Summary
This article constructs a new, simple, yet rigorous fiscal rule as an alternative for the current (new) rules in the Stability and Growth Pact of the European Union. One problem with the current rules of maximum debt of 60 % and maximum deficit of 3 % is that they are ex nihilo and completely arbitrary and ad hoc, based on some assumptions and average debt levels of the early 1990s. The present approach takes a rigorous approach using solvency constraints and stochastic differential equations. The rule presented here is thus robust with respect to underlying parameters. The S2 indicator of the European commission is both mathematically and economically meaningless, and the reference values have no theoretically robust basis. That is why a new approach is needed.
The idea is that the required primary balance ratio target is determined via considering the inter-temporal solvency constraint of the sovereign and assuming a certain simple mean-reverting fiscal rule. The rule presented differentiates across Member states and is based on actual primary deficits, debt ratios and historical adjustment rates. The possible implementation of the rule is discussed and its links to the discussion of a fiscal stabilization function is elaborated as an alternative to legally binding fiscal rules.
Introduction
Fiscal policy coordination and economic policy coordination more generally are becoming evermore important in the Economic and Monetary Union (EMU) of the EU, as we have witnessed the end of ultra low interest rates on government bonds. The relatively high indebtedness of Member states might nevertheless force the ECB Governing Council to keep its monetary policy stance loose longer than previously expected, and thus to keep the yield curve relatively low across all maturities.
The fundamental rules governing public debt and deficits in EU are laid down in the primary legislation of the EU. The Treaty on Functioning of the European Union (TFEU) provides that Member states’ public debt ratios shall not exceed 60 % of GDP and public deficits shall not exceed 3 % of GDP. Article 126 of TFEU and the reference values in the protocols of the TFEU are the basis on which relevant secondary legislation provides further legally binding regulations. Various complex set of codes of conduct give further guidance on how to interpret and operationalize the complex set of rules.
Given that the historical record concerning the effectiveness of fiscal rules in the EU is debatable at best, one might argue whether fiscal rules are needed in the first place. There is however evidence that fiscal rules have had some effect in terms of steering national budgetary developments, see (De Jong et al 2020). Due to impediments concerning orderly sovereign debt restructuring however, fiscal rules or at least policy incentives in some form will likely be needed in the future as well, as sovereign debt restructurings might prove to be difficult and cause unexpected consequences for the Euro area as a whole. On the other hand, a full convergence process where one-size-fits all monetary policy would actually work in the Euro area ideally is hard to imagine any time soon. This would be the ideal state of affairs. One price of money and monetary policy across the Euro area means currently too low interest rates for some, and too low risk premia for others. Ultimately, the divergences in competitiveness, differences in productivity together with weak mobility of labour and capital across Member states are the fundamental roots of economic challenges in EMU (Mundell 1961). It should be remembered nevertheless that the Euro area and EMU are essentially politically motivated constructions (Jonung and Drea 2010).
In terms of fiscal policy coordination and economic governance, the question of expert rules vs. democratic accountability is another important issue when considering what kind of centralized economic governance is politically sustainable in the long run in EU (Dawson and Maricut-Akbik 2021). One of the problems with fiscal rules is indeed that fiscal policy is at the core of coercive power of national politics. The national parliaments in Member states hold the power to tax, borrow and to spend. Budgetary power is the crown jewel of national parliaments in Member states. Democratic legitimacy for any fiscal policy must ultimately come from the accountability of the relevant political decision-makers. This is the essence of the principle of subsidiarity in terms of political accountability and democratic legitimacy. On the other hand, if fiscal policy powers are taken away de facto from national governments and national parliaments, then accountability, economic or political, should not reside at the national level either. This problem is at the heart of EMU.
