Abstract
The influential paper by Reinhart and Rogoff (Reinhart, C. M., and K. S. Rogoff. 2010. “Growth in a Time of Debt.” The American Economic Review 100: 573–578.) has triggered a debate about the effects of the public debt on GDP growth. They argue that a debt-to-GDP ratio of over 90 percent has a deleterious effect on long-run economic growth. In this paper, we examine the inter-temporal relationship between public debt and GDP growth rates. We examine debt-to-GDP thresholds in nonlinear panel models, using various econometric strategies, methodologies, and data samples. We also evaluate confidence intervals around the estimated thresholds to determine the accuracy of estimated thresholds. Our results demonstrate that in the majority of estimated models, threshold values are not uniquely defined and the estimated coefficients are insignificant in most model specifications, as in Enders, Falk, and Siklos (Enders, W., B. L. Falk, and P. Siklos. 2007. “A Threshold Model of Real US GDP and the Problem of Constructing Confidence Intervals in TAR Models.” Studies in Nonlinear Dynamics & Econometrics 11: 1322.). Next, we examine the inter-temporal relationship between the public debt and economic growth using structural panel data models as well as reduced form panel VAR models. In contrast to the standard presumption in the literature, we find that the inter-temporal effect of economic growth on the public debt is strong, but the effect of the public debt on economic growth is weak. We find similar results in sub-samples that include countries where the public debt is over 90 percent of GDP.
Funding source: European Social Fund
Award Identifier / Grant number: SPIRITH
Funding source: Hrvatska Zaklada za Znanost
Award Identifier / Grant number: 7031
Funding statement: Financial support from European Social Fund (Funder Id: 10.13039/501100004895 and Grant Number: SPIRITH) and Hrvatska Zaklada za Znanost (Funder Id: 10.13039/501100004488 and Grant Number: 7031).
A Appendix
A.1 Data description and literature survey
Survey of literature.
Authors | Feedback effect | Reverse causality | Confidence bands | Endogenous threshold | Number of Regimes | Local currency GDP | Non-overlapping frequency | Sys-GMM |
---|---|---|---|---|---|---|---|---|
Reinhart and Rogoff (2010) | ∘ | ∘ | ∘ | ∘ | 3 | ∘ | ∘ | ∘ |
Kumar and Woo (2010) | ∘ | ∘ | ∘ | ∘ | 3 | ∘ | · | · |
Caner, Grennes, and Koehler-Geib (2010) | ∘ | ∘ | ∘ | • | 2 | ∘ | ∘ | ∘ |
Cecchetti, Mohanty, and Zampolli (2011) | ∘ | ∘ | ∘ | • | 2 | ∘ | ∘ | ∘ |
Checherita-Westphal and Rother (2012) | ∘ | ∘ | ∘ | ∘ | 2 | ∘ | • | • |
Egert (2012) | ∘ | ∘ | ∘ | • | 2–4 | ∘ | • | ∘ |
Minea and Parent (2012) | ∘ | ∘ | ∘ | • | 4 | ∘ | ∘ | ∘ |
Panizza and Presbitero (2014) | ∘ | ∘ | ∘ | ∘ | linear | ∘ | ∘ | ∘ |
Kourtellos, Stengos, and Tan (2012) | ∘ | ∘ | ∘ | • | 2 | ∘ | • | • |
Baum, Checherita-Westphal, and Rother (2013) | ∘ | ∘ | ∘ | • | 2 | ∘ | ∘ | • |
Herndon, Ash, and Pollin (2013) | ∘ | ∘ | ∘ | ∘ | 2 | ∘ | ∘ | ∘ |
Afonso and Jalles (2013) | ∘ | ∘ | ∘ | • | 2 | ∘ | • | • |
Eberhardt and Presbitero (2013) | ∘ | • | ∘ | ∘ | linear | ∘ | ∘ | ∘ |
Lof and Malinen (2014) | ∘ | • | ∘ | ∘ | linear | ∘ | ∘ | ∘ |
Pescatori, Sandri, and Simon (2014) | ∘ | ∘ | ∘ | ∘ | 2 | ∘ | ∘ | ∘ |
Chudik et al. (2017) | ∘ | ∘ | ∘ | • | 2 | ∘ | ∘ | ∘ |
“•” denote that the paper employs or controls for the specific methodological characteristics while “∘” denotes that the paper does not.
