Interpretation and limits of sustainability tests in public finance

Abstract

Public debt is considered sustainable if discounted net repayments are expected to cover the initial debt issuance, i.e. if the government’s inter-temporal budget constraint is expected to hold. With risk-averse lenders and an uncertain economic environment, Bohn (1995) stresses that this constraint relies on a stochastic discount factor which depends on lenders’ preferences. To get round the difficulty related to the specification of private agents’ preferences in empirical analysis, Bohn (1998) suggests to estimate fiscal reaction functions describing how primary surplus reacts to indebtedness. After having solved the econometric issues arising when primary surplus and debt have a very different persistence (with a nonparametric approach) or are both integrated (with parametric tests), we estimate fiscal reaction functions for France and Greece. There remain important limitations and interpretation difficulties that are common to all econometric sustainability tests.

Keywords:

• inter-temporal budget constraint
• unit-roots
• co-integration
• fiscal reaction function
• nonparametric tests

JEL Classification:

• C12
• E62
• F34
• H60
• H62

Acknowledgements

The authors thank Guillaume Cléaud, Virginie Coudert, Élise Coudin, Éric Dubois, Corinne Prost, Lukas Reiss and participants at the Banque de France/BETA Conference on Macroeconomic and Financial Vulnerability Indicators in Advanced Economies (Strasbourg, September 2012) for comments on an earlier version.

Notes

¹ This choice for the discount rate cannot be justified according to Bohn (1995), and it makes the transversality condition and the intertemporal budget constraint ad hoc. This issue will be addressed in Section ‘Transversality condition with stochastic discount factor’.

² In his 1998 paper, Bohn alternatively considers a stationary or a (strictly) bounded process . In the appendix available on his web page, he details the proof with a (strictly) bounded process only.

³ Since May 2011, French national accounts are in base 2005 and encompass financial accounts since 1995 only. In the following, we rely on the last available accounts in base 2000.

⁴ General government debt in the sense of the Maastricht Treaty is defined as the sum of total deposits (F2), securities excluding stocks and derivatives (F3 – F34) and credits registered on the liability side (F4). These aggregates are precisely defined in the 1993 System of National Accounts (1993SNA).

⁵ With available annual and quarterly national accounts, we also estimated quarterly fiscal variables for the general government sector. Using net borrowing (B9A) as a quarterly indicator and Chow and Lin’s (1971) method, we estimated a quarterly net debt for the general government. Moreover, it is also possible to obtain a quarterly structural primary surplus, using a standard quadratic interpolation of potential GDP providing a quarterly output gap. Thus, the various fiscal variables defining a fiscal reaction function can be estimated at a quarterly frequency for France for the 1980Q1–2007Q4 period (see details in Lamé et al. (2013)). However, the same statistical approach could not be replicated for Greece due to the lack of long enough quarterly national accounts.

⁶ We assume from the start that unit-root tests do not allow us to differentiate between a formally integrated and a very persistent series for usual sample sizes. If one is absolutely sure to regress a stationary series on an integrated one, the true value of the coefficient cannot be different from zero so that the hypothesis on the existence of a fiscal reaction function would have to be rejected. Therefore, we do not rely on econometric estimations when surplus and debt have different orders of integration.

⁷ Notice that this difficulty is never taken into account in the empirical literature estimating fiscal reaction functions. In particular, Mendoza and Ostry (2008) only report estimation results with an AR(1) residual. The fact that a significantly positive reaction of primary surplus to indebtedness implies sustainability in this case is not proven.

⁸ Remember that we only consider cases where surplus and debt have the same order of integration. If they have different orders of integration, the true value of can only be 0.

⁹ KPSS statistics for the residuals of regressions (1) to (4) of Table 2 are, respectively, 0.073, 0.058, 0.102 and 0.104 to be compared with Shin (1994) asymptotic critical value at 10% of 0.231.

¹⁰ With estimated quarterly data (interpolated from the annual national accounts), net debt and both surpluses ratios are I(1) and co-integrated. Applying once again the Stock and Watson (1993) method leads to the same conclusion for French debt sustainability (i.e., no evidence of a significantly positive fiscal reaction function). Details on the quarterly data set and estimations are available in Lamé et al. (2013).

¹¹ KPSS statistics for the residuals of regressions (1)–(4) of Table 3b are, respectively, 0.117, 0.121, 0.104 and 0.112, the Shin (1994) asymptotic critical value at 10% being 0.231.