Threshold Effect of Debt_to_GDP Ratio on GDP per Capita

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investigated extensively recently. This paper employs panel threshold regression model to investigate the panel threshold effect of debt/GDP ratio on GDP per ...
Threshold Effect of Debt_to_GDP Ratio on GDP per Capita with Panel Threshold Regression Model： The Case of OECD Countries Tsangyao Chang Department of Finance, Feng Chia University

Gengnan Chiang, Ph.D. Student Ph.D. Program in Business Feng Chia University

Abstract Deficits and debt and their relationships with other macroeconomic variables have been investigated extensively recently. This paper employs panel threshold regression model to investigate the panel threshold effect of debt/GDP ratio on GDP per capita in OECD countries. The finding is that there exists a single threshold value of debt/GDP ratio which may result in threshold effect and asymmetrical responses of GDP per capita to debt/GDP ratio in OECD countries. Our result is consistent with the stimulus view (Eisner 1984) but inconsistent with the crowding-out view (Friedman 1990) during the researching period. The result indicates that the threshold value of debt/GDP ratio is 66.636%, which is higher than the Maastricht criteria and Stability and Growth Pact, which specifies two fiscal criteria -- a public deficits/GDP ratio of 3% and a public debt/GDP ratio of 60%.

Keywords: Stimulus View, Crowding-out View, Ricardian view, Panel Threshold Effect

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Corresponding author: Department of Finance, Feng Chia University, Taichung, Taiwan. TEL: 886 - 4-24517250 ext. 4150. E-mail: [email protected]

1. Introduction and Review of Literature Government debt may facilitate or deter economic growth, depending on the level of debt. When economic growth is slow or when the private sector does not have incentives to invest, the government may need to pursue fiscal and/or monetary policy to stimulate the economy and may resort to debt financing. On the other hand, when economic growth is normal or above the long-term trend, an increase in government debt may be detrimental to real GDP growth. This is because an increase in debt may push interest rates upward and reduce private investment. The fiscal stability, as defined in the Maastricht Treaty, has ranked among the most important policy objectives of the European Union. Its role further increased after 1997: the Stability and Growth Pact ratified in the Treaty of Amsterdam established that the Maastricht fiscal criteria would not merely be entry conditions for EMU membership but would continue to apply after candidate countries joined the monetary union. There are three major different views of the impact of public debt on economic growth. The stimulus view (Eisner, 1992) argues that if deficits and debt are measured correctly, higher deficits and debt will stimulate employment, consumption, investment, economic growth. Eisner (1992) is optimistic about the deficits and debt issue. He indicates that a constant debt/GDP ratio may be maintained so that the debt does not grow faster than the GDP. The crowding-out view (Friedman, 1988) maintains that higher deficits and debt will reduce economic growth due to rising interest rates and lower investment and capital formation. The Ricardian view (Barro, 1989) holds that deficits and debt do not have any impacts on economic growth because the decrease in future income and consumption due to more tax burdens will offset the increase in current government spending. Based on these different views, there should have a non-linear relationship between public debt and economic growth rate. This paper intends to examine the relationship between debt/GDP ratio and GDP per capita in OECD countries. We apply panel threshold regression model developed by Hansen (1996) to test whether there exists a non-linear relationship between debt/GDP ratio and GDP per capita. The paper is organized as follows: Section 2 introduces the data and variables; Section 3 discusses some methodological and econometric issues, while Section 4 and 5 discuss the empirical results of the panel unit root tests, the panel threshold analysis and offers some conclusions.

2. Data and Variables 2.1 Data Collection The data obtained from online statistical databases of SourceOECD for the yearly sample period from 1990 to 2004, consists 225 observations of GDP per capita, Gross fixed capital formation per GDP ratio, employment rate, and debt to GDP ratio for the 15 OECD countries. These countries are Australia, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Japan · Korea, Norway, Spain, UK, and USA.

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2.2 Variable Design 2.2.1 Explained Variable (Dependent variable) We choose GDP per capita as dependent variable. GDP per capita is measured by US$. As we know, GDP per capita is a good proxy variable of GDP. 2.2.2 Explanatory Variable There are two categories of explanatory variables in our panel data examination. The first is the threshold variable, which is the key variable to be investigated whether there is an asymmetric threshold effect of debt/GDP ratio on GDP per capita. Second, category of explanatory variable is control variables, which are employment rate and Gross fixed capital formation per GDP ratio. They are presumed to have influences upon the GDP per capita. All data are retrieved from the online statistical database of SourceOECD.

