Is it inverted U? Testing relationships between debt and growth: new evidence from smooth transition kink regression
Abstract
This study examines the inverted U-shaped relationship between public debt and economic growth rates in 44 countries, covering developed, developing, and underdeveloped economies, using data from 1970 to 2020. Unlike previous studies, which often use quadratic regression, threshold, and kink regression models that may not accurately capture the true relationship, we employ the smooth transition kink regression model for this analysis. Our results show that an inverted U-shaped relationship exists in 8 out of the 44 countries studied. The turning point of this relationship, where debt levels shift from beneficial to detrimental, ranges from 23.817% to 96.674%, highlighting the variance in optimal debt levels across different countries. These findings confirm the presence of the inverted U-shaped relationship but reject the notion of a universal turning point applicable to all countries.
First published online 17 March 2025
Keyword : debt, economic growth, inverted U, smooth transition kink regression, turning point
How to Cite
Yamaka, W., & Maneejuk, P. (2025). Is it inverted U? Testing relationships between debt and growth: new evidence from smooth transition kink regression. Technological and Economic Development of Economy, 1-21. https://doi.org/10.3846/tede.2025.22611
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Asravor, R. K., Arthur, L. A., Acheampong, V., Lamptey, C., & Yeboah, M. (2023). Domestic debt sustainability and economic growth: Evidence from Ghana. Research in Globalization, 7, Article 100144. https://doi.org/10.1016/j.resglo.2023.100144
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Beqiraj, E., Fedeli, S., & Forte, F. (2018). Public debt sustainability: An empirical study on OECD countries. Journal of Macroeconomics, 58, 238–248. https://doi.org/10.1016/j.jmacro.2018.10.002
Bentour, E. M. (2021). On the public debt and growth threshold: One size does not necessarily fit all. Applied Economics, 53(11), 1280–1299. https://doi.org/10.1080/00036846.2020.1828806
Caner, M., Grennes, T. J., & Köhler-Geib, F. F. N. (2010). Finding the tipping point – When sovereign debt turns bad. World Bank Conference on Debt Management. SSRN. https://doi.org/10.2139/ssrn.1612407
Cerra, V., & Saxena, S. C. (2008). Growth dynamics: The myth of economic recovery. American Economic Review, 98(1), 439–457. https://doi.org/10.1257/aer.98.1.439
Checherita-Westphal, C., & Rother, P. (2012). The impact of high government debt on economic growth and its channels: An empirical investigation for the euro area. European Economic Review, 56(7), 1392–1405. https://doi.org/10.1016/j.euroecorev.2012.06.007
Doğan, İ., & Bilgili, F. (2014). The non-linear impact of high and growing government external debt on economic growth: A Markov Regime-switching approach. Economic Modelling, 39, 213–220. https://doi.org/10.1016/j.econmod.2014.02.032
Eberhardt, M., & Presbitero, A. F. (2015). Public debt and growth: Heterogeneity and non-linearity. Journal of International Economics, 97(1), 45–58. https://doi.org/10.1016/j.jinteco.2015.04.005
Elmendorf, D. W., & Mankiw, N. G. (1999). Government debt In Handbook of macroeconomics (Vol. 1; pp. 1615–1669) Elsevier. https://doi.org/10.1016/S1574-0048(99)10038-7
Égert, B. (2015). Public debt, economic growth and nonlinear effects: Myth or reality? Journal of Macroeconomics, 43, 226–238. https://doi.org/10.1016/j.jmacro.2014.11.006
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Jameson, K. P. (2003). Is it possible to de-dollarize?: The case of Ecuador. International Journal of Political Economy, 33(1), 42–60. https://doi.org/10.1080/08911916.2003.11042890
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Hansen, B. E. (1999). Threshold effects in non-dynamic panels: Estimation, testing, and inference. Journal of Econometrics, 93(2), 345–368. https://doi.org/10.1016/S0304-4076(99)00025-1
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Herndon, T., Ash, M., & Pollin, R. (2014). Does high public debt consistently stifle economic growth? A critique of Reinhart and Rogoff. Cambridge Journal of Economics, 38(2), 257–279. https://doi.org/10.1093/cje/bet075
Heimberger, P. (2023). Do higher public debt levels reduce economic growth? Journal of Economic Surveys, 37(4), 1061–1089. https://doi.org/10.1111/joes.12536
International Monetary Fund. (n.d). Historical Public Debt Database. https://www.imf.org/external/datamapper/datasets/DEBT
Kristensen, P. H. (2015). Fighting the financial crisis: The social construction and deconstruction of the financial crisis in Denmark. In Research in the sociology of organizations: Vol. 43. Elites on trial (pp. 371–398). Emerald Group Publishing. https://doi.org/10.1108/S0733-558X20150000043025
Law, S. H., Ng, C. H., Kutan, A. M., & Law, Z. K. (2021). Public debt and economic growth in developing countries: Nonlinearity and threshold analysis. Economic Modelling, 98, 26–40. https://doi.org/10.1016/j.econmod.2021.02.004
Lind, J. T., & Mehlum, H. (2010). With or without U? The appropriate test for a U‐shaped relationship. Oxford Bulletin of Economics and Statistics, 72(1), 109–118. https://doi.org/10.1111/j.1468-0084.2009.00569.x
Liu, Z., & Lyu, J. (2021). Public debt and economic growth: Threshold effect and its influence factors. Applied Economics Letters, 28(3), 208–212. https://doi.org/10.1080/13504851.2020.1740157
Liu, P.-Z., Narayan, S., Ren, Y.-S., Jiang, Y., Baltas, K., & Sharp, B. (2022). Re-examining the income–CO2 emissions nexus using the new kink regression model: Does the Kuznets curve exist in G7 countries? Sustainability, 14(7), Article 3955. https://doi.org/10.3390/su14073955
Luukkonen, R., Saikkonen, P., & Teräsvirta, T. (1988). Testing linearity in univariate time series models. Scandinavian Journal of Statistics, 15(3), 161–175.
