% of GDP, but the relationship between these will reverse after exceeding 90% of the debt-to-GDP ratio, suggesting that higher debt is related to lower economic growth. Using the Johansen cointegration approach, Osinubi, Dauda, and Olaleru (2010) find evidence of a nonlinear relationship between external debt and economic growth in Nigeria, and they indicate that the estimated value of the turning point is 60% debt-to-GDP ratio. Focusing on 12 euro area countries' debt-growth nexus, Checherita-Westphal and Rother (2012) indicate that there is a nonlinear impact of public debt on per capita GDP growth rate with the debt turning point at about 90-100% of GDP. Dogan and Bilgili (2014) employ a Markov regime-switching approach and find evidence of the negative and nonlinear effects of private and public external debts on economic growth. In addition, they indicate that the negative effects mainly come from the public external debt. For a sample of West German federal states, Mitze and Matz (2015) show evidence of an inverted U-shaped debt-growth nexus with the threshold value for a 46% debt-to-GDP ratio in the long run, and further find evidence of a U-shaped relationship between the 5-year lagged debt and economic growth. Using 118 countries including developing, emerging, and advanced economies, Eberhardt and Presbitero (2015) estimate the linear and nonlinear relationship between public debt and economic growth. They find that in the linear model, there is a positive long-run impact of public debt on economic growth, but no evidence of the short-run relationship between public debt and economic growth. They also find evidence of an inverted U-shaped debt-growth nexus in most countries.

Third, in addition to using the debt-to-GDP ratio as a threshold, some of the empirical studies adopt other potential economic and institutional variables as the thresholds to estimate the nonlinear relationship between debt and economic growth. Kourtellos, Stengos, and Tan (2013) consider 15 variables as the thresholds to examine the nonlinear debt-growth nexus for 82 countries. They find evidence of the nonlinear impacts of debt on economic growth in 9 of 15 cases, and show that a higher public debt results in a lower economic growth for these countries in the low-democracy regime, but in the high-democracy regime, public debt does not significantly influence economic growth. Using the debt-to-GDP ratio and financial stress index as thresholds, Proano, Schoder, and Semmler (2014) indicate that in the low-debt regime and the low levels of financial stress regime the debt positively affects economic growth for each individual country. Besides, there is a negative and significant effect of debt on economic growth in the high-debt regime or the high levels of financial stress regime, respectively, in Greece and Portugal and in Belgium, Italy, and Japan. In the panels of countries, they find a significantly positive impact of debt on economic growth in the non-European Monetary Union (non-EMU) countries with the low debt-to-GDP ratio and in the northern and south EMU countries with the high debt-to-GDP ratio. And, the negative relationships between debt and economic growth are found in the EMU countries when the financial stress index is a threshold. Using the quartile dummy interaction variables, Abbas and Christensen (2010) analyze the nonlinear effects of debt on economic growth and find evidence of a Laffer curve (inverted U-shaped) relationship between domestic debt and economic growth. Besides, they also find that in the high-risk regime, a higher debt is related to a lower economic growth, but there is a positive effect of debt on economic growth in the low-risk regime.

III. METHODOLOGY

The two-regime PSTR model with fixed effects is defined as follows:

(1) [Y.sub.it] = [a.sub.i]+[b.sub.1][DEBT.sub.i,t]+[b.sub.2][DEBT.sub.i,t]g ([RISK.sub.i,t];[gamma],[theta]) + [[epsilon].sub.i,t],

where Y means economic growth; DEBT is the ratio of government debt to GDP; RISK represents the country risk indices including composite risk (COM), political risk (POL), financial risk (FIN), and economic risk (ECON), respectively; [epsilon] is the error term; t = 1,2,... ,T time periods; and i=1,2,... ,N individual countries. The function g([RISK.sub.i,t]; [gamma], [theta]) is a transition function of the observable variable [RISK.sub.i,t], continuous and bounded between 0 and 1.

Following Gonzalez, Terasvirta, and van-Dijk (2005) and Colletaz and Hurlin (2006), this study considers the following transition function:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [theta] = ([[theta].sub.1], .... [[theta].sub.m])' denotes a m-dimensional vector of location parameters. The parameter [gamma] determines the slope of the transition, and it determines the smoothness of the transition, that is, the speed of the transition from one regime to another. Furthermore, the restrictions [gamma] > 0 and [[theta].sub.1] [less than or equal to]... [less than or equal to] [[theta].sub.m] are imposed for identification.

The PSTR model has two main advantages as follows. First, it provides a parametric approach of the cross-country heterogeneity and the time instability of the coefficient of [DEBT.sub.i,t] switching smoothly based on the transition function g([RISK.sub.i,t];[gamma],[theta]). We define the combined coefficients of [DEBT.sub.i,t] for i-th country at time t as a weighted average of parameters ([b.sub.1],[b.sub.2]), respectively, as follows:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Second, the PSTR model allows for a continuum of an intermediate regime between two extremes. Due to heterogeneous beliefs, countries may not take actions instantly and identically at the same time. Thus, the PSTR model is more realistic for the different correlations between economic growth and debt for each country.

Besides, it is worth noting that if we only focus on the bivariate model, then the empirical results may suffer from omitted variable bias (Lutkepohl 1982). To improve omission variable bias, this study uses a multivariate model as follows:

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where the estimated transition function g([RISK.sub.i,t]; [gamma], [theta]) is obtained from the estimated results of Equation (1); I means investment; S is savings; INF represents inflation rate; POP is population growth; TO is trade openness. Similarly, in the estimation of the multivariate model, we specify lagged terms of each independent variable as the instrumental variables to improve the potential endogeneity bias by employing two-stage least squares (2SLS) regression approach.

IV. DATA AND EMPIRICAL RESULTS

A. Data Specifications

This study uses annual and unbalanced panel data covering 61 countries for the period 1985-2009. (3) To find out whether the different income levels and different debt levels have different relationships between public debt and economic growth, this study further classifies the countries into two income groups and two debt groups based on their income levels and debt levels. (4) Tables B1 and B2 of Appendix B list two income groups--27 high-income (US$12,276 or more) and 34 low-income (US$12,275 or less) countries--and two debt groups--38 high-debt (53.86 or more) and 23 low-income (53.85 or less) countries, respectively. Economic growth is the percentage growth rate of real GDP per capita obtained from the World Development Indicators (WDI) Database of the World Bank. Debt measured by the ratio of gross public debt to GDP comes from the Historical Public Debt Database of the Fiscal Affairs Department, International Monetary Fund.