If one wants to restore fiscal powers and political accountability back to national parliaments, then one should have some credible mechanism to restructure sovereign debt in times of crisis without having to resort to excessively intrusive EU-wide financial assistance programs like for example in Greece in 2010-2015. This approach goes hand in hand with the reasoning of market discipline, in which bond markets would discipline the Member states from spending recklessly (Benassy-Quere et al 2018). As democratic accountability cannot be easily extended to the Council of the EU or to the Eurogroup or the European Commission or even to the European Parliament, one can argue that the de jure and de facto fiscal powers of these institutions should be rather constrained. This in turn would suggest that we would need to re-design the fiscal rules in such a way that there is more automaticity in the operation of the rules and less discretion by the Ecofin Council, or the European Commission, for example. Moreover, the rules could be less legally binding and act more as healthy incentives.
It has been argued that fiscal rules in EU are too complicated, too opaque and too pro-cyclical (Leiner-Killinger and Nerlich 2019). Moreover, there is evidence that enforcement of the rules has been not entirely satisfactory and perhaps one way to move forward would be to focus more on reputational aspects such as ”naming and shaming” (Debrun and Jonung 2019). Furthermore, it has been suggested that rules should be more Member state -specific in the sense that for example the required amount of debt reduction yearly should take into account the variations of debt levels between Member states (European Fiscal Board 2021). The use of structural variables such as potential GDP and derivations from it such as structural balances have been criticized as well (Kamps and Leiner-Killinger 2019). Structural variables such as potential GDP and structural deficit are difficult to estimate and verify. Given how much fiscal rules intrude in the national sphere of political competencies, rules should be based on verifiable variables and easily replicable models and scenarios.
In the current set of rules, the reference values for all Member states are ultimately fixed in the TFEU. The present approach would take a differentiated approach in the sense that for each Member state, the required target for primary balance ratio would be determined based on the current debt ratio and current primary balance ratio in particular. Such a differentiated approach could make sense due to fact that there is no scientific basis for determining what amount of public debt is sustainable to begin with. According to the inter-temporal solvency constraint, almost arbitrary ratios of public debt could be sustainable, if they are off-set by future primary surpluses. That is why it makes sense to revoke the current reference values for debt and deficits and to switch to a differentiated approach. These changes would however require a Treaty change. In the current new set of rules, each Member state must comply with a net expenditure path, which replaced the 1/20th adjustment rule. The rules are fundamentally flawed still, as the reference targets are not based analytically on any economic fundamentals.
The model
The present approach focuses on the inter-temporal solvency requirement of a Member state. Therefore, there is differentiation across Member states by construction. A fiscal rule set out below guarantees solvency in the long run statistically, when it is assumed that the primary balance ratio variable follows as random process. It is assumed that the effective interest rate on public debt as well as the rate of nominal GDP growth are constants.
The basic accounting identity debt dynamics differential equation in continuous time is given by
$$\dot{d(t)}=(i-g)d(t)-b(t)$$
This differential equation for debt dynamics was derived for example in (Lindgren 2021). d is the debt-to-GDP -ratio, b is the primary balance-to-GDP -ratio, i is the effective interest rate on debt and g is the nominal growth rate. The debt dynamics equation comes from the identities :
$$\dot{D}=iD-B$$
and
$$\dot{Y}=gY$$
In other words, debt stock grows due to interest expenses and primary deficits and nominal GDP Y grows at some exponential rate g. Using the basic rules of differentiation, one arrives to the differential equation above.
The inter-temporal solvency condition for the sovereign can be derived by multiplying both sides with the discount factor:
$$e^{-(i-g)t}$$
and integrating both sides from zero to infinity over time:
$$\int_{0}^{\infty}e^{-(i-g)t}\dot{d(t)}dt=-\int_{0}^{\infty}-(i-g)e^{-(i-g)t}d(t)dt-\int_{0}^{\infty}e^{-(i-g)t}b(t)dt$$
$$\int_{0}^{\infty}e^{-(i-g)t}\dot{d(t)}dt+\int_{0}^{\infty}-(i-g)e^{-(i-g)t}d(t)dt=-\int_{0}^{\infty}e^{-(i-g)t}b(t)dt$$
$$e^{-(i-g)t}d(t)_{0}^{\infty}=-\int_{0}^{\infty}e^{-(i-g)t}b(t)dt$$
$$d(0)=\int_{0}^{\infty}e^{-(i-g)t}b(t)dt$$
The inter-temporal solvency constraint above provides that the current debt-to-GDP -ratio must equal the future stream of primary balances ratios discounted with the interest-growth differential. In practice it means that given some debt ratio initially, as long as the sovereign is in the market, the expected primary balance, growth and interest must be tuned so that the identity holds at all times. In particular, the S2-indicator developed by the European commission does not make mathematically or economically any sense. This is due to the fact that the solvency constraint holds always, unless we are in a Ponzi-scheme. Mathematically to avoid this state of affairs, we require
$$\lim_{t\rightarrow \infty}e^{-(i-g)t}d(t)=0.$$
In effect then, if there would be a sustainability gap in terms of the S2-indicator, it would mean that the transversality condition does not hold, and the integrals do not converge, therefore making the model meaningless. The solvency condition must be understood in the sense that as long as country is in the bond markets, given the debt and the current interest rates, the expectation of the market as regards growth and primary balances are such that the equality holds.
