# **_I. Introduction_**

Public debt has increased substantially for countries at all income levels as a result of the current global economic crisis. Historical evidence indicates that increases in debt persist for years following financial crises (Reinhart and Rogoff 2010; Scott 2010). In addition, projections of standard measures of public debt relative to GDP for the next 30 years indicate that debt levels are unsustainable for many countries (Cecchetti, Moharty, and Zampolli 2010). Taking account of the implicit public debt associated with social security, medical care, and contingent liabilities would reveal a substantially magnified debt problem (Cecchetti, Moharty, and Zampolli 2010).

The increase in public debt has raised concerns over whether it is starting to hit levels at which it might slow economic growth. Does such a “tipping point” exist? How strong would the growth impact be if debt surpassed the threshold? What would happen if debt stayed at elevated levels for an extended period of time?

According to Reinhart and Rogoff (2010), the answer to the first question is “yes.” Using histograms summarizing evidence from 44 developed and developing economies, they find a threshold of 90 percent central government debt to GDP, after which the real growth rate declines. This threshold has received considerable attention in the press, which has referred to it as a “tipping point” (Pozen 2010). The threshold has practical significance, because the United States and many other countries have either reached this point or are projected to reach it soon and remain above it for years.

If debt thresholds exist, there are theoretical and empirical reasons why they might vary by country income. Debt may play out differently in low-income countries, because of less developed domestic financial markets; a different degree of openness (Frankel and Romer 1999; Levine and Renelt 1992); and different institutions (Acemoglu and others 2003; Alfaro and others 2008). Debt levels in low-income countries may also have different implications for growth through the inflation channel. Governments in countries without well-developed bond markets have resorted to monetizing government debt by selling bonds to their central banks. As a result, empirical studies have found a connection between fiscal deficits and inflation in low-income countries but no systematic connection in high- income countries (Catao and Terrones 2005; Pattillo, Poirson, and Ricci 2002).

This article analyzes thresholds in long-term average public debt to GDP ratios and the differential impact of debt on long-term GDP growth below and above such a threshold. It relies on estimates first introduced by Hansen (1996, 2000) and takes into account country characteristics such as initial GDP, inflation, and trade openness.

The analysis contributes to the literature by providing an econometrically rigorous analysis of the impact of long-run average public debt to GDP ratios on long-run average growth rates. It differs from the literature in three significant ways. First, the literature focuses primarily on the nexus between external debt and growth (see, for example, Cordella, Ricci, and Ruiz-Arranz 2010; Pattillo, Poirson, and Ricci 2002, 2004). In contrast, this chapter analyzes the nexus between total public debt and growth. Second, other studies (Cordella, Ricci, and Ruiz-Arranz 2010; Pattillo, Poirson, and Ricci 2002, 2004; and 2