Country risk data are obtained from the ICRG risk data constructed by the PRS Group. The ICRG rating contains 22 variables listed in Table B3 of Appendix B. Of 22 variables, 5 are for economic risk, 12 for political risk, and 5 for financial risk; composite risk is considered for all of the 22 variables. These indices assess a country's political stability, ability to finance its official, commercial, and trade debt obligations, its economic strengths and weaknesses on a comparable basis, and whole country risk, respectively. Composite and political risk ratings are from 0 (highest risk) to 100 (lowest risk), and economic and financial-risk ratings range from 0 (highest risk) to 50 (lowest risk). The control variables include investment measured in the ratio of gross fixed capital formation to GDP, savings measured in the ratio of gross saving to GDP, inflation rate, population growth, trade openness measured in the ratio of exports and imports to GDP, and all of them come from WDI. All variables are stationary. (5)

Tables 1 and 2 present the descriptive statistics and correlation coefficients of all variables, respectively. According to Table 1, per capita GDP growth of countries in this study range from -19.38% (Gabon in 1987) to 30.34% (Nigeria in 2004), and it is 1.87% on average. In our sample, Luxembourg records the lowest ratio of gross governmental debt to GDP (6.95%) on average. The results show that countries with high-income levels and with low-debt levels have relatively higher risk scores, suggesting that these countries lie in the relatively safer political, economic, and financial-risk environments. Furthermore, Table 1 also shows that high-income countries have a lower debt-GDP ratio than low-income countries, and economic growth is higher for countries with low debt-GDP ratio than for countries with high debt-GDP ratio confirmed by the results of Table 2. Table 2 shows a significantly negative relationship between economic growth and debt-GDP ratio, suggesting that a country increases its debt-GDP ratio, and then its economic growth will reduce. The positive and negative correlations of economic growth and country risk indices and of debt-GDP ratio and country risk indices show that a country lying in a lower risk environment can have a higher economic growth and a lower debt-GDP ratio. Besides, increases in investment, savings, and trade openness could stimulate economic growth; on the contrary, increases in inflation ratio and population growth would reduce economic growth.

B. Empirical Results

Results of the Bivariate Models. We firstly examine whether there is a regime-switching effect between public debt and economic growth by using the country risk indices, that is, composite, economic, political, and financial-risk indices, as thresholds. And then, we determine the number of transition functions to confirm the number of regimes in the PSTR model. The results of the three tests for a nonlinearity of the PSTR model are reported in Table 3. We find that the null hypothesis of linearity ([H.sub.0]: r = 0) can be rejected at the 1% significance level, but the null hypothesis of the PSTR model with two regimes cannot be rejected at the 5% significance level. This result indicates that the basic PSTR model is a two-regime model. That is, under the different country risk levels, there will be different relationships between economic growth and debt.

After confirming the existing nonlinear effect of country risk levels on the economic growth-debt nexus, the choice of the model with m = 1 or m = 2 should be further examined. The choice criterion is the PSTR model with m = 2 if the rejection of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the strongest one (the statistic [F.sub.2] is the largest one), otherwise the PSTR model with m= 1 is chosen. Table 4 shows that the statistic [F.sub.3] is the largest vis-a-vis other statistics when the PSTR model is used with composite, economic, and political risk indices as thresholds, and that for financial-risk index as a threshold, the statistic [F.sub.1] is the largest statistic. Thus, the PSTR model with m = 1 is chosen in this study.

Table 5 reports the estimated results of the PSTR model with four country risk indices including composite, economic, political, and financial-risk indices. As shown in Table 5, the estimated slope parameters ([gamma]) are small (0.3260, 0.3383, 1.3532, 0.2040) in all cases, suggesting that the transition function is continuous and smooth (see Figures 1A-1D). It implies that the effects of the country risk indices on the relationship between public debt and economic growth smoothly switch from one regime to another. In the first regime, when the values of transition variables ([RISK.sub.i,t]) are less than the estimated threshold values ([theta]), the transition functions (g) approach to zero, and then the coefficients of DEBT are given by [b.sub.1]. In the second regime, the transition functions approach to one when the values of the transition variables are larger than the estimated threshold values, and then the coefficients of DEBT are given by [b.sub.1]+[b.sub.2]g([RISK.sub.i,t];[gamma],[theta]).

By using the composite risk index as a threshold, the results show that in the high-risk regime with a lower ICRG risk score, the estimated coefficient of public debt is significantly negative (-0.0077) and turns into positive (0.0760) in the low-risk regime with a higher ICRG risk score. It suggests that an increase in public debt will harm economic growth for countries with higher whole country risks, whereas it can help stimulate economic growth when a country's whole country risk is lower. This finding is consistent with the results of Abbas and Christensen (2010). Next, we further classify the country risk into the economic, political, and financial risks. We can find that the estimated coefficients of public debt are negative and positive in high- and low-risk regimes in the economic and financial-risk cases, respectively, indicating that an increase in public debt can raise economic growth when the economic and financial risks transfer to a low-risk regime. As for using political risk index as a threshold, the negative impact of public debt on economic growth mitigates as the political risk decreases.

In summary, our results show that in the higher risk environments, if a country increases its public debt, then its economic growth will reduce. On the contrary, for a country with the lower country risks, an increase in public debt can help to stimulate its economic growth except when under a political risk environment. A policy implication emerges that if a country tends to raise its economic growth by way of raising public debt or reducing the negative impact of public debt on its economic growth, it should correspondingly stabilize its politics, increase the ability to finance its debt obligations, and strengthen its economy to reduce its country risk.

Results of the Multivariate Models and Subsamples. To improve omission variable bias, this study further considers five control variables, that is, investment, savings, inflation rate, population growth, and trade openness, into our estimation model. According to Table 6, the null hypotheses of F-test and Hausman test can be rejected at the 1% significance level, indicating that the fixed-effect model is more appropriate at each case. (6) The estimated coefficients of debt are roughly consistent with the results of the bivariate model, indicating the empirical results vary little. As for switching from a high-risk regime to a low-risk one, the negative impacts of public debt on economic growth diminish in the political and financial risks, and the impacts change from negative to positive in the composite and economic risks. As to the results of control variables, the results show that a country will have a lower economic growth with an increase in its population growth. Checherita-Westphal and Rother (2012), Kourtellos, Stengos, and Tan (2013), and Spilioti and Vamvoukas (2015) also find that an increase in population growth harms economic growth. However, our results show insignificant impacts of investment, savings, inflation, and trade openness on economic growth.

