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Public debt and macroeconomic activity: a predictive analysis for advanced economies

  • Deniz Baglan and Emre Yoldas EMAIL logo


Using post-war data on advanced economies, we find that a higher public debt ratio predicts marginally slower GDP growth under the assumption of a linear relationship. This result is robust to strong persistence in debt ratio, which may cause finite sample bias in estimation and inference. In the nonlinear framework, we find only weak support for piece-wise linear models that explicitly incorporate the idea of a debt tipping point. The threshold estimates from such models are subject to a high level of uncertainty and are sensitive to assumptions on minimum number of observations in each regime. However, using a flexible semiparametric model we uncover that the predictive function is highly complex and behaves quite differently at low, intermediate and high levels of debt. Of particular interest to the recent debate on effects of higher public indebtedness on growth, we find that average annual GDP growth gradually declines by about 0.5% as debt ratio climbs from about 75% to 100%, with most of the effect taking place over the 85–95% range.

Corresponding author: Emre Yoldas, Federal Reserve Board, 20th and C Streets NW, Washington, DC 20551, USA, Phone: +1-202-973-7302, e-mail:


Monte Carlo simulations

In this appendix, we conduct simulations to assess finite sample performance of the threshold and semiparametric models implemented in the paper under model misspecification. For simplicity, we restrict our attention to the one-period case and consider Equation 1 with p=h=1. We parametrize the model as follows: ϕ1=0.4, αi=i0.5(N+1)N, and xi,t =4+ψixi,t–1+νi,t . In addition, the autoregressive roots of the process for x are specified as being local-to-unity, such that ψi =1+ci /T, which reflects the near-integrated dynamics of the debt ratio. The local to unity parameters (ci ) are drawn from a uniform distribution with support [–10, –2]. The innovations (ui,t , νi,t ) are drawn from normal distribution with E[ui,t ]=E[νi,t ]=0, σu =σν =3, and Corr(ui,t , νi,t )=–0.3, ∀i, t. For f(·) we consider piecewise-linear, quadratic, and cubic cases as follows:




For DGP-1, we consider τ∈{20, 40, 60} and set the predictive coefficients equal to the empirical estimates from our data set (see Table 4). The other DGPs are designed to generate smooth nonlinear functions in the support of x. Estimation is carried out as described in the main text for both the threshold and the semiparametric specifications. We set the number of Monte Carlo replications equal to 1000 and pick the sample size N=20, T=50 to closely resemble the data at hand. To evaluate model performance, we estimate f(·) under the assumption of both the threshold and semiparametric specifications regardless of the true DGP and assess the result of misspecification in each case. We evaluate the estimated function at x∈{10, 20, 30, 40, 50, 60, 70, 80} for each replication and report the median estimated value of f(x) across all replications for each model along with the value associated with the true DGP.

Panels A to C in Figure A.1 summarize results under the threshold DGPs. For the case of τ=20 shown in panel a the semiparametric model suggests a turning point around 25 and the point estimates remain closer to the true DGP than those from the threshold model for values of x above the threshold. For τ=40, the semiparametric model yields a largely accurate signal about the turning point, but its overall fit appears poor. The threshold model performs well with respect to goodness of fit below the threshold as well as estimating the threshold itself. Finally, in case of τ=60, the semiparametric model suggest two turning points, but the second one located closer to the true threshold is more significant in magnitude. In terms of goodness of fit, the semiparametric model performs close to the threshold model below the threshold, with the exception of very small values of x. Overall, the semiparametric model’s performance is satisfactory in terms of estimating the turning point in the underlying discontinuous function as well as goodness of fit in the regime with the larger number of observations despite violation of the smoothness assumption.

Figure A.1: Fit of the Semiparametric and Threshold Models under the Threshold DGP. (A): τ=20. (B): τ=40. (C): τ=60.Median fitted values across 1,000 Monte Carlo simulations are reported for the threshold and semiparametric models. True DGP is DGP-1 in the text.
Figure A.1:

Fit of the Semiparametric and Threshold Models under the Threshold DGP. (A): τ=20. (B): τ=40. (C): τ=60.

Median fitted values across 1,000 Monte Carlo simulations are reported for the threshold and semiparametric models. True DGP is DGP-1 in the text.

Panels A and B in Figure A.2 illustrate the cases of quadratic (DGP-2) and cubic (DGP-3), respectively. In the quadratic case, shown in panel a, the goodness of fit of the semiparametric specification is remarkable as the underlying function fulfills the basic assumption of smoothness. The threshold model is useful in signaling the turning point in the underlying function, but performs poorly in goodness of fit. The relative flatness of the estimated function under the threshold assumption suggest that the accompanying confidence intervals would be relatively large. The differences between the two estimation strategies become even more evident when the true DGP is of the cubic form. In this case, the semiparametric model continues to perform well, but the threshold model signals only the second turning point and generally suffers from a positive bias in point estimates.

Figure A.2: Fit of the Semiparametric and Threshold Models under Polynomial DGPs. (A): DGP-2. (B): DGP-3.Median fitted values across 1,000 Monte Carlo simulations are reported for the threshold and semiparametric models. See the text for DGP-1 and DGP-2.
Figure A.2:

Fit of the Semiparametric and Threshold Models under Polynomial DGPs. (A): DGP-2. (B): DGP-3.