Maneejuk, P., Yamaka, W., & Sriboonchitta, S. (2021). Does the Kuznets curve exist in Thailand? A two decades’ perspective (1993–2015). Annals of Operations Research, 300(2), 545–576. https://doi.org/10.1007/s10479-019-03425-6
Kumar, M., & Woo, J. (2010). Public debt and growth (IMF Working Paper No. 10/174). International Monetary Fund. https://doi.org/10.5089/9781455201853.001
North, D. C. (2018). Institutional change: A framework of analysis. In Social rules (pp. 189–201). Routledge. https://doi.org/10.4324/9780429497278-13
Okwoche, P. U., & Makanza, C. S. (2023). Public debt and economic growth in sub-Saharan Africa: Nonlinearity and threshold effects. Cogent Economics & Finance, 11(2), Article 2256125. https://doi.org/10.1080/23322039.2023.2256125
Panizza, U., & Presbitero, A. F. (2013). Public debt and economic growth in advanced economies: A survey. Swiss Journal of Economics and Statistics, 149, 175–204. https://doi.org/10.1007/BF03399388
Reinhart, C. M., & Rogoff, K. S. (2010). Growth in a time of debt. American Economic Review, 100(2), 573–578. https://doi.org/10.1257/aer.100.2.573
Ren, Y. S., Jiang, Y., Narayan, S., Ma, C.-Q., & Yang, X.-G. (2022). Marketisation and rural energy poverty: Evidence from provincial panel data in China. Energy Economics, 111, Article 106073. https://doi.org/10.1016/j.eneco.2022.106073
Ren, Y. S., Kuang, X., & Klein, T. (2024). Does the urban–rural income gap matter for rural energy poverty? Energy Policy, 186, Article 113977. https://doi.org/10.1016/j.enpol.2023.113977
Sadiq, M., Yousaf, S. U., Anser, M. K., Khan, H. u. R., Sriyanto, S., Zaman, K., Van Tu, D., & Anis, S. N. M. (2023). The role of debt financing in the relationship between capital structure, firm’s value, and macroeconomic factors: To throw caution to the wind. The Quarterly Review of Economics and Finance, 87, 212–223. https://doi.org/10.1016/j.qref.2020.11.001
Swamy, V. (2020). Debt and growth: Decomposing the cause and effect relationship. International Journal of Finance & Economics, 25(2), 141–156. https://doi.org/10.1002/ijfe.1729
Teräsvirta, T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association, 89(425), 208–218. https://doi.org/10.1080/01621459.1994.10476462
Teräsvirta, T. (1998). Modelling economic relationships with smooth transition regressions. In D. E. A. Giles & A. Ullah (Eds.), Handbook of applied economic statistics (pp. 507–552). Marcel Dekker.