This study further investigates whether countries with different income and debt levels have different relationships between public debt and economic growth. Tables 7 and 8 show the empirical results of the multivariate models for highland low-income countries, respectively. For both income levels, we find that the estimated coefficients of debt are significantly positive under the regime of low composite and economic risks, suggesting that a country's economy grows as it increases public debt in the lower composite and economic risk environments. Besides, the results show that under the regime of the low composite and economic risk, the estimated coefficients of debt for high-income countries are smaller than those for low-income countries. This result suggests that when the whole country risk and economic risk is low, the sensitivity of the impact of public debt on economic growth is high for low-income countries but low for high-income countries.

The potential reason may be explained by the convergence hypothesis. The high-income countries have more per capita capital stock and more per capita real GDP than the low-income countries, and thus an increase in public debt will have a smaller effect on economic growth for the high-income countries. When regarding the political and financial-risk indices as threshold, the estimated coefficients of debt are insignificant for the high-income countries, but for the low-income countries they are significantly negative under the regime of high political and financial risks. The difference may be due to high-income countries having better political and financial systems than low-income countries.

Next, this study obtains the threshold value of the ratio of debt to GDP by estimating the equation: [Y.sub.i,t] = [[alpha], + [[beta].sub.1] [DEBT.sub.i,t] + [[beta].sub.2][DEBT.sub.i,t]g([DEBT.sub.i,t];[gamma],[theta]) + [e.sub.i,t] The estimated coefficients of DEBT are 0.0381 and -0.0018 in the first and second regimes, respectively, showing evidence of the different debt-growth nexus under low and high debt-GDP ratios. The estimated threshold value is 53.85%. Under a low debt-GDP ratio, an increase in debt can enhance economic growth; however, when the debt-GDP ratio exceeds 53.58%, economic growth will be reduced as debt rises. The results also imply that countries with low and high debt-GDP ratios may have different characteristics. We then classify our sample into high- and low-debt countries based on this value. Tables 9 and 10 report the empirical results of the multivariate models for high- and low-debt countries, respectively. We can find that the estimated coefficients of debt are smaller for the high-debt countries than those for the low-debt countries, suggesting that the high-debt countries have a smaller sensitivity of economic growth with respect to a change in debt compared to the low-debt countries. It implies that the impact of public debt on economic growth becomes small in the higher ratio of public debt to GDP. Besides, for both highland low-debt countries, the coefficient's signs of the debt are consistent. An increase in public debt will reduce economic growth in the regime of the high composite and economic risks, but it can instead stimulate economic growth in the regime of the low composite and economic risks. As to the political and financial-risk cases, the results show a negative impact of public debt on economic growth under the higher risk levels, whereas the impacts will diminish or disappear under the lower risk levels. It suggests that the negative impacts of public debt on economic growth will be weakened as the political and financial-risks decrease.

V. CONCLUDING REMARKS

As an important impact of public debt on economic growth rises especially for the period of financial and economic crises, there are many empirical studies that investigate the relationship between public debt (i.e., external and/or internal debt) and economic growth. Most of the studies on the nonlinear debt-growth nexus use models with the debt-to-GDP ratio as a threshold to find evidence of an inverted U-shaped relationship between them, suggesting a higher debt results in a lower economic growth. Contrary to these, this study analyzes whether the public debt impacts the economic growth differently under different levels of the country risks. To this end, we employ the advanced PSTR model with the country risk indices, that is, the composite, economic, political, and financial-risk indices, as the thresholds to estimate the nonlinear relationship between public debt and economic growth for a panel of 61 countries.

The empirical results are summarized as follows. First, in the bivariate PSTR model, the results show that there are the different relationships between public debt and economic growth under the different country risk environments. In the high-risk regime, a higher level of public debt results in a lower economic growth. But, a country with the low composite, economic, and financial-risk environments increases its public debt, and this leads to a higher economic growth. When the political risk switches to a low-risk regime, the negative impact of public debt on economic growth mitigates. This result is roughly confirmed by the results of the multivariate models.

Second, for countries with the high- and low-income levels, an increase in public debt can stimulate economic growth in the regime of low composite and economic risks but harm economic growth in the regime of high ones. The sensitivity of the impacts of public debt on economic growth is higher for the low-income countries than for the high-income countries. Additionally, in the political and financial risks, no evidence of the debt-growth nexus is found in the high-income countries, but the relations are significantly negative in the high political and financial risks.

Third, for countries with the high- and low-debt levels, the results show a smaller sensitivity of economic growth with respect to a change in the public debt levels in the high-debt countries as compared with the low-debt countries. In the high-risk environments, an increase in public debt can harm economic growth, regardless of the levels of public debt. There is a positive relationship between public debt and economic growth in the low levels of the whole and economic risks, whereas the negative impacts of public debt on economic growth for a country with the low political and financial risks reveal the inverse relationship.

The policy implications of our results illustrate that first, to reduce country risk by stabilizing the country's politics and policies, by raising the ability to finance debt obligations and strengthening economy, a country can grow its economy by way of an increase in its public economy. Second, the impacts of public debt on economic growth are different for countries with different income and public debt levels and in the different risk environments. In order not to harm economic growth, a country should borrow appropriately based on its economic situation and risk environment.

APPENDIX A

THE ESTIMATION PROCEDURE OF THE PSTR MODEL

For the nonlinearity test, the null hypothesis of linearity is [H.sub.0].[gamma] = 0, which indicates that our model is a linear model. However, the classical tests have no standard distribution when the PSTR model is unidentified under the null hypothesis--this is the so-called Davies Problem (Davies 1977). To solve this problem we replace the transition function g([DEBT.sub.i,t]; [gamma], [theta]) by its first-order Taylor expansion around the null hypothesis [gamma] = 0. After re-parameterization, the auxiliary regression based on m = 1 and m = 2, respectively, can be written as:

(A1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where parameter vectors [b*.sub.2] and [b**.sub.2] are multiples of [gamma], [[LAMBDA].sub.0. = g([RISK.sub.i,t];[gamma] = 0,[theta]) = 1/2, and [u.sub.i,t] = [[epsilon].sub.i,t] + R([RlSK.sub.i,t];[gamma],[theta]). and where R([RISK.sub.i,t]; [gamma], [theta]) is the remainder of the Taylor expansion.

To test the linearity against the PSTR model, following Colletaz and Hurlin (2006), this study applies the Lagrange multiplier (LM), F-version LM. and pseudo-LR tests and their statistics are defined as follows:

(A3) LM = TN ([SSR.sub.0] - [SSR.sub.1]) /[SSR.sub.0],

(A4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A5) LR = -2 [log [SSR.sub.1] - log [SSR.sub.0]].

