# Interpretation and limits of sustainability tests in public finance

Gildas Lamé, Matthieu Lequien, Pierre-Alain Pionnier

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Direction des Études et Synthèses Économiques

G 2013 / 05

Interpretation and limits of sustainability tests
in public finance

Gildas LAMÉ, Matthieu LEQUIEN
and Pierre-Alain PIONNIER

Document de travail

<figure><img src="image_2.png" /></figure>

Institut National de la Statistique et des Études Économiques
INSTITUT NATIONAL DE LA STATISTIQUE ET DES ÉTUDES ÉCONOMIQUES

Série des documents de travail
de la Direction des Études et Synthèses Économiques

G 2013 / 05

Interpretation and limits of sustainability tests
in public finance

Gildas LAMÉ*, Matthieu LEQUIEN*
and Pierre-Alain PIONNIER*

MARCH 2013

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 earlier versions.

<footnote>* Département des Études Économiques - Division Études Macroéconomiques, CREST
Timbre G220 - 15, bd Gabriel Péri - BP 100 - 92244 MALAKOFF CEDEX</footnote>
# 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 intertemporal 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 non-parametric approach) or are both integrated (with parametric tests), we estimate fiscal reaction functions for France and for Greece. The empirical results highlight the remaining limitations and interpretation difficulties that plague these econometric sustainability tests.

**Keywords:** Intertemporal budget constraint; unit-roots; cointegration; fiscal reaction function; non-parametric tests

# Interprétation et limites des tests de soutenabilité
des finances publiques

## Résumé

La dette publique est dite soutenable lorsque la somme actualisée des remboursements anticipés couvre l'émission initiale de dette, c'est-à-dire lorsque la contrainte budgétaire intertemporelle de l'État est vérifiée. Dans un contexte où les prêteurs sont averses au risque et où l'environnement économique est incertain, Bohn (1995) montre que cette contrainte fait intervenir un facteur d'escompte stochastique qui dépend des préférences des agents. Afin de contourner la difficulté liée à la spécification de ces préférences dans les études empiriques, Bohn (1998) suggère d'estimer des fonctions de réaction fiscale décrivant comment le surplus primaire réagit à l'endettement. Après avoir résolu les difficultés qui se présentent en pratique lorsque le surplus primaire et la dette ont des persistances très différentes (avec une approche non-paramétrique) ou sont tous les deux intégrés (avec une approche paramétrique), nous estimons des fonctions de réaction fiscale pour la France et pour la Grèce. Les résultats mettent en évidence le fait que les tests économétriques de soutenabilité présentent des difficultés d'interprétation et des limites importantes, même lorsqu'ils sont correctement spécifiés.

**Mots clés** : Contrainte de budget intertemporelle ; racine unitaire ; cointégration ; fonction de réaction fiscale ; tests non-paramétriques

**Code JEL** : C12, E62, F34, H60, H62
# Contents

Introduction 4

I Literature review on usual indicators and tests 5

I.1 Frequently used indicators 5

I.2 Economic framework 6

I.3 Usual econometric tests and their limits 7

II Transversality condition and stochastic discount factor 9

II.1 Transversality condition with stochastic discount factor 9

II.2 About the example presented by Bohn (1995) 11

III Empirical results 12

III.1 Data description 13

III.2 Estimation of a fiscal reaction function when primary surplus and debt are integrated 15

III.3 Estimation of a fiscal reaction function when primary surplus and debt are both stationary, the latter being much more persistent than the former 15

III.4 Non-parametric tests 17

III.5 Empirical results for France 18

III.6 Empirical results for Greece 21

Conclusion 25

A Appendix 26

A.1 Sufficient sustainability condition based on the fiscal reaction function 26

A.2 Stationarity of the error term and the control variables is not sufficient 28

A.2.1 An example with weak stationarity 28

A.2.2 An example with strong stationarity 28

A.3 Debt cannot be at the same time $I(m)_{m \ge 0}$ in level and $I(k)_{k \ge 0}$ after discounting 29

A.4 Proof of proposition I.1 29

A.5 Description of the French quarterly data 30
Introduction

Public debt sustainability is a major concern in Europe at least since the outbreak of
the Euro Area sovereign debt crisis. Public debt dynamics in countries such as Greece
is particularly monitored. But even before the Great Recession, many industrial
countries showed persistent deficits and an increasing public debt. Evaluating the
sustainability of fiscal policy had naturally come under the spotlight. The Pébereau
(2005) and Champsaur-Cotis (2010) administrative reports illustrate this concern for
France.

How to define a sustainable debt? A possible definition is given by the IMF (2002): debt has to “satisf[y] the present value budget constraint without a major correction in the balance of income and expenditure given the costs of financing [the government] faces in the market”. Obviously it is not straightforward to precisely determine what a “major correction” is. Does it refer to a change in the reaction function of government’s revenue and spending to the business cycle or to public debt, or to a sizeable adjustment of public finances, without any change to the usual reaction function? If a government already has, in the past, taken successful measures to curb high indebtedness and faces again the same situation, should it be considered insolvent according to the IMF definition?

In this paper we favor the more usual term of sustainability over solvency. It refers
to the ability of a government to pay back its debt with the discounted sum of the
primary surpluses generated in the future. As Wyplosz (2007) noticed, the notion
of sustainability is essentially forward-looking since it is the future balances that
matter. Nevertheless public debt sustainability is often assessed with econometric
tests on past data. Boissinot et al. (2004) concluded with standard tests that French
public debt was (weakly) sustainable.

Potential behavioral breaks, in the past or between the end of the sample of
available data and the near future, represent a first hurdle to interpret these tests'
results. From a logical point of view, the only question they give an answer to is: does
the management of public finances as observed in the past justify that investors buy
or refuse to buy public debt? Indeed rational investors buy debt securities only under
the condition that the discounted repayments by the government cover the initial debt
issuance, i.e. when they believe that the government intertemporal budget constraint
holds.

Besides the possible behavioral breaks, Bohn (2007) has underscored that usual
tests rely on sustainability conditions that are only sufficient. This weakens their
interpretation. As long as investors keep on buying public debt securities, the re-
jection of a sufficient condition of sustainability can therefore be interpreted in two
different ways. Either they expect the government to follow in the future a different
policy because it can freely adjust its expenditures and receipts. Or they do base
their analysis on the past behavior of public finances, but with different lenses than
the econometrician, and another sufficient condition for sustainability could justify
their buying of public debt.

Following a review of the usual tests and of the sufficient sustainability conditions
they lean on, we focus on the specification of the government intertemporal budget
constraint. Bohn (1995) has stressed that writing this constraint with the interest
rate on public debt is not always justified. With risk averse lenders and an uncertain
economic environment, this constraint relies on a stochastic discount factor depending
on lenders' preferences.

To get round the difficulty related to the specification of private agents’ prefer-
ences in empirical analysis, Bohn (1998) suggests to estimate fiscal reaction functions
describing how primary surplus reacts to indebtedness. We show that this procedure
is valid only under strict technical assumptions and entails econometric difficulties.
After having solved the econometric issues arising when primary surplus and debt
have a very different persistence (with a non-parametric approach) or are both inte-
grated (with parametric tests), we estimate fiscal reaction functions for France and
for Greece in the last part of this study. The empirical results highlight the lim-
itations and interpretation difficulties that plague these econometric sustainability
tests. These difficulties are perfectly illustrated in the Greek case as the estimation of
the fiscal reaction function on past data indicates that Greek public finances can be
considered sustainable in 2007. Similar results for Greece are obtained by Mendoza
and Ostry (2008) who also estimate fiscal reaction functions. Conversely, results of
non-parametric and parametric tests in the French case are more mitigated but they
do not indicate a significantly positive fiscal reaction function over the years 1978-
2007. This result is at odds with subsequent developments. Indeed, French public
debt has increased markedly after the end of the estimation sample, investors have
continued to consider French public indebtedness as sustainable and borrowing costs
have remained low, or even very low.

# I Literature review on usual indicators and tests

I.1 Frequently used indicators

Public debt sustainability analysis generally starts from the debt accumulation equa-
tion: $d_t = \frac{1+i_t}{1+y_t} d_{t-1} - s_t$, $d_t$ being the end of period $t$ stock of debt divided by GDP, $i_t$ the interest rate, $y_t$ the GDP growth rate and $s_t$ the primary balance over GDP.

A simple and widely used indicator is the primary balance stabilizing the debt over
GDP ratio. Primary balance (i.e.: balance before interest payments) is the variable
under the short term control of the government. The stabilizing primary balance is
given by the formula $s_t^* = \left( \frac{1+i_t}{1+y_t} - 1 \right) d_t$, or $s_t^* \approx (\bar{i} - \bar{y}) d_t$, $\bar{i}$ and $\bar{y}$ being exogenous
variables. The intuition is that a country able to stabilize its indebtedness without a
major effort can be regarded as safe, a debt reduction requiring only a minimal further
improvement of the primary balance. On the contrary, a debt stabilizing primary
balance which cannot be reached without a substantial effort signals difficulties to
control the evolution of public debt.

In the same spirit, the primary balance required to bring back debt to 60% of
GDP (or whatever level considered to be safe) over a given period of time may be
computed. Predictable costs to come can also be taken into account, typically the
ageing costs (OECD; EC, 2011), or those stemming from a possible bailout of the
banking system (Benassy-Quéré, 2012; EC, 2011).<fnref n="1" /> The justification for such an

<footnote n="1">¹This computation is harder to interpret because it involves episodes with very low probability but far-reaching consequences.</footnote>
indicator is the following: if the effort to reach a given debt ratio within a reasonable horizon is deemed too large to be credible, then the country's sustainability can be questioned. The same ideas can be applied to government revenue (or spending) rather than to its surplus in order to answer the following question: by how much must taxes be raised to stabilize the debt to GDP ratio or to balance the budget (Blanchard, 1990)?

All these sustainability analysis are based upon the assumption of exogenous interest rates and GDP growth rates. They abstract from any feedback that fiscal policy may have on these variables (a deficit reduction is not neutral on the growth rate of the economy, either in the short or in the long run, nor on the interest rate). A solution to the first remark is to repeat the analysis with different scenarios for the path of the exogenous variables. If sustainability is accepted (respectively rejected) for a pessimistic (optimistic) scenario, one can be more confident in their diagnosis than with only a central scenario. However conflicting results, depending on the evolution scenarios for the exogenous variables, may also appear. This is the approach chosen by the IMF and the World Bank for their joint *Debt Sustainability Assessments*, which are studied by Wyplosz (2007). They consist in attaching probabilities to different scenarios for the years ahead and infer a range of possible levels for public debt.

## I.2 Economic framework

With $D_t$ the end of period $t$ stock of debt, $r_t$ the interest rate and $S_t$ the primary balance in period $t$, the accounting identity governing the evolution of the stock of debt is: $D_t = D_{t-1}(1 + r_t) - S_t$. Variables can be nominal, real or expressed as a ratio of GDP. The interest rate is thus respectively the nominal rate $i_t$ paid on debt, the real rate or the rate defined by $1 + r_t = (1 + i_t)/(1 + y_t)$, $y_t$ standing for nominal GDP growth. $D_t$ can be written as a function of expected surpluses with a simplifying assumption on future interest rates. The literature often considers $r_t = r > 0$ constant, or $\mathbb{E}_t[r_{t+1}] = r > 0$ for example. One obtains recursively:

$$D_t = \sum_{i=1}^{N} \frac{\mathbb{E}_t[S_{t+i}]}{(1+r)^i} + \frac{\mathbb{E}_t[D_{t+N}]}{(1+r)^N} \quad (1)$$

With rational lenders, the supply of debt meets a demand if the transversality condition (TC ad hoc) holds. It is the case when the expected debt discounted at a rate $r$ converges to 0,<fnref n="2" /> meaning that lenders expect that debt will be paid back in full through discounted expected primary surpluses, which is exactly the intertemporal budget constraint (IBC ad hoc):

$$D_t = \sum_{i=1}^{\infty} \frac{\mathbb{E}_t[S_{t+i}]}{(1+r)^i} \quad (\text{IBC ad hoc}) \\ \lim_{N \to \infty} \frac{\mathbb{E}_t[D_{t+N}]}{(1+r)^N} = 0 \quad (\text{TC ad hoc})$$

Both preceding constraints are equivalent, and they are valid when debt is sustainable.

<footnote n="2">²This 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 II.1.</footnote>
Within this framework it appears that stabilizing the debt to GDP ratio is not a necessary sustainability condition. Debt can be regarded as sustainable even if the ratio of debt over GDP increases whenever the interest rate is larger than the growth rate, which is the case when the economy is dynamically efficient.

The relevant choice of the discount rate will be dealt with later (see II.1). For now we address the interpretation issue of the usual econometric tests: are they based on sufficient and necessary sustainability conditions, or only sufficient ones?

## I.3 Usual econometric tests and their limits

One of the first major contributions to the econometric literature on public debt sustainability is Hamilton and Flavin (1986).<fnref n="3" /> In this article, the interest rate is constant: it is the ex post real interest rate earned on one-period government bonds over an average year. The authors test the transversality condition $\lim_{N \to \infty} \frac{\mathbb{E}_t[D_{t+N}]}{(1+r)^{t+N}} = 0$ against the alternative that the limit exists and is strictly positive: $\lim_{N \to \infty} \frac{\mathbb{E}_t[D_{t+N}]}{(1+r)^{t+N}} = A_0 > 0$. Under the alternative and given past data, economic agents expect part of the debt never to be paid back. In this case the accounting identity (2) can be rewritten:

$$D_t = \mathbb{E}_t \sum_{i=1}^{\infty} \frac{S_{t+i}}{(1+r)^i} + A_0(1+r)^t \quad (2)$$

If debt follows a process of type (2) and if $\{S_t\}$ is stationary, it is then equivalent to test the stationarity of $D_t$ and the nullity of $A_0$. Hamilton and Flavin find that $S_t$ and $D_t$ are stationary<fnref n="4" /> and infer the nullity of $A_0$ and the sustainability of the American public debt.

Other authors have chosen an approach based on the variables determining debt's variation, such as the deficit or public spending and revenue.

Trehan and Walsh (1988) assume that the interest rate is constant and that revenue $T_t$ and (without interest) spending $G_t$ are at most $I(1)$. In this case, they show that the transversality condition (TC ad hoc) holds if total deficit (including interests) is stationary. This condition is equivalent to the existence of a cointegrating relationship between $G_t^r$ (spending with interests) and $T_t$ (revenue).

Quintos (1995) further proves that a $I(2)$ debt is compatible with the transversality condition $\lim_{N \to \infty} \frac{\mathbb{E}_t[D_{t+N}]}{(1+r)^N} = 0$.<fnref n="5" /> In this case, debt $\mathbb{E}_t[D_{t+N}]$ behaves, in probability, like a polynomial in $N$,<fnref n="6" /> but this polynomial is asymptotically dominated by the exponentially-growing discount factor. Bohn (2007) broadens this result and proves

<footnote n="3">³These authors make substantial efforts to improve debt and deficit data (to subtract from the deficit the interest payments and the seigniorage revenue for instance, or to deal with the gold stock in the United States). The notation $S_t$ is therefore slightly different in their paper.</footnote>

<footnote n="4">⁴ADF test: rejection of the unit root hypothesis at 10% (but not 5%) for debt and primary balance.</footnote>

<footnote n="5">⁵This is what Quintos (1995) calls weak sustainability. Boissinot et al. (2004) show that French public finances are weakly sustainable over the period 1978-2002 because general government's expenditures and receipts are bound by a cointegrating relationship $T_t = \alpha + \beta \cdot G_t^r + \epsilon_t$ with $0 < \beta < 1$. However, they report that the coefficient $\beta$ is declining over time and lower than in the U.S. and other European countries.</footnote>

<footnote n="6">⁶One can use Bohn's (2007) proposition 1 to prove $\mathbb{E}_t[D_{t+N}] = O_p(N^2)$ when $D_t \sim I(2)$ process.</footnote>
that sustainability holds when debt is integrated of arbitrarily high order (i.e.: when debt is $I(m)$). Hence, the existence of a cointegrating relationship between revenue $T_t$ and spending (including interests) $G_t^r$ is not a necessary sustainability condition either. If these variables are integrated of orders $m_T$ and $m_G$ respectively, but not cointegrated, the order of integration of debt will be $m$ with $m \le \max(m_1, m_2) + 1$, ensuring that the transversality condition $\lim_{N \to \infty} \frac{\mathbb{E}_t[D_{t+N}]}{(1+r)^N} = 0$ holds.

