metadata: authors: 0: author: Frank,Nathaniel
1: author: Ley,Eduardo
count: World
docna: 0: docna: Refinements to the probabilistic approach to
            fiscal sustainability analysis
docty: Policy Research Working Paper
subtopic: Debt Relief and HIPC,Macro-Fiscal Policy,Economic Conditions and Volatility,Economic Adjustment and Lending,Public Sector Economics,External Debt,International Trade and Trade Rules,Public Finance Decentralization and
            Poverty Reduction,Debt Markets
teratopic: Macroeconomics and Economic Growth,Finance and Financial Sector Development,Private Sector Development,International Economics and Trade
abstracts: cdata!: This paper relaxes some key assumptions
            in the probabilistic approach to fiscal sustainability.
            First, the authors identify structural breaks over the
            sample period used to estimate the covariance matrix of the
            shocks to the debt ratios. Second, the assumption of
            normality of the shocks is dropped by modeling their
            respective empirical distribution directly, which makes it
            possible to quantify asymetries and thick tails. Third, the
            use of fiscal reaction functions is avoided by focusing
            attention on debt-stabilizing balances.
repnme: repnme: Refinements to the probabilistic approach
            to fiscal sustainability analysis
display_title: Refinements to the probabilistic
            approach to fiscal sustainability analysis
listing_relative_url: /research/2008/09/9820457/refinements-probabilistic-approach-fiscal-sustainability-analysis
topicv3: Macroeconomic Vulnerability and Debt
            m1326057 1104,Fiscal Sustainability m1326901 1097,Trade m1326924 698,Fiscal Policy m1327144 445,Debt Sustainability Framework m1327215 1139
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Finance and Financial Sector Development,Private Sector Development,International Economics and Trade
no_of_pages: 14
author_keys: 0: author_key: 943610
1: author_key: 913182
model_extractions: WPS4709 Policy ReseaRch WoRking PaPeR 4709 Refinements to the Probabilistic Approach to Fiscal Sustainability Analysis _Nathaniel Frank Eduardo Ley_ The World Bank Economic Policy and Debt Department September 2008
Policy ReseaRch WoRking PaPeR 4709

# **Abstract**

This paper relaxes some key assumptions in the probabilistic approach to fiscal sustainability. First, the authors identify structural breaks over the sample period used to estimate the covariance matrix of the shocks to the debt ratios. Second, the assumption of normality of the shocks is dropped by modeling their respective empirical distribution directly, which makes it possible to quantify asymetries and thick tails. Third, the use of fiscal reaction functions is avoided by focusing attention on debt-stabilizing balances.

This paper—a product of the Economic Policy and Debt Department—is part of a larger effort in the department to study issues related to debt sustainability. Policy Research Working Papers are also posted on the Web at http://econ.worldbank. org. The author may be contacted at eley@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Refinements to the Probabilistic Approach to Fiscal Sustainability Analysis**

## Nathaniel Frank

_Nuffield College, University of Oxford, U.K._ Eduardo Ley _The World Bank, Washington DC, U.S.A._

**Keywords.** Fiscal sustainability, structural change, SVAR, bootsrap **JEL Classification System.** F34, H60, C50

**Address.** nathaniel.frank@nuffield.ox.ac.uk and eley@worldbank.org
# **1. Introduction**

The joint Bank-IMF debt-sustainability stress tests look at the debt-dynamics behavior under large changes of several of the variables involved, keeping all else constant. These shocks are applied to interest rates, exchange rates, or growth—without changing the values of other endogenous variables.

Celasun, Debrun and Ostry (2007, CDO henceforth) discuss the limitations of this approach and propose a probabilistic scenario analysis, using a stochastic framework to draw constellations of values for the variables driving the debt dynamics. For this purpose, CDO estimate a VAR for the non-fiscal components of the system. Under the assumption of joint normality they produce debt fan charts—by drawing from the fitted residual multivariate normal distribution, and iterating forward the law of motion of the debt-to-GDP ratio, along an estimated fiscal reaction function. Budina and van Wijnbergen (2007), and Bandeira _et al._ (2007) apply this framework to several country cases, and discuss how it improves the traditional Bank-IMF debt-sustainability framework.