Here, [SSR.sub.0] is the panel sum of squared residuals under [H.sub.0] (linear panel model with individual effects), [SSR.sub.1] is the panel sum of squared residuals under [H.sub.1] (PSTR model with two regimes), and K is the number of explanatory variables. (7) If we reject the linearity hypothesis, then we can further test whether there are other transition functions by testing the null hypothesis of no further additive nonlinearity.

We next eliminate the individual effects [a.sub.i] by removing individual-specific means. The individual means in Equation (1) are expressed as follows:

(A6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [[bar.[Y.sub.i]] [[bar.[DEBT.sub.i]], [[bar.[w.sub.i]]([gamma], [theta]), and [[bar.[[epsilon].sub.i] are individual means. Subtracting Equation (A6) from Equation (1) yields:

(A7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In order to improve the potential endogeneity bias, we adopt the instrumental variable estimators, which are [Z.sub.i,t] = ([DEBT.sub.i,t],... , [DEBT.sub.i.t-j]) in our study. Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Given a couple ([gamma],[theta]), the estimate can then be yielded by using the instrumental variables as follows:

(A8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

APPENDIX B

See Tables B1 to B4.
List of Countries Classified into 27 High-Income and 34 Low-Income
Countries

27 High-Income Countries

Australia  Ireland      Portugal
Austria    Israel       Spain
Belgium    Italy        Sweden
Canada     Japan        Switzerland
Denmark    South Korea  U.K.
Finland    Luxembourg   United States
France     Netherlands  Uruguay
Germany    New Zealand
Greece     Norway
Iceland    Oman

34 Low-Income Countries

Algeria         Honduras    Panama
Bangladesh      Indonesia   Papua New Guinea
Bolivia         Kenya       Paraguay
Botswana        Madagascar  Peru
Brazil          Malawi      Philippines
China           Malaysia    South Africa
Dominican Rep.  Mexico      Sri Lanka
Ecuador         Morocco     Sudan
El Salvador     Nicaragua   Thailand
Ethiopia        Niger       Togo
Gabon           Nigeria
Gambia          Pakistan

Notes: Countries are divided according to 2919 gross national income
(GNI) per capita, calculated using the World Bank Atlas method. The
two groups include: low income, $12,275 or less; and high income,
$12,276 or more.

TABLE B2
List of Countries Classified into 38 High-Debt and 23 Low-Debt
Countries

38 High-Debt Countries

Algeria         Greece            Niger
Austria         Honduras          Nigeria
Belgium         Ireland           Pakistan
Bolivia         Israel            Panama
Brazil          Italy             Philippines
Canada          Japan             Portugal
Denmark         Kenya             Sri Lanka
Dominican Rep.  Madagascar        Sudan
Ecuador         Malawi            Sweden
Ethiopia        Malaysia          Togo
Gabon           Morocco           United States
Gambia          New Zealand       Uruguay
Germany         Nicaragua

23 Low-Debt Countries

Australia       Indonesia         Paraguay
Bangladesh      South Korea       Peru
Botswana        Luxembourg        South Africa
China           Mexico            Spain
El Salvador     Netherlands       Switzerland
Finland         Norway            Thailand
France          Oman              U.K.
Iceland         Papua New Guinea

Notes: Countries are divided according to the threshold value 53.85
which is obtained by the PSTR model with the ratio of debt to GDP as a
threshold. The two groups include: low debt, 53.85 or less; and high
debt, 53.86 or more.

TABLE B3
Risk Components of ICRG Risk Rating

Economic risk
GDP per head
Real GDP growth
Annual inflation rate
Budget balance as a percentage of GDP
Current account as a percentage of GDP
Political risk
Government stability
Socioeconomic conditions
Investment profile
Internal conflict
External conflict
Corruption
Military in politics
Religious tensions
Law and order
Ethnic tensions
Democratic accountability
Bureaucracy quality
Financial risk
Foreign debt as a percentage of GDP
Foreign debt service as a percentage of exports of goods and services
Current account as a percentage of exports of goods and services
Net international liquidity as months of import cover
Exchange rate stability

Source: International country risk guide (ICRG).

TABLE B4
Results of the Maddala and Wu ADF Panel Unit-Root Tests

Variable               Y             DEBT          COM

                       617.73 (***)  360.59 (***)  436.45 (***)
                        (0.000)       (0.000)       (0.000)
High-income countries
                       221.70 (***)  135.15 (***)  197.26 (***)
                        (0.000)       (0.000)       (0.000)
Low-income countries
                       396.02 (***)  225.44 (***)  239.19 (***)
                        (0.000)       (0.000)       (0.000)
High-debt countries
                       399.47 (***)  217.59 (***)  264.47 (***)
                        (0.000)       (0.000)       (0.000)
Low-debt countries
                       218.26 (***)  143.00 (***)  171.98 (***)
                        (0.000)       (0.000)       (0.000)

Variable               ECO           POL           FIN

                       462.26 (***)  441.53 (***)  352.13 (***)
                        (0.000)       (0.000)       (0.000)
High-income countries
                       164.82 (***)  203.41 (***)  140.93 (***)
                        (0.000)       (0.000)       (0.000)
Low-income countries
                       297.43 (***)  238.12 (***)  211.20 (***)
                        (0.000)       (0.000)       (0.000)
High-debt countries
                       280.38 (***)  276.57 (***)  203.20 (***)
                        (0.000)       (0.000)       (0.000)
Low-debt countries
                       181.87 (***)  164.96 (***)  148.93 (***)
                        (0.000)       (0.000)       (0.000)

Variable               I             S             INF

                       447.90 (***)  416.04 (***)  537.40 (***)
                        (0.000)       (0.000)       (0.000)
High-income countries
                       223.35 (***)  182.31 (***)  201.06 (***)
                        (0.000)       (0.000)       (0.000)
Low-income countries
                       224.56 (***)  233.72 (***)  336.34 (***)
                        (0.000)       (0.000)       (0.000)
High-debt countries
                       279.19 (***)  239.54 (***)  341.59 (***)
                        (0.000)       (0.000)       (0.000)
Low-debt countries
                       168.71 (***)  176.50 (***)  195.81 (***)
                        (0.000)       (0.000)       (0.000)

Variable               POP           TO

                       614.33 (***)  352.96 (***)
                        (0.000)       (0.000)
High-income countries
                       232.84 (***)  161.87 (***)
                        (0.000)       (0.000)
Low-income countries
                       381.49 (***)  191.09 (***)
                        (0.000)       (0.000)
High-debt countries
                       390.24 (***)  227.81 (***)
                        (0.000)       (0.000)
Low-debt countries
                       224.09 (***)  125.15 (***)
                        (0.000)       (0.000)

Notes: The model with drift is used. The null hypothesis is that the
variable has a unit root. P values are in parentheses.
(***)Indicates the 1% significance level.