Procedures testing if debt is integrated of order $m$, against an alternative where its order of integration is strictly larger than $m$, therefore cannot reject the transversality condition. Sustainability holds both under the null and the alternative. In a nutshell, the null hypothesis is a sufficient but not necessary sustainability condition.

Trehan and Walsh (1991) do not restrict debt to be $I(m)$. They show that the transversality condition holds if primary surplus $S_t$ and debt $D_{t-1}$ are linked by a stationary linear combination ($S_t - \alpha D_{t-1} = \epsilon_t \sim I(0)$) and if the quasi-difference of the primary surplus $S_t - \lambda S_{t-1}$ with $\lambda \in [0, 1+r]$ is $I(0)$ and has a zero mean.<fnref n="7" /> It follows:

$$D_t - \lambda D_{t-1} = (S_{t+1} - \lambda S_t)/\alpha - (\epsilon_{t+1} - \lambda \epsilon_t)/\alpha \sim I(0)$$

With $\lambda$ in the interval $[1, 1+r]$, debt is explosive but sustainable because it is discounted by $(1+r) > \lambda$. Bohn (2007) notices that debt is not $I(m)$ in this case, whatever the order of integration $m$. This underscores once again that having an $I(m)$ public debt is just a sufficient sustainability condition, but not a necessary one.

Wilcox (1989) has a special place in the econometric literature on sustainability.<fnref n="8" /> The variable of interest in his article is real debt discounted at date $(t+i)$ with the realized yield on public debt between date $t$ (reference year) and date $(t+i)$, i.e.: $\frac{D_{t+i}}{(1+r)^i}$. It is necessary for the transversality condition to hold that discounted real debt is stationary with its unconditional mean equal to zero.<fnref n="9" /> In this case, $\lim_{N \to \infty} \mathbb{E}_t[\frac{D_{t+N}}{(1+r)^N}] = 0$. Estimating the unconditional mean of the discounted real debt is the purpose of Wilcox's test.

Wilcox's framework is not the same as in Bohn (2007) where it is debt in level (nominal or real) which is integrated of order $m$. It can be shown that debt cannot be at the same time $I(m)$ in level and stationary after discounting (see annex A.3). It is however possible to generalize Bohn's results to a wider class of processes including those analyzed by Bohn and Wilcox (proof in annex A.4):

**Proposition I.1.** Let $f$ be a deterministic and discrete function of time.

1. If $D_{t+n}/f(n) \sim I(m)$, with $m \ge 0$ and $f(n) = o((1+r)^n/n^m)$, then debt verifies the transversality condition (TC ad hoc).

<footnote n="7">⁷Bohn (2007) notices that Trehan and Walsh (1991) implicitly consider a positive fiscal reaction function: $S_t = \alpha D_{t-1} + \epsilon_t$ with $0 < \alpha$.</footnote>

<footnote n="8">⁸However, it is not an isolated contribution. The method described by Wilcox (1989) has recently been adapted by Davig (2005) to allow for behavioral breaks in the data generating process of discounted debt.</footnote>

<footnote n="9">⁹When discounted real debt is not stationary, two cases are possible: either the conditional mean $\mathbb{E}_t[\frac{D_{t+N}}{(1+r)^N}]$ does not have a limit when $n$ tends to infinity, or it is equal to a random variable and not necessarily to 0.</footnote>
2. If $D_{t+n}/f(n) \sim I(0)$ with $f(n) = O((1+r)^n)$ and $\mathbb{E}[D_{t+n}/f(n)] = 0$, then debt verifies the transversality condition (TC ad hoc).

In particular, whatever $r_0 < r$, $D_{t+n}/(1+r_0)^n \sim I(m)$ is a sufficient condition for the ad hoc transversality condition to hold. Furthermore, if $D_{t+n}/(1+r)^n \sim I(0)$ with mean zero, then the transversality condition also holds: it is the particular case studied by Wilcox (1989). Hamilton and Flavin (1986) also belong to this special case, since equation (2) shows that the conditions of the second case are verified when $A_0 = 0$. Finally the first case with a constant function $f$ corresponds to the entire set of processes considered by Bohn (2007).

All the articles described so far make use of the interest rate on public debt in the transversality condition and, except Wilcox (1989), they make one of the following assumptions to characterize the evolution of this interest rate:

* $r_t = r > 0$.

* $r_t$ is not autocorrelated and $\mathbb{E}_t[r_{t+1}] = r > 0$.

* $r_t$ is a stationary process with mean $r > 0$.

Beyond the interpretation issues related to the rejection of only sufficient conditions, the previous econometric tests show another weakness, associated with the choice of a very specific discount factor in the intertemporal budget constraint. We now come to this issue.

# II Transversality condition and stochastic discount factor

## II.1 Transversality condition with stochastic discount factor

In order to illustrate the choice of the relevant discount factor, we follow Bohn (1995) and consider a simplified endowment economy. At each date, a representative agent receives a random endowment $Y_t$ that he cannot store. A fixed proportion $g$ of this endowment is consumed by the government. This public consumption is financed by a tax and the issuance of government bonds to be repaid at a later date. In this decentralized economy, the Euler equation determines the government bond yield ensuring that households effectively consume a fraction $(1-g)$ of their endowment at each date. Using this Euler equation, one can price any security contingent on a specific state of nature being realized. We denote by $s_t$ the different states of nature, by $h_t = (s_t, h_{t-1})$ the history at date $t$ and by $\pi(s_t|h_{t-1})$ the probability of state $s_t$ being realized conditional on history $h_{t-1}$ at previous date.

Private agents maximize their intertemporal utility function:

$$ \sum_{i=0}^{+\infty} \sum_{h_{t+i}} \beta^i \pi(h_{t+i} | h_t) U[C_{t+i}(h_{t+i})] = \mathbb{E}_t \left[ \sum_{i=0}^{+\infty} \beta^i U[C_{t+i}] \right] $$
Given the absence of arbitrage at the optimum, one can determine the price (i.e.: how many units of consumption goods) private agents are willing to invest at time t in exchange for one additional unit in the history $h_{t+j}$ at time $(t + j)$:

$$q(h_{t+j}|h_t) = \beta^j \pi(h_{t+j}|h_t) \frac{U'[C_{t+j}(h_{t+j})]}{U'[C_t(h_t)]}$$

The yield of a government bond issued at time $t$ and offering a total return $(1 + r_t(j))^j$ in every state of nature at time $t + j$ is given by the following formula:

$$\frac{1}{(1 + r_t(j))^j} = \sum_{h_{t+j}} \beta^j \pi(h_{t+j}|h_t) \frac{U'[C_{t+j}(h_{t+j})]}{U'[C_t(h_t)]} = \mathbb{E}_t \left[ \beta^j \frac{U'[C_{t+j}]}{U'[C_t]} \right]$$

In the same way, one can also price government debt at time $t$ with payoff $D_{t+n}(h_{t+n})$ at time $t + n$ for every history $h_{t+n}$, given history $h_t$:

$$\sum_{h_{t+n}} \beta^n \pi(h_{t+n}|h_t) \frac{U'[C_{t+n}(h_{t+n})]}{U'[C_t(h_t)]} D_{t+n}(h_{t+n}) = \mathbb{E}_t \left[ \beta^n \frac{U'[C_{t+n}]}{U'[C_t]} D_{t+n} \right]$$

The relevant transversality condition in a stochastic environment becomes:

$$\lim_{n \to +\infty} \mathbb{E}_t \left[ \beta^n \frac{U'[C_{t+n}]}{U'[C_t]} D_{t+n} \right] = 0 \qquad (\text{TC})$$

A strictly positive limit implies that private agents could have a higher intertemporal utility by consuming more at time $t$ and lending less to the government. The country would then refinance itself indefinitely without ever fully repaying the principal as in a Ponzi scheme. Thus, rational investors would not be willing to hold such assets. By contradiction, this shows that the transversality condition (TC) always holds in equilibrium.

This condition is different from the usual transversality condition that is often used in the literature:

$$\begin{aligned} & \mathbb{E}_t \left[ \beta^n \frac{U'[C_{t+n}]}{U'[C_t]} D_{t+n} \right] \\ &= \mathbb{E}_t \left[ \beta^n \frac{U'[C_{t+n}]}{U'[C_t]} \right] \mathbb{E}_t [D_{t+n}] + \mathrm{Cov}_t \left[ \beta^n \frac{U'[C_{t+n}]}{U'[C_t]}, D_{t+n} \right] \\ &= \frac{\mathbb{E}_t [D_{t+n}]}{(1 + r_t(n))^n} + \mathrm{Cov}_t \left[ \beta^n \frac{U'[C_{t+n}]}{U'[C_t]}, D_{t+n} \right] \end{aligned}$$

Depending on the sign of the covariance term, it could be easier or more difficult for the usual transversality condition to hold. In the case of a deterministic economy or with risk-neutral private agents (with $U[C_t] = \frac{C_t^{1-\epsilon}}{1-\epsilon}$, $\epsilon = 0 \Rightarrow U'(C_{t+n}) = U'(C_t) = 1$), the transversality condition with uncertainty (TC) actually boils down to the usual (TC ad hoc). With risk-averse agents in a stochastic economy, both conditions will not in general coincide as it would require $D_{t+n}$ and $\beta^n \frac{U'[C_{t+n}]}{U'[C_t]}$ to be uncorrelated. Of course, it is unlikely to have a zero correlation between these two variables because (marginal utility of) consumption certainly depends on the
budgetary and fiscal stance of the government. Bohn (1995) provides an example in which the debt to GDP ratio remains constant. In this example, the ad hoc transversality condition can be rejected whereas the relevant one in a stochastic setting is always satisfied.

In a stochastic setting, the intertemporal budget constraint becomes:

$$D_t = \sum_{n \ge 0} \left\{ \frac{\mathbb{E}_t [T_{t+n} - G_{t+n}]}{(1+r_t(n))^n} + \text{Cov}_t \left( \beta^n \frac{U'[C_{t+n}]}{U'[C_t]}, T_{t+n} - G_{t+n} \right) \right\} \quad (\text{IBC})$$

## II.2 About the example presented by Bohn (1995)

We consider the endowment economy defined previously and examine the case where the government issues debt so that the debt/GDP ratio measured at the end of each period and in every state of nature is constant: $\frac{D_t(h_t)}{Y_t(h_t)} = d$. Taxes are adjusted so that public spending always represents a constant proportion $g$ of the endowment $Y_t$. Equilibrium in the goods' market therefore implies that agents' consumption is a constant proportion of the endowment at each period: $C_t = (1 - g)Y_t$. This fiscal policy will be shown to be sustainable according to the transversality condition in a stochastic setting but not always with the usual one.

We use a CRRA instantaneous utility function with risk aversion denoted $\epsilon^{10}$: $U[C_t] = \frac{C_t^{1-\epsilon}}{1-\epsilon}$. The evolution of the endowment is supposed to be log-normal: $\frac{Y_t}{Y_{t-1}} = 1 + y_t$ with $\log(1 + y_t) \sim N(\mu, \sigma^2)$. Finally, we assume that the agents' intertemporal utility is finite given the properties of this process. Therefore the general term of this positive-term series converges to 0 as $t$ approaches infinity.

$$\lim_{n \to +\infty} \mathbb{E}_t [\beta^n U[C_{t+n}]] = \frac{(1-g)^{1-\epsilon}}{1-\epsilon} \lim_{n \to +\infty} \mathbb{E}_t [\beta^n Y_{t+n}^{1-\epsilon}] = 0$$

Given our assumptions, the transversality condition in a stochastic setting holds. Indeed,

$$\lim_{n \to +\infty} \mathbb{E}_t \left[ \beta^n \frac{U'[C_{t+n}]}{U'[C_t]} D_{t+n} \right] = \frac{d(1-g)^{-\epsilon}}{U'[C_t]} \lim_{n \to +\infty} \mathbb{E}_t \left[ \beta^n Y_{t+n}^{1-\epsilon} \right] = 0$$

We now write the risk-free rate on a loan between date $t$ and date $t+n$:

$$\frac{1}{(1+r_t(n))^n} = \mathbb{E}_t \left[ \beta^n \frac{U'[C_{t+n}]}{U'[C_t]} \right] = \mathbb{E}_t \left[ \beta^n \prod_{i=1}^n (1+y_{t+i})^{-\epsilon} \right]$$

<footnote n="10">¹⁰A CRRA utility function is used in this example for the sake of simplicity. It is a well-known fact that this model does not allow to reproduce the pattern (i.e. the low values) of the risk-free interest rate with reasonable values of time preference, consumption volatility and risk aversion. But this example only aims at illustrating the differences between the stochastic discount factor and the riskless discount factor in a simple setting. Research in the joint modeling of economic fluctuations and asset returns is still active. We will circumvent the difficulty associated with the relevant specification of the stochastic discount factor in the empirical section of this paper.</footnote>
We can then compare the riskless rate with the expectation of the debt variable at time $t+n$ in order to see whether or not the usual transversality condition holds:<fnref n="11" />

$$ \frac{1}{(1 + r_t(n))^n} = \beta^n \exp \left( -\epsilon \mu n + \frac{\epsilon^2 \sigma^2 n}{2} \right) $$

$$ \mathbb{E}_t[D_{t+n}] = dY_t \mathbb{E}_t \left[ \prod_{i=1}^{n} (1 + y_{t+i}) \right] = dY_t \exp \left( \mu n + \frac{\sigma^2 n}{2} \right) $$

$$ \lim_{n \to +\infty} \frac{\mathbb{E}_t[D_{t+n}]}{(1 + r_t(n))^n} = 0 \Leftrightarrow (\epsilon - 1)\mu - (1 + \epsilon^2)\frac{\sigma^2}{2} - \log(\beta) > 0 $$

For sufficiently high values of the risk aversion parameter $\epsilon$ and of the variance $\sigma^2$, the usual transversality condition could be rejected whereas the relevant one in a stochastic setting would always be satisfied.

### III Empirical results

To get round the difficulty related to the estimation of a general equilibrium model and to the specification of private agents' preferences, Bohn (1998) suggests to estimate a fiscal reaction function describing how primary surplus reacts to public debt. He shows that a positive link is a sufficient condition for sustainability. The theoretical justification, given here in appendix, for estimating a fiscal reaction function is adapted from the unpublished appendix of Bohn (1998). We complement the original proof with an important precision concerning the control variables and the error term in the fiscal reaction function. The proof is relevant only if these variables are bounded. We provide a counter-example showing that it does not work with weakly stationary control variables and error term.<fnref n="12" /> Details are available in the appendix at the end of the paper.