3. Methodologies 3.1 Panel Unit Root Models Panel data unit root tests have been proposed as alternative more powerful tests than those based on individual time series unit roots tests, see Levin, Lin and Chu (2002), Im, Pesaran and Shin (2003), and Breitung (2000) to mention a few of the popular tests used in economics to test purchasing power parity (PPP) and growth convergence in macro panels using country data over time. Banerjee (1999), Phillips and Moon (2000), Baltagi and Kao (2000), Breitung and Pesaran (2005) provide some early reviews of this literature. One of the advantages of panel unit root tests is that their asymptotic distribution is standard normal. This is in contrast to individual time series unit roots which have non-standard asymptotic distributions. But these tests are not without their critics. The test, proposed by Levin, Lin and Chu (2002), hereafter denoted by LLC, is applicable for homogeneous panels where the AR coefficients for unit roots are in particular assumed to be the same across cross-sections. The null hypothesis is that each individual time series contains a unit root against the alternative that each time series is stationary. As Maddala (1999) pointed out, the null may be fine for testing convergence in growth among countries, but the alternative restricts every country to converge at the same rate. Im, Pesaran and Shin (2003), hereafter denoted by IPS, allow for heterogeneous panels and propose panel unit root tests which are based on the average of the individual ADF unit root tests computed from each time series. The null hypothesis is that each individual time series contains a unit root while the alternative allows for some but not all of the individual series to have unit roots. One major criticism of both the LLC and IPS tests is that they require cross-sectional independence. This is a restrictive assumption given the cross-section correlation and spillovers across countries, states and regions.

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Maddala and Wu (1999) and Choi (2001) proposed combining the p-values from the individual unit root ADF tests applied to each time series. Once again, these tests follow a standard normal limiting distribution. They have the advantage that N, the number of cross-sections, can be finite or infinite; the time series can be of different length; and the alternative allows some groups to have unit roots while others may not. Hansen’s (1999) panel threshold regression model is in fact an extension of the traditional least squared estimation method. It requires that variables considered in the model need to be stationary in order to avoid the so-called spurious regression. Firstly, the study will process the unit root test. Since the data are all panel in our investigation, both well known IPS and Maddala-Wu techniques are employed for the panel unit root tests. The result of the stationary test for each panel shows that all the variables are most likely to be presumed to carry stationary characteristics since the null of unit root are mostly rejected, especially in the findings from LLC test. These stationary findings enable us to further estimations of the panel threshold regression.

3.2 The Panel Threshold Model 3.2.1 The Single Threshold Model 3.2.1.1 Estimating a Single Threshold This subsection introduces the panel threshold model by Hansen (1999, 2000). Starting with the single threshold case, the equation for a balanced panel with threshold effects is given as: if d it ≤ γ ⎧µ + θ ′hit + α 1 d it + ε it y it = ⎨ i (1) if d it > γ ⎩ µ i + θ ′h it +α 2 d it + ε it

θ = (θ1 ,θ 2 )′ ,

′ hit = (lit , g it )

where θ1 ,θ 2 are the coefficients of control variables lit :employment rate and g it : gross fixed capital formation per GDP ratio. Another threshold regression model of (1) is to set: y it = µ i + θ ′hit + α 1 d it I (d it ≤ γ ) + α 2 d it I (d it > γ ) + ε it

where I (•) represents indicator function.

⎡ hit ⎤ The above equation can be written as y it = µ i + [θ ′, α ′]⎢ ⎥ + ε it ( ) γ d it ⎣ ⎦ ⎡d it I (d it ≤ γ )⎤ or y it = µ i + β ′xit (γ ) + ε it , where d it (γ ) = ⎢ ⎥, ⎣d it I (d it > γ )⎦ α = (α 1 , α 2 )′ , β = (θ ′, α ′), xit = (hit′ , d it′ (γ )) . y it = µ i + β 1′ x it I (d it ≤ γ

