# Conditional Logit with one Binary Covariate: Link between the Static and Dynamic Cases

Romain Aeberhardt, Laurent Davezies

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Direction des Études et Synthèses Économiques

G 2010 / 18

Conditional Logit with one Binary Covariate:
Link between the Static and Dynamic Cases

Romain AEBERHARDT et Laurent DAVEZIES

Document de travail
INSTITUT NATIONAL DE LA STATISTIQUE ET DES ÉTUDES ÉCONOMIQUES

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

G 2010 / 18

Conditional Logit with one Binary Covariate:
Link between the Static and Dynamic Cases

Romain AEBERHARDT et Laurent DAVEZIES*

DÉCEMBRE 2010

We are grateful to Magali Beffy, Bo Honoré as well as participants at the 15th International Conference on Panel Data in Bonn (July 2009) for helpful discussions. We also thank Pauline Givord for thoroughly reading the proofs and providing us with suggestions to improve the paper. The views expressed herein are attributable to the authors and do not reflect those of INSEE.

<footnote>* Département des Études Économiques d'Ensemble - 15, bd Gabriel Péri - BP 100 - 92244 MALAKOFF CEDEX</footnote>
# Conditional Logit with one Binary Covariate:
Link between the Static and Dynamic Cases

## Abstract

Disentangling state dependence from unobserved heterogeneity is a common issue in economics. It arises for instance when studying transitions between different states on the labor market. When the outcome variable is binary, one of the usual strategies consists in using a conditional logit model with an appropriate conditioning suitable for a dynamic framework.

Although static conditional logit procedures are widely available, these procedures cannot be used directly in a dynamic framework. Indeed, it is inappropriate to use them with a lag dependent variable in the list of regressors. Moreover, reprogramming this kind of procedures in a dynamic framework can prove quite cumbersome because the likelihood can have a very high number of terms when the number of periods increases.

Here, we consider the case of a conditional logit model with one binary regressor which can be either exogenous or the lagged dependent variable itself. We provide closed forms for the conditional likelihoods in both cases and show the link between them.

These results show that in order to evaluate a conditional logit model with one lag of state dependence and no other covariate, it is possible to simply generate a two variable dataset and use standard procedures originally intended for models without state dependence. Moreover, the closed forms help reduce the computational burden even in the static case in which preimplemented procedures usually exist.

**Keywords:** conditional logit, state dependence, binary model, incidental parameter

# Logit conditionnel avec une covariable binaire :
lien entre les cas statiques et dynamiques

## Résumé

Identifier les effets relevant de la dépendance d'état (c'est-à-dire de la trajectoire passée) tout en contrôlant des effets de variables inobservées est un problème classique en économétrie. C'est par exemple le cas lorsqu'on étudie les transitions d'individus entre différents états sur le marché du travail. Quand la variable d'intérêt est binaire, une des stratégies usuelles consiste à utiliser un modèle logit conditionnel.

Bien que les procédures informatiques permettant d'estimer des modèles de type logit conditionnel dans un cadre statique soient largement disponibles dans les logiciels statistiques, ces procédures ne doivent pas être utilisées directement dans le cas d'un modèle dynamique. Les utiliser en incluant naïvement la variable dépendante retardée dans la liste des régresseurs conduit à des estimations non convergentes. De plus, programmer la vraisemblance de ce type de modèles dans un cadre dynamique peut se révéler délicat car le nombre de termes dans la vraisemblance conditionnelle augmente exponentiellement avec le nombre de périodes d'observation.

Dans ce document, nous considérons un modèle logit conditionnel avec comme explicatives soit un régresseur binaire exogène, soit la variable d'intérêt retardée. Dans les deux cas, nous explicitons des formes fermées de la vraisemblance conditionnelle et nous mettons en évidence la relation entre ces deux expressions. En particulier, pour estimer un logit conditionnel avec une dépendance d'état d'une période et sans autre covariable, nous démontrons qu'il est possible de générer simplement une base de données constituée de deux variables et d'appliquer les procédures standards développées pour le cadre statique. De plus au prix de la programmation d'une maximisation, les formes fermées permettent de tirer parti du caractère binaire de la variable explicative pour réduire drastiquement les temps de calculs, y compris dans le cas statique pour lequel les procédures disponibles sont parfois lentes.

**Mots-clés :** Logit conditionnel, dépendance d'état, modèle binaire, paramètres incidents

**Classification JEL :** C23, C25, J62
# 1 Introduction

Disentangling state dependence from unobserved heterogeneity is a common issue in economics. While the former corresponds to the lasting effect of the past trajectory on the state or behavior of an individual, the latter corresponds to the effect of all other relevant individual characteristics which can not be controlled by the researcher. This question arises for instance when studying transitions between different states on the labor market. An application of such a method concerning subsidized training and youth employment can be found for instance in Magnac (2000). Indeed, being able to distinguish between these two aspects can be extremely important in terms of policy targeting. For instance, one can imagine that if state dependence is very high, voluntary policies aiming at bringing unemployed people back to jobs could have long term positive effects, whereas if there is no state dependence, efforts should be made to improve individual characteristics for instance through more education or on-the-job training.

When the outcome variable is binary, one of the usual strategies consists in using a conditional logit model with an appropriate conditioning suitable for a dynamic framework as developed in Chamberlain (1985). The conditional logit is a common procedure when dealing with unobserved heterogeneity in panel data econometrics when the outcome is binary and the covariates are exogenous, in particular when there is no state dependence. Indeed, classical maximum likelihood estimators are not consistent when the number of estimated parameters increases at the same rate as the number of observations. The conditional logit approach rules out this incidental parameters issue which arises with panel data. Seminal papers on this topic include Rasch (1960) and Andersen (1973), while Magnac (2004) generalizes this approach to other distribution families.

In such a framework with exogenous covariates one needs only to condition on the number of occurrences of each state. When there is state dependence, for instance when the outcome at date $t$ depends on the outcome at date $t-1$, the exogeneity of the covariates is lost. However it is still possible to use a similar approach to make the individual fixed effect disappear but with another conditioning statistic. In that case, there must be at least four observations by individual for the model to be identified.

Although static conditional logit procedures are widely available, these procedures cannot
be used directly in a dynamic framework. Indeed, it is inappropriate to use them with a lag dependent variable in the list of regressors. Moreover, reprogramming this kind of procedures in a dynamic framework can prove quite cumbersome because the likelihood can have a very high number of terms when the number of periods increases.

Here, we consider the case of a conditional logit model with one binary regressor which can be either exogenous or the lagged dependent variable itself. We provide closed forms for the conditional likelihoods in both cases and show the link between them. These results show that in order to evaluate a conditional logit model with one lag of state dependence and no other covariate, it is possible to simply generate a two-variable dataset and use standard procedures originally devised for a framework without state dependence. Moreover, the closed forms help reduce the computational burden even in the static case in which preimplemented procedures usually exist.