In practice, we will estimate the following regression where $\mu_t$ comprises control variables and a structural error term:

$$ \frac{S_t}{Y_{t-1}} = \alpha + \beta \frac{D_{t-1}}{Y_{t-1}} + \mu_t \quad (3) $$

It is slightly different from the one proposed by Bohn (1998), for two reasons. First, we change the date convention: $D_t$ is now the end of period $t$ debt whereas it is beginning of period $t$ debt in Bohn (1998). Second, we divide primary surplus $S_t$ and debt $D_t$ by the GDP of period $t-1$. In this way, the right-hand-side variable $\frac{D_{t-1}}{Y_{t-1}}$ is

$$ \begin{align*} \log(1 + y_t) &\sim \mathcal{N}(\mu, \sigma^2) \\ &\Rightarrow \log \prod_{i=1}^{n} (1 + y_{t+i})^{-\epsilon} \sim \mathcal{N}(-\epsilon\mu n, \epsilon^2\sigma^2 n) \\ &\Rightarrow \mathbb{E}_t \left[ \prod_{i=1}^{n} (1 + y_{t+i})^{-\epsilon} \right] = \exp \left( -\epsilon\mu n + \frac{\epsilon^2\sigma^2 n}{2} \right) = \left( \mathbb{E} \left[ (1 + y_t)^{-\epsilon} \right] \right)^n \end{align*} $$

<footnote n="11">¹¹With the log-normal hypothesis made for the endowment variation, it can be inferred that:</footnote>

<footnote n="12">¹²In his 1998 paper, Bohn alternatively considers a stationary or a (strictly) bounded process $\mu_t$. In the appendix available on his web-page, he details the proof with a (strictly) bounded process only.</footnote>
fully predetermined and the regression coefficient $\beta$ is not subject to an asymptotic simultaneity bias. In the appendix, we prove that a significantly positive $\beta$ in this specification ensures sustainability, relying on the additional assumption that the interest rate on public debt is bounded. In his specification, Bohn divides primary surplus and beginning of period $t$ debt by the GDP of period $t$. He estimates the following regression, with his own date convention on debt:

$$ \frac{S_t}{Y_t} = \alpha + \beta \frac{D_t}{Y_t} + \mu_t $$

Because GDP of period $t$ depends on the primary surplus of period $t$, his estimation is subject to a simultaneity bias, even if $D_t$ (beginning of period $t$ debt) is predetermined.

This method entails other econometric difficulties when the persistence of the primary surplus is very different from the persistence of debt. We will describe a non-parametric method in order to deal with this econometric issue and apply it to French data. We will also consider Greek data where primary surplus and debt ratios are both integrated series. In this case, a parametric (cointegration) method will be considered. But first of all, we start with a description of the available data.

### III.1 Data description

French national accounts in base 2000 include a financial account for general government from 1978 on.<fnref n="13" /> General government debt can be either defined as financial liabilities or as financial liabilities net of financial assets (gross debt or net debt thereafter). Notice that none of these definitions exactly match general government debt as it is defined in the Maastricht Treaty. In this treaty, debt consists in a subcomponent of general government's financial liabilities taken at their book value rather than at their market value.<fnref n="14" /> It is also worth noting that debt, in the different definitions we consider, is never netted from non-financial assets such as land, buildings and infrastructures which are considered more difficult to liquidate if the government needs cash to repay creditors.

Moreover, Reinhart and Rogoff (2010) have constructed long time series of public debt for several countries including France. Reinhart and Rogoff's series for France coincides with general government debt as it is defined in the Maastricht Treaty after 1978. For the period before 1978, their series most likely represents financial liabilities of the central government only.

From an economic point of view, the most relevant variable seems to be (financial) net debt. Indeed, nationalizations and privatizations from the 1980s and 1990s led to movements of the same sign on the asset and liability sides of the general government balance sheet. Even if net debt may contain more measurement errors than gross debt, we will rely on it in the following for these economic reasons.

<footnote n="13">¹³Since 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.</footnote>

<footnote n="14">¹⁴General 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) (cf. Bourges 2007). These aggregates are precisely defined in the 1993 System of National Accounts (1993 SNA).</footnote>
Fiscal data available in the annual national accounts (base 2000) only cover a time span of 30 years (1978-2007). As quarterly national accounts in the same base are also available, it is possible to obtain a richer sample for our subsequent empirical analysis, i.e. net debt and primary surplus (structural or not) on a quarterly basis from 19801 to 2007Q4. 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, we obtained a quarterly structural primary surplus, using a standard quadratic interpolation of annual potential GDP providing a quarterly output gap. Details on the construction of the quarterly data set are available in appendix A.5.

<figure><img src="image_3.png" /><figcaption>Figure 1: French public debt from 1949 to 2007 and structural primary surplus over 1978-2007 (% of GDP).</figcaption></figure>

The evolution of Greek debt, primary and structural primary surpluses to GDP ratios is depicted on Figure 2. Greece has been able to reduce its primary deficit rapidly during the 1990s after its debt ratio had started to increase at the beginning of the 1980s. Afterwards, it maintained a positive primary surplus until 2002, allowing to stabilize the debt ratio around 100% of GDP. Only Maastricht debt is available for Greece in international databases. The structural primary surplus is obtained using the European Commission estimates of the output gap (AMECO database), and a budgetary sensitivity of 0.43 (as computed in European Commission, 2005). Unfortunately, the statistical approach used for France to obtain higher-frequency fiscal variables could not be replicated for Greece due to the lack of long enough quarterly national accounts.
<figure><img src="image_4.png" /><figcaption>Figure 2: Greek debt, primary and structural primary surpluses over 1978-2007 (% of GDP). Data are taken from the AMECO (March 2011) database. Over 1995-2007, they correspond to those published by Eurostat in February 2012.</figcaption></figure>

### III.2 Estimation of a fiscal reaction function when primary surplus and debt are integrated

When primary surplus and public debt are both integrated time series, the fiscal reaction function is a cointegrating relationship. A finite-sample bias might appear if the evolution of the debt / GDP ratio is correlated to the primary surplus / GDP ratio (cf. III.3). To eliminate this bias, Stock and Watson (1993) recommend to include leads and lags of public debt's variation in the regression:

$$ \frac{S_t}{Y_{t-1}} = \alpha + \beta \frac{D_{t-1}}{Y_{t-1}} + \sum_{i=-n}^{n} \gamma_i \left( \frac{D_{t+i-1}}{Y_{t+i-1}} - \frac{D_{t+i-2}}{Y_{t+i-2}} \right) + \mu_t \quad (4) $$

### III.3 Estimation of a fiscal reaction function when primary surplus and debt are both stationary, the latter being much more persistent than the former

The following regression has to be estimated (cf. *supra* for date conventions):

$$ \frac{S_t}{Y_{t-1}} = \alpha + \beta \frac{D_{t-1}}{Y_{t-1}} + \mu_t $$

Results of this regression are difficult to interpret when the primary surplus/GDP ratio is stationary and the debt/GDP ratio is also stationary but very persistent.<fnref n="15" />

<footnote n="15">¹⁵We 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 β coefficient cannot be different from</footnote>
This is a pure econometric issue, not an economic one.

First of all, suppose that the regressor is formally I(1). The error term $\mu_t$ is most likely correlated with the evolution of the debt/GDP ratio between the end of period $t-1$ and the end of period $t$. Indeed, an increase in primary surplus leads to a decrease in debt, everything else held equal. In such a case, the estimator $\hat{\beta}$ has a non-standard asymptotic distribution and a finite-sample bias. The bias is present even when the regressor is predetermined as it is in our case. Thus, it is not a simultaneity bias. Despite the superconvergence property of the estimator, this finite-sample bias is particularly impeding for samples of standard sizes and can lead us to over-reject $H_0$ ($\beta = 0$) using a Student test with usual critical values.

With a finite sample, the same difficulty arises for time series that are not formally integrated but simply very persistent (cf. Mankiw and Shapiro (1986) for an empirical illustration and Banerjee and Dolado (1988) for a theoretical explanation). The sign and the size of this bias depend on the unknown correlation between the error term and the evolution of the debt/GDP ratio.

The existence of this bias casts doubt on the results obtained from panel regressions with numerous countries having a persistent debt/GDP ratio such as in Mendoza and Ostry (2008) and the study by the European Commission (PFR 2011).

A first way to eliminate the finite sample bias would be to add an additional lag of the debt/GDP ratio in the regression (3), which gives:

$$ \frac{S_t}{Y_{t-1}} = \alpha + \beta \frac{D_{t-1}}{Y_{t-1}} + \gamma \frac{D_{t-2}}{Y_{t-2}} + \mu_t \quad (5) $$

Even when the debt ratio is integrated, estimators $\hat{\beta}$ and $\hat{\gamma}$ converge in $\sqrt{T}$ to standard normal distributions centered at $\beta$ and $\gamma$. Indeed, regression (5) can be rewritten differently with these coefficients associated with stationary variables. We use the fact that the difference $\frac{D_{t-1}}{Y_{t-1}} - \frac{D_{t-2}}{Y_{t-2}}$ is stationary. It is a direct application of a theorem by Sims, Stock and Watson (1990). Simulations done by Galbraith and al. (1987) show that using this method yields excellent results in the case of regressors that are not formally integrated processes but only very persistent.

This parametric method could solve the aforementioned econometric problems due to heterogeneous persistence, but we will not rely on it in the present context for two reasons. First, it would require to make strong assumptions on the stochastic properties of the debt to GDP ratio (e.g.: bounded process) to comply with the proof given in appendix if $\frac{D_{t-2}}{Y_{t-2}}$ is considered as a control variable. Second, it is not obvious to extend Bohn's proof to the case of fiscal reaction functions with lags of the debt/GDP ratio and/or additional lags of the surplus/GDP ratio. Computations become extremely cumbersome in this case.<fnref n="16" />

<footnote>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.</footnote>

<footnote n="16">¹⁶Notice 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.</footnote>
### III.4 Non-parametric tests

The problem arising from the correlation between primary surplus innovations and future values of debt can also be solved using non-parametric tests, without additional lags in the equation. According to Campbell and Dufour (1997), if $\frac{S_t}{Y_{t-1}}$ is independent from the past (in particular from $\frac{D_{t-1}}{Y_{t-1}}$ under the null hypothesis $\beta = 0$) and has a median $b_0$, then the finite-sample exact distribution of the sign statistic $S_g(b_0) = \sum_{t=1}^n u[(\frac{S_t}{Y_{t-1}} - b_0)(\frac{D_{t-1}}{Y_{t-1}} - \hat{m}_{t-1})]$ is known, where $u(z) = 1$ if $z \ge 0$ and $u(z) = 0$ if $z < 0$, and $\hat{m}_{t-1}$ is the empirical median of the first $t-1$ observations of the debt ratio. Moreover, if the primary surplus ratio has a continuous and symmetric distribution about $b_0$, then we also know the exact distribution of the signed rank statistic $SR_g(b_0) = \sum_{t=1}^n u[(\frac{S_t}{Y_{t-1}} - b_0)(\frac{D_{t-1}}{Y_{t-1}} - \hat{m}_{t-1})]R_t^+(b_0)$ where $R_t^+(b_0)$ denotes the rank of $|\frac{S_t}{Y_{t-1}} - b_0|$ among $|\frac{S_1}{Y_0} - b_0|, \dots, |\frac{S_n}{Y_{n-1}} - b_0|$ sorted in ascending order, that is $R_t^+(b_0) = \sum_{j=1}^n u[|\frac{S_t}{Y_{t-1}} - b_0| - |\frac{S_j}{Y_{j-1}} - b_0|]$.

Both tests rely on the comparison of the signs of $\frac{S_t}{Y_{t-1}} - b_0$ and $\frac{D_{t-1}}{Y_{t-1}} - \hat{m}_{t-1}$. If $\beta$ is positive, both primary surplus and debt will tend to be above or below their median at the same time, meaning that $(\frac{S_t}{Y_{t-1}} - b_0)(\frac{D_{t-1}}{Y_{t-1}} - \hat{m}_{t-1})$ will be more frequently positive than negative. In such a case, the sign statistic $S_g(b_0)$ and the signed rank statistic $SR_g(b_0)$ will be positive and far from 0. In contrast with a negative $\beta$, $\frac{S_t}{Y_{t-1}} - b_0$ and $\frac{D_{t-1}}{Y_{t-1}} - \hat{m}_{t-1}$ will generally display opposite signs, entailing sign and signed rank statistics near 0.

When the median $b_0$ of the primary surplus ratio is unknown, Campbell and Dufour (1997) propose two strategies. The first strategy consists in computing the above statistics with the empirical estimator $\tilde{b}_0$ of the median $b_0$ on the whole sample. However, finite sample distributions of test statistics are not available in this case. The second strategy consists in three steps: first, an exact confidence interval of level $\alpha_1$ for $b_0$ is computed; then, test statistics of level $\alpha_2$ are computed for each value inside the confidence interval; finally, these statistics are combined with the confidence interval for $b_0$ using Bonferroni's inequality in order to end up with a finite-sample exact non-parametric test at the desired level $\alpha_1 + \alpha_2 = \alpha$.

These non-parametric tests have several advantages compared with the frequently used parametric tests. No restriction is imposed either on the correlation between innovations of the primary surplus ratio and future values of the debt ratio, or on the nature of the innovations generating primary surplus and debt: they can be heteroscedastic and follow non-normal distributions. These tests also rely on exact finite-sample critical values. Numerical simulations done by Campbell and Dufour (1997) show that these test statistics do not wrongly over-reject the null hypothesis and display a power at least similar to standard t-tests in finite samples.

However, these non-parametric tests are only valid under the assumption that the primary surplus ratio is not autocorrelated under the null hypothesis. This assumption seems to be more acceptable if we consider the cyclically-adjusted (i.e. structural) primary surplus ratio rather than the non-cyclically adjusted primary surplus ratio. Therefore, we only present results of the non-parametric tests when the dependent variable is the structural primary surplus ratio. Notice that this choice amounts to follow Bohn's (1998) advice and to control for the cyclical evolution of the primary
surplus ratio (see III.5). Campbell and Dufour (1997) also suggest a method to take
into account autocorrelated innovations by considering two subsamples. The first one
only contains observations at even dates and the second one those at odd dates. A
test of level α/2 on each of them will actually amount to an α-level test on the whole
sample.

### III.5 Empirical results for France

Fiscal reaction functions are only estimated on the 1978-2007 sample so that national accounts data are definitive and output gap estimates are more reliable. Indeed, the output gap appears to be a potentially important variable determining the primary surplus / GDP ratio and is most likely correlated with the debt to GDP ratio. Bohn (1998) also suggests to include the output gap in the regression. But rather than directly estimating the elasticity of primary surplus to output gap because we would need instrumental variables to do it properly, we rely on the elasticity of 0.5 computed for France by Guyon and Sorbe (2009). We use the output gap computed by the European Commission (AMECO database) rather than an HP filter because the estimate of the European Commission relies on a production function and is therefore more structural. Since most revisions of this series seem to be concentrated on the last 3 or 4 years, the output gap series computed until 2007 is considered to be reliable.

Considering usual stationarity tests (ADF, KPSS and ERS, see Table 1a), both gross and net debt ratios seem to be I(1) whereas the cyclically-unadjusted primary surplus ratio seems to be I(0). However, the KPSS and ERS unit-root tests lead to inconclusive results for the structural primary surplus. Since we consider that it is not possible for these tests to distinguish between formally integrated series and stationary but very persistent series with the available data, we will assume first that both primary surplus ratios and the net debt ratios are formally I(1), and then that all these variables are stationary with possibly high persistence.<fnref n="17" />

First considering that all series are I(1), we apply the Stock and Watson (1993) method to estimate the fiscal reaction function for France. Results are presented in Table 2. The coefficient on the debt to GDP ratio is never significant. A Shin (1994) test does not reject the cointegration hypothesis between debt and the primary surpluses.<fnref n="18" />

If we assume now that the cyclically-adjusted primary surplus and net financial debt ratios are stationary but the latter very persistent, we apply non-parametric tests introduced by Campbell and Dufour (1997) to implement the sustainability analysis. Specification (3) is used and right unilateral tests are computed. The significance of the fiscal reaction coefficient is assessed at a level of 5%. Sign and signed-rank statistics are computed using either the empirical median estimate of the structural primary surplus ratio (median-estimate tests) or a confidence interval for this median (bounds tests).