Data sets and subsamples.
Time period | Frequency | N | T | |
---|---|---|---|---|
Data Set A | 1960–2009 | 5-year non-overlapping averages | 261 | 10 |
Data Set B | 1960–2009 | annual | 262 | 50 |
Data Set C | 1880–2009 | annual | 262 | 130 |
OECD economies | 1960–2009 | 5-year non-overlapping averages | 34 | 10 |
Non-OECD economies | 1960–2009 | 5-year non-overlapping averages | 185 | 10 |
Data Set B, debt>90% | 1960–2009 | annual | 259 | 50 |
Data Set C, debt>90% | 1880–2009 | annual | 262 | 130 |
Data sources and explanations.
Variable | Source |
---|---|
Main Variables | |
Public debt to GDP ratio | Abbas et al. (2010) |
GDP in local currency units | The World Bank (2014) |
GDP in PPP | Maddison (2010) |
Control Variables | |
Secondary school enrollment | Barro and Lee (2010) |
Gross fixed capital formation in percent of GDP | The World Bank (2014) |
Imports and Exports of goods and services as a percent of GDP | The World Bank (2014) |
Age dependency ratio (percent of working-age population) | The World Bank (2014) |
Total population | The World Bank (2014) |
Consumer price index (2005 = 100) | The World Bank (2014) |
Average maturity on new external debt commitments in years | The World Bank (2014) |
Data availability for public debt in OECD and non-OECD countries.
Country | Time period | Country | Time period | Country | Time period |
---|---|---|---|---|---|
Albania | 1994–2009 | Gambia | 1973–2009 | Norway* | 1880–2009 |
Algeria | 1970–2009 | Georgia | 1995–2009 | Oman | 1973–2009 |
Angola | 1995–2009 | Germany* | 1880–2009 | Pakistan | 1951–2009 |
Antigua and Barb. | 1998–2009 | Ghana | 1962–2009 | Panama | 1953–2009 |
Argentina | 1884–2009 | Greece* | 1884–2009 | Papua New Guinea | 1973–2007 |
Armenia | 1993–2009 | Grenada | 1970–2009 | Paraguay | 1970–2009 |
Australia* | 1901–2009 | Guatemala | 1923–2009 | Peru | 1918–2009 |
Austria* | 1880–2009 | Guinea | 1990–2009 | Phillipines | 1948–2009 |
Azerbaijan | 1993–2009 | Guinea-Bissau | 1986–2009 | Poland* | 1986–2009 |
Bahamas | 1968–2009 | Guyana | 1963–2009 | Portugal* | 1880–2009 |
Bahrain | 1974–2009 | Haiti | 1970–2009 | Qatar | 1990–2009 |
Bangladesh | 1974–2009 | Honduras | 1926–2009 | Romania | 1990–2009 |
Barbados | 1970–2009 | Hungary* | 1928–2009 | Russian Fed. | 1885–2009 |
Belarus | 1994–2009 | Iceland* | 1951–2009 | Rwanda | 1970–2009 |
Belgium* | 1880–2009 | India | 1948–2009 | Samoa | 1970–2009 |
Belize | 1976–2009 | Indonesia | 1976–2009 | Sao Tome & Principe | 1995–2007 |
Benin | 1970–2009 | Iran | 1970–2009 | Saudi Arabia | 1991–2009 |
Bhutan | 1982–2009 | Ireland* | 1929–2009 | Senegal | 1970–2009 |
Bolivia | 1970–2009 | Israel* | 1972–2009 | Serbia | 2000–2009 |
Bosnia & Herz. | 1998–2009 | Italy* | 1880–2009 | Seychelles | 1973–2009 |
Botswana | 1972–2009 | Jamaica | 1963–2009 | Sierra Leone | 1970–2009 |