What is critical however is that the constraint only makes sense when the interest-growth differential is positive, but this is not always the case empirically, see (Blanchard 2019), otherwise the present value integral does not necessarily converge. Furthermore, there must be conditions on the primary balance ratio variable, namely the primary balance ratio growth must be suppressed by the discount rate. We will assume thus that the primary balance ratio variable grows slower than exponentially when time tends to infinity.
What is clear in the real world is that the future primary balance ratios are not known ex ante. From a risk management point of view, the primary balance ratio is then a stochastic process. This in turn means that we cannot prima facie judge when sovereign debt is sustainable or not. Instead, we can however assume that the primary balance ratio follows some specified stochastic process and then we can ask under what circumstances or with what conditions the current debt ratio can be sustained with the discounted stream of future primary balances ratios.
Suppose that the rate at which the primary balance ratio is adjusted towards some reference value is given by the parameters:
$$\mu \in R$$
$$\theta >0$$
Where mu is the target and theta is the adjustment rate. The fiscal rule dictates that given an assumed primary balance ratio adjustment with some rate, a primary balance ratio target is set. From the policy perspective, the key is to determine an appropriate value for the primary balance target ratio. As it is evident that the actual empirical primary balance ratio variable will not match exactly this fiscal policy rule, we add Brownian noise to the model to obtain directly an Ornstein-Uhlenbeck stochastic process for the primary balance ratio variable:We may assume that the primary balance evolves according to a stochastic differential equation
$$db(t)=\theta(\mu-b)dt+\sigma dW(t)$$
The solution for this stochastic differential equation is given by:
$$b(t)=b(0)e^{-\theta t}+\mu(1-e^{-\theta t})+\sigma\int_{0}^{t}e^{-\theta (t-s)}dW(s)$$
As the stochastic integral above is a symmetric, normally distributed random variable, with distribution
$$N~\left(0,\int_{0}^{t}e^{-2\theta (t-s)}ds \right)$$
and considering that the solvency constraint considers an infinite horizon, as the stationary distribution of the process has a mean mu, it is reasonable to consider the expectation of the Ornstein-Uhlenbeck process at time t. The expectation for the process is given by:
$$E(b(t))=b(0)e^{-\theta t}+\mu(1-e^{-\theta t})$$
This expected primary balance ratio can then be inserted in the solvency condition. The solvency condition for public debt is given by:
$$d(0)=\int_{0}^{\infty}e^{-(i-g)t}\left(b(0)e^{-\theta t}+\mu(1-e^{-\theta t})\right)dt$$
The integrals can be solved analytically, to give
$$\mu=\frac{(i-g)(i-g+\theta)}{\theta}d(0)-\frac{i-g}{\theta}b(0)$$
The parameters could be estimated in principle from data. So, given the historical adjustment rate, which could be realistic politically speaking, we might set up individual targets for debt ratios. Interest rates and growth rates can be estimated from data as well. The model could be discretized for actual use, when in effect the debt dynamic differential equation becomes a difference equation and the stochastic model for the primary balance DE could be replaced with some AR-process.