Results are reported in Table 1b. Using the empirical median estimate on the sample, the null hypothesis cannot be rejected: the p-value is 0.64% for the sign

<footnote n="17">¹⁷Remember 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 β can only be 0.</footnote>

<footnote n="18">¹⁸KPSS statistics for the residuals of regression (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.</footnote>
<table><caption>Table 1a: France 1978-2007. Order of integration of fiscal variables with t-stat. ***(**,*) indicates rejection of the null hypothesis of non-stationarity (ADF, ERS) at a 1% (5%,10%) level and †††(††,†) rejection of the null of stationarity (KPSS) at a 1% (5%, 10%) level</caption><thead><tr><th rowspan="2">Variable</th><th rowspan="2">Order of integration</th><th colspan="3">Level</th><th colspan="3">1st difference</th></tr><tr><th>ADF</th><th>KPSS</th><th>ERS</th><th>ADF</th><th>KPSS</th><th>ERS</th></tr></thead><tbody><tr><td>S/GDP(-1)</td><td>0</td><td>-3.11**</td><td>0.13</td><td>0.79***</td><td>-4.26***</td><td>0.08</td><td>1.77***</td></tr><tr><td>S struct/GDP(-1)</td><td>0/1</td><td>-2.49</td><td>0.17</td><td>4.34</td><td>-5.75***</td><td>0.07</td><td>2.26**</td></tr><tr><td>D<sub>net</sub>/GDP</td><td>1</td><td>-1.58</td><td>0.64††</td><td>24.22</td><td>-3.31**</td><td>0.26</td><td>2.91**</td></tr><tr><td>D<sub>gross</sub>/GDP</td><td>1</td><td>-0.64</td><td>0.67††</td><td>95.60</td><td>-3.43**</td><td>0.12</td><td>0.31***</td></tr></tbody></table>

<table><caption>Table 1b: France 1978-2007. Under $H_0$, primary surplus ratios and debt ratios are independent. Right unilateral tests are performed on the statistics $Sg$, $SRg$, $SB$ and $SRB$. p-values are indicated in the table. $Q_L$ is the smallest value taken by the test statistic on the confidence interval defined for $b_0$. $Q_U$ is the largest value</caption><thead><tr><th rowspan="2">S struct/GDP(-1)</th><th colspan="4">Median-Estimate Tests</th><th colspan="4">Bound Tests</th></tr><tr><th>Sg</th><th>Interpretation</th><th>SRg</th><th>Interpretation</th><th>SB</th><th>Interpretation</th><th>SRB</th><th>Interpretation</th></tr></thead><tbody><tr><td>Total sample</td><td>0.64</td><td>H<sub>0</sub> not rejected</td><td>0.66</td><td>H<sub>0</sub> not rejected</td><td>Q<sub>L</sub> 0.97</td><td>Q<sub>U</sub> 0.03</td><td>Inconclusive 0.84</td><td>H<sub>0</sub> not rejected</td></tr><tr><td>Sub-sample A</td><td>0.40</td><td>H<sub>0</sub> not rejected</td><td>0.64</td><td>H<sub>0</sub> not rejected</td><td>0.91</td><td>0.00</td><td>Inconclusive 0.88</td><td>H<sub>0</sub> not rejected</td></tr><tr><td>Sub-sample B</td><td>0.21</td><td>H<sub>0</sub> not rejected</td><td>0.24</td><td>H<sub>0</sub> not rejected</td><td>0.79</td><td>0.01</td><td>Inconclusive 0.56</td><td>H<sub>0</sub> not rejected</td></tr></tbody></table>

<footnote>Note: For median-estimate tests, relying on the empirical median estimate $b_0$ of the structural primary surplus / GDP(-1) ratio, significance is tested at a 5% level (2.5% for the subsamples).</footnote>

<footnote>For bounds tests, a 99% confidence interval $J(0.01)$ is first constructed for the median $b_0$ on the whole sample (99.5% on each subsample). $H_0$ is rejected if, for all $b \in J(0.01)$ ($J(0.005)$ for subsamples), the test statistic is above the 4% critical value (2% for subsamples). $H_0$ is not rejected if, for all $b \in J(0.01)$ ($J(0.005)$ for subsamples), the test statistic is less than the 6% critical value (3% for subsamples). It may occur that $Q_L$ is less than the 4% (2%) critical value but that $Q_U$ is above the 6% (3%) critical value. In this case, test results are said to be inconclusive.</footnote>
<table><thead><tr><th></th><th>(1)<br>S/GDP(-1)</th><th>(2)<br>S/GDP(-1)</th><th>(3)<br>S struct/GDP(-1)</th><th>(4)<br>S struct/GDP(-1)</th></tr></thead><tbody><tr><td>D(-1)/GDP(-1)</td><td>0.0196<br>(0.0143)</td><td>0.0203<br>(0.0151)</td><td>-0.0131<br>(0.0175)</td><td>-0.0126<br>(0.0165)</td></tr><tr><td>D(+1)/GDP(+1) - D/GDP</td><td>-0.0473<br>(0.0582)</td><td></td><td>-0.0515<br>(0.0698)</td><td></td></tr><tr><td>D/GDP - D(-1)/GDP(-1)</td><td>-0.136<br>(0.0849)</td><td>-0.145*<br>(0.0765)</td><td>-0.110*<br>(0.0587)</td><td>-0.132**<br>(0.0489)</td></tr><tr><td>D(-1)/GDP(-1) - D(-2)/GDP(-2)</td><td>-0.133**<br>(0.0576)</td><td>-0.0907<br>(0.0583)</td><td>-0.000308<br>(0.0777)</td><td>0.00590<br>(0.0636)</td></tr><tr><td>D(-2)/GDP(-2) - D(-3)/GDP(-3)</td><td>-0.116<br>(0.0713)</td><td>-0.0827<br>(0.0780)</td><td>-0.00972<br>(0.0767)</td><td>0.0213<br>(0.0665)</td></tr><tr><td>D(-3)/GDP(-3) - D(-4)/GDP(-4)</td><td>-0.0243<br>(0.0575)</td><td></td><td>0.0491<br>(0.0532)</td><td></td></tr><tr><td>Constant</td><td>-0.624<br>(0.446)</td><td>-0.914**<br>(0.360)</td><td>-0.469<br>(0.417)</td><td>-0.502<br>(0.379)</td></tr><tr><td>Observations</td><td>25</td><td>27</td><td>25</td><td>27</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.460</td><td>0.428</td><td>0.005</td><td>0.020</td></tr></tbody></table>

Standard errors in parentheses

* p < 0.10, ** p < 0.05, *** p < 0.01

<caption>Table 2: France 1978-2007. OLS estimates with Newey-West standard errors</caption>
statistic and 0.66% for the signed-rank statistic. Using a confidence interval for
the median of the structural primary surplus ratio, the null hypothesis is not rejected
either (cf. details under Table 1b). Like Campbell and Ghysels (1995), we then divide
the sample in two parts and apply the same non-parametric tests on each subsample
so that the assumption of non-autocorrelated residuals becomes more credible. Under
the null hypothesis, this assumption means that structural primary surplus ratios are
non-autocorrelated in each subsample. These robustness checks confirm our previous
results, indicating a lack of response of primary surplus to indebtedness.

We then perform the same analysis with quarterly data interpolated from the
annual national accounts, yielding similar results. Table 3a shows stationarity tests
for these fiscal variables, indicating that net debt and both surplus ratios are I(1)
and cointegrated. Applying once again the Stock and Watson (1993) method leads
to the same conclusion for French debt sustainability: no evidence of a significantly
positive fiscal reaction function, as reported in Table 3b.

As a conclusion for the French case, results of parametric and non-parametric tests
are mitigated but they do not indicate a significantly positive fiscal reaction function
in the past.<fnref n="19" /> So, to the extent private investors used the fiscal reaction function as a
device to assess sustainability, they probably anticipated a strengthening of the fiscal
reaction even before the start of the financial crisis to justify their buying of French
public debt. However, French public debt continued to increase after the end of the
estimation sample and French borrowing costs remained low, or even very low.

### III.6 Empirical results for Greece

Debt and primary surplus ratios may be both considered as I(1) for this country. Therefore, the fiscal reaction function is estimated using Stock and Watson (1993) method. Results are presented in Table 4b. The coefficient on the debt to GDP ratio is estimated at around 0.1 for the 1978-2007 period, depending on the specification. It is always significant at a 1% level. This estimate is very high, implying that a 10 points increase in the debt ratio leads to a 1 point increase in the (structural) primary surplus, thus pointing strongly towards sustainability. A Shin (1994) test does not reject the cointegration hypothesis between (structural) primary surplus and debt ratios.<fnref n="20" /> Notice that Greece also appears as a country with very sustainable public finances in Mendoza and Ostry (2008) who also estimate fiscal reaction functions.

Of course, this result may seem confusing when one considers the recent eco-
nomic developments in Greece. This should be an important warning for the users
of econometric sustainability tests. Greece is actually unable to finance its public
debt on the market although its past fiscal reaction function points to a sustainable
indebtedness. In fact, investors probably anticipated that Greece would be unable to
apply this fiscal reaction function at higher debt levels. This is exactly the issue that
Bi and Leeper (2012) deal with using a general equilibrium model. Their conclusion

<footnote n="19">¹⁹The estimation of a fiscal reaction function for Germany is not considered in this paper. Indeed the huge challenges following the German reunification probably caused a break in the fiscal reaction function. Furthermore the treatment of the privatizations of eastern companies in the early 1990's through the Treuhandanstalt should be taken into account.</footnote>

<footnote n="20">²⁰KPSS statistics for the residuals in regressions (1) to (4) of Table 4b are respectively 0.117, 0.121, 0.104 and 0.112, the Shin (1994) asymptotic critical value at 10% being 0.231.</footnote>
<table><caption>Table 3a: France 1980Q1-2007Q4. Order of integration of quarterly fiscal variables with t-stat. ***(**,*) indicates rejection of the null hypothesis of non-stationarity (ADF,ERS) at a 1% (5%,10%) level and †††(††,†) rejection of the null of stationarity (KPSS) at a 1% (5%, 10%) level</caption><thead><tr><th rowspan="2">Variable</th><th rowspan="2">Order of integration</th><th colspan="3">Level</th><th colspan="3">1st difference</th></tr><tr><th>ADF</th><th>KPSS</th><th>ERS</th><th>ADF</th><th>KPSS</th><th>ERS</th></tr></thead><tbody><tr><td>S/GDP(-1)</td><td>1</td><td>-2.13</td><td>0.20</td><td>7.30</td><td>-14.18***</td><td>0.10</td><td>0.66***</td></tr><tr><td>S struct/GDP(-1)</td><td>1</td><td>-2.68*</td><td>0.18</td><td>9.87</td><td>-14.68***</td><td>0.06</td><td>0.51***</td></tr><tr><td>D<sub>net</sub>/GDP</td><td>1</td><td>-1.69</td><td>1.12 † † †</td><td>31.87</td><td>-3.70***</td><td>0.26</td><td>2.28**</td></tr></tbody></table>

<table><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr><tr><th></th><th>S /GDP(-1)</th><th>S /GDP(-1)</th><th>S struct /GDP(-1)</th><th>S struct /GDP(-1)</th></tr></thead><tbody><tr><td>D(-1)/GDP(-1)</td><td>0.003<br>(0.003)</td><td>0.003<br>(0.002)</td><td>-0.003<br>(0.003)</td><td>-0.003<br>(0.003)</td></tr><tr><td>D(+1)/GDP(+1) - D/GDP</td><td>0.005<br>(0.079)</td><td></td><td>-0.036<br>(0.0634)</td><td></td></tr><tr><td>D/GDP - D(-1)/GDP(-1)</td><td>-0.206***<br>(0.069)</td><td>-0.182**<br>(0.072)</td><td>-0.143**<br>(0.066)</td><td>-0.188<br>(0.061)</td></tr><tr><td>D(-1)/GDP(-1) - D(-2)/GDP(-2)</td><td>0.078<br>(0.056)</td><td>0.100<br>(0.062)</td><td>0.083<br>(0.058)</td><td>0.094<br>(0.058)</td></tr><tr><td>D(-2)/GDP(-2) - D(-3)/GDP(-3)</td><td>-0.010<br>(0.064)</td><td>-0.158<br>(0.074)</td><td>-0.027<br>(0.054)</td><td>-0.027<br>(0.070)</td></tr><tr><td>D(-3)/GDP(-3) - D(-4)/GDP(-4)</td><td>-0.130<br>(0.080)</td><td></td><td>-0.003<br>(0.071)</td><td></td></tr><tr><td>Constant</td><td>-0.008***<br>(0.002)</td><td>-0.008***<br>(0.002)</td><td>-0.004<br>(0.003)</td><td>-0.004<br>(0.003)</td></tr><tr><td>Observations</td><td>107</td><td>109</td><td>107</td><td>109</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.42</td><td>0.41</td><td>0.12</td><td>0.15</td></tr></tbody></table>

Standard errors in parentheses

*p < 0.10, **p < 0.05, ***p < 0.01

<caption>Table 3b: France 1980Q1-2007Q4. OLS estimates with Newey-West standard errors. D denotes the French general government net debt</caption>
<table><caption>Table 4a: Greece 1978-2007. Order of integration of fiscal variables with t-stat. ***(**,*) indicates rejection of the null hypothesis of non-stationarity (ADF,ERS) at a 1% (5%,10%) level and †††(††,†) rejection of the null of stationarity (KPSS) at a 1% (5%, 10%) level</caption><thead><tr><th rowspan="2">Variable</th><th rowspan="2">Order of integration</th><th colspan="3">Level</th><th colspan="3">1st difference</th></tr><tr><th>ADF</th><th>KPSS</th><th>ERS</th><th>ADF</th><th>KPSS</th><th>ERS</th></tr></thead><tbody><tr><td>S/GDP(-1)</td><td>1</td><td>-1.68</td><td>0.31</td><td>4.61</td><td>-6.05***</td><td>0.14</td><td>1.80***</td></tr><tr><td>S struct/GDP(-1)</td><td>1</td><td>-1.79</td><td>0.33</td><td>4.74</td><td>-5.67***</td><td>0.14</td><td>1.76***</td></tr><tr><td>D/GDP</td><td>1</td><td>-1.36</td><td>0.66 † †</td><td>158.86</td><td>-4.71***</td><td>0.25</td><td>1.96**</td></tr></tbody></table>

<table><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr><tr><th></th><th>S/GDP(-1)</th><th>S/GDP(-1)</th><th>S struct/GDP(-1)</th><th>S struct/GDP(-1)</th></tr></thead><tbody><tr><td>D(-1)/GDP(-1)</td><td>0.112***<br>(0.0273)</td><td>0.102***<br>(0.0218)</td><td>0.103***<br>(0.0333)</td><td>0.0966***<br>(0.0260)</td></tr><tr><td>D(+1)/GDP(+1) - D/GDP</td><td>0.0158<br>(0.0708)</td><td></td><td>-0.0272<br>(0.0732)</td><td></td></tr><tr><td>D/GDP - D(-1)/GDP(-1)</td><td>-0.0634<br>(0.110)</td><td>-0.0623<br>(0.0914)</td><td>-0.0580<br>(0.113)</td><td>-0.0502<br>(0.0973)</td></tr><tr><td>D(-1)/GDP(-1) - D(-2)/GDP(-2)</td><td>0.0604<br>(0.131)</td><td>0.0229<br>(0.134)</td><td>0.0488<br>(0.151)</td><td>0.0144<br>(0.153)</td></tr><tr><td>D(-2)/GDP(-2) - D(-3)/GDP(-3)</td><td>-0.0267<br>(0.107)</td><td>-0.0130<br>(0.100)</td><td>-0.0217<br>(0.111)</td><td>-0.00514<br>(0.103)</td></tr><tr><td>D(-3)/GDP(-3) - D(-4)/GDP(-4)</td><td>0.0494<br>(0.101)</td><td></td><td>0.0487<br>(0.108)</td><td></td></tr><tr><td>Constant</td><td>-9.577***<br>(2.626)</td><td>-8.675***<br>(1.633)</td><td>-8.857**<br>(3.290)</td><td>-8.487***<br>(2.116)</td></tr><tr><td>Observations</td><td>25</td><td>27</td><td>25</td><td>27</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.470</td><td>0.506</td><td>0.356</td><td>0.396</td></tr></tbody></table>

Standard errors in parentheses

* p < 0.10, ** p < 0.05, *** p < 0.01

<caption>Table 4b: Greece 1978-2007. OLS estimates with Newey-West standard errors</caption>
is that the default risk does not only depend on a fiscal reaction function but also
on the fact that the product of taxes cannot grow indefinitely to stabilize debt above
a certain threshold due to economic and social constraints (Laffer curve). It is also
possible that the 2000's increase in the share of foreign holders of public debt has
changed the fiscal reaction function or the reaction of the market to new develop-
ments in public finance. Given that our analysis uses the most accurate data as of
2012 for the period 1978-2007, it is very likely that the same analysis with 2007 data
would have pointed even more strongly towards sustainability. Yet the uncovering of
the misleading fiscal figures in 2010 certainly undermined the investors' confidence
in the Greek government, their statistics and their ability to react according to the
estimated fiscal reaction function.
Conclusion

This paper has recalled the weaknesses associated with the first generation of sus-
tainability tests in public finance. Some of them can be overcome using Bohn's
suggestion to estimate fiscal reaction functions linking primary surplus and public
debt. A positive link is a sufficient sustainability condition, under the strong con-
dition that the control variables and the error term are bounded. In practice, since
this method also entails econometric difficulties when primary surplus and debt have
a very different persistence or are both integrated, we have put forward parametric
and non-parametric methods in order to deal with these issues.