Brazil | 1880–2009 | Japan* | 1880–2009 | Singapore | 1963–2009 |
Brunei Dar. | 2001–2007 | Jordan | 1970–2009 | Slovak Rep.* | 1992–2009 |
Bulgaria | 1992–2009 | Kazakhstan | 1993–2009 | Slovenia* | 1993–2009 |
Burkina Faso | 1976–2009 | Kenya | 1961–2009 | Solomon Islands | 1980–2009 |
Burundi | 1964–2009 | Korea* | 1958–2009 | South Africa | 1914–2009 |
Cambodia | 1996–2009 | Kuwait | 1971–2009 | Spain* | 1880–2009 |
Cameroon | 1970–2009 | Kyrgyz Rep. | 1995–2009 | Sri Lanka | 1951–2009 |
Canada* | 1880–2009 | Lao | 1989–2009 | St. Kitts and Nevis | 1984–2009 |
Cape Verde | 1981–2009 | Latvia | 1994–2009 | St. Lucia | 1981–2009 |
Central African Rep. | 1970–2009 | Lebanon | 1970–2009 | St. Vincent & Grens. | 1975–2009 |
Chad | 1970–2009 | Lesotho | 1973–2009 | Sudan | 1992–2009 |
Chile* | 1970–2009 | Liberia | 1973–2009 | Suriname | 1971–2009 |
China (Mainland) | 1984–2009 | Libya | 1973–2009 | Swaziland | 1970–2009 |
China (Hong Kong) | 2001–2009 | Lithuania | 1994–2009 | Sweden* | 1880–2009 |
Colombia | 1958–2009 | Luxembourg* | 1974–2009 | Switzerland* | 1899–2009 |
Comoros | 1982–2009 | Macedonia | 1995–2009 | Syrian Arab Rep. | 1970–2009 |
Congo, Dem. Rep. of | 1970–2009 | Madagascar | 1971–2009 | Taiwan | 1997–2009 |
Congo, Rep. of | 1970–2009 | Malawi | 1970–2009 | Tajikistan | 1998–2009 |
Costa Rica | 1950–2009 | Malaysia | 1953–2009 | Tanzania | 1970–2009 |
Cote d’Ivoire | 1979–2009 | Maldives | 1978–2009 | Thailand | 1954–2009 |
Croatia | 1994–2009 | Mali | 1970–2009 | Togo | 1975–2009 |
Cyprus | 1970–2009 | Malta | 1965–2009 | Tonga | 1985–2009 |
Czech Rep.* | 1993–2009 | Mauritania | 1977–2009 | Trinidad & Tobago | 1963–2009 |
Denmark* | 1880–2009 | Mauritius | 1970–2009 | Tunisia | 1970–2009 |
Djibouti | 1993–2009 | Mexico* | 1914–2009 | Turkey* | 1936–2009 |
Dominica | 1975–2009 | Moldova | 1995–2009 | Turkmenistan | 1997–2009 |
Dominican Rep. | 1970–2009 | Mongolia | 1992–2007 | Uganda | 1970–2009 |
Ecuador | 1939–2009 | Montenegro | 2002–2009 | United Kingdom* | 1880–2009 |
Egypt | 1929–2009 | Morocco | 1965–2009 | Ukraine | 1992–2009 |
El Salvador | 1939–2009 | Mozambique | 1999–2009 | United Arab Emirates | 1973–2009 |
Equatorial Guinea | 1980–2009 | Myanmar | 1970–2009 | United States* | 1880–2009 |
Eritrea | 1995–2009 | Namibia | 1993–2009 | Uruguay | 1970–2009 |
Estonia* | 1995–2009 | Nepal | 1970–2009 | Uzbekistan | 1998–2009 |
Ethiopia | 1970–2009 | Netherlands* | 1880–2009 | Vanuatu | 1981–2007 |
Fiji | 1970–2009 | New Zealand* | 1880–2009 | Venezuela | 1920–2009 |
Finland* | 1914–2009 | Nicaragua | 1970–2009 | Vietnam | 1992–2009 |
France* | 1880–2009 | Niger | 1970–2009 | Yemen | 1992–2009 |
Gabon | 1970–2009 | Nigeria | 1968–2009 | Zambia | 1970–2009 |
Zimbabwe | 1964–2009 |
* indicates OECD countries in Table 2. Source: Abbas et al. (2010).