This paper builds on this work, and explores some methodological refinements to the CDO fiscal sustainability analysis. First, we allow for structural breaks in the data-generation mechanism, which are identified through the application of Markov Switching models. Second, the assumption of normally distributed shocks is relaxed and bootstrapping techniques are used to make draws directly from their empirical distributions. This allows for a better risk assessment as the tail behaviour and asymmetries in the debt projections are more precisely quantified. Third, the estimation of the fiscal reaction function is replaced by inference with regard to the required primary balances consistent with sustainable fiscal policy.

This paper is organized as follows. Section 2 outlines the standard debt-sustainability framework and motivation of the research. Section 3 discusses the proposed methodology. Section 4 presents results for emerging market economies, and Section 5 conducts policy evaluation against a benchmark of fiscal sustainability. Finally, Section 6 concludes.

# **2. Debt-Sustainability Framework**

Using _d_ for debt and _b_ for the government balance (expressed as percentages of GDP), _g_ for real GDP growth, _α_<sup>_f_</sup> for the share of foreign-denominated government debt, and _β_<sup>_f_</sup> as the share of the tradable sector in GDP, the debt-dynamics are given by: ˆ where _et_ is the rate of nominal depreciation of the local currency, and _ıt_ = _α_<sup>_h_</sup> _i_<sup>_h_</sup> _t_<sup>+</sup><sup>_αfif_</sup> _t_<sup>and</sup> ˆ _πt_ = _β_<sup>_h_</sup> _πt_<sup>_h_+</sup><sup>_βfπ_</sup> _t_<sup>_f_are the effective interest rate and GDP deflator—which are weighted averages</sup> We acknowledge useful comments from Fernando Blanco, Carlos Braga, Tihomir Stucka, Rogier van den Brink, Sweder van Wijnbergen, and participants at seminars at the World Bank and at the Banca d’Italia workshop on Fiscal Sustainability (Perugia, April 2008). We also thank Nina Budina, Oya Celasun and Xavier Debrun for useful conversations and sharing their data with us. The views expressed in this paper are the authors’, and do not necessarily reflect those of the World Bank or its executive directors.

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of domestic and foreign rates (Ley, 2006). Equations (1)–(3) can be combined to obtain the familiar expression driving public-debt dynamics: The Bank-Fund joint debt-sustainability framework (DSF) analyses the behavior of equation (4) under some stress tests. Thus, large shocks are applied interest rates, exchange rates, or growth— keeping other endogenous variables fixed, and the subsequent behavior of the debt-dynamics is studied. CDO discuss the limitations of this approach and implement a probabilistic scenario analysis that addresses some of the shortcomings of the standard DSF.

# _2.1. Refinements_

As mentioned, CDO develop a stochastic framework to draw joint shocks for the variables involved in (4). First, a VAR comprised of the aforementioned input variables such as growth, interest and depreciation rates is estimated. Second, a fiscal reaction function is computed, yielding the statistical relationship between the primary balances, past levels of debt and the output gap. Finally, shocks are repeatedly drawn from the approximated joint Normal distribution, based on the VARestimated covariance matrix, which are in turn used in the forward iteration of a debt equation and the fiscal reaction function. The resulting fan charts thus provide a probability distribution for future debt levels, which are contrasted against the DSF criteria.

In this paper methodological refinements are proposed, as we identify three issues which remain unaddressed by this technique.

- [1] **Structural Breaks** . Estimation conducted for emerging market economies often includes episodes that feature financial crises— _e.g._ , Mexico in 1995, Asia in 1997, Turkey in 2001 and Argentina in 2002. During such periods, significant jumps in interest rate spreads, exchange rates and GDP growth have historically been observed. This implies that the assumption of stationarity of the data generating processes cannot be ensured. In this context, estimation of a standard unvarying VAR is problematic. Consequently, inference with regard to the debt forecasts may be inappropriate, as the former is used in the input projections whereas the stochastic simulations are based on the latter. In this paper we allow for structural breaks which are identified through a Markov Switching VAR. Further estimation is then conducted over periods exhibiting constancy in the data generating processes, which ensures consistent

- [2] **Normality** . The assumption of normality with regard to the underlying shock distribution constitutes a severe limitation of the analysis in CDO. The resulting imposition of symmetry does not adequately reflect the empirical tail behaviour of economic variables, especially during period of financial distress. Furthermore, any inferred symmetry of the debt projections may merely be a construct of this assumption and thus conceals the true degree and shape of risk exposure. We replace the normality assumption by direct inference on the joint distribution of the shocks. Identification of stable sub-samples allows for the application of bootstrapping techniques. Consistent resampling of the data and repeated estimation implies that the resulting residuals converge to their true underlying counterpart. This then allows for the analysis of any

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non-normality such as asymmetry and for the exact specification of the tail behaviour of the shocks.