But even the second generation of sustainability tests has strong empirical limi-
tations, as we have shown using French and Greek national accounts over the last 30
years. Because Greece generated an enormous increase of its primary surplus during
the 1990s, it appears to fulfill this sufficient sustainability condition in 2007. This
result is clearly at odds with recent economic developments in this country. As for
France, results of parametric and non-parametric sustainability tests do not indi-
cate a significantly positive fiscal reaction function over the years 1978-2007. Again,
this result is at odds with subsequent developments. Indeed, French public debt has
increased markedly after the end of the estimation sample, investors have contin-
ued to consider French public indebtedness as sustainable and borrowing costs have
remained low, or even very low.

Our results highlight the limits of econometric sustainability tests. Even if they
are correctly specified, they only give an answer to the following question: is it
rational for an investor, using only the past reaction of primary surplus to debt, to
lend money to a government? In fact, fiscal reaction functions can evolve strongly
according to the circumstances and the sustainability of a country's public finance
depends above all on the quality and strength of its institutions.
# A Appendix

## A.1 Sufficient sustainability condition based on the fiscal reaction function

This appendix gives a theoretical justification for estimating fiscal reaction functions. It is adapted from Bohn's (1998) unpublished appendix. Compared to Bohn's original proof, date conventions have been changed: $D_t$ is now the end of period $t$ debt whereas it is the beginning of period $t$ debt in Bohn (1998) and the interest rate on a loan made in period $t$ is $R_t$ instead of $R_{t+1}$. We also divide primary surplus $S_t$ and debt $D_t$ by the GDP of period $(t-1)$ $Y_{t-1}$ (see III for an econometric justification, related to the estimation of the fiscal reaction function). Finally, the public debt accumulation equation becomes: $D_t = (D_{t-1} - S_t)(1 + R_t)$. This accounting equation means that debt at the end of period $t$ already includes the interest burden that is due for period $(t+1)$. In period $t$, households lend $D_{t-1} - S_t$ to the government and will be repaid $(D_{t-1} - S_t)(1 + R_t)$ in period $(t+1)$. As a consequence, the equation linking the households' stochastic discount factor and the risk-free interest rate on public debt is $E_t[u_{t+i,1} \cdot (1 + R_{t+i})] = 1$.

The debt accumulation equation can be divided by the GDP of period $t$:

$$d_t \equiv \frac{D_t}{Y_t} = \left( \frac{D_{t-1}}{Y_{t-1}} - \frac{S_t}{Y_{t-1}} \right) \cdot (1 + R_t) \frac{Y_{t-1}}{Y_t} \equiv \left( \frac{D_{t-1}}{Y_{t-1}} - \frac{S_t}{Y_{t-1}} \right) \cdot x_t$$

Suppose that the fiscal reaction function is of the following form, with $0 < \rho < 1$:

$$s_t \equiv \frac{S_t}{Y_{t-1}} = \rho \frac{D_{t-1}}{Y_{t-1}} + \mu_t$$

Like in Bohn (1998), $\mu_t$ comprises control variables and a structural error term.

Primary surplus can then be taken out of the equation governing the evolution of public debt. By successive iterations, we get:

$$d_{t+n} = \left( \prod_{j=1}^{n} x_{t+j} \right) (1-\rho)^n d_t - \sum_{i=1}^{n} \left( \prod_{j=i}^{n} x_{t+j} \right) (1-\rho)^{n-i} \mu_{t+i}$$

We can note that this equation implicitly assumes that there is no default, which underlies the only additional technical assumption that we need compared to Bohn (1998): the interest rate $R_t$ is bounded, i.e. $0 < m \le 1 + R_t \le M$. This implies, given the positivity of $u_{t+i,1}$, that: $mu_{t+i,1} \le u_{t+i,1}(1 + R_{t+i}) \le Mu_{t+i,1} \Rightarrow \frac{1}{M} \le E_t[u_{t+i,1}] \le \frac{1}{m}$.

We deduce in the next steps:

$$\frac{\mathbb{E}_t[u_{t,n} \cdot D_{t+n}]}{Y_t} = \mathbb{E}_t \left[ u_{t,n} \cdot \prod_{j=1}^{n} (1 + y_{t+j}) \cdot d_{t+n} \right] \\ = (1 - \rho)^n \cdot \mathbb{E}_t \left[ u_{t,n} \cdot \prod_{j=1}^{n} (1 + y_{t+j}) \cdot \prod_{j=1}^{n} x_{t+j} \right] \cdot d_t \\ - \sum_{i=1}^{n} (1 - \rho)^{n-i} \cdot \mathbb{E}_t \left[ u_{t,n} \cdot \prod_{j=1}^{n} (1 + y_{t+j}) \cdot \prod_{j=i}^{n} x_{t+j} \cdot \mu_{t+i} \right]$$
$$
\begin{align*}
&= (1 - \rho)^n \cdot \mathbb{E}_t \left[ u_{t,n} \cdot \prod_{j=1}^{n} (1 + R_{t+j}) \right] \cdot d_t \\
&\quad - \sum_{i=1}^{n} (1 - \rho)^{n-i} \cdot \mathbb{E}_t \left[ u_{t,n} \cdot \prod_{j=i}^{n} (1 + R_{t+j}) \cdot \prod_{j=1}^{i-1} (1 + y_{t+j}) \cdot \mu_{t+i} \right] \\
&= (1 - \rho)^n \cdot \mathbb{E}_t \left[ u_{t,1} \prod_{j=1}^{n-1} u_{t+j,1} \cdot (1 + R_{t+j}) (1 + R_{t+n}) \right] \cdot d_t \\
&\quad - \sum_{i=1}^{n} (1 - \rho)^{n-i} \cdot \mathbb{E}_t \left[ u_{t,i} \cdot \prod_{j=1}^{i-1} (1 + y_{t+j}) \cdot \prod_{j=i}^{n-1} u_{t+j,1} \cdot (1 + R_{t+j}) \cdot (1 + R_{t+n}) \cdot \mu_{t+i} \right]
\end{align*}
$$

We then use the law of iterated expectations and give an upper bound to the absolute value of $\frac{\mathbb{E}_t[u_{t,n} \cdot D_{t+n}]}{Y_t}$. Indeed, all the terms in the integrands except $\mu_t$ are positive and we assume, like Bohn (1998), that the process $\mu_t$ is bounded, meaning that there exists a $M_0$ such that the realization of $\mu_t$ in every state of nature and at each date lies between $-M_0$ and $M_0$. Therefore:

$$
\begin{align*}
\left| \frac{\mathbb{E}_t[u_{t,n} \cdot D_{t+n}]}{Y_t} \right| &\le (1-\rho)^n \cdot d_t \cdot \frac{M}{m} \\
&\quad + \sum_{i=1}^n (1-\rho)^{n-i} \cdot \mathbb{E}_t \left[ u_{t,i} \cdot \prod_{j=1}^{i-1} (1+y_{t+j}) \cdot u_{t+i,1} \cdot (1+R_{t+i}) \cdot |\mu_{t+i}| \right] M \\
&\le (1-\rho)^n \cdot d_t \frac{M}{m} + M M_0 \sum_{i=1}^n (1-\rho)^{n-i} \cdot \mathbb{E}_t \left[ u_{t,i} \cdot \prod_{j=1}^{i-1} (1+y_{t+j}) \cdot u_{t+i,1} \cdot (1+R_{t+i}) \right] \\
&\le (1-\rho)^n \cdot d_t \frac{M}{m} + M M_0 \sum_{i=1}^n (1-\rho)^{n-i} \cdot \mathbb{E}_t \left[ u_{t,i-1} \cdot u_{t+i-1,1} \cdot \prod_{j=1}^{i-1} (1+y_{t+j}) \right] \\
&\le (1-\rho)^n \cdot d_t \frac{M}{m} + \frac{M}{m} M_0 \sum_{i=1}^n (1-\rho)^{n-i} \cdot \mathbb{E}_t \left[ u_{t,i-1} \cdot \prod_{j=1}^{i-1} (1+y_{t+j}) \right]
\end{align*}
$$

By assumption, also made by Bohn (1998), the discounted value of future rev-
enues

$$
\sum_{k=1}^{n} Y_t \cdot \mathbb{E}_t \left[ u_{t,k} \cdot \prod_{j=1}^{k} (1 + y_{t+j}) \right] \text{ is finite, so that } \lim_{k \to +\infty} \mathbb{E}_t \left[ u_{t,k} \cdot \prod_{j=1}^{k} (1 + y_{t+j}) \right] = 0.
$$

It is then straightforward to show that:

$$
\lim_{n \to +\infty} \frac{\mathbb{E}_t[u_{t,n} \cdot D_{t+n}]}{Y_t} = 0
$$

This means that the existence of the postulated fiscal reaction function is sufficient for the transversality condition to hold, whatever the exact form of the stochastic discount factor. Recall that this result is valid under some technical assumptions: the control variables and the error term are bounded, the discounted value of future revenues is finite and the interest rate is bounded.
## A.2 Stationarity of the error term and the control variables is not sufficient

It is important to bear in mind that stationarity of the control variables and the error term in the fiscal reaction function together with the positivity of the coefficient on debt is not a sufficient sustainability condition (i.e.: it does not imply the transversality condition (TC)). However, if the control variables and the error term are bounded and if there is a positive $\beta$ in the fiscal reaction function, then (TC) holds. Weaker conditions on the control variables could be found, but neither boundedness in probability (which is implied by weak stationarity), nor weak stationarity, nor even strong stationarity are sufficient. An example with a weakly stationary process is given below, for which having a positive $\beta$ in the fiscal reaction function does not imply (TC). Another example with a strongly stationary process follows.

### A.2.1 An example with weak stationarity

Let $u_k \sim iid U([0, 1])$. We define $\mu_k$ and $u_{t,k} \prod_{j=1}^k (1 + y_{t+j}) \equiv X_k$ as follows:

$$ \mu_k = \begin{cases} \sqrt{k^4 - 1} & \text{if } u_k < \frac{1}{k^4} \\ \frac{-1}{\sqrt{k^4 - 1}} & \text{otherwise} \end{cases} \qquad X_k = \begin{cases} k^2 & \text{if } u_k < \frac{1}{k^4} \\ 0 & \text{otherwise} \end{cases} $$

It is straightforward to show that $\mu_k$ is weakly stationary: $E[\mu_k] = \frac{\sqrt{k^4-1}}{k^4} - \frac{1}{\sqrt{k^4-1}}(1-\frac{1}{k^4}) = 0$, $V[\mu_k] = \frac{k^4-1}{k^4} + \frac{1}{k^4-1}(1-\frac{1}{k^4}) = 1$, and all the autocorrelations are null given that $u_k$ is iid. Thus, $\mu_k$ is a weakly stationary process.

$$ \text{Furthermore } E[X_k] = \frac{k^2}{k^4} \xrightarrow{k \to +\infty} 0. $$

$$ \text{However, } E[X_k \mu_k] = \frac{k^2 \sqrt{k^4-1}}{k^4} \xrightarrow{k \to +\infty} 1. $$

In a nutshell, even in taking Bohn's (1998) date conventions and definition of the fiscal reaction function, assuming only that $\lim_{k \to +\infty} E_t \left[ u_{t,k} \cdot \prod_{j=1}^k (1 + y_{t+j}) \right] = 0$ and that $\mu_t$ is a weakly stationary process does not imply that $\lim_{k \to +\infty} E_t \left[ u_{t,k} \cdot \prod_{j=1}^k (1 + y_{t+j}) \cdot \mu_{t+k} \right] = 0$, which is essential for the proof to work.

### A.2.2 An example with strong stationarity

Let $u_k \sim iid U([0, 1])$ and $\mu_k = -\ln(u_k)$, defined almost everywhere with mean and variance 1. Since its mean and variance exist, the strongly stationary $\mu_k$ is also weakly stationary.

Let $X_k \equiv \frac{1}{k^2 u_k (\ln(u_k) - 1)^2}$. Then, using a generalized integral:

$$ E_t[X_k] = \frac{1}{k^2} \int_0^1 \frac{du}{u(\ln u - 1)^2} = \frac{1}{k^2} \left[ \frac{-1}{\ln u - 1} \right]_0^1 = \frac{1}{k^2} \xrightarrow{k \to +\infty} 0 $$

But $\forall k \in \mathbb{N}^*, E[X_k \mu_k] = +\infty$. Indeed for $0 < a < 1$, we have:

$$ \int_a^1 \frac{-\ln u \, du}{u(\ln u - 1)^2} = \left[ \frac{\ln u}{\ln u - 1} \right]_a^1 - \int_a^1 \frac{du}{u(\ln u - 1)} = \left[ -\frac{\ln a}{\ln a - 1} \right]_a^1 - [\ln(1 - \ln u)]_a^1 \xrightarrow{a \to 0^+} +\infty $$
With these $\mu_k$ and $u_{t,k} \prod_{j=1}^k (1 + y_{t+j}) = X_k$ processes, the transversality condition is therefore violated. Of course this example remains valid with both Bohn's and our notations for debt and surplus ratios.

### A.3 Debt cannot be at the same time $I(m)_{m \ge 0}$ in level and $I(k)_{k \ge 0}$ after discounting

If $X_t \sim I(m)$ and $X_0$ is known, then $\mathbb{V}[X_t] \sim O(t^{2m})$. This result can be shown by induction, the assertion being trivial for $m=0$. Let us assume the result established for every $k < m$, and let us consider a process $X_t \sim I(m)$. The process $Y_t = (1-L)X_t$ can then be defined and it is $I(m-1)$. The variance of $X_t = X_0 + Y_t + \dots + Y_1$ equals $\sum_{j=1}^t \mathbb{V}[Y_j] + \sum_{j_1, j_2=1, j_1 \neq j_2}^t \mathrm{Cov}[Y_{j_1}, Y_{j_2}]$. The first term is a sum over $1 \le j \le t$ of $O(j^{2m-2})$ terms thanks to the induction hypothesis, so it is $O(t^{2m-1})$. The second term, with Cauchy-Schwarz inequality, is a sum on $1 \le j_1 \neq j_2 \le t$ of $O(j_1^{m-1} j_2^{m-1})$ terms, thus is $O(t^{2m})$. Eventually we did prove that the variance of the process $X_t$ is $O(t^{2m})$.