B Appendix
B.1 Threshold model results with control variables and estimated statistics
Data Set A: 5-year frequency non-overlapping data (1960–2009).
FE | GMM | SYS-GMM | FE-IV | GMM-IV | |
---|---|---|---|---|---|
Regime | |||||
−0.097* | 0.185 | ||||
(−1.84) | (1.02) | ||||
bi,t | −0.005* | −0.007* | −0.012** | 0.040* | −0.009 |
(−1.79) | (−1.73) | (−2.01) | (1.84) | (−1.57) | |
Capital | 0.035*** | 0.016 | 0.028*** | 0.066*** | 0.020 |
(5.32) | (1.61) | (4.53) | (3.08) | (1.29) | |
Education | −0.008 | 0.004 | 0.004 | −0.017 | 0.022* |
(−1.28) | (0.48) | (0.94) | (−1.49) | (1.71) | |
y0 | −0.042*** | −0.116*** | −0.012*** | −0.073*** | −0.100*** |
(−6.74) | (−10.89) | (−4.48) | (−4.89) | (−7.32) | |
Population | 0.109 | 0.069 | −0.473 | 0.207 | 0.767 |
(0.22) | (0.19) | (−1.11) | (0.50) | (0.82) | |
Inflation | −0.023*** | −0.043*** | −0.027** | −0.041** | −0.054*** |
(−3.61) | (−2.65) | (−2.52) | (−2.07) | (−5.01) | |
Openness | −0.001 | −0.006 | 0.000 | −0.032*** | 0.000 |
(−0.14) | (−0.89) | (0.41) | (−2.88) | (−0.05) | |
Age dependency | −0.053*** | −0.110*** | −0.023 | −0.129*** | −0.096*** |
(−3.53) | (−5.40) | (−1.54) | (−3.55) | (−3.04) | |
Regime | |||||
−0.037 | 0.241 | ||||
(−0.57) | (1.35) | ||||
bi,t | −0.004* | −0.008*** | −0.003 | 0.089** | −0.006* |
(−1.70) | (−3.22) | (−0.89) | (2.37) | (−1.70) | |
Capital | 0.032*** | 0.030*** | 0.023*** | 0.040*** | 0.024*** |
(4.53) | (5.26) | (3.70) | (4.44) | (2.81) | |
Education | −0.013* | −0.005 | 0.001 | −0.017* | 0.007 |
(−1.78) | (−0.71) | (0.16) | (−1.80) | (0.93) | |
y0 | −0.040*** | −0.093*** | −0.011*** | −0.054*** | −0.083*** |
(−6.15) | (−11.08) | (−2.84) | (−5.46) | (−7.26) | |
Population | 0.665 | 0.426 | −0.209 | 0.013 | 0.152 |
(1.24) | (1.53) | (−0.79) | (0.04) | (0.33) | |
Inflation | −0.046*** | −0.036*** | −0.046*** | −0.032*** | −0.029*** |
(−6.52) | (−5.15) | (−4.64) | (−3.50) | (−2.70) | |
Openness | −0.002 | −0.005 | −0.001 | −0.029*** | −0.001 |
(−0.24) | (−0.74) | (−0.81) | (−2.82) | (−0.11) | |
Age dependency | −0.056*** | −0.085*** | −0.029** | −0.115*** | −0.079*** |
(−3.49) | (−5.25) | (−2.04) | (−3.78) | (−3.24) | |
−0.061 | 0.029 | −0.044 | |||
(−1.60) | (0.64) | (−0.77) | |||
Constant | −0.105 | −0.348* | 0.035 | −0.921*** | −0.19 |
(−0.49) | (−1.79) | (0.60) | (−2.87) | (−0.71) | |
Wald test results (p-values) | |||||
β1 = β2 | 0.675 | 0.818 | 0.097 | 0.047 | 0.561 |
ϕ1 = ϕ2 | 0.013 | 0.000 | 0.197 | 0.139 | 0.022 |