The benefit of this present approach compared to the actual fiscal rules used by the EU is that the required primary balance target ratio is simple, transparent and scientifically based directly on the inter-temporal solvency constraint. The debt reduction rule that used to be used in EU stipulated that that the debt ratio should converge towards the reference value of 60 per cent at a pace of 1/20 of the difference on 3-year average. This adjustment rate does not follow directly from theory. Neither in the so called preventive arm of the Stability and Growth Pact does the so-called Medium Term Objective for the structural balance has any good theoretical basis. Neither does the new net expenditure path.
From binding rules to healthy incentives: a balance between constitutional solidarity and market discipline
In spite of theoretical feasibility of any fiscal rule, it can be argued that national fiscal policies cannot be guided perfectly with some exogenous technical rules based on theoretical inter-temporal solvency considerations. On top of this challenge, the real problem is political in nature: coercive fiscal rules dictated by the European Commission and Council of the EU can be divisive, as the Council for example as a whole is not accountable to a given electorate in a given Member State. This democratic legitimacy gap cannot be solved with any particular technical solution as regards the design of fiscal rules. That is why compliance could be more fruitfully be linked to positive incentives instead.
Presumably, if the EC was asked, the European Council could establish a joint macroeconomic stabilization function within the Multiannual Financial Framework of EU and thus within the EU budget itself (this was essentially proposed in the MFF proposal of July 2025). For example, Next Generation EU (NGEU) could be modified to cater for this more permanent possibility. Due to the Corona crisis, an EU-wide recovery fund Next Generation EU was decided by the Heads of State or Government in the European Council in July 2020. NGEU allows the European Commission to issue bonds on the capital markets to fund recovery in the EU with a total face value of around 800 billion euros. As part of the agreement, it was agreed also that the Commission would propose new Own Resources for the EU to pay back the bonds issued. Such new Own Resources could be based on Emission Trading Scheme revenues, Carbon Border Adjustment Mechanism or on a digital tax on companies.
Extending the current volume of the EU budget substantially and allowing the EU to permanently borrow from capital markets would be a substantial change in the competence of the EU and thus would require a Treaty change. Access to such a macroeconomic stabilization function should require confirmed compliance with the fiscal targets as set out for example via the present approach. Participation should be completely voluntary, so that annual contributions to finance the scheme through Own Resources would need to be voluntary as well. These functional changes in the financial architecture of EU would likely require substantial changes in the Treaty.
The lack of legally binding fiscal rules would require substantial increase of market discipline in order to limit moral hazard and to prevent excessive deficits, which could be supported for example by constraining the powers of the ECB/Eurosystem to conduct idiosyncratic bond buying directed towards any single Member state. In practice, the Treaty could be amended in such a way that there would be clear provisions on the limits of the Asset Purchase Programme (APP) and Outright Monetary Transactions (OMT).
In the Euro area, impediments to orderly sovereign debt restructuring can make market discipline incredible. If there is no credible alternative to bailouts, investors will assume that ultimately sovereign debt is bought or refinanced by the local central bank or other official party. This will in turn make it possible for Member states to take on more debt, as the credit risk premia are kept low due to the impression that sovereigns will be rescued financially. For evidence on bond spreads and the role of EMU, see (Bhatt et al 2017). This potential moral hazard could lead to loss of monetary independence, inflation and other disruptions in the Euro area. On fiscal dominance, see (Sargent and Wallace 1981). The decisive role of the ECB in terms of managing bond market turmoil in EU is discussed for example in (De Grauwe 2013).
In order to foster orderly debt restructuring and credibility of market discipline, prudential regulation of banks should be improved with provisions to require banks hold sufficient amount of capital against sovereign credit risk. One of the main challenges for financial stability and orderly sovereign debt restructuring in the Euro area is the so-called vicious loop between banks and sovereigns. One key feature of this vicious loop is that domestic banks in the Member States are heavily exposed to credit risk of their domestic government. This can mean that while the perceived credit risk of a Member State is increased due to for example excessive government debt or deficits, the solvency of the banks within the Member state is deteriorated as a result, which in turn means more risk for the government. The additional risk comes from the perception that the financial market assumes that the balance sheet of the sovereign is used at least partly to bail-out the banks. Partly due to this, Banking Union was established in the Euro area in 2013 with its common supervision (ECB) and common resolution fund (Single Resolution Fund), although a common deposit insurance scheme is still missing. Debt restructurings become very difficult when the domestic banking sector cannot sustain the write-off of its sovereign exposures (Bucheit et al 2019).