Furthermore, with $X_t \sim I(m)$ and $Y_t \sim I(m')$ for $m' \le m$, Cauchy-Schwarz inequality allows to write $\mathrm{Cov}[X_t, Y_t] = O(t^{2m})$. One can establish by induction on $k \ge 0$ that there exists coefficients $\{\alpha_{k,j}\}_{0 \le j \le k}$ such that:

$$ \Delta^k \left[ \frac{D_{t+n}}{(1+r)^n} \right] = \frac{1}{(1+r)^n} \sum_{j=0}^{k} \alpha_{k,j} \Delta^j D_{t+n} $$

The $\{\alpha_{k,j}\}_{0 \le j \le k}$ can be obtained by the following recursion: $\alpha_{k+1,j} = (1+r)\alpha_{k,j-1} - r\alpha_{k,j}$ with $\alpha_{0,0} = 1$, $\alpha_{k,j} = 0$ for $j < 0$ and $j > k$.

Developing for $k \ge 0$:

$$ \mathbb{V} \left[ \Delta^k \left[ \frac{D_{t+n}}{(1+r)^n} \right] \right] = \frac{1}{(1+r)^{2n}} \mathbb{V} \left[ \sum_{j=0}^k \alpha_{k,j} \Delta^j D_{t+n} \right] $$

And we notice that the term whose variance we look at is a sum of $k+1$ terms all integrated of order smaller or equal than $m$. Developing the variance enables to write it as a sum of $(k+1)+k(k+1)$ terms which are all $O((t+n)^{2m})$. We can then infer that $\mathbb{V}[\Delta^k \left[ \frac{D_{t+n}}{(1+r)^n} \right]] = O((t+n)^{2m}/(1+r)^{2n})$, which means that for every $k \ge 0$, this variance will converge towards 0 when $n$ goes to infinity. Hence, the $k$ times differentiated discounted debt cannot be a stationary non-zero process for any $k \ge 0$.

### A.4 Proof of proposition I.1

**Proposition I.1.** Let $f$ be a deterministic and discrete function of time.

1. If $D_{t+n}/f(n) \sim I(m)$, with $m \ge 0$ and $f(n) = o((1+r)^n/n^m)$, then debt verifies the transversality condition (TC ad hoc).

2. If $D_{t+n}/f(n) \sim I(0)$ with $f(n) = O((1+r)^n)$ and $\mathbb{E}[D_{t+n}/f(n)] = 0$, then debt verifies the transversality condition (TC ad hoc).
The proof of the first part is very close to that of proposition 1 in Bohn (2007). Noting $d_{t+n} = D_{t+n}/f(n)$ and assuming that this process is $I(m)$, we can write, with Bohn's notations:

$$d_{t+n} = \sum_{k=0}^{m-1} p_k(n) \Delta^k d_t + \sum_{i=1}^{n} p_{m-1}(i) \Delta^m d_{t+(n+1-i)}$$

This implies:

$$\mathbb{E}_t[D_{t+n}]/(1+r)^n = \frac{f(n)}{(1+r)^n} \left( \sum_{k=0}^{m-1} p_k(n) \Delta^k d_t + \sum_{i=1}^{n} p_{m-1}(i) \mathbb{E}_t[\Delta^m d_{t+(n+1-i)}] \right).$$

Since $\Delta^k d_t$ is known at time $t$ and $p_k(n) = O(n^k)$, $\sum_{k=0}^{m-1} p_k(n) \Delta^k d_t = O(n^{m-1})$.

Moreover, $\mathbb{E}_t[\Delta^m d_{t+(n+1-i)}] \xrightarrow{n \to +\infty} \mu = \mathbb{E}[\Delta^m d_t]$ and $\sum_{i=1}^{n} p_{m-1}(i) = O(n^m)$, implying $\sum_{i=1}^{n} p_{m-1}(i) \mathbb{E}_t[\Delta^m d_{t+(n+1-i)}] = O_p(n^m)$.

$$\text{Finally, } \left( \sum_{k=0}^{m-1} p_k(n) \Delta^k d_t + \sum_{i=1}^{n} p_{m-1}(i) \mathbb{E}_t[\Delta^m d_{t+(n+1-i)}] \right) = O_p(n^m).$$

$$\text{Hence, } \mathbb{E}_t[D_{t+n}]/(1+r)^n \xrightarrow{n \to +\infty} 0.$$

The proof of the second part is straightforward noting that $\lim_{n \to +\infty} \mathbb{E}_t[D_{t+n}/f(n)] = \mathbb{E}[D_{t+n}/f(n)] = 0$ given the stationarity of $D_{t+n}/f(n)$.

## A.5 Description of the French quarterly data

Quarterly data on general government net surplus $S_t$ (B9A) as well as interest payments 21 are extracted from the quarterly national accounts (base 2000, INSEE). General government quarterly primary surplus can be simply deduced from those two series. The corresponding cyclically-adjusted primary surplus requires the computation of an output gap at the same frequency. We therefore construct a quarterly potential GDP with a quadratic interpolation of the annual potential GDP provided by the European Commission (in base 2005, not available in base 2000). We can then compute a quarterly output gap for France using real quarterly GDP (quarterly national accounts in base 2005 as well). Using the same elasticity of primary surplus with respect to output gap as for annual data (0.5), we obtain a quarterly cyclically-adjusted primary surplus.

General government net financial debt is only published on an annual basis. Its evolution is linked to surplus by the following equation:

$$\Delta D_{net,t} = -S_t + Adj_t$$

where $Adj_t$ is an adjustment term reflecting revaluation of assets and liabilities in the government balance sheet.

The quarterly evolution of net financial debt can be deduced from the quarterly surplus. Chow and Lin's (1971) method is used to compute the adjustment term at a quarterly frequency under the constraint that debt annual evolution is equal

<footnote n="21">21 We use net interest paid (D41 paid minus received) to be coherent with of our choice of the net debt ratio.</footnote>
to its 4 quarterly evolutions over the year. Surplus and net financial debt at a quarterly frequency are finally divided by nominal quarterly GDP (same date for debt, previous date for surplus) in order to estimate the fiscal reaction function at a quarterly frequency. Note that the coefficient on debt is therefore divided by about 4.

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      <td>B. CREPON et G. DUREAU<br>Investissement en recherche-développement : analyse de causalités dans un modèle d'accélérateur généralisé</td>
      <td>G 9309</td>
      <td>L. BLOCH - B. CŒURE<br>Profitabilité de l'investissement productif et transmission des chocs financiers</td>
      <td>G 9409</td>
      <td>D. EYSSARTIER, P. MAIRE<br>Impacts macro-économiques de mesures d'aide au logement - quelques éléments d'évaluation</td>
      <td>G 9606</td>
      <td>C. DOZ - F. LENGLART<br>Factor analysis and unobserved component models: an application to the study of French business surveys</td>
    </tr>
    <tr>
      <td>G 9113</td>
      <td>J.L. BRILLET, H. ERKEL-ROUSSE, J. TOUJAS-BERNATE<br>"France-Allemagne Couplées" - Deux économies vues par une maquette macro-économétrique</td>
      <td>G 9310</td>
      <td>J. BOURDIEU - B. COLIN-SEDILLOT<br>Les théories sur la structure optimale du capital : quelques points de repère</td>
      <td>G 9410</td>
      <td>F. ROSENWALD<br>Suivi conjoncturel de l'investissement</td>
      <td>G 9607</td>
      <td>N. GREENAN - D. GUELLEC<br>La théorie coopérative de la firme</td>
    </tr>
    <tr>
      <td>G 9201</td>
      <td>W.J. ADAMS, B. CREPON, D. ENCAOUA<br>Choix technologiques et stratégies de dissuasion d'entrée</td>
      <td>G 9311</td>
      <td>J. BOURDIEU - B. COLIN-SEDILLOT<br>Les théories sur la structure optimale du capital : quelques points de repère</td>
      <td>G 9411</td>
      <td>C. DEFEUILLEY - Ph. QUIRION<br>Les déchets d'emballages ménagers : une analyse économique des politiques française et allemande</td>
      <td>G 9607</td>
      <td></td>
    </tr>
  </tbody>
</table>
<table><tr><td>G 9608</td><td>N. GREENAN - D. GUELLEC<br>Technological innovation and employment<br>reallocation</td></tr><tr><td>G 9609</td><td>Ph. COUR - F. RUPPRECHT<br>L'intégration asymétrique au sein du continent<br>américain : un essai de modélisation</td></tr><tr><td>G 9610</td><td>S. DUCHENE - G. FORGEOT - A. JACQUOT<br>Analyse des évolutions récentes de la productivité apparente du travail</td></tr><tr><td>G 9611</td><td>X. BONNET - S. MAHFOUZ<br>The influence of different specifications of wages-prices spirals on the measure of the NAIRU: the case of France</td></tr><tr><td>G 9612</td><td>PH. COUR - E. DUBOIS, S. MAHFOUZ, J. PISANI-FERRY<br>The cost of fiscal retrenchment revisited: how strong is the evidence?</td></tr><tr><td>G 9613</td><td>A. JACQUOT<br>Les flexions des taux d'activité sont-elles seulement conjoncturelles ?</td></tr><tr><td>G 9614</td><td>ZHANG Yingxiang - SONG Xueqing<br>Lexique macroéconomique Français-Chinois</td></tr><tr><td>G 9701</td><td>J.L. SCHNEIDER<br>La taxe professionnelle : éléments de cadrage économique</td></tr><tr><td>G 9702</td><td>J.L. SCHNEIDER<br>Transition et stabilité politique d'un système redistributif</td></tr><tr><td>G 9703</td><td>D. GOUX - E. MAURIN<br>Train or Pay: Does it Reduce Inequalities to Encourage Firms to Train their Workers?</td></tr><tr><td>G 9704</td><td>P. GENIER<br>Deux contributions sur dépendance et équité</td></tr><tr><td>G 9705</td><td>E. DUGUET - N. IUNG<br>R & D Investment, Patent Life and Patent Value<br>An Econometric Analysis at the Firm Level</td></tr><tr><td>G 9706</td><td>M. HOUBEBINE - A. TOPIOL-BENSAÎD<br>Les entreprises internationales en France : une analyse à partir de données individuelles</td></tr><tr><td>G 9707</td><td>M. HOUBEBINE<br>Polarisation des activités et spécialisation des départements en France</td></tr><tr><td>G 9708</td><td>E. DUGUET - N. GREENAN<br>Le biais technologique : une analyse sur données individuelles</td></tr><tr><td>G 9709</td><td>J.L. BRILLET<br>Analyzing a small French ECM Model</td></tr><tr><td>G 9710</td><td>J.L. BRILLET<br>Formalizing the transition process: scenarios for capital accumulation</td></tr><tr><td>G 9711</td><td>G. FORGEOT - J. GAUTIÉ<br>Insertion professionnelle des jeunes et processus de déclassement</td></tr><tr><td>G 9712</td><td>E. DUBOIS<br>High Real Interest Rates: the Consequence of a Saving Investment Disequilibrium or of an insufficient Credibility of Monetary Authorities?</td></tr><tr><td>G 9713</td><td>Bilan des activités de la Direction des Études et Synthèses Économiques - 1996</td></tr></table>

<table><tr><td>G 9714</td><td>F. LEQUILLER<br>Does the French Consumer Price Index Overstate Inflation?</td></tr><tr><td>G 9715</td><td>X. BONNET<br>Peut-on mettre en évidence les rigidités à la baisse des salaires nominaux ?<br>Une étude sur quelques grands pays de l'OCDE</td></tr><tr><td>G 9716</td><td>N. IUNG - F. RUPPRECHT<br>Productivité de la recherche et rendements d'échelle dans le secteur pharmaceutique français</td></tr><tr><td>G 9717</td><td>E. DUGUET - I. KABLA<br>Appropriation strategy and the motivations to use the patent system in France - An econometric analysis at the firm level</td></tr><tr><td>G 9718</td><td>L.P. PELÉ - P. RALLE<br>Âge de la retraite : les aspects incitatifs du régime général</td></tr><tr><td>G 9719</td><td>ZHANG Yingxiang - SONG Xueqing<br>Lexique macroéconomique français-chinois, chinois-français</td></tr><tr><td>G 9720</td><td>M. HOUBEBINE - J.L. SCHNEIDER<br>Mesurer l'influence de la fiscalité sur la localisation des entreprises</td></tr><tr><td>G 9721</td><td>A. MOUROUGANE<br>Crédibilité, indépendance et politique monétaire<br>Une revue de la littérature</td></tr><tr><td>G 9722</td><td>P. AUGERAUD - L. BRIOT<br>Les données comptables d'entreprises<br>Le système intermédiaire d'entreprises<br>Passage des données individuelles aux données sectorielles</td></tr><tr><td>G 9723</td><td>P. AUGERAUD - J.E. CHAPRON<br>Using Business Accounts for Compiling National Accounts: the French Experience</td></tr><tr><td>G 9724</td><td>P. AUGERAUD<br>Les comptes d'entreprise par activités - Le passage aux comptes - De la comptabilité d'entreprise à la comptabilité nationale - A paraitre</td></tr><tr><td>G 9801</td><td>H. MICHAUDON - C. PRIGENT<br>Présentation du modèle AMADEUS</td></tr><tr><td>G 9802</td><td>J. ACCARDO<br>Une étude de comptabilité générationnelle pour la France en 1996</td></tr><tr><td>G 9803</td><td>X. BONNET - S. DUCHÈNE<br>Apports et limites de la modélisation « Real Business Cycles »</td></tr><tr><td>G 9804</td><td>C. BARLET - C. DUGUET - D. ENCAOUA - J. PRADEL<br>The Commercial Success of Innovations<br>An econometric analysis at the firm level in French manufacturing</td></tr><tr><td>G 9805</td><td>P. CAHUC - Ch. GIANELLA - D. GOUX - A. ZILBERBERG<br>Equalizing Wage Differences and Bargaining Power - Evidence form a Panel of French Firms</td></tr><tr><td>G 9806</td><td>J. ACCARDO - M. JLASSI<br>La productivité globale des facteurs entre 1975 et 1996</td></tr></table>