Note however that the dynamic procedure studied here is only suitable when there are no other varying covariates. This may seem very restrictive but in fact, first, the model takes into account, in a very flexible way, all the individual characteristics which are constant over time, and second, in the case of varying but stationary covariates, it is always possible to use a stronger conditioning. This extension consists in restricting the sample to individuals whose covariates do not change between two consecutive periods (see for instance Honoré and Kyriazidou, 2000).

The second part will give an idea of the method on a simple case, the third part compares the conditional likelihoods in the static and dynamic frameworks, provides closed forms for the corresponding likelihoods and shows how to generate an appropriate dataset which can be used for the estimation of a conditional logit model with state dependence using standard procedures intended for static conditional logit models. The last part concludes. Examples of programs which generate such an appropriate dataset as well as full proofs of the results are provided in appendix.

## 2 Introductory example

The minimum number of periods needed to identify the state dependence parameter in a dynamic conditional logit model is four (Chamberlain, 1985). In this section we consider such a
model with four time periods, one lag of state dependence and no other covariates than the constant individual unobserved heterogeneity. Then we show that the corresponding likelihood can be interpreted as that of a conditional logit with two time periods and one exogenous binary covariate.

For this example as well as for the rest of the article, we will use the following notations: $y_{it}$, $z_{it}$, $x_{it}$ will all be binary variables; $i$ and $t$ represent respectively individuals and time periods; $y$ will be reserved to the dynamic model, while $z$ and $x$ will be respectively the dependent and explanatory variables for the static model. In both types of models $\alpha_i$ will represent the individual unobserved heterogeneity which is constant over time.

## 2.1 Conditional Logit example in a dynamic framework with four time periods

We consider the following model:

$$y_{it} = 1_{\{\alpha_i + y_{it-1} \delta + \varepsilon_{it} > 0\}} \quad \text{where the } \varepsilon_{it} \text{ have a logistic probability distribution}$$

This model can also be characterized by:

$$P(y_{it} | y_{it-1}, \alpha_i) = \frac{e^{y_{it}(\alpha_i + y_{it-1}\delta)}}{1 + e^{\alpha_i + y_{it-1}\delta}} \quad (1)$$

In order to make the $\alpha_i$ vanish, one usually conditions on $y_{i1}$, $y_{i4}$ and $y_{i2} + y_{i3} = 1$ (corresponding to individuals switching state between periods 2 and 3). With this particular conditioning the remaining sets of events to consider correspond to the following:

$$A_i = \{y_{i1}, y_{i2} = 0, y_{i3} = 1, y_{i4}\} \quad \text{and} \quad B_i = \{y_{i1}, y_{i2} = 1, y_{i3} = 0, y_{i4}\}$$
The probabilities of these two events are:

$$
\begin{align*}
\mathbb{P}(A_i|\alpha_i) &= \mathbb{P}(y_{i4}|y_{i3} = 1, \alpha_i)\mathbb{P}(y_{i3} = 1|y_{i2} = 0, \alpha_i)\mathbb{P}(y_{i2} = 0|y_{i1}, \alpha_i)\mathbb{P}(y_{i1}|\alpha_i) \\
&= \frac{e^{\alpha_i} e^{y_{i4}(\delta+\alpha_i)}}{(1+e^{\alpha_i+y_{i1}\delta})(1+e^{\alpha_i})(1+e^{\alpha_i+\delta})}\mathbb{P}(y_{i1}|\alpha_i) \\
\mathbb{P}(B_i|\alpha_i) &= \frac{e^{y_{i1}\delta+\alpha_i} e^{y_{i4}\alpha_i}}{(1+e^{\alpha_i+y_{i1}\delta})(1+e^{\alpha_i+\delta})(1+e^{\alpha_i})}\mathbb{P}(y_{i1}|\alpha_i)
\end{align*}
$$

hence,

$$
\begin{align*}
\mathbb{P}(A_i|A_i \cup B_i, \alpha_i) &= \frac{e^{y_{i4}\delta}}{e^{y_{i1}\delta} + e^{y_{i4}\delta}} \\
\mathbb{P}(B_i|A_i \cup B_i, \alpha_i) &= \frac{e^{y_{i1}\delta}}{e^{y_{i1}\delta} + e^{y_{i4}\delta}}
\end{align*}
$$

therefore, the conditional likelihood does not depend on αᵢ and can be written as:

$$
\mathbb{P}(y_{i2}, y_{i3} | y_{i1}, y_{i4}, y_{i2} + y_{i3} = 1) = \frac{e^{\delta y_{i2} y_{i1}} e^{\delta y_{i4} y_{i3}}}{e^{\delta y_{i1}} + e^{\delta y_{i4}}} \quad (2)
$$

Note that $\mathbb{P}(y_{i2}, y_{i3} | y_{i1}, y_{i4}, y_{i2} + y_{i3} = 0)$ and $\mathbb{P}(y_{i2}, y_{i3} | y_{i1}, y_{i4}, y_{i2} + y_{i3} = 2)$ do not depend on $\delta$ and therefore the estimation strategy consisting in maximizing the conditional likelihood relies only on the individuals who change state between periods 2 and 3.

2.2 Conditional Logit example in a static framework with two inde-
pendent time periods

We now turn to a conditional logit model with two time periods, no state dependence and one
binary exogenous variable:

$$
z_{it} = \mathbb{1}_{\{\alpha_i + x_{it}\delta + \varepsilon_{it} > 0\}} \quad \text{where the } \varepsilon_{it} \text{ have a logistic probability distribution}
$$

This model can also be characterized by:

$$
\mathbb{P}(z_{it} = 1 | x_{it}, \alpha_i) = \frac{e^{\alpha_i + x_{it} \delta}}{1 + e^{\alpha_i + x_{it} \delta}} \quad (3)
$$
Hence, with the same kind of calculations as before,

$$ \mathbb{P}(z_{i1}, z_{i2} | z_{i1} + z_{i2} = 1, x_{i1}, x_{i2}) = \frac{e^{\delta z_{i1} x_{i1}} e^{\delta z_{i2} x_{i2}}}{e^{\delta x_{i1}} + e^{\delta x_{i2}}} \quad (4) $$

Note that, as in the dynamic case, $\mathbb{P}(z_{i1}, z_{i2} | z_{i1} + z_{i2} = 0)$ and $\mathbb{P}(z_{i1}, z_{i2} | z_{i1} + z_{i2} = 2)$ do not depend on $\delta$ and therefore the estimation strategy consisting in maximizing the conditional likelihood relies only on the individuals who change state between periods 1 and 2.

Note that this model is identified only on the individuals who change state between the two periods.

## 2.3 Link between the static and the dynamic frameworks

In this simple case, if you consider a four-period dynamic model ($y_{i1}$, $y_{i2}$, $y_{i3}$, $y_{i4}$) and a two-period static model (($z_{i1}$, $x_{i1}$), ($z_{i2}$, $x_{i2}$)) such that $z_{i1} = y_{i2}$, $x_{i1} = y_{i1}$, $z_{i2} = y_{i3}$ and $x_{i2} = y_{i4}$, both conditional likelihoods are equal. That means, that with four time periods, if you feed a standard conditional logit procedure designed for a static framework with a two-period dataset such as in Table 1a, the software will maximize the “right” conditional likelihood of a dynamic framework. Note that reshaping the data as in Table 1b will not give a consistent estimator of the state dependence parameter with standard conditional logit procedures although it could have seemed intuitive to run a conditional logistic regression on the lagged dependent variable when looking at Equations (1) and (3).