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) + β 2′ x it I (d it

> γ

) + ε it ,

(2)

where I (•) is an indicator function. The error term ε it is independent and identically distributed with zero mean and finite variance σ 2 . The subscript i stands for the cross-sections with (1 ≤ i ≤ N ) and t indexes time (1 ≤ t ≤ T ) . The dependent are scalar, the regressor x it is a variable y it and the threshold variable d it k-dimensional vector of exogenous variables. x it and y it are assumed to be stationary variables. x it may contain variables with slope coefficients constrained to be the same in the two regimes, which have no effect on the following distribution theory. If the threshold variable d it is below or above a certain value of d it , namely γ , then the regressor x it has a different impact on y it represented by coefficients β 1 ≠ β 2 . In many applications, the threshold variable d it may be an element of x it but this is not necessarily the case. In our application, y it is GDP per capita and d it is a measure of debt/GDP ratio. Hansen (1999, 2000) chooses a fixed effect approach to estimate Equation (2). After removing the individual specific means α i , the slope coefficient β can be estimated (for given γ ) by ordinary least squares (OLS). Restating Equation (2) as: y it = α i + β ′xit (γ ) + ε it , (3)

⎛ xit (qit ≤ γ )⎞ ⎟⎟ and β = (β 1′β 2′ )′ , the OLS estimator of β is obtained by where xit (γ ) = ⎜⎜ ⎝ xit (qit > γ )⎠ −1 ) β (γ ) = ⎛⎜ X * (γ )′ X * (γ )⎞⎟ X * (γ )′ Y * . (4) ⎝ ⎠ X * and Y * denote the stacked data over all individuals after removing the individual ) ) specific means. The vector of regression residuals is ε (γ ) = Y * − X * (γ )β (γ ) and the sum of squared errors can be written as −1 ′⎛ ) ′⎞ ′) ′ ′ S1 (γ ) = ε * (γ ) ε * (γ ) = Y * ⎜⎜ I − X * (γ ) ⎛⎜ X * (γ ) X * (γ )⎞⎟ X * (γ ) ⎟⎟Y * . (5) ⎠ ⎝ ⎝ ⎠ In a second step, Hansen (2000) suggests the estimation of the threshold γ by least squares, implying ) γ = arg min S1 (γ ). (6) γ

) ) ) The resulting estimate for the slope coefficient is obtained by β = β (γ ) . The residual ) ) ) vector is ε * = ε * (γ ) and the residual variance is defined as 1 1 ) ′) ) ) σ2 = ε*ε* = S1 (γ )⋅ (7) N (T − 1) N (T − 1)

3.2.1.2 Testing for a Threshold ) Having estimated the single threshold γ , it is important to check whether the threshold is in fact statistically significant. Obviously, the null hypothesis ”no threshold effect in

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Equation (2)” is equivalent to

H 0 : β1 = β 2 . Note that standard tests have non-standard distributions since under H 0 the threshold is not identified. For fixed-effects equations, Hansen (1996) therefore suggests a bootstrap method to simulate the asymptotic distribution of the likelihood ratio test. Under the null hypothesis of no threshold, the model is y it = α i + β 1′xit + ε it . (8) After the fixed effects transformation, the equation can be written as y it* = β 1' xit* + ε it* .

(9)

~ The OLS estimator of β 1 is β 1 , the residuals are ε~it* and the sum of squared errors is ′ S 0 = ε~it* ε~it* . Then, the likelihood ratio test of H 0 is based on the test statistic

) S 0 − S1 (γ ) F1 = , σˆ 2

(10)

) where σ 2 is the residual variance defined in (7). Hansen (1996) shows that a bootstrap procedure achieves the first-order asymptotic distribution, so p-values constructed from the bootstrap are asymptotically valid.