Ueshina, M., & Nakamura, T. (2019). An inverted U-shaped relationship between public debt and economic growth under the golden rule of public finance. Theoretical Economics Letters, 9(6), 1792–1803. https://doi.org/10.4236/tel.2019.96114
World Bank. (n.d.). World Development Indicators. https://databank.worldbank.org/source/world-development-indicators
Yang, L., & Su, J.-J. (2018). Debt and growth: Is there a constant tipping point? Journal of International Money and Finance, 87, 133–143. https://doi.org/10.1016/j.jimonfin.2018.06.002
Ardagna, S., Caselli, F., & Lane, T. (2007). Fiscal discipline and the cost of public debt service: Some estimates for OECD countries. The BE Journal of Macroeconomics, 7(1). https://doi.org/10.2202/1935-1690.1417
Arsić, M., Mladenović, Z., & Nojković, A. (2021). Debt uncertainty and economic growth in emerging European economies: Some empirical evidence. Emerging Markets Finance and Trade, 57(12), 3565–3585. https://doi.org/10.1080/1540496X.2019.1700364
Asravor, R. K., Arthur, L. A., Acheampong, V., Lamptey, C., & Yeboah, M. (2023). Domestic debt sustainability and economic growth: Evidence from Ghana. Research in Globalization, 7, Article 100144. https://doi.org/10.1016/j.resglo.2023.100144
Baum, A., Checherita-Westphal, C., & Rother, P. (2013). Debt and growth: New evidence for the euro area. Journal of International Money and Finance, 32, 809–821. https://doi.org/10.1016/j.jimonfin.2012.07.004
Beqiraj, E., Fedeli, S., & Forte, F. (2018). Public debt sustainability: An empirical study on OECD countries. Journal of Macroeconomics, 58, 238–248. https://doi.org/10.1016/j.jmacro.2018.10.002
Bentour, E. M. (2021). On the public debt and growth threshold: One size does not necessarily fit all. Applied Economics, 53(11), 1280–1299. https://doi.org/10.1080/00036846.2020.1828806
Caner, M., Grennes, T. J., & Köhler-Geib, F. F. N. (2010). Finding the tipping point – When sovereign debt turns bad. World Bank Conference on Debt Management. SSRN. https://doi.org/10.2139/ssrn.1612407
Cerra, V., & Saxena, S. C. (2008). Growth dynamics: The myth of economic recovery. American Economic Review, 98(1), 439–457. https://doi.org/10.1257/aer.98.1.439
Checherita-Westphal, C., & Rother, P. (2012). The impact of high government debt on economic growth and its channels: An empirical investigation for the euro area. European Economic Review, 56(7), 1392–1405. https://doi.org/10.1016/j.euroecorev.2012.06.007
Doğan, İ., & Bilgili, F. (2014). The non-linear impact of high and growing government external debt on economic growth: A Markov Regime-switching approach. Economic Modelling, 39, 213–220. https://doi.org/10.1016/j.econmod.2014.02.032
Eberhardt, M., & Presbitero, A. F. (2015). Public debt and growth: Heterogeneity and non-linearity. Journal of International Economics, 97(1), 45–58. https://doi.org/10.1016/j.jinteco.2015.04.005
Elmendorf, D. W., & Mankiw, N. G. (1999). Government debt In Handbook of macroeconomics (Vol. 1; pp. 1615–1669) Elsevier. https://doi.org/10.1016/S1574-0048(99)10038-7
Égert, B. (2015). Public debt, economic growth and nonlinear effects: Myth or reality? Journal of Macroeconomics, 43, 226–238. https://doi.org/10.1016/j.jmacro.2014.11.006
James, J. A. (1984). Public debt management policy and nineteenth-century American economic growth. Explorations in Economic History, 21(2), 192–217. https://doi.org/10.1016/0014-4983(84)90025-1
Jameson, K. P. (2003). Is it possible to de-dollarize?: The case of Ecuador. International Journal of Political Economy, 33(1), 42–60. https://doi.org/10.1080/08911916.2003.11042890
Haans, R. F., Pieters, C., & He, Z. L. (2016). Thinking about U: Theorizing and testing U‐and inverted U‐shaped relationships in strategy research. Strategic Management Journal, 37(7), 1177–1195. https://doi.org/10.1002/smj.2399
Hansen, B. E. (1999). Threshold effects in non-dynamic panels: Estimation, testing, and inference. Journal of Econometrics, 93(2), 345–368. https://doi.org/10.1016/S0304-4076(99)00025-1
Hansen, B. E. (2017). Regression kink with an unknown threshold. Journal of Business & Economic Statistics, 35(2), 228–240. https://doi.org/10.1080/07350015.2015.1073595
Herndon, T., Ash, M., & Pollin, R. (2014). Does high public debt consistently stifle economic growth? A critique of Reinhart and Rogoff. Cambridge Journal of Economics, 38(2), 257–279. https://doi.org/10.1093/cje/bet075
Heimberger, P. (2023). Do higher public debt levels reduce economic growth? Journal of Economic Surveys, 37(4), 1061–1089. https://doi.org/10.1111/joes.12536