In the following section we shall see that the link between the conditional likelihoods of static and dynamic models can be generalized to more than four time periods.

<table><caption>Table 1: Rearrangements with 4 time periods</caption><thead><tr><th colspan="3">(a) Good one</th><th colspan="3">(b) Bad one</th></tr><tr><th>t</th><th>z<sub>i</sub></th><th>x<sub>i</sub></th><th>t</th><th>z<sub>i</sub></th><th>x<sub>i</sub></th></tr></thead><tbody><tr><td>1</td><td>y<sub>i2</sub></td><td>y<sub>i1</sub></td><td>1</td><td>y<sub>i2</sub></td><td>y<sub>i1</sub></td></tr><tr><td>2</td><td>y<sub>i3</sub></td><td>y<sub>i4</sub></td><td>2</td><td>y<sub>i3</sub></td><td>y<sub>i2</sub></td></tr><tr><td></td><td></td><td></td><td>3</td><td>y<sub>i4</sub></td><td>y<sub>i3</sub></td></tr></tbody></table>
### 3 Generalization for any $T \ge 4$

Here we consider a binary outcome with $T \ge 4$ periods in the dynamic framework: $y = (y_{i1}, \dots, y_{iT})$ and $T' \ge 2$ in the static framework: $z = (z_{i1}, \dots, z_{iT'})$. Because in the dynamic framework, the trajectories such that $\sum_{t=2}^{T-1} y_{it} = 0$ or $\sum_{t=2}^{T-1} y_{it} = T - 2$ are uninformative, estimation is made without these observations and in this section we assume without loss of generality but for convenience in notations that such observations are dropped from the data. In the following, individuals such that $\sum_{t=2}^{T-1} y_{it} \notin \{0, T-2\}$ are called “movers” (in $y$). Similarly, trajectories such that $\sum_{t=1}^{T'} z_{it} = 0$ or $\sum_{t=1}^{T'} z_{it} = T'$ will not be considered, and individuals such that $\sum_{t=1}^{T'} z_{it} \notin \{0, T'\}$ are called “movers” (in $z$).

#### 3.1 Likelihood of a conditional logit with one lag of state dependence but no other varying covariates

Equation (2) can easily be extended to $T \ge 4$:

$$ \mathbb{P}(y_{i1}, \dots, y_{iT} | y_{i1}, \sum_{t=2}^{T-1} y_{it}, y_{iT}) = \frac{\exp\left(\sum_{t=2}^{T} y_{it} y_{it-1} \delta\right)}{\sum_{\tilde{y} \in B(T)} \exp\left(\sum_{t=2}^{T} \tilde{y}_{it} \tilde{y}_{it-1} \delta\right)} \quad (5) $$

where $B(T) = \{ (\tilde{y}_{i1}, \dots, \tilde{y}_{iT}) | \tilde{y}_{i1} = y_{i1}, \tilde{y}_{iT} = y_{iT}, \sum_{t=2}^{T-1} \tilde{y}_{it} = \sum_{t=2}^{T-1} y_{it} \}$ is the set of all possible trajectories with the same first and last states and the same occurrences of each state as in the observed trajectory between $t = 2$ and $t = T - 1$. Intuitively, identification is achieved by analyzing if the visits in state 1 are rather concentrated or evenly distributed along the trajectory. Therefore, the conditional logit compares individual trajectories with the same number of visits in each state. Moreover, if there is state dependence, the states in the first and last periods will not be independent from the distribution of states in the rest of the trajectory, so it seems natural to also condition on the first and last periods.

However, Equation (5) depends on the set $B(T)$ which can become cumbersome to compute as $T$ increases: the number of terms for a trajectory such that $\sum_t y_t = T/2$ increases as $O(2^{T(1-1/T)T/\sqrt{T-1}})$. For instance, for $T = 5$ the number of terms is at most 10, but for $T = 10$ it is
252 and for $T = 20$ it is greater than 180,000. A simpler closed form can therefore be helpful to estimate $\delta$.

**Lemma 3.1** (Closed form of a conditional logit with state dependence).

For $T \ge 4$ and for any mover's trajectory $y$, the likelihood of a conditional logit with one lag of state dependence but no other varying covariate can be written as :

$$ \mathbb{P}(y_{i1}, \dots, y_{iT} | y_{i1}, \sum_{t=2}^{T-1} y_{it}, y_{iT}) = \left[ \sum_{j=\max(0, 2\sum_{t} y_{it} - T + 1 - y_{1} - y_{T})}^{\sum_{t} y_{it} - 1 - y_{1}y_{T}} \binom{\sum_{t} y_{it} - 1}{j} \binom{T - \sum_{t} y_{it} - 1}{\sum_{t} y_{it} - j - y_{1} - y_{T}} \exp\left\{\left(j - \sum_{t=2}^{T} y_{t}y_{t-1}\right) \delta\right\} \right]^{-1} $$

The number of terms in the previous expression is bounded by $T/2 - 1$ and can be easily computed even when $T$ is larger than 20 or 30.

Proof : see appendix.

## 3.2 Likelihood of a conditional logit with one covariate but no state dependence

Equation (4) can easily be extended to $T \ge 2$:

$$ \mathbb{P}(z_{i1}, \dots, z_{iT'} | \sum_{t=1}^{T'} z_{it}, x_{i1}, \dots, x_{iT'}) = \frac{\exp\left(\sum_{t=1}^{T'} z_{it}x_{it}\delta\right)}{\sum_{\tilde{z} \in B'(T')} \exp\left(\sum_{t=1}^{T'} \tilde{z}_{it}x_{it}\delta\right)} \quad (6) $$

where $B'(T') = \{(\tilde{z}_{i1}, \dots, \tilde{z}_{iT'}) | \sum_{t=1}^{T'} \tilde{z}_{it} = \sum_{t=1}^{T'} z_{it}\}$ is the set of all trajectories with the same occurrences of each state as in the observed trajectory between $t = 1$ and $t = T'$. Identification is intuitively achieved by the covariance of $x$ and $z$ for a known number of visits in each state.

Once again, the maximization of Likelihood (6) can be a computational burden because the number of elements in the set $B'(T')$ increases exponentially with $T$. But when $X$ is binary, a lot of trajectories $\tilde{z} \in B'(T')$ share the same value for $\sum_{t=1}^{T'} \tilde{z}_{it}x_{it} \in [0, T']$. If we define $B'(T', k) = B'(T') \cap \{(\tilde{z}_{i1}, \dots, \tilde{z}_{iT'}) | \tilde{z}_{it}x_{it} = k\}$, and $n_k = \#B'(T', k)$ the denominator of 6
becomes $\sum_{k=0}^{T'} n_k \exp(k\delta)$, and a simpler expression of the likelihood can be maximized. The following lemma gives the closed form obtained with this method.