In the following, we adopt the bootstrap method by Hansen (1999) but modify the procedure. Hansen (1999) has a large number of cross sections ( N → ∞ ) but only a few time periods. In contrast, the number of countries in our sample is ten but T is large. 3.2.1.3 Confidence Intervals for Threshold Estimate and Slope Coefficients ) In case of a threshold effect, i.e. β1 ≠ β 2 , the estimate γ is consistent for the true value ) of γ , say γ 0 . Since the asymptotic distribution of the threshold estimate γ is highly non-standard, Hansen (2000) uses the likelihood ratio statistic for tests on γ to form confidence intervals for γ . The null hypothesis is H 0 : γ = γ 0 and the likelihood ratio statistic is given by ) S (γ ) − S (γ ) LR1 (γ ) = 1 ) 2 1 (11)

σ

The null hypothesis is rejected for large values of LR1 (γ 0 ) . Hansen (2000) shows that there is an asymptotic distribution for T → ∞ or N → ∞ to form valid asymptotic confidence intervals for γ . He demonstrates that the distribution function has the inverse

(

)

c(α ) = −2 ln 1 − 1 − α from which it is easy to calculate critical values, e.g. the 5% critical value is 7.35 and the 1% critical value is 10.59. The test rejects the hypothesis H 0 : γ = γ 0 at the asymptotic level α if LR1 (γ 0 ) exceeds c(α ) . The

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asymptotic (1 − α ) confidence interval for γ is the set of values of γ such that LR1 (γ ) ≤ c(α ) . Note that this confidence interval construction can produce highly asymmetric confidence intervals for γ . ) The asymptotic distribution of the slope coefficients β is more straightforward, ) ) ) ) although the estimate β = β (γ ) depends on the threshold estimate γ . Hansen (2000) ) shows that inference on β can proceed as if the threshold estimate γ were the true ) ) value. Therefore, β is asymptotically normal with covariance matrix V estimated by −1

) ⎛ N T * ) * ) ′ ⎞ )2 V = ⎜ ∑∑ xit (γ )xit (γ ) ⎟ σ . ⎝ i =1 t =1 ⎠ 3.2.2 Multiple Thresholds 3.2.2.1 Estimating Multiple Thresholds In many applications, there may be more than only one threshold. For example, there are two thresholds accounting for non-linearity in the relationship between inflation and growth in Europe, see Cuaresma and Silgoner (2004). Fortunately, the testing and estimation procedure by Hansen (1999, 2000) allows for the possibility of multiple thresholds. In the following, we illustrate the methods for the double threshold model since these methods extend in straightforward way to higher order threshold models. The double threshold model has the form y it = α i + β1′xit I (q it ≤ γ 1 ) + β 2′ xit I (γ 1 < q it < γ 2 ) + β 3′ xit I (γ 2 < qit ) + ε it

(12)

with γ 1 < γ 2 . Equation (12) can be estimated by OLS since for given threshold (12) is linear in slopes. The sum of squared residuals S (γ 1 , γ 2 ) can be calculated as in the single threshold model and the joint least squares estimates of (γ 1 , γ 2 ) are the values which jointly minimize S (γ 1 , γ 2 ) . Since a grid search over (γ 1 , γ 2 ) requires approximately

(NT )2

regressions, it is important that – as Hansen (1999) demonstrates – sequential estimation is consistent. In the first stage, γˆ1 is the threshold estimate which minimizes S1 (γ ) defined in (5). Given the first-stage estimate γˆ1 , the criterion for the second stage is in Hansen’s (1999) notation given by

⎧S (γˆ1 , γ 2 ) ⎪ S 2γ (γ 2 ) = ⎨ ⎪⎩S (γ 2 , γˆ1 )

if

γˆ1 < γ 2

if

γ 2 < γˆ1

(13)

The second-stage threshold estimate can then be written as

γˆ 2γ = arg min S 2γ (γ 2 ) γ2

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(14)

As Bai (1997) has shown, the estimator for γ 2 is asymptotically efficient. However, since γˆ1 was obtained from a sum of squared residuals function which neglects the second threshold, γˆ1 is not efficient. Bai (1997) suggests a third-stage estimation to get an asymptotically efficient estimator for γ 1 . Holding the second-stage estimate γˆ 2γ fix, the third-stage criterion is ⎧ S γ 1 , γˆ 2γ if γ 1 < γˆ 2γ ⎪ γ S1 = ⎨ γ (15) if γˆ 2γ < γ 1 ⎪⎩S γˆ2 , γ 2

( (

) )

Then, the estimate for γ 1 is obtained by

γˆ1γ = arg min S1γ (γ 1 ). γ1

(16)