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YI-BIN CHIU and CHIEN-CHIANG LEE (*)

(*) The authors are grateful to the Editor and four anonymous referees for helpful comments and suggestions.

Chiu: Doctor, School of Business Administration. Southwestern University of Finance and Economics, Chengdu, 611130, China. Phone +86-28-87092184, Fax +86-28-87092768, E-mail yibin.chiu@gmail.com

Lee: Doctor, Department of Finance, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan. Phone +886-7-5252000, Fax +886-7-5254899, E-mail cclee@cm.nsysu.edu.tw

ABBREVIATIONS

2SLS: Two-Stage Least Squares

ADF: Augmented Dickey-Fuller

ARDL: Autoregressive Distributed Lag

EMU: European Monetary Union

FMOLS: Fully Modified Ordinary Least Squares

GDP: Gross Domestic Product

GNI: Gross National Income

ICRG: International Country Risk Guide

LM: Lagrange Multiplier

OECD: Organization for Economic Co-operation and Development

OLS: Ordinary Least Squares

PSTR: Panel Smooth Transition Regression

VAR: Vector Autoregressions

WDI: World Development Indicators

(1.) Fiscal space is the distance between debt limit and current debt level (Ghosh et al. 2013).

(2.) These 14 countries include Australia. Austria, Finland. Germany, Greece, Japan, the Netherlands, Spain. Sweden, the United States, and the United Kingdom.

(3.) The selected countries are based on data availability for all variables. We delete the countries which have a loss of more data in one or two more variables used in this study.

(4.) According to 2010 gross national income (GNI) per capita using the World Bank Atlas method, countries with an income level of US$12,276 or more belong to the high-income countries, while the low-and middle-income countries have income levels of US$12,275 or less. Besides, we use the PSTR model: [Y.sub.i,t] = [[alpha].sub.i] + [[beta].sub.1][DEBT.sub.i,t] + [[beta].sub.2][DEBT.sub.i,t]g([DEBT.sub.i,t]; [gamma], [theta]) + [e.sub.i,t] to estimate the threshold value of debt, which is 53.85%.

(5.) The Augmented Dickey-Fuller (ADF) panel unil-root test developed by Maddala and Wu (1999). which is more suitable to examine the unbalanced panel data than other tests, is used. In our study, the model with drift is used. According to Table 3, the null hypothesis of a unit root can be rejected at the 1% significance level.

(6.) The null hypothesis of the F-test is using the panel ordinary least squares (OLS) model, and the null hypothesis of the Hausman test is using the random-effect model.

(7.) The LM and pseudo-LR statistics have a chi-square distribution with mK degrees of freedom, while the F statistics have an approximate F(mK, TN - N - m(K + 1)) distribution.
TABLE 1
Descriptive Statistics of Variables in Levels

                       Economic  Debt     Composite  Economic
                       Growth    (DEBT,   Risk       Risk
Variables              (Y, %)    %)       (COM)      (ECO)

Mean                     1.87      66.91  69.83      35.46
SD                       3.83      70.71  13.75       6.29
Maximum                 30.34    2092.92  94.00      48.50
Minimum                -19.38       3.24  23.00       1.00
High-income countries
Mean                     2.09      59.37  80.90      39.22
SD                       2.78      33.10   7.21       4.07
Maximum                 11.77     210.25  94.00      48.50
Minimum                 -8.71       4.00  48.50      18.50
Low-income countries
Mean                     1.69      72.99  61.04      32.47
SD                       4.49      89.82  11.10       6.14
Maximum                 30.34    2092.92  84.75      45.00
Minimum                -19.38       3.24  23.00       1.00
High-debt countries
Mean                     1.48      84.63  67.09      34.24
SD                       3.82      83.90  13.96       6.50
Maximum                 30.34    2092.92  92.00      47.50
Minimum                -19.38       8.07  23.00       1.00
Low-debt countries
Mean                     2.51      38.13  74.35      37.48
SD                       3.77      18.77  12.11       5.35
Maximum                 15.79     108.27  94.00      48.50
Minimum                -14.39       3.24  34.50      18.00

                       Political  Financial
                       Risk       Risk       Investment
Variables              (POL)      (FIN)      (I, %)

Mean                   67.96      36.12      21.38
SD                     15.97       8.31       5.92
Maximum                97.00      50.00      46.10
Minimum                13.00       6.00       4.56
High-income countries
Mean                   81.43      41.01      22.46
SD                      9.07       5.63       3.93
Maximum                97.00      50.00      36.06
Minimum                36.00      21.00       9.63
Low-income countries
Mean                   57.27      32.23      20.51
SD                     11.57       8.04       7.02
Maximum                78.50      50.00      46.10
Minimum                13.00       6.00       4.56
High-debt countries
Mean                   65.27      34.58      20.46
SD                     16.11       8.46       5.82
Maximum                94.00      50.00      46.10
Minimum                13.00       6.00       4.56
Low-debt countries
Mean                   72.41      38.65      22.94
SD                     14.72       7.39       5.77
Maximum                97.00      50.00      45.96
Minimum                28.00      12.00      12.02

                                                   Population  Trade
                        Saving          Inflation  Growth      Openness
Variables              (S, %) (INF, %)             (POP, %)    (TO, %)

Mean                    21.15              32.66    1.55        69.16
SD                       9.25             390.70    1.05        40.21
Maximum                 57.86           11749.64    6.10       349.85
Minimum                -24.00             -11.69   -1.61        10.75
High-income countries
Mean                    22.03               5.43    0.77        72.62
SD                       5.99              15.51    0.74        44.18
Maximum                  0.01             304.58    6.02       349.85
Minimum                 40.50              -4.48   -0.43        15.92
Low-income countries
Mean                    20.44              53.89    2.16        66.38
SD                      11.13             520.20    0.82        36.51
Maximum                 57.86           11749.64    6.10       220.41
Minimum                -24.00             -11.69   -1.61        10.75
High-debt countries
Mean                    19.23              34.74    1.70        66.87
SD                       9.06             412.59    1.13        36.59
Maximum                 57.86           11749.64    6.10       220.41
Minimum                -24.00             -11.69   -1.61        10.75
Low-debt countries
Mean                    24.30              29.15    1.29        73.04
SD                       8.68             351.11    0.83        45.44
Maximum                 53.35            7481.66    4.63       349.85
Minimum                  0.01              -1.41   -0.30        13.18