**Lemma 3.2** (Closed form of a conditional logit with one binary covariate but without state dependence).

For $T' \ge 2$ and for any mover's trajectory $z$, the likelihood of conditional logit with one binary covariate but no state dependence can be written as :

$$ \mathbb{P}(z_{i1}, \dots, z_{iT'} | \sum_{t=1}^{T'} z_{it}, x_{i1}, \dots, x_{iT'}) = \left[ \sum_{j=\max(0, \sum_{t=1}^{T'} z_{it} + \sum_{t=1}^{T'} x_{it} - T')}^{\min(\sum_{t=1}^{T'} z_{it}, \sum_{t=1}^{T'} x_{it})} \binom{\sum_{t=1}^{T'} x_{it}}{j} \binom{T' - \sum_{t=1}^{T'} x_{it}}{\sum_{t=1}^{T'} z_{it} - j} \exp\left\{\left(j - \sum_{t=1}^{T'} x_{it}z_{it}\right) \delta\right\} \right]^{-1} $$

Proof: see appendix.

## 3.3 Link between the static and dynamic frameworks

The aim is to appropriately choose $z = (z_{it})_{1\le t \le T'}$ and $x = (x_{it})_{1\le t \le T'}$, such that the conditional likelihood in a static framework corresponds to the likelihood in a dynamic one.

Many statistical softwares provide procedures to estimate conditional logit models without state dependence, but not to estimate such models with state dependence. Despite the fact that 3.1 gives simple expression of the likelihood, econometricians who would like to estimate a conditional logit model with state dependence could be tempted to use standard procedures. The following theorem gives sufficient conditions for the two likelihoods to be the same.

**Theorem 3.3** (Conditions to link the conditional likelihoods of dynamic and static conditional logit models).

The likelihood of a dynamic model such as 3.1 and the likelihood of a static model with only one binary covariate such as 3.2 are the same if and only if

$$ 1. T' = T - 2 \text{ and } (\sum_{t=1}^{T-2} z_{it} = \sum_{t=2}^{T-1} y_{it} \text{ or } \sum_{t=1}^{T-2} z_{it} = T - 2 - \sum_{t=2}^{T-1} y_{it}) $$
2. • for y such that $0 < \sum_{t=2}^{T-1} y_{it} < T - 2$ and $1 < \sum_{t=1}^{T} y_{it} < T - 1$

$$
\left\{
\begin{array}{l}
\text{There are } \sum_{t=2}^{T} y_{it}y_{it-1} \text{ periods such that } (z_{it}, x_{it}) = (1,1) \\
\text{There are } \sum_{t=1}^{T} y_{it} - y_{i1} - y_{iT} - \sum_{t=2}^{T} y_{it}y_{it-1} \text{ periods such that } (z_{it}, x_{it}) = (1,0) \\
\text{There are } \sum_{t=1}^{T} y_{it} - 1 - \sum_{t=2}^{T} y_{it}y_{it-1} \text{ periods such that } (z_{it}, x_{it}) = (0,1) \\
\text{There are } T - 1 - 2 \sum_{t=1}^{T} y_{it} + \sum_{t=2}^{T} y_{it}y_{it-1} + y_{i1} + y_{iT} \text{ periods such that } (z_{it}, x_{it}) = (0,0)
\end{array}
\right.
\quad \text{or}
$$

$$
\left\{
\begin{array}{l}
\text{There are } \sum_{t=2}^{T} y_{it}y_{it-1} \text{ periods such that } (z_{it}, x_{it}) = (0,0) \\
\text{There are } \sum_{t=1}^{T} y_{it} - y_{i1} - y_{iT} - \sum_{t=2}^{T} y_{it}y_{it-1} \text{ periods such that } (z_{it}, x_{it}) = (0,1) \\
\text{There are } \sum_{t=1}^{T} y_{it} - 1 - \sum_{t=2}^{T} y_{it}y_{it-1} \text{ periods such that } (z_{it}, x_{it}) = (1,0) \\
\text{There are } T - 1 - 2 \sum_{t=1}^{T} y_{it} + \sum_{t=2}^{T} y_{it}y_{it-1} + y_{i1} + y_{iT} \text{ periods such that } (z_{it}, x_{it}) = (1,1)
\end{array}
\right.
\begin{array}{l}
\bullet \text{ for y such that } (\sum_{t=2}^{T-1} y_{it} = 1 \text{ and } y_{i1} = y_{iT} = 0) \text{ or such that } (\sum_{t=2}^{T-1} y_{it} = T-3 \text{ and} \\
y_{i1} = y_{iT} = 1)
\end{array}
$$

$$ (\forall t \le T - 2 \ x_{it} = 0 \quad \text{or} \quad \forall t \le T - 2 \ x_{it} = 1) \quad \text{and} \quad (\sum z \in \{1, T - 3\}) $$

Proof: see Appendix

Note that the trajectories such that $\sum_{t=2}^{T-1} y_{it} = \sum_{t=1}^{T} y_{it} = 1$ or $\sum_{t=2}^{T-1} y_{it} = \sum_{t=1}^{T} y_{it} - 2 = T - 3$ are the uninformative trajectories because $\sum_{t=2}^{T} \tilde{y}_{it} \tilde{y}_{it-1}$ is constant when $\tilde{y}$ vary in $B(T)$. These special cases are degenerate ones. In these cases, $\#B(T) = T - 2$ and the conditional likelihood is equal to $\frac{1}{T-2}$, to ensure equality of the likelihood $z$ must be in the same state at $T - 3$ periods and $x$ must be constant. In the other cases, if $y$ is such that $0 < \sum_{t=2}^{T-1} y_{it} < T - 2$ and $1 < \sum_{t=1}^{T} y_{it} < T - 1$, the likelihood of the dynamic model depends on $\delta$ and this dependence impose more restrictions on $z$ and $x$ to ensure the equality of the two likelihoods.
dependence with a program which estimates conditional logit models without state dependence. After removing the observations such that $\sum_{t=2}^{T-1} y_{it} \in \{0, T-2\}$, it suffices to generate a new dataset with two binary covariates as described above, and then to apply the maximization of the conditional likelihood in the static framework.

Note that, the uninformative trajectories such that $\sum_{t=2}^{T-1} y_{it} = \sum_{t=1}^{T} y_{it} = 1$ or $\sum_{t=2}^{T-1} y_{it} = \sum_{t=1}^{T} y_{it} - 2 = T - 3$ do not require any special treatment. Indeed, it is equivalent to remove them from the analysis or to keep them and use the above transformation which will lead to uninformative static trajectories anyway.