Finance ministers of the EU (Eurogroup in extended format) are currently discussing on how to mitigate the vicious loop by considering amending prudential regulation in terms of capital requirements for sovereign bonds. Currently, the EU legislation does not generally require banks to hold capital against credit risk from EU sovereigns. Contractual terms in EU sovereign bonds should be further optimized as well so that collective action clauses would mitigate the so-called creditor coordination problem (Bucheit and Gulati 2018). One major impediment in terms of orderly sovereign debt restructuring could be contagion to other vulnerable Member states (Ehrmann and Fratzscher 2017).
The debate on a fiscal union of EU, i.e. the future of economic policy and fiscal policy coordination and possible need to establish a central fiscal capacity in EMU, has been on-going for many years. Especially relevant question is whether a fiscal stabilization function could be established to smoothen idiosyncratic shocks in individual Member States. Such elements have been proposed and discussed for example in (Benassy-Quere et al 2018).
The simple fiscal rule proposed in this research article would depend crucially on the ability of the EU to create incentives for Member states to comply with the fiscal target. Current secondary legislation includes provisions to sanction Member states if there is severe non-compliance. However, these sanctions have never been used. Indeed, for political reasons it is unlikely that direct sanctions could be credibly instated in the first place. Politically, it could be easier to establish criteria to have an access to a macroeconomic stabilization function based on compliance, than to try to penalize Member states directly using deposited fines or other penalties. One option could be measure for example the cumulative deviation from the fiscal target and determine an access quota to such a macroeconomic stabilization function. Such an incentive scheme would therefore be based on the principles of a fair insurance – the pay-off from the insurance scheme should depend on the past behaviour of the policy holder. In various insurance policies it is common that the first-loss cost depends on the past behaviour of the policy holder. From the perspective of smaller ”frugal” Member states it is clear that for any joint macroeconomic stabilization criteria to become reality, strict conditionality will likely be needed (Schoeller 2021).
The Economic and Monetary Union will remain incomplete for the foreseeable future. This does not however mean that improvements cannot be agreed on. The key balancing act is how to balance risk sharing, good incentives and market discipline. On the other hand, risk sharing must be constitutional in terms of national parliaments and democratically legitimate. If fiscal rules were to be made more flexible, non-binding and differentiated across Member states, likely from a political point of view, market disicpline needs strengthening. Ultimately the future of the fiscal union must be a compromise between all Member states and therefore it needs to strike the right balance. One option to support market discipline would be to amend the compentencies of the ECB in such a way that the Eurosystem could not buy government bonds without a limit. Currently, the yield curve reflects predominantly the unconventional monetary policy stance of the ECB. If the actors and investors in the capital markets assume that the central bank will ultimately buy bonds of Member states with solvency risks, the functioning of market discipline could be impaired. Moreover, it has been documented that the large scale buying activity of Eurosystem might also increase the imbalances in th be TARGET2-settlement system in the Eurosystem (Bundesbank 2018). These imbalances might cause large budgetary risks for Member states in case that the dissolution of the Euro area cannot be ruled out (Bundesbank 2018). Risks stemming from monetary policy operations – direct or indirect – are substantially more opaque compared to for example liabilities stemming from the NGEU. Therefore, from the point of view of constitutionality, it could be fruiful to try to contain the risks in monetary policy operations via establishing a joint macroeconomic stabilization function instead within the EU legislative framework.
All and all, it seems that the fiscal union architecture would need preferably amendments in the primary legislation of the union. The present model for a fiscal rule combined with a macroeconomic stabilization function within the EU budget would be hardly compatible with the current provisions of the Treaties. Similarly, the European Stability Mechanism and the NGEU would be better anchored via explicit provisions in the TFEU and also any changes to the competence of the ECB or the ESCB would likely require a Treaty change as well.
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