TABLE 2
Coefficients of the Correlation Matrix for Full Sample (61 countries)

      Y              DEBT           COM            ECO

Y     1
DEBT  -0.1716 (***)  1
      (0.000)
COM    0.2106 (***)  -0.3028 (***)  1
      (0.000)        (0.000)
ECO    0.3176 (***)  -0.3742 (***)   0.8327 (***)  1
      (0.000)        (0.000)        (0.000)
POL    0.1222 (***)  -0.2221 (***)   0.9448 (***)   0.6787 (***)
      (0.000)        (0.000)        (0.000)        (0.000)
FIN    0.2238 (***)  -0.2873 (***)   0.8629 (***)   0.6964 (***)
      (0.000)        (0.000)        (0.000)        (0.000)
I      0.2650 (***)  -0.1859 (***)   0.3706 (***)   0.3395 (***)
      (0.000)        (0.000)        (0.000)        (0.000)
s      0.3097 (***)  -0.3104 (***)   0.4228 (***)   0.5201 (***)
      (0.000)        (0.000)        (0.000)        (0.000)
INF   -0.1041 (***)   0.0839 (***)  -0.1331 (***)  -0.1634 (***)
      (0.000)        (0.001)        (0.000)        (0.000)
POP   -0.1793 (***)   0.1279 (***)  -0.6686 (***)  -0.5070 (***)
      (0.000)        (0.000)        (0.000)        (0.000)
TO     0.0689 (***)  -0.0999 (***)   0.3044 (***)   0.3295 (***)
      (0.007)        (0.000)        (0.000)        (0.000)

      POL            FIN            I              S

Y
DEBT

COM

ECO

POL   1

FIN    0.6913 (***)  1
      (0.000)
I      0.3118 (***)   0.3688 (***)  1
      (0.000)        (0.000)
s      0.2876 (***)   0.4541 (***)   0.6019 (***)  1
      (0.000)        (0.000)        (0.000)
INF   -0.0976 (***)  -0.1335 (***)  -0.0548**      -0.0579 (**)
      (0.000)        (0.000)        (0.036)        (0.030)
POP   -0.6542 (***)  -0.5704 (***)  -0.2625 (***)  -0.2492 (***)
      (0.000)        (0.000)        (0.000)        (0.000)
TO     0.2826 (***)   0.2353 (***)   0.1263 (***)   0.2913 (***)
      (0.000)        (0.000)        (0.000)        (0.000)

      INF            POP      TO

Y
DEBT

COM

ECO

POL

FIN

I

s

INF   1

POP    0.0405        1
      (0.120)
TO    -0.0679 (***)  -0.0213  1
      (0.009)        (0.408)

Notes: P values are in parentheses. (***) and (**) indicate the 1% and
5% significance levels, respectively.

TABLE 3
Tests for Remaining Nonlinearity of the PSTR

                                             Model
Model                               (1)           (2)

Threshold
Variable                            COM           ECO
[H.sub.0]:r = 0 vs [H.sub.1] :r=1
LM                                  39.349 (***)  104.205 (***)
                                    (0.000)        (0.000)
LM,                                 12.840 (***)   35.851 (***)
                                    (0.000)        (0.000)
LR                                  40.003 (***)  108.430 (***)
                                    (0.000)        (0.000)
[H.sub.0]:r= 1 vs [H.sub.1] :r = 2
LM                                   2.430          2.743
                                    (0.119)        (0.098)
L[M.sub.F]                           2.306          2.618
                                    (0.129)        (0.106)
LR                                   2.433          2.745
                                    (0.119)        (0.098)


Model                               (3)           (4)

Threshold
Variable                            POL           FIN
[H.sub.0]:r = 0 vs [H.sub.1] :r=1
LM                                  44.676 (***)  24.204 (***)
                                    (0.000)       (0.000)
LM,                                 14.660 (***)   7.827 (***)
                                    (0.000)       (0.000)
LR                                  45.473 (***)  24.423 (***)
                                    (0.000)       (0.000)
[H.sub.0]:r= 1 vs [H.sub.1] :r = 2
LM                                   1.188         1.173
                                    (0.276)       (0.279)
L[M.sub.F]                           1.130         1.119
                                    (0.288)       (0.290)
LR                                   1.189         1.174
                                    (0.276)       (0.279)

Notes: Under [H.sub.0], the LM and LR statistics have an asymptotic
[chi square](mK) distribution, whereas the L[M.sub.F] has an
asymptotic F(mK, TN - N - m(K + 1)) distribution. Moreover, r is the
number of transition function. P values are in parentheses.
(***) Indicates the 1 % significance level.

TABLE 4
Tests for Choosing the PSTR Model

Model                                                      (1)
Threshold Variable                                         COM

[F.sub.3]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:
[[delta].sub.3], = 0)                                       7.187 (***)
                                                           (0.000)
[F.sub.2]
([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:
[[delta].sub.2]=0|[[delta].sub.3] =0)                       3.243 (**)
                                                           (0.021)
[F.sub.1]                                                   2.293 (*)
([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],:
[[delta].sub.1] =0| [[delta].sub.2]= [[delta].sub.3] = 0)
                                                           (0.076)

Model                                                      (2)
Threshold Variable                                         ECO

[F.sub.3]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:
[[delta].sub.3], = 0)                                      20.437 (***)
                                                           (0.000)
[F.sub.2]
([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:
[[delta].sub.2]=0|[[delta].sub.3] =0)                       9.907 (***)
                                                           (0.000)
[F.sub.1]                                                   4.715 (***)
([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],:
[[delta].sub.1] =0| [[delta].sub.2]= [[delta].sub.3] = 0)
                                                           (0.003)

Model                                                      (3)
Threshold Variable                                         POL

[F.sub.3]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:
[[delta].sub.3], = 0)                                       8.444 (***)
                                                           (0.000)
[F.sub.2]
([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:
[[delta].sub.2]=0|[[delta].sub.3] =0)                       2.447 (*)
                                                           (0.062)
[F.sub.1]                                                   3.628**
([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],:
[[delta].sub.1] =0| [[delta].sub.2]= [[delta].sub.3] = 0)
                                                           (0.013)