3.2.2.2 Testing for the Number of Thresholds

Let us now determine the number of thresholds in a multiple threshold model. Again, the procedure is illustrated in the double threshold model, since the generalization to more than two thresholds is straightforward. In the single threshold model F1 in (10) is obtained as the test statistic for a test of no thresholds against one threshold. If F 1 rejects the null of no threshold, we need a further test to discriminate between one and two thresholds. The minimized sum of squared errors from the second stage threshold estimate γˆ 2γ is S 2γ (γˆ 2γ ) with the variance estimate σˆ 2 = S 2γ (γˆ 2γ ) / N (T − 1) . Thus, the likelihood ratio statistic for a test of one versus two thresholds is given by F2 =

S1 (γˆ1 ) − S 2γ (γˆ 2γ ) σˆ 2

(17)

The null of one threshold is rejected if F2 is large. The bootstrap procedure to approximate the asymptotic p-value for the likelihood ratio test works as for the single-threshold case. The threshold variable d it and the regressors xit are fixed in repeated bootstrap samples. The bootstrap errors will be drawn from the residuals calculated under the alternative hypothesis, i.e. from the residuals from least squares regression of Equation (12). Specifically, we draw (with replacement) error samples from the empirical distribution, namely ε it# . Now we generate the dependent variable y it# under the null hypothesis of one threshold using the equation

yit# = βˆ1′xit I (qit ≤ γˆ ) + βˆ 2′ xit I (qit > γˆ ) + ε it#

(18)

Equation (18) depends on the least squares estimates from the single threshold model βˆ1 , βˆ , and γˆ . The test statistic F can be calculated and repeating this procedure a large 2

2

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number of times will provide the bootstrap p-value. Note that in the generalized case the sequential testing sequence stops if e.g. the null of a maximum number of (K − 1) thresholds is rejected but the null of at most K thresholds is not. 3.2.2.3 Confidence Intervals

Following Bai (1997), the threshold estimators γˆ1γ and γˆ 2γ have the same asymptotic distributions as the threshold estimate in the single threshold model. Consequently, the confidence intervals for the two threshold parameters are constructed in the same way as in the single threshold case. We calculate S γ (γ ) − S 2γ (γˆ 2γ ) S1γ (γ ) − S1γ (γˆ1γ ) γ ( ) LR2γ (γ ) = 2 and LR γ = 1 σˆ 2 σˆ 2 where S 2γ (γ ) and S1γ (γ ) are defined in (13) and (15), respectively. Then, the asymptotic (1 − α ) confidence regions for the threshold estimates are the set of values of γ with LR2γ (γ ) ≤ c(α ) and LR1γ (γ ) ≤ c(α ) .

4. Empirical Results Hansen’s (1999) panel threshold regression model is in fact an extension of the traditional least squared estimation method. It requires that all the variables considered in the model have to be stationary in order to avoid the so-called spurious regression. We process the panel unit root tests as our first step in this paper. Since the data are all panel in our investigation, both well known IPS, Maddala and Wu , and Hadri techniques are employed for the panel unit tests.

4.1 Empirical Results for the Panel Unit Root Tests Table 1 and Table 2 show the descriptive statistics of cross-sectional data for each country and longitudinal data for each variable. From the cross-sectional perspective, the average of GDP per capita is US$22,773. The largest country of GDP per capita is the USA. The average of Gross Fixed Capital Formation per GDP is 21.64%. The highest country of Gross Fixed Capital Formation per GDP is Norway. The lowest country is Japan. The average of Employment Rate is 65.1%. The highest country of Employment Rate is Spain. The lowest country is France. The average of debt/GDP is 64.75%. The highest country of debt/GDP ratio is Korea. The lowest country is Norway. From the longitudinal perspective, the overall GDP per capita among the fifteen countries for each year is increasing from 1990 to 2004. ＜Insert Table 1 about here＞ ＜Insert Table 2 about here＞

Table 3 presents the empirical results of the panel unit root tests. Both IPS and Maddala-Wu panel unit root tests reject the null hypothesis of unit root, and Hadri can

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not reject the null hypothesis of no unit root. Table 4 shows the bootstrap distribution and the critical values for the panel unit root tests. The result of the stationary test for each panel (dependent variable, threshold variable, and control variables) shows that all the variables are all stationary. These stationary findings enable us to go further estimations of the panel threshold regression without worrying about the spurious regression. ＜Insert Table 3 about here＞ ＜Insert Table 4 about here＞

