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«WP/16/178 Optimal Debt Policy Under Asymmetric Risk by Julio Escolano and Vitor Gaspar © 2016 International Monetary Fund WP/16/178 IMF Working ...»

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Optimal Debt Policy Under Asymmetric Risk

by Julio Escolano and Vitor Gaspar

© 2016 International Monetary Fund WP/16/178

IMF Working Paper

Fiscal Affairs Department

Optimal Debt Policy Under Asymmetric Risk

Prepared by Julio Escolano and Vitor Gaspar1

Authorized for distribution by Vitor Gaspar

August 2016

IMF Working Papers describe research in progress by the author(s) and are published to elicit

comments and to encourage debate. The views expressed in IMF Working Papers are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF management.

Abstract In the paper we show that, most of the time, smooth reduction in the debt ratio is optimal for tax-smoothing purposes when fiscal risks are asymmetric, with large debt-augmenting shocks more likely than commensurate debt reducing shocks. Asymmetric risks are a feature of 200 years of data for the U.S. and the U.K.: rare but recurrent large surges of the debt-to-GDP ratio, followed by very gradual but persistent declines over long periods. More informal evidence from many other countries suggests that asymmetry is a general feature of fiscal shocks. The gradual smooth reduction in the public debt to GDP ratio is not a response to past developments. Instead it is optimal given recurrent fiscal risks and the empirical characteristics of fiscal shocks. The behavior of the debt-to-GDP ratio in the U.K. and the U.S.

seems roughly compatible with the prescriptions of the tax-smoothing model.

JEL Classification Numbers: E60, E61, E62, E65, H21, H62, H63 Keywords: Government Debt, Optimal Debt Policies, Fiscal Risks, Fiscal Shocks.

Author’s E-Mail Address: JEscolano@img.org and VGaspar@imf.org International Monetary Fund, Fiscal Affairs Department. This paper should not be reported as representing the views of the IMF. The views expressed in this paper are those of the authors and do not necessarily represent those of the IMF or IMF policy.

Content Page


I. Introduction

II. Evidence from Debt History

III. Optimal Debt Policy

IV. Optimal Debt Policy under Skewed Shocks

V. How Skewed are Debt Shocks?

VI. Conclusions



1. Symmetry Tests Results


1. United Kingdom: National/Government Debt

2. United States: Federal Government Debt

3. United Kingdom: Histogram of the First Differences of the Debt Ratio

4. United States: Histogram of the First Differences of the Debt Ratio


The global financial crisis of 2008 and its aftermath resulted in large increases in public debt ratios to GDP. Ostry, Ghosh, and Espinoza (2015) argue that fiscal authorities should not aim at a primary balance surplus beyond what is necessary to pay the higher interest bill entailed by the additional debt.2 Rather they should just aim at stabilizing the debt ratio at its current level. The set-up used here, as well as in Ostry, Ghosh, and Espinoza (2015), abstracts from counter-cyclical stabilization policies and rollover risk, and instead focuses on intertemporal considerations associated with government financing and tax smoothing. In this paper, we simplify the framework in Ostry, Ghosh, and Espinoza by disregarding public investment. Instead, we extend long-term optimal debt policy a la Barro (1979 and 1986) to consider stochastic and recurrent shocks to the fiscal position and, hence, to the debt ratio.

The question we ask is whether countries that do not face binding financing constraints should gradually reduce high public debt to GDP ratios. That question is distinct from debt reduction forced by the risk of an immediate loss of market access. Only a few advanced economies, which experienced large debt ratio increases since 2008, faced adverse market conditions for rolling over or increasing their outstanding debt stock. For the remaining advanced countries, including some of the largest economies in the world, debt reduction policies are, at this time, a matter of choice.

The choice of debt policy entails an inter-temporal trade-off. As argued in Ostry, Ghosh, and Espinoza (2015), keeping the debt ratio constant is optimal when the marginal deadweight loss incurred today equals the marginal expected net present value of future gains. Minimizing the net present value of inter-temporal deadweight losses implies tax smoothing: if expenditure is expected to remain constant in the future, tax smoothing implies a tax ratio set permanently at the level that just pays the annual constant expenditure and the interest on the inherited debt. In this case, debt will also be expected to remain at the current level.

Importantly, policy decisions regarding this inter-temporal trade-off must be made in the face of recurrent fiscal risk. As the recent financial crisis showed and the earlier history of debt confirms, public debt ratios have been subject to very substantial disturbances. While the size of the debt accumulation prompted by the crisis of 2008 stands out in post-WWII history, it has certainly not been the first or the largest upward shock to public debt from a broader historical perspective, nor will it be the last.

Thus, to analyze the optimal response to the debt surge after the 2008 global financial crisis, the approach here will be to consider this surge as a (particularly bad) draw from an enduring stochastic process. From this standpoint, we show that whether gradual reduction in the debt ratio is optimal hinges on the distribution of debt shocks. If the distribution of shocks were symmetric, reducing debt now to pay down in advance future adverse shocks would not be more Primary balance is used henceforth to denote fiscal revenue less expenditure before interest payments. Thus the primary balance equals the net lending by the government (or overall balance) plus interest payments. The concept is sometimes denoted gross primary balance—since it nets out interest payments from expenditure, but not interest receipts from revenue.

justified than increasing debt now on account of future favorable shocks. Indeed, in the case of symmetric shocks or if no further shocks were expected in the future, the optimal policy would be to stabilize the debt at current levels, making no deliberate attempt to reduce or increase debt ratios—as argued in Ostry, Ghosh, and Espinoza (2015).

