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Public debt and economic growth conundrum: nonlinearity and inter-temporal relationship

  • Vladimir Arčabić ORCID logo EMAIL logo , Josip Tica , Junsoo Lee and Robert J. Sonora
Published/Copyright: February 13, 2018

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

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

Table 5:

Survey of literature.

AuthorsFeedback effectReverse causalityConfidence bandsEndogenous thresholdNumber of RegimesLocal currency GDPNon-overlapping frequencySys-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
  1. “•” denote that the paper employs or controls for the specific methodological characteristics while “∘” denotes that the paper does not.

Table 6:

Data sets and subsamples.

Time periodFrequencyNT
Data Set A1960–20095-year non-overlapping averages26110
Data Set B1960–2009annual26250
Data Set C1880–2009annual262130
OECD economies1960–20095-year non-overlapping averages3410
Non-OECD economies1960–20095-year non-overlapping averages18510
Data Set B, debt>90%1960–2009annual25950
Data Set C, debt>90%1880–2009annual262130
Table 7:

Data sources and explanations.

VariableSource
Main Variables
 Public debt to GDP ratioAbbas et al. (2010)
 GDP in local currency units The World Bank (2014)
 GDP in PPPMaddison (2010)
Control Variables
 Secondary school enrollmentBarro 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)
Table 8:

Data availability for public debt in OECD and non-OECD countries.

CountryTime periodCountryTime periodCountryTime period
Albania1994–2009Gambia1973–2009Norway*1880–2009
Algeria1970–2009Georgia1995–2009Oman1973–2009
Angola1995–2009Germany*1880–2009Pakistan1951–2009
Antigua and Barb.1998–2009Ghana1962–2009Panama1953–2009
Argentina1884–2009Greece*1884–2009Papua New Guinea1973–2007
Armenia1993–2009Grenada1970–2009Paraguay1970–2009
Australia*1901–2009Guatemala1923–2009Peru1918–2009
Austria*1880–2009Guinea1990–2009Phillipines1948–2009
Azerbaijan1993–2009Guinea-Bissau1986–2009Poland*1986–2009
Bahamas1968–2009Guyana1963–2009Portugal*1880–2009
Bahrain1974–2009Haiti1970–2009Qatar1990–2009
Bangladesh1974–2009Honduras1926–2009Romania1990–2009
Barbados1970–2009Hungary*1928–2009Russian Fed.1885–2009
Belarus1994–2009Iceland*1951–2009Rwanda1970–2009
Belgium*1880–2009India1948–2009Samoa1970–2009
Belize1976–2009Indonesia1976–2009Sao Tome & Principe1995–2007
Benin1970–2009Iran1970–2009Saudi Arabia1991–2009
Bhutan1982–2009Ireland*1929–2009Senegal1970–2009
Bolivia1970–2009Israel*1972–2009Serbia2000–2009
Bosnia & Herz.1998–2009Italy*1880–2009Seychelles1973–2009
Botswana1972–2009Jamaica1963–2009Sierra Leone1970–2009
Brazil1880–2009Japan*1880–2009Singapore1963–2009
Brunei Dar.2001–2007Jordan1970–2009Slovak Rep.*1992–2009
Bulgaria1992–2009Kazakhstan1993–2009Slovenia*1993–2009
Burkina Faso1976–2009Kenya1961–2009Solomon Islands1980–2009
Burundi1964–2009Korea*1958–2009South Africa1914–2009
Cambodia1996–2009Kuwait1971–2009Spain*1880–2009
Cameroon1970–2009Kyrgyz Rep.1995–2009Sri Lanka1951–2009
Canada*1880–2009Lao1989–2009St. Kitts and Nevis1984–2009
Cape Verde1981–2009Latvia1994–2009St. Lucia1981–2009
Central African Rep.1970–2009Lebanon1970–2009St. Vincent & Grens.1975–2009
Chad1970–2009Lesotho1973–2009Sudan1992–2009
Chile*1970–2009Liberia1973–2009Suriname1971–2009
China (Mainland)1984–2009Libya1973–2009Swaziland1970–2009
China (Hong Kong)2001–2009Lithuania1994–2009Sweden*1880–2009
Colombia1958–2009Luxembourg*1974–2009Switzerland*1899–2009
Comoros1982–2009Macedonia1995–2009Syrian Arab Rep.1970–2009
Congo, Dem. Rep. of1970–2009Madagascar1971–2009Taiwan1997–2009
Congo, Rep. of1970–2009Malawi1970–2009Tajikistan1998–2009
Costa Rica1950–2009Malaysia1953–2009Tanzania1970–2009
Cote d’Ivoire1979–2009Maldives1978–2009Thailand1954–2009
Croatia1994–2009Mali1970–2009Togo1975–2009
Cyprus1970–2009Malta1965–2009Tonga1985–2009
Czech Rep.*1993–2009Mauritania1977–2009Trinidad & Tobago1963–2009
Denmark*1880–2009Mauritius1970–2009Tunisia1970–2009
Djibouti1993–2009Mexico*1914–2009Turkey*1936–2009
Dominica1975–2009Moldova1995–2009Turkmenistan1997–2009
Dominican Rep.1970–2009Mongolia1992–2007Uganda1970–2009
Ecuador1939–2009Montenegro2002–2009United Kingdom*1880–2009
Egypt1929–2009Morocco1965–2009Ukraine1992–2009
El Salvador1939–2009Mozambique1999–2009United Arab Emirates1973–2009
Equatorial Guinea1980–2009Myanmar1970–2009United States*1880–2009
Eritrea1995–2009Namibia1993–2009Uruguay1970–2009
Estonia*1995–2009Nepal1970–2009Uzbekistan1998–2009
Ethiopia1970–2009Netherlands*1880–2009Vanuatu1981–2007
Fiji1970–2009New Zealand*1880–2009Venezuela1920–2009
Finland*1914–2009Nicaragua1970–2009Vietnam1992–2009
France*1880–2009Niger1970–2009Yemen1992–2009
Gabon1970–2009Nigeria1968–2009Zambia1970–2009
Zimbabwe1964–2009
  1. * indicates OECD countries in Table 2. Source: Abbas et al. (2010).