4.2 Empirical Results for the Panel Threshold Regression Models This paper applies the threshold theory proposed by Hansen (1999) and hypothesize that debt/GDP ratio and GDP per capita have asymmetric nonlinear relationship. This paper follows the bootstrap method to get the approximation of F statistic and then calculate the p-value. We test single threshold, double threshold, and triple threshold effect respectively. Table 5 presents the empirical results of test for single, double and triple threshold effects. After repeating bootstrap procedure 300 times for each of the panel threshold tests, we find that the test for single threshold is statistically significant for the dependent variable of GDP per capita. Both double and triple threshold is statistically insignificant. We thus conclude that there exists a single threshold effect of debt/GDP ratio on the GDP per capita. ＜Insert Table 5 about here＞ ＜Insert Table 6 about here＞

When there exists a single threshold effect of the debt/GDP ratio on the GDP per capita, all observation are split into two regimes, a low debt/GDP ratio level and a high debt/GDP ratio level, depending on whether the threshold variable d it is smaller or larger than the threshold value ( γ ). The regimes are distinguished by differing regression slopes, βˆ , and βˆ . Table 6 represents the regression slope estimates, standard errors 1

2

and heterogeneous standard errors for two regimes. The estimated model from empirical finding can be expressed as follows: y it = 129.78 xit I (d it ≤ γˆ ) + 60.54 xit I (d it > γˆ ) + ε it

The estimated threshold value ( γˆ ) is 66.636%, and two coefficients ( βˆ1 =129.78, βˆ 2 =60.54) are all positive with the evidence that the βˆ1 in the low level of debt/GDP ratio and βˆ 2 in the high level of debt/GDP ratio are both significant at the 1% level under the consideration of both homogenous standard errors and heterogeneous standard errors. The empirical result indicates that when the level of debt/GDP is lower than the threshold value of 66.636%, the increase of debt/GDP ratio can improve the GDP per 10

capita. As the debt/GDP ratio is above this threshold value, the upward effect on the GDP per capita is less than lower level of debt/GDP ratio. The threshold effect is stronger in lower level of debt/GDP ratio than in higher level of debt/GDP ratio. ＜Insert Table 7 about here＞

The influences of two control variables upon the GDP per capita are observed in Table 7. The coefficients of two control variables are both statistically significant at the 1% level under the consideration of both homogenous standard errors and heterogeneous standard errors. The estimated coefficient of the first control variable of Gross fixed capital formation per GDP ratio is negative. It represents the negative relationship between the Gross fixed capital formation per GDP ratio and GDP per capita. The estimated coefficient of the second control variable of employment rate is positive. It shows the positive relationship between the employment rate and GDP per capita.

5. Conclusions This paper contributes to previous literature in three aspects. First, we employ three different panel unit root tests for our panel data in order to avoid the so-called spurious regression. Second, we apply advanced panel threshold regression model developed by Hansen (1999) to test if there exists a “threshold” of optimal debt/GDP ratio on GDP per capita. Third, two related control variables are considered to make our nonlinear function more persuadable. The paper applies panel threshold regression model to examine whether debt/GDP ratio affects the GDP per capita in OECD countries. Also, we intend to test whether there exists an optimal debt/GDP ratio, which leads to the asymmetric relationship between the debt/GDP ratio and GDP per capita. The empirical results of testing for the influence of debt/GDP on the GDP per capita indicate that the threshold value ( γˆ ) is 66.636%. There exists the effect of the stimulus view when the debt/GDP ratio is lower than the threshold value, but it does not exist the effect of crowding-out view when the debt/GDP ratio is more than thresholds value. We find that there exists single threshold effect and the coefficients are all positive and significant for two regimes. Our results identify that the GDP per capita is positively related to debt/GDP level, with lower than 66.636% debt/GDP level countries having a higher coefficient, but the positive effect decreases when debt/GDP ratio increases. The results of this paper are more consistent with the stimulus view, but inconsistent with the crowding-out view. Our results indicate that OECD countries should use public debt wisely to improve their GDP per capita.

