Fiscal sustainability using growth-maximizing debt targets

Abstract

This article highlights the importance of debt-related fiscal rules and derives growth-maximizing public debt ratios from a simple theoretical model. On the basis of evidence on the productivity of public capital, we estimate public debt targets that governments should maintain if they wish to maximize growth for panels of OECD, EU and euro area countries. These are not arbitrary numbers, but are founded on long-run optimizing behaviour assuming that governments implement the golden rule of financing; that is, they contract debt only to finance public investment. Our estimates suggest that the euro area should target debt levels of around 50% of GDP if member states are to have common targets. That is about 15% points lower than the estimate for the growth-maximizing debt ratio in our OECD sample and comfortably within the Stability and Growth Pact’s debt ceiling of 60% of GDP. We also indicate how forward-looking budget reaction functions fit into a debt targeting framework.

Keywords:

• public debt
• public capital
• economic growth
• golden rule of financing

JEL Classification:

• H63
• E22
• O40

Notes

¹ See, for example, Dixit and Lambertini (2003) or Hughes Hallett and Weymark (2007).

² The revised Stability and Growth Pact now includes high debt ratios in the medium-term budgetary objectives that countries are asked to achieve. Moreover, if the current budgetary position falls short of the medium-term objective, high-debt countries are to implement more ambitious adjustment plans to achieve them. Finally, for countries with debt ratios above 60% of GDP, an excessive deficit procedure can be launched if the debt ratio is deemed not to be sufficiently diminishing – meaning the debt ratio should diminish annually by at least 1/20th of the difference between the actual debt ratio and the 60% of GDP reference value.

³ It might be thought that a debt target allows greater flexibility, which governments might exploit to run large deficits, but imposing a debt brake/golden rule effectively rules this out since the rest of the budget has to be in balance.

⁴ Equation 1 displays constant returns to scale overall, but also crucially between aggregate public and private sector inputs (and within private production). Without the second-order conditions for a maximum, the search for growth will lead to steadily escalating debt – with financing costs being the only constraint. Default then becomes unavoidable.

⁵ L is normalized to 1 in Aschauer (2000). But in general, Equation 3 shows that φ is the optimal ratio of public to private inputs.

⁶ The 22 OECD economies covered are Australia (AUS), Austria (AUT), Belgium (BEL), Canada (CAN), Switzerland (CHE), Denmark (DNK), Finland (FIN), France (FRA), Germany (DEU), Greece (GRC), Ireland (IRL), Iceland (ISL), Italy (ITA), Japan (JPN), Netherlands (NLD), Norway (NOR), New Zealand (NZL), Portugal (PRT), Spain (ESP), Sweden (SWE), the UK (GBR) and the US (USA). The EU-14 countries appear in italics, and EA-11 in bold italics.

⁷ We focus on (and use in this article) the production function approach, which is in line with our theoretical model. This is the most frequently employed of three main approaches of the empirical literature on the marginal productivity of public capital. The other two are the cost function approach and the vector autoregressive approach.

⁸ Performed on demeaned data to render cross-sectionally independent disturbances. The test allows for heterogeneous short-run dynamics for different countries in the panel.

⁹ As implemented in Stata by Persyn and Westerlund (2008).

¹⁰ As implemented in Blackburne and Frank (2007), namely, (i) a modified fixed-effects estimator; (ii) the mean-group estimator of Pesaran and Smith (1995); and (iii) the pooled mean-group estimator.

¹¹ As implemented in Stata based on Sarafidis and De Hoyos (2006).

¹² The estimates for the OECD are marginally higher at 0.22 than those found in Kamps (2006) for the same sample of countries and a shorter time period. These results are also comparable to 0.203 in Holz-Eakin (1994), but lower than the 0.30 in Aschauer (2000) using a panel estimation across US states. Applying a nonlinear estimation model, Kamps (2005) finds a very similar coefficient (0.208) for the EU-14 group and calculates a growth-maximizing ratio of public capital-to-GDP ratio of 42.3% using data for the period 1970 to 2000.

¹³ See Vance (2006). For more details and another application to euro area countries, see Checherita and Rother (2012).

¹⁴ The confidence interval for the euro area optimal debt ratio seems wide, but this is mostly because of the smaller cross-country sample size. Moreover, the SE is less than one-quarter the average debt ratio.

¹⁵ We thank a reviewer for the suggestions in this direction.

¹⁶ Only between 66% and 68% of GDP across the three robustness checks under Models 2 and 3. Under Model 1, in line with previous estimates, the variation is somewhat higher: d* is at about 60% of GDP in the robustness check (i), 42% for case (ii) and 54% for case (iii). Results of the robustness checks are available upon request.

¹⁷ However, one must also reckon with the possibility that debt fatigue (a point beyond which tax revenues cannot be made to rise) may set in. This possibility is captured by the line AB, drawn to intersect (r – g)d at d₂. This line says that, whereas policymakers may make little effort to raise a primary surplus at low levels of debt, they may well find they are unable to do so (or the political consequences of attempting to do so are too severe) at high levels. Beyond d₂, primary surpluses will be too small to stop the debt burden rising. Risk premia at this point will rotate the (r – g)d line upwards.