B Appendix

B.1 Threshold model results with control variables and estimated statistics

Table 9:

Data Set A: 5-year frequency non-overlapping data (1960–2009).

FEGMMSYS-GMMFE-IVGMM-IV
Regime qi,tdθ
yi,t1−0.097*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)
Capital0.035***0.0160.028***0.066***0.020
(5.32)(1.61)(4.53)(3.08)(1.29)
Education−0.0080.0040.004−0.0170.022*
(−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)
Population0.1090.069−0.4730.2070.767
(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−0.001−0.0060.000−0.032***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 qi,td>θ
yi,t1−0.0370.241
(−0.57)(1.35)
bi,t−0.004*−0.008***−0.0030.089**−0.006*
(−1.70)(−3.22)(−0.89)(2.37)(−1.70)
Capital0.032***0.030***0.023***0.040***0.024***
(4.53)(5.26)(3.70)(4.44)(2.81)
Education−0.013*−0.0050.001−0.017*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)
Population0.6650.426−0.2090.0130.152
(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)
yi,t1−0.0610.029−0.044
(−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 = β20.6750.8180.0970.0470.561
ϕ1 = ϕ20.0130.0000.1970.1390.022
  1. *, ** 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.

Table 10:

Data Set B: short-run annual data (1960–2009).

FEGMMSYS-GMMFE-IVGMM-IV
Regime qi,tdθ
yi,t10.136**0.155***
(2.32)(7.01)
bi,t0.0070.007**−0.0130.010***0.011
(1.05)(2.18)(−1.09)(4.43)(0.69)
Capital0.0090.036***0.0180.024***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)
y00.0000.291***−0.014*0.0010.295***
(.)(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)
Openness0.001−0.089***0.0030.002−0.068***
(0.19)(−17.63)(1.21)(0.65)(−3.33)
Age dependency−0.014−0.0470.026−0.021**0.057
(−1.09)(−1.21)(0.75)(−2.50)(1.12)


Regime qi,td>θ
yi,t10.111***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)
Capital0.027***0.034***0.0170.023***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)
y00.0020.282***−0.0040.0000.297***
(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)
Openness0.002−0.088***−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)
yi,t10.088***0.0900.080**
(4.89)(0.91)(2.00)
Constant0.0870.000−3.543*0.0590.000
(0.60)(.)(−1.92)(0.75)(.)


Wald test results (p-values)
β1 = β20.0690.0000.8440.0330.530
ϕ1 = ϕ20.0110.0000.0000.0250.190
  1. See notes in Table 9.

Table 11:

Data Set C: long-run annual data (1880–2009).

FEGMMSYS-GMMFE-IVGMM-IV
Regime qi,tdθ
yi,t10.237***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 qi,td>θ
yi,t10.151***0.117***
(3.50)(6.37)
bi,t−0.002−0.016−0.0100.000−0.025
(−1.15)(−1.24)(−0.72)(0.28)(−0.03)
yi,t10.139***0.148**0.102
(7.27)(2.48)(0.07)
Constant−0.0030.081***0.0630.027***−0.125
(−0.23)(2.99)(1.27)(4.22)(−0.04)


Wald test results (p-values)
β1=β20.1180.9570.6980.0370.984
  1. See notes in Table 9.

Figure 3: 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.
Figure 3: 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.
Figure 3: 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.
Figure 3:

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).


Published Online: 2018-2-13

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