Median fitted values across 1,000 Monte Carlo simulations are reported for the threshold and semiparametric models. See the text for DGP-1 and DGP-2.

In general, this Monte Carlo exercise shows that the semiparametric model performs well in signaling a turning point even when the underlying assumption of smoothness is violated. It also appears that the threshold model can be useful in estimating turning points when the underlying function is a smooth low-degree polynomial. The semiparametric model has better goodness of fit properties under model misspecification. We obtain qualitatively similar results under different numerical parametrizations.


Baker, S., N. Bloom, and S. Davis. 2013. “Measuring Economic Policy Uncertainty.” Chicago Booth research paper, (13–02).10.3386/w21633Search in Google Scholar

Baum, A., C. Checherita-Westphal, and P. Rother. 2013. “Debt and Growth: New Evidence for the Euro Area.” Journal of International Money and Finance 32: 809–821.10.1016/j.jimonfin.2012.07.004Search in Google Scholar

Bosworth, B., B. Collins, and S. Margaret. 2003. “The Empirics of Growth: An Update.” Brookings Papers on Economic Activity 2003: 113–206.10.1353/eca.2004.0002Search in Google Scholar

Caner, M., T. Grennes, and F. Koehler-Geib. 2010. “Finding the Tipping Point – when Sovereign Debt Turns Bad.” The World Bank Policy Research Working Paper, No. 5391.10.1596/9780821384831_CH03Search in Google Scholar

Cecchetti, S., M. Mohanty, and F. Zampolli. 2011. “The Real Effects of Debt.” BIS Working paper, No. 352.Search in Google Scholar

Cecherita, C. and P. Rother. 2012. “The Impact of High Government Debt on Economic Growth and its Channels: An Empirical Investigation for the Euro Area.” European Economic Review 56: 1392–1405.10.1016/j.euroecorev.2012.06.007Search in Google Scholar

Clark, T. and M. McCracken. 2012. “In-Sample Tests of Predictive Ability.” Journal of Econometrics 170: 1–14.10.1016/j.jeconom.2010.09.012Search in Google Scholar

Cukierman, A. and A. Meltzer. 1989. “A Political Theory of Government Debt and Deficits in a Neo-Ricardian Framework.” American Economic Review 79: 713–732.Search in Google Scholar

Eberhardt, M. and A. Presbitero. 2013. “This Time they are different: Heterogeneity and Nonlinearity in the Relationship between Debt and Growth.” IMF Working Paper No. 13/248.10.5089/9781484309285.001Search in Google Scholar

Égert, B. 2015a. “The 90% Public Debt Threshold: The Rise and Fall of a Stylised Fact.” Applied Economics 47: 3756–3770.10.2139/ssrn.2304242Search in Google Scholar

Égert, B. 2015b. “Public Debt, Economic Growth and Nonlinear Effects: Myth or Reality?” Journal of Macroeconomics 43: 226–238.10.1016/j.jmacro.2014.11.006Search in Google Scholar

Elliott, G., T. Rothenberg, and J. Stock. 1996. “Efficient Tests for an Autoregressive Unit Root.” Econometrica 64: 813–836.10.3386/t0130Search in Google Scholar

Elmeskov, J. and D. Sutherland. 2012. “Post-Crisis Debt Overhang: Growth Implications across Countries.” Available at SSRN 1997093.10.2139/ssrn.1997093Search in Google Scholar

Hansen, B. 1996. “Inference when a Nuisance Parameter is not Identified under the Null Hypothesis.” Econometrica 64: 413–430.10.2307/2171789Search in Google Scholar

Herndon, T., M. Ash, and R. Pollin. 2014. “Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff.” Cambridge Journal of Economics 38: 257–279.10.1093/cje/bet075Search in Google Scholar

Hjalmarsson, E. 2010. “Predicting Global Stock Returns.” Journal of Financial and Quantitative Analysis 45: 49–80.10.1017/S0022109009990469Search in Google Scholar

Kasparis, I., E. Andreou, and P. Phillips. 2015. “Nonparametric Predictive Regression.” Journal of Econometrics 185: 468–494.10.1016/j.jeconom.2014.05.015Search in Google Scholar

Kumar, M. and J. Woo. 2010. “Public Debt and Growth.” IMF Working Paper 10/174.10.5089/9781455201853.001Search in Google Scholar

Reinhart, C. and K. Rogoff. 2010a. “Growth in a Time of Debt.” American Economic Review: Papers and Proceedings 100: 573–578.10.3386/w15639Search in Google Scholar

Reinhart, C. and K. Rogoff. 2010b. Errata: “Growth in a Time of Debt”. mimeo Harvard University.10.3386/w15639Search in Google Scholar

Stambaugh, R. 1999. “Predictive Regressions.” Journal of Financial Economics 54: 375–421.10.3386/t0240Search in Google Scholar

Su, L. and A. Ullah. 2006. “Profile Likelihood Estimation of Partially Linear Panel Data Models with Fixed Effects.” Economics Letters 92: 75–81.10.1016/j.econlet.2006.01.019Search in Google Scholar

Woodford, M. 1990. “Public Debt as Private Liquidity.” American Economic Review 80: 382–388.Search in Google Scholar

Supplemental Material:

The online version of this article (DOI: 10.1515/snde-2014-0075) offers supplementary material, available to authorized users.

Published Online: 2015-12-15
Published in Print: 2016-6-1

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