## 3.5 Examples of data generation with $T = 6$

The following two numerical examples are derived using corollary 3.4:

$$1. y = (0, 1, 1, 1, 0, 1) \text{ becomes} \left\{ \begin{array}{ll} \begin{array}{cc} z & x \\ \hline 1 & 1 \\ 1 & 1 \end{array} & \sum_{t=2}^{T} y_t y_{t-1} = 2 \\ \\ \begin{array}{cc} 1 & 0 \\ \hline 0 & 1 \end{array} & \sum_{t=1}^{T} y_t - y_1 - y_T - \sum_{t=2}^{T} y_t y_{t-1} = 1 \\ \\ \sum_{t=1}^{T} y_t - 1 - \sum_{t=2}^{T} y_t y_{t-1} = 1 \end{array} \right.$$

$$2. y = (1, 0, 1, 0, 0, 1) \text{ becomes} \left\{ \begin{array}{ll} \begin{array}{cc} z & x \\ \hline 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ \hline 0 & 0 \end{array} & \sum_{t=1}^{T} y_t - y_1 - y_T - \sum_{t=2}^{T} y_t y_{t-1} = 1 \\ \\ \sum_{t=1}^{T} y_t - 1 - \sum_{t=2}^{T} y_t y_{t-1} = 2 \\ \\ T - 1 - 2 \sum_{t=1}^{T} y_t + y_1 + y_T + \sum_{t=2}^{T} y_t y_{t-1} = 1 \end{array} \right.$$

## 4 Conclusion

In the case of a binary outcome with one lag of state dependence and individual unobserved heterogeneity, we provide a simple closed form for the conditional likelihood. Moreover, we show that such a conditional likelihood is the same as that of a conditional logit model with one
binary exogenous variable and no state dependence. Therefore these results show that in order to evaluate a conditional logit model with one lag of state dependence, it is possible to simply generate a two-variable dataset and use standard procedures originally intended for a framework without state dependence. Examples of programs which can generate such a dataset are provided in appendix A. Proofs of lemmas and theorems are provided in appendix B. Extensions to more than two states and more than one lag of state dependence are left for further research.
References

ANDERSEN, E. B. (1973): *Conditional inference and models for measuring*. Mentalhygiejnisk
Forlag.

CHAMBERLAIN, G. (1985): "Heterogeneity, omitted variable bias, and duration dependence," in *Longitudinal Analysis of Labor Market Data*, ed. by J. J. Heckman, and B. Singer. Cambridge University Press.

HONORÉ, B. E., AND E. KYRIAZIDOU (2000): “Panel Data Discrete Choice with Lagged Dependent Variables,” *Econometrica*, 68(4).

MAGNAC, T. (2000): “Subsidised training and youth employment: distinguishing unobserved heterogeneity from state dependence in labour market histories,” *The Economic Journal*, 110.

————— (2004): “Panel Binary Variables and Sufficiency: Generalizing Conditional Logit,” *Econometrica*, 72(6), 1859–1876.

RASCH, G. (1960): *Probabilistic Models for Some Intelligence and Attainment Tests*. Denmark
Paedagogiske Institut.
# Appendix

Appendix A provides a SAS macro and a piece of R code which help reshape datasets in a way that makes them directly usable by *traditional* conditional logit procedures. Appendix B gives the proofs concerning the closed forms of the conditional likelihoods in the static and in the dynamic case as well as the proof of the link between them.

# A Examples of programs

## A.1 SAS

### A.1.1 Preimplemented procedure for the static framework

Estimation of a conditional logit in a static framework using a preimplemented procedure :

```sas
/*Example assuming dataset OBS contains three variables :
-I for the individuals
-Z for the LHS variable
-X for the RHS variable
*/
proc logistic data=obs desc;
  strata i;
  model z=x;
run;
```

### A.1.2 Faster estimation for the static framework

A faster computation can be obtained using lemma (3.2)

```sas
data obs2;
  set obs;
  zx=z*x;
run;

proc summary data=obs2 nway;
  class i;
```
var z x zx;

output out=tab(rename=(_freq_=_t)) sum=sumx sumx sumxz;

run;

proc iml;

use tab;

read all var {sumxz} into sumxz;

read all var {sumx} into sumx;

read all var {sumz} into sumz;

read all var {t} into t;

/*LOG-LIKELIHOOD*/

start logvrais delta global(sumxz, sumx, sumz, t);

value={0};

do i=1 to nrow(t);

j=do(max(0, sumx[i,1]+sumx[i,1]-t[i,1]), min(sumx[i,1], sumx[i,1]), 1);

value=value-log((comb(sumx[i,1], j)#comb(t[i,1]-sumx[i,1], sumx[i,1]-j)#exp((j-sumxz[i,1])*delta))[+]);

end;

return(value);

finish;

optn={1 0};

delta0={0};

call nlpnra(rc, delta, 'logvrais', delta0, optn);

/*STANDARD DEVIATION*/

start varas delta global(sumxz, sumx, sumz, t);

value={0};

do i=1 to nrow(t);

j=do(max(0, sumx[i,1]+sumx[i,1]-t[i,1]), min(sumx[i,1], sumx[i,1]), 1);

value=value

+(((j-sumxz[i,1])*comb(sumx[i,1], j)#comb(t[i,1]-sumx[i,1], sumx[i,1]-j)#exp((j-sumxz[i,1])*delta))[+])**2

/((comb(sumx[i,1], j)#comb(t[i,1]-sumx[i,1], sumx[i,1]-j)#exp((j- sumxz[i,1])*delta))[+])*2;

end;
value=1/nrow(t)*value;
return(value);
finish;
ec=1/sqrt(nrow(t)*varas delta));

/*PRINT THE RESULTS (ESTIMATION AND STANDARD DEVIATION)*/
print delta ec;
close; quit; run;

### A.1.3 Reshaping the data to estimate the dynamic model using the preimple-
mented procedure intended for static models

%macro dyn2sta( table_in=, /* entry table (must be sorted by ident and time) */
table_out=, /* output table */
ident=, /* individual identifier */
time=, /* period identifier */
state=, /* state variable (0 or 1) in the original dataset */
static=, /* LHS variable in the new dataset */
static_1= /* RHS variable in the new dataset */
);
data &table_out.(drop=_lagstate _sumY _sumYLY _Y1 _T _k
_n11 _n10 _n01 _n00);
set &table_in.;
by &ident. &time.;
retain _lagstate _sumY _sumYLY _Y1 _T;
if first.&ident. then do;
_lagstate=&state.;
_sumY=&state.;
_sumYLY=0;
_Y1=&state.;
_T=1;
end;
else do;
_T= _T+1;
_sumY= _sumY+&state.;
_sumYLY=_sumYLY+_lagstate*&state.;
```
__lagstate=&state.;
if last.&ident. and 0<__sumY - __Y1 - &state.__<T-2 and 1<__sumY<__T-1
    and __T>=4 then do;
    __n11=__sumYLY;
    __n10=__sumY - __Y1 - &state.__ - __sumYLY;
    __n01=__sumY - 1 - __sumYLY;
    __n00=__T - 2 - __n11 - __n10 - __n01;

    if __n11>0 then do __k=1 to __n11;
        &static.=1;
        &static_1.=1;
        output;
    end;

    if __n10>0 then do __k=1 to __n10;
        &static.=1;
        &static_1.=0;
        output;
    end;

    if __n01>0 then do __k=1 to __n01;
        &static.=0;
        &static_1.=1;
        output;
    end;

    if __n00>0 then do __k=1 to __n00;
        &static.=0;
        &static_1.=0;
        output;
    end;

end;

end;

run;

%mend;
```