- [3] **Fiscal Reaction Function** . CDO makes inference with regard to the dynamics between primary balances, lagged debt and the output gap by estimating a fiscal reaction function, which is subject to severe estimation and model uncertainty. In this paper we avoid its introduction by inverting equation (4). As a result, we specify a policy which is consistent with fiscal sustainability, such as debt stabilisation, and by drawing repeated shocks from the true error distribution, we make probabilistic inference with regard to the implied balances. This allows us to escape the aforementioned data constraints and for the evaluation of current policy against such a sustainability benchmark.

Other methodological differences introduced here include the amendment of the debt equation in order to account for tradables which are proxied by the export-to-GDP ratio. Furthermore, we do not assume that interest rate shocks affect the entire debt stock, but rather differentiate between its maturity structure such that merely the short term and a uniformly distributed fraction of the medium to long term debt is rolled over each period. Finally, with regard to data, our estimation is based on the fiscal panel and the input variables provided by CDO, except for the definition of the interest rate for foreign denominated debt. Whereas they employ the deflated US T-Bill rates as a proxy for borrowing costs in foreign markets, we incorporate interest rate spreads in the form of the Emerging Markets Bond Index (EMBI) as we believe that this more appropriate for emerging market countries.

# **3. Methodological Refinements**

# _3.1. Markov Switching VAR_

The Markov Switching VAR, as proposed by Hamilton (1989) and Krolzig (1997), differs from its linear counterpart by allowing the structural coefficients and the covariance matrix to be dependent on an unobserved state variable _St_ , which is assumed to follow a _k_ -dimensional Markov chain. This is of importance in our context, as we expect the joint distribution of the shocks to be non-constant across our sample period.

Furthermore, estimation of this model allows for inference with regard to the probabilities of being in the respective states of the world, such that any structural breaks are identified by regime switches.

# _3.2. Bootstrap_

As discussed above, this paper replaces the assumption of normally distributed shocks imposed in CDO by direct inference with regard to their true joint distribution. To this end we employ nonparametric bootstrapping techniques on the stationary sub-periods exhibiting constancy in terms 3
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# **8. References**

- Bandiera, Luca, Nina Budina, Michel Klijn, and Sweder van Wijnbergen (2007) “The ‘How To’ of Fiscal Sustainability: A Technical Manual for Using the Fiscal Sustainability Tool” World Bank Policy Research Working Paper No 4170

- Budina, Nina, and Sweder van Wijnbergen (2007) “Quantitative Approaches to Fiscal Sustainability Analysis: A New WorldBank Tool Applied to Turkey” World Bank Policy Research Working Paper No 4169

- Celasun, Oya , Xavier Debrun, and Jonathan D. Ostry (2007) “Primary Surplus Behavior and Risks to Fiscal Sustainability in Emerging Market Countries: A Fan-Chart Approach,” _IMF Staff Papers_ , 53(3): 401–425.

- Hamilton, J. D. (1989) “A new approach to the economic analysis of nonstationary time series and the business cycle,” _Econometrica_ 57, 357–384.

- Krolzig, H.-M. (1997), _Markov Switching Vector Autoregressions: Modelling, Statistical Inference and Application to Business Cycle Analysis_ , Lecture Notes in Economics and Mathematical Systems, 454, Springer-Verlag, Berlin.

- Ley, E. (2006) “Fiscal (and External) Sustainability,” (Unpublished, The World Bank), available at http://129.3.20.41/eps/pe/papers/0310/0310007.pdf

- Politis, D.N. and Romano, J. (1992) “A circular block-resampling procedure for stationary data,” in _Exploring the Limits of Bootstrap_ , edited by Raoul LePage and Lynne Billard, John Wiley, 263–270.

- Politis, D. N. and H. White (2004) “Automatic block-length selection for the dependent bootstrap,” _Econometric Reviews_ 23(1): 53–70. (See also: A. Patton, D.N. Politis, and H. White (2008) “Correction to: ‘Automatic Block-Length Selection for the Dependent Bootstrap’ by D. Politis and H. White.”)

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