Model                                                      (4)
Threshold Variable                                         FIN

[F.sub.3]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:
[[delta].sub.3], = 0)                                       0.995
                                                           (0.394)
[F.sub.2]
([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]:
[[delta].sub.2]=0|[[delta].sub.3] =0)                       0.547
                                                           (0.650)
[F.sub.1]                                                   6.271 (***)
([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],:
[[delta].sub.1] =0| [[delta].sub.2]= [[delta].sub.3] = 0)
                                                           (0.000)

Notes: [F.sub.1], [F.sub.2], and [F.sub.3] have an asymptotic
F(mK,TN-N-m(K+1)) distribution. The PSTR model with m = 2 is chosen if
the rejection of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
is the strongest one, otherwise the PSTR model with m = 1 is chosen.
P values are in parentheses.
(***), (**), and (*) indicate the 1%, 5%, and 10% significance levels.
respectively. The decision on the choice between the PSTR model with
m = 1 and m = 2 is indicated in the last row.

TABLE 5
Estimated Results of the PSTR Model

Model                (1)            (2)            (3)
Threshold
Variable             COM            ECO            POL

DEBT                 -0.0077 (*)    -0.0092 (**)   -0.0287 (***)
                     (0.0041)       (0.0040)       (0.0054)
DEBT*g                0.0837 (***)   0.1006 (***)   0.0259 (***)
                     (0.0137)       (0.0098)       (0.0047)
Location             83.9794        40.4959        40.3495
parameters, [theta]
Slope                 0.3260         0.3383         1.3532
parameters, [gamma]

Model                (4)
Threshold
Variable             FIN

DEBT                 -0.0347 (***)
                     (0.0066)
DEBT*g                0.0357 (***)
                     (0.0082)
Location             15.5000
parameters, [theta]
Slope                 0.2040
parameters, [gamma]

Notes: The standard errors (S.E.) are corrected for
heteroskedasticity. S.E. are in parentheses.
(***), (**), and (*) indicate the 1%, 5%, and 10% significance levels,
respectively.

TABLE 6
Estimated Results of the Multivariate Model for Full Sample

Threshold
Variable                COM              ECO
Model                   FE               FE

DEBT                      -0.0376 (***)    -0.0354 (***)
                          (0.0065)         (0.0059)
DEBT*g                     0.0963 (***)     0.1112 (***)
                          (0.0157)         (0.0117)
I                          0.0003           0.0548
                          (0.0467)         (0.0436)
S                         -0.0120          -0.0581
                          (0.0427)         (0.0389)
INF                       -0.0012          -0.0010
                          (0.0009)         (0.0009)
POP                       -1.13]9 (***)    -0.7755 (**)
                          (0.3340)         (0.3214)
TO                        -0.0150          -0.022 (**)
                          (0.0110)         (0.0106)
C                          6.2402 (***)     5.1331 (***)
                          (1.4867)         (1.3985)
Number of observations  1071             1093
F-test (p value)           0.0000           0.0000
Hausman test (p value)     0.0000           0.0000

Threshold
Variable                POL              FIN
Model                   FE               FE

DEBT                      -0.0508 (***)    -0.0588 (***)
                          (0.0095)         (0.0141)
DEBT*g                     0.0243 (***)     0.0348 (**)
                          (0.0074)         (0.0155)
I                         -0.0426          -0.0466
                          (0.0469)         (0.0440)
S                          0.0156           0.0028
                          (0.0405)         (0.0360)
INF                       -0.0012          -0.0012
                          (0.0009)         (0.0009)
POP                       -1.0759 (***)    -0.8402 (***)
                          (0.3382)         (0.3099)
TO                        -0.0174          -0.0144
                          (0.0111)         (0.0104)
C                          7.0043 (***)     6.7498 (***)
                          (1.5258)         (1.4063)
Number of observations  1082             1158
F-test (p value)           0.0000           0.0000
Hausman test (p value)     0.0000           0.0001

Notes: The standard errors (S.E.) are in parentheses. C is the
constant term. FE means the fixed-effect model. To reject the
hypotheses of F-test and Hausman test means that the fixed-effect
model is more appropriate.
(***) and (**) indicate the 1% and 5% significance levels,
respectively.

TABLE 7
Estimated Results of the Multivariate Model for High-Income Countries

Threshold Variable      COM             ECO             POL
Model                   FE              FE              FE

DEBT                     -0.0241 (**)    -0.0287 (***)   -0.0095
                         (0.0101)        (0.0086)        (0.0131)
DEBT*g                    0.0847 (***)    0.0950 (***)    0.0033
                         (0.0121)        (0.0102)        (0.0112)
I                         0.1551 (**)     0.1513 (**)     0.0659
                         (0.0759)        (0.0651)        (0.0748)
S                         0.1440 (***)    0.0852 (*)      0.2703 (***)
                         (0.0511)        (0.0485)        (0.0471)
INF                       0.0146          0.0405 (***)    0.0030
                         (0.0169)        (0.0155)        (0.01735)
POP                      -2.2932 (***)   -1.7793 (***)   -1.8728 (***)
                         (0.4140)        (0.3693)        (0.4098)
TO                       -0.0211 (**)    -0.0340 (***)   -0.0241 (**)
                         (0.0107)        (0.0101)        (0.0110)
C                        -2.0483         -0.4729         -2.1469
                         (2.4488)        (2.1890)        (2.4772)
Number of observations  497             547             522
F-test (p value)          0.0000          0.0000          0.0000
Hausman test (p value)    0.0000          0.0000          0.0000

Threshold Variable      FIN
Model                   FE

DEBT                     -0.0168
                         (0.0992)
DEBT*g                    0.0082
                         (0.1015)
I                         0.0741
                         (0.0780)
S                         0.2495 (***)
                         (0.0489)
INF                       0.0057
                         (0.0171)
POP                      -1.9623 (***)
                         (0.4309)
TO                       -0.0240 (**)
                         (0.0121)
C                        -1.6838
                         (2.5354)
Number of observations  518
F-test (p value)          0.0000
Hausman test (p value)    0.0000

Notes: The standard errors (S.E.) are in parentheses. C is the
constant term. FE means the fixed-effect model. To reject the
hypotheses of F-test and Hausman test means that the fixed-effect
model is more appropriate.
(***), (**), and (*) indicate the 1%, 5%, and 10% significance levels,
respectively.