### A.1.4 Estimation of the dynamic model using lemma (3.1)

For fast computation (necessary when $n > 10000$), instead of using `proc logistic` reshape the data and use lemma (3.2) or equivalently use lemma (3.1) as follows.
%macro dyn2iml( table_in=, /* entry table (must be sorted by ident and time) */
table_out=, /* output table with variables : */
/* _Y1, _YT, _sumY, _sumYLY */
ident=, /* individual identifier */
time=, /* period identifier */
state=, /* state variable (0 or 1) in the original dataset */
);
data &table_out.(drop= lagstate);
set &table_in.;
by &ident. &time.;
retain lagstate sumY sumYLY Y1 T;
if first.&ident. then do;
    lagstate=&state.;
    sumY=&state.;
    sumYLY=0;
    Y1=&state.;
    T=1;
end;
else do;
    T=T+1;
    sumY=sumY+&state.;
    sumYLY=sumYLY+lagstate*&state.;
    lagstate=&state.;
    if last.&ident. and 0<sumY - Y1 - &state.<T-2 and 1<sumY<T-1
        and T>=4 then do;
        YT=&state.;
        output;
    end;
end;
run;
%mend;
/*Example assuming dataset OBS contains three variables :
-I for the individuals
-T for the periods
-Y for the dependant variable
*/
%dyn2iml(table_in=OBS,
table_out=tab,
ident=I,
time=T,
state=Y)

proc iml;

use tab;

read all var {__sumY} into sumy;

read all var {__sumYLY} into sumyly;

read all var {__Y1} into y1;

read all var {__YT} into yT;

read all var {__T} into T;

/*LOG-LIKELIHOOD*/

start logvrais (delta) global (sumy, sumyly, y1, yt, t);

value={0};

do i=1 to nrow(t);

j=do(max(0,2*sumy[i,1]-t[i,1]+1-y1[i,1]-yT[i,1]),sumy[i,1]-1-y1[i,1]*yT[i,1],1);

value=value-log((comb(sumy[i,1]-1,j)#comb(t[i,1]-sumy[i,1]-1, sumy[i,1]-j-y1[i,1]-yT[i,1])*exp((j-sumyly[i,1])*delta))[+]);

end;

return(value);

finish;

optn={1 0};

delta0={0};

call nlpnra (rc, delta, 'logvrais', delta0, optn);

/*STANDARD DEVIATION*/

start varas (delta) global (sumy, sumyly, y1, yt, t);

value={0};

do i=1 to nrow(t);

j=do(max(0,2*sumy[i,1]-t[i,1]+1-y1[i,1]-yT[i,1]),sumy[i,1]-1-y1[i,1]*yT[i,1],1);

value=value+(

(
(j-sumyly[i,1])*comb(sumy[i,1]-1,j)*comb(t[i,1]-sumy[i,1]-1, sumy[i,1]-j-y1[i,1]-yT[i,1])*exp((j-sumyly[i,1])*delta)
)[+]
)**2/(
 comb(sumy[i,1]-1,j)*comb(t[i,1]-sumy[i,1]-1, sumy[i,1]-j-y1[i,1]-yT[i,1])*exp((j-sumyly[i,1])*delta)
)[+]
)**2;
end;
value=1/nrow(t)*value;
return(value);
finish;
ec=1/sqrt(nrow(t)*varas delta));
print delta ec;
close; quit;
run;

## A.2 R

### A.2.1 Preimplemented procedure for the static framework

#######
# Example assuming dataset base.sta contains three variables:
# -I for the individuals
# -Z for the LHS variable
# -X for the RHS variable
#######

#### conditional logit
library(survival)
res <- clogit(Z ~ X + strata(I), data=base.sta)
summary(res)

### A.2.2 Reshaping the data to estimate the dynamic model using the preimplemented procedure intended for static models
####

```r
# example of a program which transforms a dataset with 3 variables
```

```r
# - ID individual identifier
```

```r
# - T time variable
```

```r
# - binary state variable Y
```

```r
# on which you want to perform a conditional logit analysis with state dependence,
```

```r
# into a dataset with 4 variables:
```

```r
# - ID
```

```r
# - T
```

```r
# - binary state variable Z
```

```r
# - binary "modified lagged state variable" X
```

```r
# which can be used directly with standard conditional logit procedures
```

####

```r
### set working directory and load original data base
```

```r
#setwd("")
```

```r
#base <- read.csv("", sep="", header=T)
```

```r
### the dataset must be sorted by ID and T
```

```r
### change names into ID, T and Y
```

```r
# names(base)[names(base)=="Old.Y.Name"] <- "Y"
```

### names(base)

```r
### number of observations for each individual
```

```r
base agg <- aggregate(base$ID, by=base["ID"], length)
```

```r
names(base.agg)[names(base.agg)="x"] <- "nbobs"
```

```r
### first and last observation for each individual
```

```r
base.agg$Y.1 <- aggregate(base$Y, by=base["ID"], head, n=1)[, "x"]
```

```r
base.agg$Y.T <- aggregate(base$Y, by=base["ID"], tail, n=1)[, "x"]
```

```r
### sum of Y between 1 and T
```

```r
base.agg$sum.Y <- aggregate(base$Y, by=base["ID"], sum)[, "x"]
```

```r
### lag of Y: LY, put 0 for the first period of each individual
```
LY <- c(0, base$Y[-length(base$Y)])

LY[c(1, cumsum(base agg$nbobs)[-nrow(base agg)]+1)] <- 0

### sum of Y*Y_1 between 2 and T

base agg$sum.YLY <- aggregate(base$Y*LY, by=base["ID"], sum)[, "x"]

### we keep only the individuals such that

0 < sumY - Y.1 - Y.T < T-2

1 < sumY < T-1

base aggident <- subset(base agg,
  sum.Y - Y.1 - Y.T < nbobs - 2 &
  sum.Y - Y.1 - Y.T > 0 &
  sum.Y < nbobs - 1 &
  sum.Y > 1)

names(base aggident)[names(base aggident)="sum.YLY"] <- "n.11"

base aggident$n.10 <- base aggident$sum.Y - base aggident$Y.1 -
  base aggident$Y.T - base aggident$n.11

base aggident$n.01 <- base aggident$sum.Y - 1 - base aggident$n.11

base aggident$n.00 <- base aggident$nbobs - 2 - base aggident$n.11 -
  base aggident$n.10 - base aggident$n.01

### new data frame with ID, LHS variable: ZZ, RHS variable: XX

repseq <- do. call(c, as. list(t(base aggident[, c("n.11", "n.10", "n.01", "n.00")])))

base dyn <- data frame(ID=rep(base aggident$ID, base aggident$nbobs-2),
  ZZ=rep中央(c(1,1,0,0), nrow(base aggident)), repseq),
  XX=rep中央(c(1,0,1,0), nrow(base aggident)), repseq))

### conditional logit

library(survival)

res <- clogit(ZZ ~ XX + strata(ID), data=base dyn)

summary(res)
# B Proofs

## B.1 Proof of 3.1

**Lemma B.1** (Link between the number of occurrences of each state and the transitions from one state to another).

Let

* $T \ge 4$ the number of time periods,

* $j_{\ell, \ell'}$, $(\ell, \ell') \in \{0, 1\}^2$ the number of transitions from state $\ell$ to state $\ell'$,

* $k_\ell$, $\ell \in \{0, 1\}$ the number of occurrences of state $\ell$,

* $y_1$ and $y_T$ the first and last states,

the knowledge of $k_1$ (and therefore also $k_0 = T - k_1$), $y_1$, $y_T$ and $j_{11}$ determines $j_{00}$, $j_{10}$ and $j_{01}$ and conversely.