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Sawhney, B. L., and William R. D.(1994), "Public Debt, Deficits and Economic Growth: A Cross-Country Analysis," Southern Business and Economic Journal, 281-296. Smyth, D. J. and Y. Hsing(1995), "In Search of An Optimal Debt Ratio for Economic Growth, " Cotemporary Economic Policy, 13(4), 51-59 .Tanzi, V. and H. H. Zee(1997), “Fiscal Policy and Long-Run Growth,” IMF Staff Papers, 44(2), 179-209. Tong, H.,(1978) "On a Threshold Model, in C.H. Chen (ed.), Pattern Recognition and Signal PROAessing, " Amsterdam: Sijthoff & Noordhoff, 1978, 101-141.

14

Table 1 Cross-sectional data for each country variables

statistics Australia Belgium Canada Demark Finland France Germany Greece Ireland Japan Korea Norway Spain UK USA mean 23270 23676 24655 25102 22479 18624 23193 23398 14996 22755 23993 14111 28153 22700 30483 maximum 31231 30851 31395 31932 30594 25582 29554 28605 21689 35767 29664 20907 38765 31436 39732 GDP per capita minimum 16758 18038 19301 18753 17226 13405 17802 18063 11142 12972 18826 8203 18021 16440 23012 Std.Dev 4786 4096 4250 4496 4624 4099 3897 3196 3326 7893 3151 3831 7384 5026 5399 mean 22.92 20.29 19.60 18.99 19.45 24.45 19.05 21.09 21.96 20.56 27.59 33.68 20.00 16.86 18.05 Gross Fixed Capital maximum 24.69 22.46 21.62 20.44 28.42 27.83 21.57 23.55 25.49 24.96 32.32 38.89 25.17 20.51 19.91 Formation per GDP minimum 20.94 18.52 17.91 16.91 15.69 21.57 17.44 17.37 18.60 15.50 23.81 29.09 17.35 15.74 16.17 Std.Dev 1.16 0.99 0.96 1.07 3.19 2.11 1.16 1.94 2.27 3.33 2.67 3.76 2.04 1.17 1.16 mean 67.34 57.62 69.17 74.95 65.48 53.57 60.25 65.10 55.47 57.94 69.07 62.17 75.08 70.91 72.37 maximum 69.51 60.92 72.55 76.47 74.14 62.05 62.49 67.06 59.64 65.52 70.02 63.75 78.28 72.67 74.10 Employment Rate minimum 64.13 54.45 66.39 72.36 59.94 47.40 58.36 63.84 53.07 50.69 68.23 59.19 71.29 68.24 70.81 Std.Dev 1.75 2.01 2.09 1.32 3.87 4.95 1.40 0.85 1.92 6.08 0.50 1.43 2.55 1.57 1.15

Debt per GDP

mean maximum minimum Std.Dev

28.91 43.38 17.82 8.73

122.83 140.67 98.69 13.30

87.86 100.76 72.18 9.79

66.58 87.73 52.85 11.20

51.64 65.99 16.49 14.05

62.30 75.56 47.73 9.38

60.62 74.65 38.61 11.65

55.00 104.33 63.14 107.42 67.92 114.36 94.62 156.34 37.92 79.58 29.38 64.77 9.60 11.34 26.22 33.73

11.19 36.42 45.26 67.72 19.58 51.18 53.73 75.39 5.19 27.52 33.04 58.04 5.60 7.07 6.76 6.14

Note :

1. Yearly sample period from 1990 to 2004. 2. The unit of each variable : GDP per capita is US$; Gross Fixed Capital Formation per GDP is percentage; Employment Rate is percentage; Debt per GDP is percentage.

15

variables

statistics mean maximum GDP per capita minimum Std.Dev mean Gross Fixed maximum Capital Formation per minimum GDP Std.Dev mean maximum Employment Rate minimum Std.Dev mean maximum Debt per GDP minimum Std.Dev Note :