*, ** and *** indicate statistical significance at 10%, 5% and 1% levels respectively. t-statistics are in parenthesis. p-values from the Wald test on β1 = β2 or ϕ1 = ϕ2 are reported, where ϕi = (ρi, βi, δi)’ for i = 1, 2. FE is the fixed effects model, GMM is generalized method of moments, SYS-GMM is the System-GMM model, FE-IV is fixed effects with instrumental variables and GMM-IV is GMM with instrumental variables.
Data Set B: short-run annual data (1960–2009).
FE | GMM | SYS-GMM | FE-IV | GMM-IV | |
---|---|---|---|---|---|
Regime | |||||
0.136** | 0.155*** | ||||
(2.32) | (7.01) | ||||
bi,t | 0.007 | 0.007** | −0.013 | 0.010*** | 0.011 |
(1.05) | (2.18) | (−1.09) | (4.43) | (0.69) | |
Capital | 0.009 | 0.036*** | 0.018 | 0.024*** | 0.021 |
(1.34) | (6.50) | (0.97) | (6.72) | (0.78) | |
Population | −0.659** | −0.849* | 0.455 | −0.429*** | −1.272* |
(−2.41) | (−1.78) | (0.42) | (−3.64) | (−1.73) | |
y0 | 0.000 | 0.291*** | −0.014* | 0.001 | 0.295*** |
(.) | (9.21) | (−1.83) | (0.60) | (3.82) | |
Inflation | −0.051*** | −0.033*** | −0.035*** | −0.030*** | −0.085** |
(−2.86) | (−6.10) | (−2.98) | (−6.21) | (−2.25) | |
Openness | 0.001 | −0.089*** | 0.003 | 0.002 | −0.068*** |
(0.19) | (−17.63) | (1.21) | (0.65) | (−3.33) | |
Age dependency | −0.014 | −0.047 | 0.026 | −0.021** | 0.057 |
(−1.09) | (−1.21) | (0.75) | (−2.50) | (1.12) | |
Regime | |||||
0.111*** | 0.140*** | ||||
(3.07) | (5.21) | ||||
bi,t | −0.008*** | −0.007** | −0.010 | −0.000 | −0.011 |
(−2.94) | (−2.29) | (−0.96) | (−0.02) | (−0.26) | |
Capital | 0.027*** | 0.034*** | 0.017 | 0.023*** | 0.034** |
(6.23) | (6.77) | (1.35) | (6.54) | (2.36) | |
Population | −0.529*** | −1.955*** | 0.749 | −0.730*** | −1.927 |
(−4.01) | (−4.51) | (0.71) | (−5.00) | (−1.47) | |
y0 | 0.002 | 0.282*** | −0.004 | 0.000 | 0.297*** |
(0.36) | (8.96) | (−0.64) | (.) | (3.85) | |
Inflation | −0.019*** | −0.015*** | −0.011** | −0.015*** | −0.014** |
(−4.72) | (−6.48) | (−2.32) | (−4.50) | (−2.18) | |
Openness | 0.002 | −0.088*** | −0.005*** | 0.001 | −0.069*** |
(0.41) | (−16.69) | (−3.21) | (0.23) | (−3.21) | |
Age dependency | −0.007 | −0.036 | −0.003 | −0.017* | 0.067 |
(−0.82) | (−0.90) | (−0.06) | (−1.73) | (1.30) | |
0.088*** | 0.090 | 0.080** | |||
(4.89) | (0.91) | (2.00) | |||
Constant | 0.087 | 0.000 | −3.543* | 0.059 | 0.000 |
(0.60) | (.) | (−1.92) | (0.75) | (.) | |
Wald test results (p-values) | |||||
β1 = β2 | 0.069 | 0.000 | 0.844 | 0.033 | 0.530 |
ϕ1 = ϕ2 | 0.011 | 0.000 | 0.000 | 0.025 | 0.190 |
See notes in Table 9.