<table><tr><td>G 9807</td><td>Bilan des activités de la Direction des Études et Synthèses Économiques - 1997</td></tr><tr><td>G 9808</td><td>A. MOUROUGANE<br>Can a Conservative Governor Conduct an Comodative Monetary Policy?</td></tr><tr><td>G 9809</td><td>X. BONNET - E. DUBOIS - L. FAUVET<br>Asymétrie des inflations relatives et menus costs : tests sur l'inflation française</td></tr><tr><td>G 9810</td><td>E. DUGUET - N. IUNG<br>Sales and Advertising with Spillovers at the firm level: Estimation of a Dynamic Structural Model on Panel Data</td></tr><tr><td>G 9811</td><td>J.P. BERTHIER<br>Congestion urbaine : un modèle de trafic de pointe à courbe débit-vitesse et demande élastique</td></tr><tr><td>G 9812</td><td>C. PRIGENT<br>La part des salaires dans la valeur ajoutée : une approche macroéconomique</td></tr><tr><td>G 9813</td><td>A.Th. AERTS<br>L'évolution de la part des salaires dans la valeur ajoutée en France reflète-t-elle les évolutions individuelles sur la période 1979-1994 ?</td></tr><tr><td>G 9814</td><td>B. SALANIÉ<br>Guide pratique des séries non-stationnaires</td></tr><tr><td>G 9901</td><td>S. DUCHÈNE - A. JACQUOT<br>Une croissance plus riche en emplois depuis le début de la décennie ? Une analyse en comparaison internationale</td></tr><tr><td>G 9902</td><td>Ch. COLIN<br>Modélisation des carrières dans Destinie</td></tr><tr><td>G 9903</td><td>Ch. COLIN<br>Évolution de la dispersion des salaires : un essai de prospective par microsimulation</td></tr><tr><td>G 9904</td><td>B. CREPON - N. IUNG<br>Innovation, emploi et performances</td></tr><tr><td>G 9905</td><td>B. CREPON - Ch. GIANELLA<br>Wages inequalities in France 1969-1992<br>An application of quantile regression techniques</td></tr><tr><td>G 9906</td><td>C. BONNET - R. MAHIEU<br>Microsimulation techniques applied to intergenerational transfers - Pensions in a dynamic framework: the case of France</td></tr><tr><td>G 9907</td><td>F. ROSENWALD<br>L'impact des contraintes financières dans la décision d'investissement</td></tr><tr><td>G 9908</td><td>Bilan des activités de la DESE - 1998</td></tr><tr><td>G 9909</td><td>J.P. ZOYEM<br>Contrat d'insertion et sortie du RMI<br>Évaluation des effets d'une politique sociale</td></tr><tr><td>G 9910</td><td>Ch. COLIN - FI. LEGROS - R. MAHIEU<br>Bilans contributifs comparés des régimes de retraite du secteur privé et de la fonction publique</td></tr><tr><td>G 9911</td><td>G. LAROQUE - B. SALANIÉ<br>Une décomposition du non-emploi en France</td></tr><tr><td>G 9912</td><td>B. SALANIÉ<br>Une maquette analytique de long terme du marché du travail</td></tr><tr><td>G 9913</td><td>Ch. GIANELLA<br>Ch. GIANELLA<br>Local unemployment and wages</td></tr></table>

<table><tr><td>Bis</td><td>Une estimation de l'élasticité de l'emploi peu qualifié à son coût</td></tr><tr><td>G 9913</td><td>Division « Redistribution et Politiques Sociales »<br>Le modèle de microsimulation dynamique DESTINIE</td></tr><tr><td>G 9914</td><td>E. DUGUET<br>Macro-commandes SAS pour l'économie des panels et des variables qualitatives</td></tr><tr><td>G 9915</td><td>R. DUHAUTOIS<br>Évolution des flux d'emplois en France entre 1990 et 1996 : une étude empirique à partir du fichier des bénéfices réels normaux (BRN)</td></tr><tr><td>G 9916</td><td>J.Y. FOURNIER<br>Extraction du cycle des affaires : la méthode de Baxter et King</td></tr><tr><td>G 9917</td><td>B. CRÉPON - R. DESPLATZ - J. MAIRESSE<br>Estimating price cost margins, scale economies and workers' bargaining power at the firm level</td></tr><tr><td>G 9918</td><td>Ch. GIANELLA - Ph. LAGARDE<br>Productivity of hours in the aggregate production function: an evaluation on a panel of French firms from the manufacturing sector</td></tr><tr><td>G 9919</td><td>S. AUDRIC - P. GIVORD - C. PROST<br>Évolution de l'emploi et des coûts par qualification entre 1982 et 1996</td></tr><tr><td>G 2000/01</td><td>R. MAHIEU<br>Les déterminants des dépenses de santé : une approche macroéconomique</td></tr><tr><td>G 2000/02</td><td>C. ALLARD-PRIGENT - H. GUILMEAU - A. QUINET<br>The real exchange rate as the relative price of nontrables in terms of tradables: theoretical investigation and empirical study on French data</td></tr><tr><td>G 2000/03</td><td>J.-Y. FOURNIER<br>L'approximation du filtre passe-bande proposée par Christiano and Fitzgerald</td></tr><tr><td>G 2000/04</td><td>Bilan des activités de la DESE - 1999</td></tr><tr><td>G 2000/05</td><td>B. CREPON - F. ROSENWALD<br>Investissement et contraintes de financement : le poids du cycle<br>Une estimation sur données françaises</td></tr><tr><td>G 2000/06</td><td>A. FLIPO<br>Les comportements matrimoniaux de fait</td></tr><tr><td>G 2000/07</td><td>R. MAHIEU - B. SÉDILLOT<br>Microsimulations of the retirement decision: a supply side approach</td></tr><tr><td>G 2000/08</td><td>C. AUDENIS - C. PROST<br>Déficit conjoncturel : une prise en compte des conjonctures passées</td></tr><tr><td>G 2000/09</td><td>R. MAHIEU - B. SÉDILLOT<br>Équivalent patrimonial de la rente et souscription de retraite complémentaire</td></tr><tr><td>G 2000/10</td><td>R. DUHAUTOIS<br>Ralentissement de l'investissement : petites ou grandes entreprises ? industrie ou tertiaire ?</td></tr><tr><td>G 2000/11</td><td>G. LAROQUE - B. SALANIÉ<br>Temps partiel féminin et incitations financières à l'emploi</td></tr><tr><td>G2000/12</td><td>Ch. GIANELLA<br>Local unemployment and wages</td></tr></table>
G2001/13 B. CREPON - Th. HECKEL
- Informatisation en France : une évaluation à partir de données individuelles
- Computerization in France: an evaluation based on individual company data

G2001/01 F. LEQUILLER
- La nouvelle économie et la mesure de la croissance du PIB
- The new economy and the measurement of GDP growth

G2001/02 S. AUDRIC
La reprise de la croissance de l'emploi profite-t-elle aussi aux non-diplômés ?

G2001/03 I. BRAUN-LEMAIRE
Évolution et répartition du surplus de productivité

G2001/04 A. BEAUDU - Th. HECKEL
Le canal du crédit fonctionne-t-il en Europe ? Une étude de l'hétérogénéité des comportements d'investissement à partir de données de bilan agrégées

G2001/05 C. AUDENIS - P. BISCOURP - N. FOURCADE - O. LOISEL
Testing the augmented Solow growth model: An empirical reassessment using panel data

G2001/06 R. MAHIEU - B. SÉDILLOT
Départ à la retraite, irréversibilité et incertitude

G2001/07 Bilan des activités de la DESE - 2000

G2001/08 J. Ph. GAUDEMET
Les dispositifs d'acquisition à titre facultatif d'annuités viagères de retraite

G2001/09 B. CRÉPON - Ch. GIANELLA
Fiscalité, coût d'usage du capital et demande de facteurs : une analyse sur données individuelles

G2001/10 B. CRÉPON - R. DESPLATZ
Évaluation des effets des dispositifs d'allégements de charges sociales sur les bas salaires

G2001/11 J.-Y. FOURNIER
Comparaison des salaires des secteurs public et privé

G2001/12 J.-P. BERTHIER - C. JAULENT
R. CONVENEVOLE - S. PISANI
Une méthodologie de comparaison entre consommations intermédiaires de source fiscale et de comptabilité nationale

G2001/13 P. BISCOURP - Ch. GIANELLA
Substitution and complementarity between capital, skilled and less skilled workers: an analysis at the firm level in the French manufacturing industry

G2001/14 I. ROBERT-BOBEE
Modelling demographic behaviours in the French microsimulation model Destinie: An analysis of future change in completed fertility

G2001/15 J.-P. ZOYEM
Diagnostic sur la pauvreté et calendrier de revenus : le cas du "Panel européen des ménages"

G2001/16 J.-Y. FOURNIER - P. GIVORD
La réduction des taux d'activité aux âges extrêmes, une spécificité française ?

G2001/17 C. AUDENIS - P. BISCOURP - N. RIEDINGER
Existe-t-il une asymétrie dans la transmission du prix du brut aux prix des carburants ?

G2002/01 F. MAGNIEN - J.-L. TAVERNIER - D. THESMAR
Les statistiques internationales de PIB par habitant en standard de pouvoir d'achat : une analyse des résultats

G2002/02 Bilan des activités de la DESE - 2001

G2002/03 B. SÉDILLOT - E. WALRAET
La cessation d'activité au sein des couples : y a-t-il interdépendance des choix ?

G2002/04 G. BRILHAULT
- Rétropolation des séries de FBCF et calcul du capital fixe en SEC-95 dans les comptes nationaux français

- Retropolation of the investment series (GFCF) and estimation of fixed capital stocks on the ESA-95 basis for the French balance sheets

G2002/05 P. BISCOURP - B. CRÉPON - T. HECKEL - N. RIEDINGER
How do firms respond to cheaper computers? Microeconometric evidence for France based on a production function approach

G2002/06 C. AUDENIS - J. DEROYON - N. FOURCADE
L'impact des nouvelles technologies de l'information et de la communication sur l'économie française - un bouclage macro-économique

G2002/07 J. BARDAJI - B. SÉDILLOT - E. WALRAET
Évaluation de trois réformes du Régime Général d'assurance vieillesse à l'aide du modèle de microsimulation DESTINIE

G2002/08 J.-P. BERTHIER
Réflexions sur les différentes notions de volume dans les comptes nationaux : comptes aux prix d'une année fixe ou aux prix de l'année précédente, séries chaînées

G2002/09 F. HILD
Les soldes d'opinion résument-ils au mieux les réponses des entreprises aux enquêtes de conjoncture ?

G2002/10 I. ROBERT-BOBÉE
Les comportements démographiques dans le modèle de microsimulation Destinie - Une comparaison des estimations issues des enquêtes Jeunes et Carrières 1997 et Histoire Familiale 1999

G2002/11 J.-P. ZOYEM
La dynamique des bas revenus : une analyse des entrées-sorties de pauvreté

G2002/12 F. HILD
Prévisions d'inflation pour la France

G2002/13 M. LECLAIR
Réduction du temps de travail et tensions sur les facteurs de production

G2002/14 E. WALRAET - A. VINCENT
- Analyse de la redistribution intragénérationnelle dans le système de retraite des salariés du privé - Une approche par microsimulation

- Intragenerational distributional analysis in the french private sector pension scheme - A microsimulation approach

G2002/15 P. CHONE - D. LE BLANC - I. ROBERT-BOBEE
Offre de travail féminine et garde des jeunes enfants

G2002/16 F. MAUREL - S. GREGOIR
Les indices de compétitivité des pays : interprétation et limites

G2003/01 N. RIEDINGER - E.HAUVY
Le coût de dépollution atmosphérique pour les entreprises françaises : Une estimation à partir de données individuelles

G2003/02 P. BISCOURP et F. KRAMARZ
Création d'emplois, destruction d'emplois et internationalisation des entreprises industrielles françaises : une analyse sur la période 1986-1992

G2003/03 Bilan des activités de la DESE - 2002

G2003/04 P.-O. BEFFY - J. DEROYON - N. FOURCADE - S. GREGOIR - N. LAÎB - B. MONFORT
Évolutions démographiques et croissance : une projection macro-économique à l'horizon 2020

G2003/05 P. AUBERT
La situation des salariés de plus de cinquante ans dans le secteur privé

G2003/06 P. AUBERT - B. CRÉPON
Age, salaire et productivité
La productivité des salariés décline-t-elle en fin de carrière ?

G2003/07 H. BARON - P.O. BEFFY - N. FOURCADE - R. MAHIEU
Le ralentissement de la productivité du travail au cours des années 1990

G2003/08 P.-O. BEFFY - B. MONFORT
Patrimoine des ménages, dynamique d'allocation et comportement de consommation

G2003/09 P. BISCOURP - N. FOURCADE
Peut-on mettre en évidence l'existence de rigidités à la baisse des salaires à partir de données individuelles ? Le cas de la France à la fin des années 90

G2003/10 M. LECLAIR - P. PETIT
Présence syndicale dans les firmes : quel impact sur les inégalités salariales entre les hommes et les femmes ?

G2003/11 P.-O. BEFFY - X. BONNET - M. DARRACQ-PARIES - B. MONFORT
MZE: a small macro-model for the euro area

G2004/01 P. AUBERT - M. LECLAIR
La compétitivité exprimée dans les enquêtes trimestrielles sur la situation et les perspectives dans l'industrie

G2004/02 M. DUÉE - C. REBILLARD
La dépendance des personnes âgées : une projection à long terme

G2004/03 S. RASPILLER - N. RIEDINGER
Régulation environnementale et choix de localisation des groupes français

G2004/04 A. NABOULET - S. RASPILLER
Les déterminants de la décision d'investir : une approche par les perceptions subjectives des firmes

G2004/05 N. RAGACHE
La déclaration des enfants par les couples non mariés est-elle fiscalement optimale ?

G2004/06 M. DUÉE
L'impact du chômage des parents sur le devenir scolaire des enfants

G2004/07 P. AUBERT - E. CAROLI - M. ROGER
New Technologies, Workplace Organisation and the Age Structure of the Workforce: Firm-Level Evidence

G2004/08 E. DUGUET - C. LELARGE
Les brevets accroissent-ils les incitations privées à innover ? Un examen microéconomique

G2004/09 S. RASPILLER - P. SILLARD
Affiliating versus Subcontracting: the Case of Multinationals

G2004/10 J. BOISSINOT - C. L'ANGEVIN - B. MONFORT
Public Debt Sustainability: Some Results on the French Case

G2004/11 S. ANANIAN - P. AUBERT
Travailleurs âgés, nouvelles technologies et changements organisationnels : un réexamen à partir de l'enquête « REPONSE »

G2004/12 X. BONNET - H. PONCET
Structures de revenus et propensions différentes à consommer - Vers une équation de consommation des ménages plus robuste en prévision pour la France

G2004/13 C. PICART
Évaluer la rentabilité des sociétés non financières

G2004/14 J. BARDAJI - B. SÉDILLOT - E. WALRAET
Les retraites du secteur public : projections à l'horizon 2040 à l'aide du modèle de microsimulation DESTINIE

G2005/01 S. BUFFETEAU - P. GODEFROY
Conditions de départ en retraite selon l'âge de fin d'études : analyse prospective pour les générations 1945 à 1974

G2005/02 C. AFSA - S. BUFFETEAU
L'évolution de l'activité féminine en France : une approche par pseudo-panel

G2005/03 P. AUBERT - P. SILLARD
Délocalisations et réductions d'effectifs dans l'industrie française

G2005/04 M. LECLAIR - S. ROUX
Mesure et utilisation des emplois instables dans les entreprises

G2005/05 C. L'ANGEVIN - S. SERRAVALLE
Performances à l'exportation de la France et de l'Allemagne - Une analyse par secteur et destination géographique

G2005/06 Bilan des activités de la Direction des Études et Synthèses Économiques - 2004

G2005/07 S. RASPILLER
La concurrence fiscale : principaux enseignements de l'analyse économique

G2005/08 C. L'ANGEVIN - N. LAÎB
Éducation et croissance en France et dans un panel de 21 pays de l'OCDE

G2005/09 N. FERRARI
Prévoir l'investissement des entreprises
Un indicateur des révisions dans l'enquête de conjoncture sur les investissements dans l'industrie.

G2005/10 P.-O. BEFFY - C. L'ANGEVIN
Chômage et boucle prix-salaires :
apport d'un modèle « qualifiés/peu qualifiés »

G2005/11 B. HEITZ
A two-states Markov-switching model of inflation in France and the USA: credible target VS inflation spiral

G2005/12 O. BIAU - H. ERKEL-ROUSSE - N. FERRARI
Réponses individuelles aux enquêtes de conjoncture et prévision macroéconomiques :
Exemple de la prévision de la production manufacturière

G2005/13 P. AUBERT - D. BLANCHET - D. BLAU
The labour market after age 50: some elements of a Franco-American comparison

G2005/14 D. BLANCHET - T. DEBRAND - P. DOURGNON - P. POLLET
L'enquête SHARE : présentation et premiers résultats de l'édition française

G2005/15 M. DUÈE
La modélisation des comportements démographiques dans le modèle de microsimulation DESTINIE

G2005/16 H. RAOUI - S. ROUX
Étude de simulation sur la participation versée aux salariés par les entreprises

G2006/01 C. BONNET - S. BUFFETEAU - P. GODEFROY
Disparités de retraite de droit direct entre hommes et femmes : quelles évolutions ?