International Monetary Fund. (n.d). Historical Public Debt Database. https://www.imf.org/external/datamapper/datasets/DEBT
Kristensen, P. H. (2015). Fighting the financial crisis: The social construction and deconstruction of the financial crisis in Denmark. In Research in the sociology of organizations: Vol. 43. Elites on trial (pp. 371–398). Emerald Group Publishing. https://doi.org/10.1108/S0733-558X20150000043025
Law, S. H., Ng, C. H., Kutan, A. M., & Law, Z. K. (2021). Public debt and economic growth in developing countries: Nonlinearity and threshold analysis. Economic Modelling, 98, 26–40. https://doi.org/10.1016/j.econmod.2021.02.004
Lind, J. T., & Mehlum, H. (2010). With or without U? The appropriate test for a U‐shaped relationship. Oxford Bulletin of Economics and Statistics, 72(1), 109–118. https://doi.org/10.1111/j.1468-0084.2009.00569.x
Liu, Z., & Lyu, J. (2021). Public debt and economic growth: Threshold effect and its influence factors. Applied Economics Letters, 28(3), 208–212. https://doi.org/10.1080/13504851.2020.1740157
Liu, P.-Z., Narayan, S., Ren, Y.-S., Jiang, Y., Baltas, K., & Sharp, B. (2022). Re-examining the income–CO2 emissions nexus using the new kink regression model: Does the Kuznets curve exist in G7 countries? Sustainability, 14(7), Article 3955. https://doi.org/10.3390/su14073955
Luukkonen, R., Saikkonen, P., & Teräsvirta, T. (1988). Testing linearity in univariate time series models. Scandinavian Journal of Statistics, 15(3), 161–175.
Maneejuk, P., Yamaka, W., & Sriboonchitta, S. (2021). Does the Kuznets curve exist in Thailand? A two decades’ perspective (1993–2015). Annals of Operations Research, 300(2), 545–576. https://doi.org/10.1007/s10479-019-03425-6
Kumar, M., & Woo, J. (2010). Public debt and growth (IMF Working Paper No. 10/174). International Monetary Fund. https://doi.org/10.5089/9781455201853.001
North, D. C. (2018). Institutional change: A framework of analysis. In Social rules (pp. 189–201). Routledge. https://doi.org/10.4324/9780429497278-13
Okwoche, P. U., & Makanza, C. S. (2023). Public debt and economic growth in sub-Saharan Africa: Nonlinearity and threshold effects. Cogent Economics & Finance, 11(2), Article 2256125. https://doi.org/10.1080/23322039.2023.2256125
Panizza, U., & Presbitero, A. F. (2013). Public debt and economic growth in advanced economies: A survey. Swiss Journal of Economics and Statistics, 149, 175–204. https://doi.org/10.1007/BF03399388
Reinhart, C. M., & Rogoff, K. S. (2010). Growth in a time of debt. American Economic Review, 100(2), 573–578. https://doi.org/10.1257/aer.100.2.573
Ren, Y. S., Jiang, Y., Narayan, S., Ma, C.-Q., & Yang, X.-G. (2022). Marketisation and rural energy poverty: Evidence from provincial panel data in China. Energy Economics, 111, Article 106073. https://doi.org/10.1016/j.eneco.2022.106073
Ren, Y. S., Kuang, X., & Klein, T. (2024). Does the urban–rural income gap matter for rural energy poverty? Energy Policy, 186, Article 113977. https://doi.org/10.1016/j.enpol.2023.113977
Sadiq, M., Yousaf, S. U., Anser, M. K., Khan, H. u. R., Sriyanto, S., Zaman, K., Van Tu, D., & Anis, S. N. M. (2023). The role of debt financing in the relationship between capital structure, firm’s value, and macroeconomic factors: To throw caution to the wind. The Quarterly Review of Economics and Finance, 87, 212–223. https://doi.org/10.1016/j.qref.2020.11.001
Swamy, V. (2020). Debt and growth: Decomposing the cause and effect relationship. International Journal of Finance & Economics, 25(2), 141–156. https://doi.org/10.1002/ijfe.1729
Teräsvirta, T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association, 89(425), 208–218. https://doi.org/10.1080/01621459.1994.10476462
Teräsvirta, T. (1998). Modelling economic relationships with smooth transition regressions. In D. E. A. Giles & A. Ullah (Eds.), Handbook of applied economic statistics (pp. 507–552). Marcel Dekker.
Ueshina, M., & Nakamura, T. (2019). An inverted U-shaped relationship between public debt and economic growth under the golden rule of public finance. Theoretical Economics Letters, 9(6), 1792–1803. https://doi.org/10.4236/tel.2019.96114
World Bank. (n.d.). World Development Indicators. https://databank.worldbank.org/source/world-development-indicators
Yang, L., & Su, J.-J. (2018). Debt and growth: Is there a constant tipping point? Journal of International Money and Finance, 87, 133–143. https://doi.org/10.1016/j.jimonfin.2018.06.002