Data Set C: long-run annual data (1880–2009).
FE | GMM | SYS-GMM | FE-IV | GMM-IV | |
---|---|---|---|---|---|
Regime | |||||
0.237*** | 0.221*** | ||||
(6.37) | (12.49) | ||||
bi,t | −0.003* | −0.016 | −0.012 | −0.001 | −0.023 |
(−1.92) | (−1.35) | (−0.75) | (−0.49) | (−0.03) | |
Regime | |||||
0.151*** | 0.117*** | ||||
(3.50) | (6.37) | ||||
bi,t | −0.002 | −0.016 | −0.010 | 0.000 | −0.025 |
(−1.15) | (−1.24) | (−0.72) | (0.28) | (−0.03) | |
0.139*** | 0.148** | 0.102 | |||
(7.27) | (2.48) | (0.07) | |||
Constant | −0.003 | 0.081*** | 0.063 | 0.027*** | −0.125 |
(−0.23) | (2.99) | (1.27) | (4.22) | (−0.04) | |
Wald test results (p-values) | |||||
0.118 | 0.957 | 0.698 | 0.037 | 0.984 |
See notes in Table 9.



Threshold values and estimated statistics (Data Set A).
Note: Potential threshold values of the debt/GDP ratio (horizontal axis) are shown against the matching RMSE, Hansen J or RSS statistics (vertical axis) obtained from a grid search. Confidence intervals are shaded areas and the vertical line represents the debt/GDP value that minimizes test statistics in the grid search.
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Supplemental Material
The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/snde-2016-0086).
©2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Introduction: Special Issue Honoring the Contributions of Walter Enders
- Improving likelihood-ratio-based confidence intervals for threshold parameters in finite samples
- Nonlinear Taylor rules: evidence from a large dataset
- Flexible Fourier form for volatility breaks
- Nonlinear evidence on the existence of jobless recoveries
- Public debt and economic growth conundrum: nonlinearity and inter-temporal relationship
- Examining the success of the central banks in inflation targeting countries: the dynamics of the inflation gap and institutional characteristics
- Evaluating the impact of the labor market conditions index on labor market forecasts
- Time-varying correlations and Sharpe ratios during quantitative easing
- Testing for a unit root against ESTAR stationarity
Articles in the same Issue
- Introduction: Special Issue Honoring the Contributions of Walter Enders
- Improving likelihood-ratio-based confidence intervals for threshold parameters in finite samples
- Nonlinear Taylor rules: evidence from a large dataset
- Flexible Fourier form for volatility breaks
- Nonlinear evidence on the existence of jobless recoveries
- Public debt and economic growth conundrum: nonlinearity and inter-temporal relationship
- Examining the success of the central banks in inflation targeting countries: the dynamics of the inflation gap and institutional characteristics
- Evaluating the impact of the labor market conditions index on labor market forecasts
- Time-varying correlations and Sharpe ratios during quantitative easing
- Testing for a unit root against ESTAR stationarity