TABLE 8
Estimated Results of the Multivariate Model for Low-Income Countries

Threshold Variable      COM             ECO             POL
Model                   FE              FE              FE

DEBT                     -0.0361 (***)   -0.0392 (***)   -0.0655 (***)
                         (0.0058)        (0.0077)        (0.0122)
DEBT*g                    0.6818 (***)    0.1215 (***)    0.0326 (***)
                         (0.1838)        (0.0266)        (0.0091)
I                         0.0002         -0.0347         -0.0448
                         (0.0598)        (0.0563)        (0.0596)
S                        -0.0525         -0.0669         -0.0702
                         (0.0569)        (0.0488)        (0.0508)
INF                      -0.0012         -0.0013         -0.0011
                         (0.0011)        (0.0011)        (0.0011)
POP                      -0.0740          0.0386          0.0324
                         (0.5045)        (0.4045)        (0.4463)
TO                        0.0089          0.0123          0.0086
                         (0.0179)        (0.0156)        (0.0170)
C                         4.5250 (***)    4.7800 (**)     6.0084 (***)
                         (2.1487)        (1.899)         (2.0795)
Number of observations  602             676             639
F-test (p value)          0.0000          0.0000          0.0000
Hausman test (p value)    0.0336          0.0162          0.0002

Threshold Variable      FIN
Model                   FE

DEBT                     -0.0652 (***)
                         (0.0161)
DEBT*g                    0.0371 (**)
                         (0.0187)
I                        -0.0833
                         (0.0573)
S                        -0.0213
                         (0.0486)
INF                      -0.0018
                         (0.0011)
POP                       0.0056
                         (0.4134)
TO                        0.0084
                         (0.0159)
C                         5.5536 (***)
                         (1.9203)
Number of observations  676
F-test (p value)          0.0000
Hausman test (p value)    0.0006

Notes: The standard errors (S.E.) are in parentheses. C is the
constant term. FE means the fixed-effect model. To reject the
hypotheses of f-test and Hausman test means that the fixed-effect
model is more appropriate.
(***) and (**) indicate the 1% and 5% significance levels,
respectively.

TABLE 9
Estimated Results of the Multivariate Model for High-Debt Countries

Threshold Variable      COM             ECO             POL
Model                   FE              FE              FE

DEBT                     -0.0356 (***)   -0.0391 (***)   -0.0536 (***)
                         (0.0072)        (0.0066)        (0.0108)
DEBT*g                    0.0865 (***)    0.0892 (***)    0.0272 (***)
                         (0.0190)        (0.0141)        (0.0082)
I                        -0.0907         -0.1292 (**)    -0.1299 (**)
                         (0.0586)        (0.0548)        (0.0617)
S                        -0.0274         -0.0528         -0.0097
                         (0.0496)        (0.0435)        (0.0499)
INF                       0.0004          0.0016          0.0005
                         (0.0018)        (0.0018)        (0.0017)
POP                      -1.1778 (**)    -0.5553         -1.0108 (**)
                         (0.4555)        (0.3663)        (0.4595)
TO                        0.0160          0.0118          0.0162
                         (0.0154)        (0.0135)        (0.0155)
C                         6.6858 (***)    6.9584 (***)    7.1236 (***)
                         (1.8258)        (1.6608)        (1.9030)
Number of observations  664             750             657
F-test (p value)          0.0000          0.0000          0.0000
Hausman test (p value)    0.0000          0.0000          0.0000

Threshold Variable      FIN
Model                   FE

DEBT                     -0.0489 (***)
                         (0.0162)
DEBT*g                    0.0270
                         (0.0177)
I                        -0.0862
                         (0.0589)
S                        -0.0084
                         (0.0477)
INF                       0.0004
                         (0.0017)
POP                      -0.9457 (**)
                         (0.4678)
TO                        0.0144
                         (0.0152)
C                         5.8959 (***)
                         (1.8112)
Number of observations  666
F-test (p value)          0.0001
Hausman test (p value)    0.0013

Notes: The standard errors (S.E.) are in parentheses. C is the
constant term. FE means the fixed-effect model. To reject the
hypotheses of F-test and Hausman test means that the fixed-effect ]
model is more appropriate.
(***) and (**) indicate the 1% and 5% significance levels,
respectively.

TABLE 10
Estimated Results of the Multivariate Model for Low-Debt Countries

Threshold Variable      COM             ECO             POL
Model                   FE              FE              FE

DEBT                     -0.0687 (***)   -0.0796 (***)   -0.0737 (***)
                         (0.0189)        (0.0166)        (0.0258)
DEBT*g                    0.1359 (***)    0.1676 (***)    0.0447**
                         (0.000)         (0.0226)        (0.0227)
I                         0.0754          0.0916          0.0227
                         (0.0728)        (0.0690)        (0.0735)
S                         0.0152         -0.0276          0.1158
                         (0.0790)        (0.0707)        (0.07128)
INF                      -0.0021 (**)    -0.0021 (**)    -0.0022 (**)
                         (0.0009)        (0.0009)        (0.0009)
POP                      -1.1545 (**)    -0.6521         -0.7459
                         (0.4485)        (0.4153)        (0.4552)
TO                       -0.0378 (**)    -0.0458 (***)   -0.0404 (***)
                         (0.0146)        (0.0136)        (0.0150)
C                         5.6676 (**)     5.9070 (**)     4.0193
                         (2.6205)        (2.4262)        (2.5849)
Number of observations  435             473             454
F-test (p value)          0.0000          0.0000          0.0009
Hausman test (p value)    0.0000          0.0000          0.0601

Threshold Variable      FIN
Model                   FE

DEBT                     -0.0949 (**)
                         (0.0418)
DEBT*g                    0.0663
                         (0.0447)
I                        -0.0070
                         (0.07135)
S                         0.1209 (*)
                         (0.0680)
INF                      -0.0025 (***)
                         (0.0009)
POP                      -0.5650
                         (0.4457)
TO                       -0.0380 (***)
                         (0.0143)
C                         4.2882 (*)
                         (2.5073)
Number of observations  473
F-test (p value)          0.0005
Hausman test (p value)    0.0163

Notes: The standard errors (S.E.) are in parentheses. C is the
constant term. FE means the fixed-effect model. To reject the
hypotheses of f-test and Hausman test means that the fixed-effect
model is more appropriate.
(***), (**), and (*) indicate the 1%, 5%, and 10% significance levels,
respectively.
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Author:Chiu, Yi-Bin; Lee, Chien-Chiang
Publication:Contemporary Economic Policy
Article Type:Report
Date:Oct 1, 2017
Words:10563
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