Table 2 Longitudinal data for each variable 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 16600 17259 17819 18284 19289 20254 21226 22376 23120 24270 26106 27178 28189 29103 30514 23012 23456 24470 25374 26636 27542 28780 30228 31485 32994 36305 37113 36609 37510 39732 8203 9195 9857 10594 11623 12818 13426 14126 13644 15047 16287 17261 18453 19279 20907 3705 3659 3763 3834 3973 3968 4154 4291 4502 4731 5410 5383 5059 5009 5242 23.75 22.61 21.56 20.69 20.69 20.86 21.15 21.61 21.93 22.06 22.00 21.70 21.17 21.26 21.53 37.09 38.89 36.89 36.34 36.42 37.31 37.49 35.62 30.35 29.73 31.09 29.54 29.09 29.92 29.51 17.43 16.25 16.17 15.50 15.69 16.35 16.54 16.48 17.54 17.17 16.97 16.62 16.46 15.91 16.33 5.29 5.94 5.57 5.58 5.47 5.43 5.36 4.75 3.49 3.29 3.68 3.44 3.63 4.16 4.12 64.83 64.14 63.38 62.54 62.80 63.65 64.02 64.59 65.11 65.93 66.89 66.94 67.13 67.06 67.50 75.42 74.64 74.48 72.36 72.43 73.93 75.31 77.03 78.28 78.04 77.90 77.46 77.11 75.76 75.99 51.78 51.15 50.46 47.98 47.40 48.28 49.26 50.70 52.45 55.01 55.86 55.61 57.70 58.92 59.64 8.49 7.95 7.68 7.75 7.94 7.86 7.83 7.94 7.73 7.33 6.73 6.44 6.04 5.58 5.35 54.28 55.72 60.67 68.50 68.72 70.59 70.70 69.07 68.05 65.91 63.90 63.10 63.49 64.31 64.17 126.18 127.83 136.91 140.67 137.68 135.17 133.47 127.70 122.63 125.67 133.97 142.28 149.40 154.03 156.34 7.79 6.75 6.36 5.65 5.19 5.45 5.86 7.54 13.13 15.60 16.33 17.36 16.63 18.63 17.82 32.09 32.61 32.74 34.06 32.46 31.06 31.49 30.68 30.66 32.27 34.03 35.76 36.24 35.86 36.10

1. Yearly sample period from 1990 to 2004. 2. The unit of each variable : GDP per capita is US$; Gross Fixed Capital Formation per GDP is percentage; Employment Rate is percentage; Debt per GDP is percentage.

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ψi ψ LM

Table 3 Panel Unit Root Tests (without breaks) Statistic P-Value

Maddala and Wu Hadri(homo) Hadri(hetero)

0.010

ψi ψ LM

-14.13

0.000

22.368 205.67 -4.706 -4.657

0.000 0.000 1.000 1.000

Table 4 Bootstrap Distribution (%) 0.025 0.050 0.100 0.900

-4.044 -3.413 -2.933

Maddala and Wu Hadri(homo) Hadri(hetero)

-2.425

2.331

0.950

0.975

0.990

2.975

3.445

4.164

-3.883 -3.480 -2.977 -2.509 2.329 3.130 4.174 4.957 5.315 6.823 9.131 10.781 35.771 47.087 56.926 64.160 -3.426 -3.117 -2.791 -2.358 2.835 3.833 4.514 5.506 -3.343 -3.071 -2.618 -2.428 2.734 4.176 4.463 4.781

Table 5 Test for Threshold Effects Test for single threshold Threshold 66.636 F1 P-value (10%, 5%, 1% critical values)

45.49 0.03** (34.33, 41.21, 54.49)

Test for double threshold Threshold

30.926, 66.636

F2 P-value (10%, 5%, 1% critical values)

6.54 0.91 (27.54, 37.62, 56.55)

Test for triple threshold Threshold

30.926, 46.729, 66.636

F3 P-value (10%, 5%, 1% critical values)

5.19 0.93 (19.53, 22.76, 33.24)

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Table 6 Single Threshold Estimate Coefficient Standard Errors Het Standard Errors

βˆ1 βˆ 2

129.78***

23.72 (5.47)

23.94

60.54 19.33 (3.13) 1. ***denotes at the significance of 1% level.

16.36

***

βˆ1 and βˆ 2 are the coefficients estimates for regimes.

2.

3. The value in ( ) is t-value.

Table 7 Test for Control Variable Coefficient estimate Standard Errors Het Standard Errors

θˆ1

-956.03***

136.27 (-7.02)

134.65

1658.17*** 95.53 (17.39) denotes at the significance of 1% level.

92.86

θˆ

2

1.

***

2. θˆ1 and θˆ2

are the regression coefficients of control variables.

3. The value in ( ) is t-value.

18