However, if the probabilistic distribution of fiscal shocks results in infrequent but large adverse (positive) shocks—as we find it is the case in the data—the optimal policy in normal times is to reduce debt ratios gradually but persistently in anticipation of future large negative events. In the past, the most prominent of these negative events were the outbreak of wars. But in present times, other events can also result in large unexpected fiscal costs. In particular, reducing public debt ratios pre-emptively can be argued on grounds of financial stability (Obstfeld, 2013), or the materialization of public contingent liabilities (Bova et al. 2016). The objective of this policy of reducing debt ratios in good times is to stabilize the (expected) debt ratio in the long run. In years when large adverse shocks materialize, they should be absorbed though borrowing. But in the absence of an emergency—that is, in most years—the optimal policy results in a moderate debt reduction. As we will show, the reduction in the debt-to-GDP ratio is a direct consequence of the distribution of shocks to public debt. Optimal policy entails that both the public debt ratio and the tax ratio behave like random walks. Nevertheless, the empirical characteristics of the distribution of shocks means that it is most likely to witness shocks below average. This bias leads to debt reduction in normal years.

Given that our analysis is motivated by the actual historical pattern of the debt ratio in the major economies of the time, we start in Section II by summarily presenting the evidence of the last two centuries for the United Kingdom and the United States. We argue that the path of debt ratios is characterized by large and sudden upward shocks that occur infrequently, and by long periods of gradual but persistent debt reduction. We focus on the United Kingdom and the United States because one of the two was the most advanced economy in the world during the historical period studied (1790-present). Moreover, both developed financial markets and institutions early on, and their sovereign debt was, for most of the period, considered as a safe asset. Thus, these sovereigns were least likely to face financing constraints. Also, consistent data on debt and GDP are available for these countries, as well as a well-researched historical economic record. Nevertheless, it is important to stress that there is evidence that positive asymmetry is a general feature of fiscal shocks that applies to a wide cross-country evidence (International Monetary Fund, 2016).

Section III then lays out a basic framework in which government debt is subject to random shocks. The policymaker seeks to smooth the tax ratio over time, subject only to a non-Ponzi game solvency constraint, but is otherwise free to accommodate any amount of debt. The optimal policy in this setting is in line with Barro (1979). After a shock to the debt ratio, the government should adjust the tax ratio and the primary balance up or down just enough to pay the new level of (growth-adjusted) interest, and the expected annual expenditure including the long-term average value of shocks (if different from zero). As a result, the actual paths of the debt and tax ratios (and of the primary balance as a ratio to GDP) will be random walks and the expected path of the debt ratio will be constant. Section IV specializes this optimal debt policy to a skewed distribution of shocks, with infrequent but large adverse shocks. Section V formally analyzes the historical fiscal shocks and test the skewness of the distribution of changes in the debt ratio. It finds that the statistical evidence is consistent with a skewed distribution of shocks.

Section VI concludes.

–  –  –

In discussing the appropriate response to recent increases in public debt, it is useful to start from the historical record. Over the past two and a quarter centuries, the path of government debt ratios in the United Kingdom and the United States were characterized by occasional large increases prompted by national emergencies such as wars and large economic crises followed by long periods of sustained reductions in debt ratios.

The debt ratio of the United Kingdom (Figure 1) reached a peak of 220 percent of GDP in 1822, after the Napoleonic wars.3 But during the following almost a century, from 1822 to 1913, the debt ratio declined more or less steadily to a historical low of 31 percent—a deliberate and sustained debt reduction policy. The rationale for such a sustained reduction in the debt to GDP ratio was part of the so-called Gladstone doctrine of public finances (Schumpeter, 1956). During these years, roughly covering the Victorian period, there were few severe downturns (Hills, Thomas, and Dimsdale, 2010). Military engagement costs—mainly in the Crimean and Boer wars—relative to the size of the economy were of a scale well below those of the preceding period (Barro, 1987) and also those to come in the 20th century.

Data for the United Kingdom in early years correspond to “national debt” and are from Hills, Thomas, and Dimsdale (2010, database updated in 2014). Data for more recent years correspond to consolidated general government debt and are from the U.K. Office for National Statistics (ONS, series code BKPX). For consistency with the data available for the earliest dates, we use GDP at current factor cost for the whole sample period (calculated like in Hills, Thomas, and Dimsdale (2010) as the difference between the ONS series codes: YBHACMVL). This results in a debt-to-GDP ratio of around 100 percent in 2014, which is higher than the debt-to-GDP ratio of about 90 percent obtained by using the headline series of GDP at current market prices.

–  –  –

Sources: Hills, Thomas, and Dimsdale (2010, updated 2014), and UK Office for National Statistics (ONS).

WWI and the recession of 1920 – 1921 prompted a sharp increase in the debt ratio, which was also followed by subsequent attempts at reduction, albeit interrupted by the depression in 1930 – 1933.4 In turn, these years were followed by a remarkable fall in the debt ratio, in the seven years (1934 – 1940) preceding WWII. As a result of the WWII effort, the debt ratio rose to 270 percent of GDP by 1946. But during 1946 – 1990 it fell again to about 34 percent. The recession in the early 1990s, raised the debt ratio to about 53 percent. And finally, the global financial crisis of 2008 raised it again from about 49 percent in 2007 to 102 percent in 2014.

Overall, for the past two centuries, national debt policies in the United Kingdom show persistent reductions in the debt ratio in the wake of a few large increases associated with wars or large recessions.

The increase in the debt ratio during 1930 – 1933 was mainly due to a decline in nominal GDP. The nominal value of debt went from 7.6 billion pounds in 1929 to 8 billion pounds in 1933 or a nominal increase of about

5.7 percent, while nominal GDP declined by more than 8.4 percent (Hills, Thomas, and Dimsdale, 2010).

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