*Proof.* immediate using:

$$ \left\{ \begin{array}{l} j_{00} + j_{01} + (1 - y_T) = k_0 \\ j_{10} + j_{11} + y_T = k_1 \\ j_{00} + j_{10} + (1 - y_1) = k_0 \\ j_{01} + j_{11} + y_1 = k_1 \end{array} \right. $$

□

**Lemma B.2** (Counting trajectories as a function of the number of 1's and the number of "11" transitions).

Let the two states be 0 and 1.

The number of trajectories of length $T$, starting with $y_1$, ending with $y_T$, with $k_1$ ($1 \le k_1 \le T - 1$) occurrences of 1 and $j_{11}$ transitions from state 1 to state 1 is:<fnref n="1" />

$$ \binom{k_1-1}{j_{11}} \binom{T-k_1-1}{k_1-j_{11}-y_1-y_T} \mathbf{1}_{\{\max(0,2k_1-T+1-y_1-y_T) \le j_{11} \le k_1-1-y_1y_T\}} $$

<footnote n="1">¹using the notation $\binom{n}{p} = \frac{n!}{(n-p)!p!}$</footnote>
Conversely, using the number of occurrences of state 0: $k_0 = T - k_1$, and the number of transitions from state 0 to state 0: $j_{00} = k_0 - k_1 + j_{11} + y_1 + y_T - 1$, the previous number of trajectories is also equal to:

$$ \binom{k_1-1}{j_{11}} \binom{k_0-1}{j_{00}} \mathbb{1}_{\{0 \le j_{11} \le k_1-1-y_1 y_T, \ 0 \le j_{00} \le k_0-1-(1-y_1)(1-y_T)\}} $$

*Proof.* To answer this question we shall introduce the following notations: let $y = (y_1, \dots, y_T)$ be a trajectory, then define $Red(y)$ the “reduced trajectory” of $y$ which is obtained by concatenation of the successive zeros and ones. For instance, $Red(1, 1, 1, 0, 0, 1, 1, 0) = (1, 0, 1, 0)$. Then, let $(0, 1)_n$ (respectively $(1, 0)_n$) be “n times” the sequence $(0, 1)$ (respectively the sequence $(1, 0)$). This leads for instance to: $Red(1, 1, 1, 0, 0, 1, 1, 0) = ((1, 0)_2)$.

The interest of defining these reduced forms lies in the fact that two trajectories with the same reduced form also share the same likelihood.

The number of 1's, $k_1$, in a trajectory of reduced form $(0, 1)_n$ or $(1, 0)_n$ is: $k_1 = n + j_{11}$ where $j_{11}$ is the number of transitions from state 1 to state 1. Indeed, noting that a trajectory of reduced form $(1, 0)_n$ will look like:

$$ \underbrace{(1, \dots, 1, 0, \dots, 0)}_{1}, \underbrace{(1, \dots, 1, 0, \dots, 0)}_{1}, \dots, \underbrace{(1, \dots, 1, 0, \dots, 0)}_{1}, $$

in each block of 1's, the number of 1's is equal to $1+\text{“the number of transitions from 1 to 1 in that block”}$. Summing over the $n$ blocks, the total number of 1's will be $j_{11} + n$.

Therefore,

* if $y_1 = y_T = 0$ then $Red(y) = 0(10)_{k_1-j_{11}}$

* $y_1 = 1$ and $y_T = 0$ then $Red(T) = (10)_{k_1-j_{11}}$

* $y_1 = 0$ and $y_T = 1$ then $Red(T) = (01)_{k_1-j_{11}}$

* $y_1 = 1$ and $y_T = 1$ then $Red(T) = 1(01)_{k_1-j_{11}-1}$

Now we have to count the number of full trajectories which lead to each of these four reduced trajectories. We use the fact that the number of occurrences of state 0 is $k_0 = T - k_1$.
The number of elements in $Red^{-1}((0,1)_{k_1-j_{11}})$ is the number of ways to make $k_1-j_{11}$ groups out of $k_1$ identical elements (the 1's), times the number of ways to make $k_1-j_{11}$ groups out of $k_0$ identical elements (the 0's). Using the fact that if you write down a list of $n$ identical elements on one line, making $p$ groups out of these $n$ elements is like setting $p-1$ separators in the $n-1$ spots between the elements, and there are $\binom{n-1}{p-1}$ ways to do so.

The answer is thus $\binom{k_1-1}{k_1-j_{11}-1}\binom{k_0-1}{k_1-j_{11}-1} = \binom{k_1-1}{j_{11}}\binom{k_0-1}{k_1-j_{11}-1}$, with $\max(0, 2k_1-T) \le j_{11} \le k_1-1$

Similar arguments can be made for the other trajectories and the results are summarized as follows:

* $\#\{Red^{-1}(0(10))_{k_1-j_{11}}\} = \binom{k_1-1}{j_{11}}\binom{k_0-1}{k_1-j_{11}} = \binom{k_1-1}{j_{11}}\binom{T-k_1-1}{k_1-j_{11}}$ for $\max(0, 2k_1-T+1) \le j_{11} \le k_1-1$

* $\#\{Red^{-1}((10))_{k_1-j_{11}}\} = \binom{k_1-1}{j_{11}}\binom{k_0-1}{k_1-j_{11}-1} = \binom{k_1-1}{j_{11}}\binom{T-k_1-1}{k_1-j_{11}-1}$ for $\max(0, 2k_1-T) \le j_{11} \le k_1-1$

* $\#\{Red^{-1}((01))_{k_1-j_{11}}\} = \binom{k_1-1}{j_{11}}\binom{k_0-1}{k_1-j_{11}-1} = \binom{k_1-1}{j_{11}}\binom{T-k_1-1}{k_1-j_{11}-1}$ for $\max(0, 2k_1-T) \le j_{11} \le k_1-1$

* $\#\{Red^{-1}(1(10))_{k_1-j_{11}-1}\} = \binom{k_1-1}{j_{11}}\binom{k_0-1}{k_1-j_{11}-2} = \binom{k_1-1}{j_{11}}\binom{T-k_1-1}{k_1-j_{11}-2}$ for $\max(0, 2k_1-T-1) \le j_{11} \le k_1-2$