G2006/02 C. PICART
Les gazelles en France

G2006/03 P. AUBERT - B. CRÉPON - P. ZAMORA
Le rendement apparent de la formation continue dans les entreprises : effets sur la productivité et les salaires

G2006/04 J.-F. OUVRARD - R. RATHELOT
Demographic change and unemployment: what do macroeconometric models predict?

G2006/05 D. BLANCHET - J.-F. OUVRARD
Indicateurs d'engagements implicites des systèmes de retraite : chiffrages, propriétés analytiques et réactions à des chocs démographiques types

G2006/06 G. BIAU - O. BIAU - L. ROUVIERE
Nonparametric Forecasting of the Manufacturing Output Growth with Firm-level Survey Data

G2006/07 C. AFSA - P. GIVORD
Le rôle des conditions de travail dans les absences pour maladie

G2006/08 P. SILLARD - C. L'ANGEVIN - S. SERRAVALLE
Performances comparées à l'exportation de la France et de ses principaux partenaires
Une analyse structurelle sur 12 ans

G2006/09 X. BOUTIN - S. QUANTIN
Une méthodologie d'évaluation comptable du coût du capital des entreprises françaises : 1984-2002

G2006/10 C. AFSA
L'estimation d'un coût implicite de la pénibilité du travail chez les travailleurs âgés

G2006/11 C. LELARGE
Les entreprises (industrielles) françaises sont-elles à la frontière technologique ?

G2006/12 O. BIAU - N. FERRARI
Théorie de l'opinion
Faut-il pondérer les réponses individuelles ?

G2006/13 A. KOUBI - S. ROUX
Une réréprétrétation de la relation entre productivité et inégalités salariales dans les entreprises

G2006/14 R. RATHELOT - P. SILLARD
The impact of local taxes on plants location decision

G2006/15 L. GONZALEZ - C. PICART
Diversification, recentrage et poids des activités de support dans les groupes (1993-2000)

G2007/01 D. SRAER
Allègements de cotisations patronales et dynamique salariale

G2007/02 V. ALBOUY - L. LEQUIEN
Les rendements non monétaires de l'éducation : le cas de la santé

G2007/03 D. BLANCHET - T. DEBRAND
Aspiration à la retraite, santé et satisfaction au travail : une comparaison européenne

G2007/04 M. BARLET - L. CRUSSON
Quel impact des variations du prix du pétrole sur la croissance française ?

G2007/05 C. PICART
Flux d'emploi et de main-d'œuvre en France : un réexamen

G2007/06 V. ALBOUY - C. TAVAN
Massification et démocratisation de l'enseignement supérieur en France

G2007/07 T. LE BARBANCHON
The Changing response to oil price shocks in France: a DSGE type approach

G2007/08 T. CHANEY - D. SRAER - D. THESMAR
Collateral Value and Corporate Investment Evidence from the French Real Estate Market

G2007/09 J. BOISSINOT
Consumption over the Life Cycle: Facts for France

G2007/10 C. AFSA
Interpréter les variables de satisfaction : l'exemple de la durée du travail

G2007/11 R. RATHELOT - P. SILLARD
Zones Franches Urbaines : quels effets sur l'emploi salarié et les créations d'établissements ?

G2007/12 V. ALBOUY - B. CRÉPON
Aléa moral en santé : une évaluation dans le cadre du modèle causal de Rubin

G2008/01 C. PICART
Les PME françaises : rentables mais peu dynamiques

G2008/02 P. BISCOURP - X. BOUTIN - T. VERGÉ
The Effects of Retail Regulations on Prices Evidence form the Loi Galland

G2008/03 Y. BARBESOL - A. BRIANT
Économies d'agglomération et productivité des entreprises : estimation sur données individuelles françaises

G2008/04 D. BLANCHET - F. LE GALLO
Les projections démographiques : principaux mécanismes et retour sur l'expérience française

G2008/05 D. BLANCHET - F. TOUTLEMONDE
Évolutions démographiques et déformation du cycle de vie active : quelles relations ?

G2008/06 M. BARLET - D. BLANCHET - L. CRUSSON
Internationalisation et flux d'emplois : que dit une approche comptable ?

G2008/07 C. LELARGE - D. SRAER - D. THESMAR
Entrepreneurship and Credit Constraints - Evidence from a French Loan Guarantee Program

G2008/08 X. BOUTIN - L. JANIN
Are Prices Really Affected by Mergers?

G2008/09 M. BARLET - A. BRIANT - L. CRUSSON
Concentration géographique dans l'industrie manufacturière et dans les services en France : une approche par un indicateur en continu

G2008/10 M. BEFFY - É. COUDIN - R. RATHELOT
Who is confronted to insecure labor market histories? Some evidence based on the French labor market transition

G2008/11 M. ROGER - E. WALRAET
Social Security and Well-Being of the Elderly: the Case of France

G2008/12 C. AFSA
Analyser les composantes du bien-être et de son évolution

Une approche empirique sur données individuelles

G2008/13 M. BARLET - D. BLANCHET - T. LE BARBANCHON
Microsimuler le marché du travail : un prototype

G2009/01 P.-A. PIONNIER
Le partage de la valeur ajoutée en France, 1949-2007

G2009/02 Laurent CLAVEL - Christelle MINODIER
A Monthly Indicator of the French Business Climate

G2009/03 H. ERKEL-ROUSSE - C. MINODIER
Do Business Tendency Surveys in Industry and Services Help in Forecasting GDP Growth?
A Real-Time Analysis on French Data

G2009/04 P. GIVORD - L. WILNER
Les contrats temporaires : trappe ou marchepied vers l'emploi stable ?

G2009/05 G. LALANNE - P.-A. PIONNIER - O. SIMON
Le partage des fruits de la croissance de 1950 à 2008 : une approche par les comptes de surplus

G2009/06 L. DAVEZIES - X. D'HAULTFOEUILLE
Faut-il pondérer ?... Ou l'éternelle question de l'économétre confronté à des données d'enquête

G2009/07 S. QUANTIN - S. RASPILLER - S. SERRAVALLE
Commerce intragroupe, fiscalité et prix de transferts : une analyse sur données françaises

G2009/08 M. CLERC - V. MARCUS
Élasticités-prices des consommations énergétiques des ménages

G2009/09 G. LALANNE - E. POULIQUEN - O. SIMON
Prix du pétrole et croissance potentielle à long terme

G2009/10 D. BLANCHET - J. LE CACHEUX - V. MARCUS
Adjusted net savings and other approaches to sustainability: some theoretical background

G2009/11 V. BELLAMY - G. CONSALES - M. FESSEAU - S. LE LAIDIER - É. RAYNAUD
Une décomposition du compte des ménages de la comptabilité nationale par catégorie de ménage en 2003

G2009/12 J. BARDAJI - F. TALLET
Detecting Economic Regimes in France: a Qualitative Markov-Switching Indicator Using Mixed Frequency Data

G2009/13 R. AEBERHARDT - D. FOUGÈRE - R. RATHELOT
Discrimination à l'embauche : comment exploiter les procédures de testing ?

G2009/14 Y. BARBESOL - P. GIVORD - S. QUANTIN
Partage de la valeur ajoutée, approche par données microéconomiques

G2009/15 I. BUONO - G. LALANNE
The Effect of the Uruguay round on the Intensive and Extensive Margins of Trade

G2010/01 C. MINODIER
Avantages comparés des séries des premières valeurs publiées et des séries des valeurs révisées - Un exercice de prévision en temps réel de la croissance trimestrielle du PIB en France

G2010/02 V. ALBOUY - L. DAVEZIES - T. DEBRAND
Health Expenditure Models: a Comparison of Five Specifications using Panel Data

G2010/03 C. KLEIN - O. SIMON
Le modèle MÉSANGE réestimé en base 2000
Tome 1 - Version avec volumes à prix constants

G2010/04 M.-É. CLERC - É. COUDIN
L'IPC, miroir de l'évolution du coût de la vie en France ? Ce qu'apporte l'analyse des courbes d'Engel

G2010/05 N. CECI-RENAUD - P.-A. CHEVALIER
Les seuils de 10, 20 et 50 salariés : impact sur la taille des entreprises françaises

G2010/06 R. AEBERHARDT - J. POUGET
National Origin Differences in Wages and Hierarchical Positions - Evidence on French Full-Time Male Workers from a matched Employer-Employee Dataset

G2010/07 S. BLASCO - P. GIVORD
Les trajectoires professionnelles en début de vie active : quel impact des contrats temporaires ?

G2010/08 P. GIVORD
Méthodes économétriques pour l'évaluation de politiques publiques
G2010/09 P.-Y. CABANNES - V. LAPÈGUE - E. POULIQUEN - M. BEFFY - M. GAINI Quelle croissance de moyen terme après la crise ?

G2010/10 I. BUONO - G. LALANNE La réaction des entreprises françaises à la baisse des tarifs douaniers étrangers

G2010/11 R. RATHELOT - P. SILLARD L'apport des méthodes à noyaux pour mesurer la concentration géographique - Application à la concentration des immigrés en France de 1968 à 1999

G2010/12 M. BARATON - M. BEFFY - D. FOUGÈRE Une évaluation de l'effet de la réforme de 2003 sur les départs en retraite - Le cas des enseignants du second degré public

G2010/13 D. BLANCHET - S. BUFFETEAU - E. CRENNER S. LE MINEZ Le modèle de microsimulation Destinie 2: principales caractéristiques et premiers résultats

G2010/14 D. BLANCHET - E. CRENNER Le bloc retraites du modèle Destinie 2: guide de l'utilisateur

G2010/15 M. BARLET - L. CRUSSON - S. DUPUCH - F. PUECH Des services échangés aux services échangeables : une application sur données françaises

G2010/16 M. BEFFY - T. KAMIONKA Public-private wage gaps: is civil-servant human capital sector-specific?

G2010/17 P.-Y. CABANNES - H. ERKEL-ROUSSE - G. LALANNE - O. MONSO - E. POULIQUEN Le modèle Mésange réestimé en base 2000 Tome 2 - Version avec volumes à prix chaînés

G2010/18 R. AEBERHARDT - L. DAVEZIES Conditional Logit with one Binary Covariate: Link between the Static and Dynamic Cases

G2011/01 T. LE BARBANCHON - B. OURLIAC - O. SIMON Les marchés du travail français et américain face aux chocs conjoncturels des années 1986 à 2007 : une modélisation DSGE

G2011/02 C. MARBOT Une évaluation de la réduction d'impôt pour l'emploi de salariés à domicile

G2011/03 L. DAVEZIES Modèles à effets fixes, à effets aléatoires, modèles mixtes ou multi-niveaux: propriétés et mises en œuvre des modélisations de l'hétérogénéité dans le cas de données groupées

G2011/04 M. ROGER - M. WASMER Heterogeneity matters: labour productivity differentiated by age and skills

G2011/05 J.-C. BRICONGNE - J.-M. FOURNIER V. LAPÈGUE - O. MONSO De la crise financière à la crise économique L'impact des perturbations financières de 2007 et 2008 sur la croissance de sept pays industrialisés

G2011/06 P. CHARNOZ - É. COUDIN - M. GAINI Wage inequalities in France 1976-2004: a quantile regression analysis

G2011/07 M. CLERC - M. GAINI - D. BLANCHET Recommendations of the Stiglitz-Sen-Fitoussi Report: A few illustrations

G2011/08 M. BACHELET - M. BEFFY - D. BLANCHET Projeter l'impact des réformes des retraites sur l'activité des 55 ans et plus: une comparaison de trois modèles

G2011/09 C. LOUVOT-RUNAVOT L'évaluation de l'activité dissimulée des entreprises sur la base des contrôles fiscaux et son insertion dans les comptes nationaux

G2011/10 A. SCHREIBER - A. VICARD La tertiairisation de l'économie française et le ralentissement de la productivité entre 1978 et 2008

G2011/11 M.-É. CLERC - O. MONSO - E. POULIQUEN Les inégalités entre générations depuis le baby-boom

G2011/12 C. MARBOT et D. ROY Évaluation de la transformation de la réduction d'impôt en crédit d'impôt pour l'emploi de salariés à domicile en 2007

G2011/13 P. GIVORD - R. RATHELOT - P. SILLARD Place-based tax exemptions and displacement effects: An evaluation of the Zones Franches Urbaines program

G2011/14 X. D'HAULTFOEUILLE - P. GIVORD - X. BOUTIN The Environmental Effect of Green Taxation: the Case of the French "Bonus/Malus"

G2011/15 M. BARLET - M. CLERC - M. GARNEO - V. LAPÈGUE - V. MARCUS La nouvelle version du modèle MZE, modèle macroéconomique pour la zone euro

G2011/16 R. AEBERHARDT - I. BUONO - H. FADINGER Learning, Incomplete Contracts and Export Dynamics: theory and Evidence form French Firms

G2011/17 C. KERDRAIN - V. LAPÈGUE Restrictive Fiscal Policies in Europe: What are the Likely Effects?

G2012/01 P. GIVORD - S. QUANTIN - C. TREVIEN A Long-Term Evaluation of the First Generation of the French Urban Enterprise Zones

G2012/02 N. CECI-RENAUD - V. COTTET Politique salariale et performance des entreprises

G2012/03 P. FÉVRIER - L. WILNER Do Consumers Correctly Expect Price Reductions? Testing Dynamic Behavior

G2012/04 M. GAINI - A. LEDUC - A. VICARD School as a shelter? School leaving-age and the business cycle in France

G2012/05 M. GAINI - A. LEDUC - A. VICARD A scarred generation? French evidence on young people entering into a tough labour market

G2012/06 P. AUBERT - M. BACHELET Disparités de montant de pension et redistribution dans le système de retraite français

G2012/07 R. AEBERHARDT - P. GIVORD - C. MARBOT Spillover Effect of the Minimum Wage in France: An Unconditional Quantile Regression Approach

G2012/08 A. EIDELMAN - F. LANGUMIER - A. VICARD Prélèvements obligatoires reposant sur les ménages: des canaux redistributifs différents en 1990 et 2010

G2012/09 O. BARGAIN - A. VICARD Le RMI et son successeur le RSA découragent-ils certains jeunes de travailler ? Une analyse sur les jeunes autour de 25 ans

G2012/10 C. MARBOT - D. ROY Projections du coût de l'APA et des caractéristiques de ses bénéficiaires à l'horizon 2040 à l'aide du modèle Destinie

G2012/11 A. AUROUX Le crédit d'impôt dédié au développement durable: une évaluation économique

G2012/12 V. COTTET - S. QUANTIN - V. RÉGNIER Coût du travail et allègements de charges: une estimation au niveau établissement de 1996 à 2008

G2012/13 X. D'HAULTFOEUILLE, P. FEVRIER et L. WILNER Demand Estimation in the Presence of Revenue Management

G2012/14 D. BLANCHET et S. LE MINEZ Joint macro/micro evaluations of accrued-to-date pension liabilities: an application to French reforms

G2013/01- F1301 T. DEROYON - A. MONTAUT et P-A PIONNIER Utilisation rétrospective de l'enquête Emploi à une fréquence mensuelle: apport d'une modélisation espace-état

G2013/02- F1302 C. TRÉVIEN Habiter en HLM: quel avantage monétaire et quel impact sur les conditions de logement?

G2013/03 A. POISSONNIER Temporal disaggregation of stock variables - The Chow-Lin method extended to dynamic models

G2013/04 P. GIVORD - C. MARBOT Does the cost of child care affect female labor market participation? An evaluation of a French reform of childcare subsidies

G2013/05 G. LAME - M. LEQUIEN - P.-A. PIONNIER Interpretation and limits of sustainability tests in public finance