Finally the number of trajectories is $\binom{k_1-1}{j_{11}}\binom{T-k_1-1}{k_1-j_{11}-y_1-y_T}$ with $\max(0, 2k_1-T+1-y_1-y_T) \le j_{11} \le k_1-1-y_1y_T$

The symmetrical expression using the 0's follows directly. $\square$

**Lemma B.3** (Closed form for the denominator of a conditional logit with state dependence).

Let $B(T, k_1, y_1, y_T)$ be the number of trajectories of length $T$, with $k_1$ 1's ($1 \le k_1 \le T-1$), starting with $y_1$ and finishing with $y_T$:

$$B(T, k_1, y_1, y_T) = \left\{ (\tilde{y}_1, \dots, \tilde{y}_T) \in \{0,1\}^T \mid \tilde{y}_{i1} = y_{i1}, \tilde{y}_{iT} = y_{iT}, \sum_{t=1}^T \tilde{y}_t = k_1 \right\}$$
Then :

$$ \sum_{\tilde{y} \in B(T, k_1, y_1, y_T)} \exp \left( \sum_{t=2}^{T} \tilde{y}_{it} \tilde{y}_{it-1} \delta \right) = \sum_{j_{11}=\max(0,2k_1-T+1-y_1-y_T)}^{k_1-1-y_1 y_T} \binom{k_1-1}{j_{11}} \binom{T-k_1-1}{k_1-j_{11}-y_1-y_T} e^{\delta j_{11}} $$

Proof. Let $A(T, k_1, y_1, y_T, j_{11}) = B(T, k_1, y_1, y_T) \cap \{(\tilde{y}_1, \dots, \tilde{y}_T) \in \{0,1\}^T \mid \sum_{t=2}^T \tilde{y}_t \tilde{y}_{t-1} = j_{11}\}$ then $B(T, k_1, y_1, y_T) = \cup_{j_{11} \in \mathbb{N}} A(T, k_1, y_1, y_T, j_{11})$

$$ \text{and } A(T, k_1, y_1, y_T, j_{11}) \cap A(T, k_1, y_1, y_T, j'_{11}) = \emptyset $$

It follows that

$$ \sum_{\tilde{y} \in B(T, k_1, y_1, y_T)} \exp \left( \sum_{t=2}^{T} \tilde{y}_{it} \tilde{y}_{it-1} \delta \right) = \sum_{j_{11} \in \mathbb{N}} \#\{A(T, k_1, y_1, y_T, j_{11})\} e^{\delta j_{11}} $$

and then, from lemma B.2:

$$ \sum_{\tilde{y} \in B(T, k_1, y_1, y_T)} \exp \left( \sum_{t=2}^{T} \tilde{y}_{it} \tilde{y}_{it-1} \delta \right) = \sum_{j_{11}=\max(0,2k_1-T+1-y_1-y_T)}^{k_1-1} \binom{k_1-1}{j_{11}} \binom{T-k_1-1}{k_1-j_{11}-y_1-y_T} e^{\delta j_{11}} $$

□

**Theorem B.4** (Closed form for the conditional likelihood of a conditional logit with two states and one lag of state dependence).

The conditional likelihood of any trajectory of length T, with $k_1$ 1's ($1 \le k_1 \le T-1$), starting with $y_1$ and finishing with $y_T$ is equal to:

$$ P(y_1, \dots, y_T | y_1, y_T, \sum_{t=1}^{T} y_t) = \frac{\exp \left( \sum_{t=2}^{T} y_t y_{t-1} \delta \right)}{\sum_{j_{11}=\max(0,2k_1-T+1-y_1-y_T)}^{k_1-1-y_1 y_T} \binom{k_1-1}{j_{11}} \binom{T-k_1-1}{k_1-j_{11}-y_1-y_T} e^{\delta j_{11}}} $$

Proof. direct consequence of lemma B.3. □

## B.2 Proof of 3.2

Consider a trajectory $(z_{it}, x_{it})_{\{1 \le t \le T'\}} \in \{0,1\}^{2T'}$ and let $n_k$ be the number of trajectories $(\tilde{z}_{it})_{\{1 \le t \le T'\}} \in \{0,1\}^{T'}$ such that $\sum_{t=1}^{T'} \tilde{z}_{it} = \sum_{t=1}^{T'} z_{it}$ and $\sum_{t=1}^{T'} \tilde{z}_{it} x_{it} = k$.
$n_k$ is equal to 0 if $k \notin [\max(\sum_{t=1}^{T'} z_{it} + \sum_{t=1}^{T'} x_{it} - T', 0), \min(\sum_{t=1}^{T'} z_{it}, \sum_{t=1}^{T'} x_{it})]$. Indeed, $\sum_{t=1}^{T'} \tilde{z}_{it}x_{it} \le \min(\sum_{t=1}^{T'} \tilde{z}_{it}, \sum_{t=1}^{T'} x_{it})$ and

$$ 
\begin{aligned}
\sum_{t=1}^{T'} \tilde{z}_{it}x_{it} &= \sum_{t=1}^{T'} x_{it} - \sum_{t=1}^{T'} (1 - \tilde{z}_{it})x_{it} \\
&\ge \sum_{t=1}^{T'} x_{it} - \min \left( T' - \sum_{t=1}^{T'} \tilde{z}_{it}, \sum_{t=1}^{T'} x_{it} \right) \\
&= \max \left( \sum_{t=1}^{T'} \tilde{z}_{it} + \sum_{t=1}^{T'} x_{it} - T', 0 \right)
\end{aligned}
$$

For $k \in [\max(\sum_{t=1}^{T'} z_{it} + \sum_{t=1}^{T'} x_{it} - T', 0), \min(\sum_{t=1}^{T'} z_{it}, \sum_{t=1}^{T'} x_{it})] \cap \mathbb{N}$, choosing a trajectory $(\tilde{z}_{it})_{\{1 \le t \le T'\}} \in \{0, 1\}^{T'}$, corresponds to choosing $k$ elements among $\sum_{t=1}^{T'} x_{it}$ (i.e. $k$ periods $t$ such that $\tilde{z}_{it} = x_{it} = 1$), and $\sum_{t=1}^{T'} z_{it} - k$ elements among $T' - \sum_{t=1}^{T'} x_{it}$ (i.e. $\sum_{t=1}^{T'} z_{it} - k$ periods $t$ such that $\tilde{z}_{it} = 1$ and $x_{it} = 0$).

So, in this case, $n_k = (\sum_{j=1}^{T'} x_{it}) (\sum_{t=1}^{T'} x_{it} - \sum_{t=1}^{T'} x_{it})$ and the result follows.

## B.3 Proof of 3.3

If $\mathcal{J}$ is a non empty subset of $\mathbb{R}$, $(\delta \mapsto \exp(k\delta))_{k \in \mathcal{J}}$ is a free family of the mappings from $\mathbb{R}$ to $\mathbb{R}$, i.e. if $\forall \delta \in \mathbb{R}$, $\sum_{k \in \mathcal{J}} \lambda_k e^{k\delta} = 0$ then, $\forall k \in \mathcal{J}$, $\lambda_k = 0$.

Using lemma 3.1 and lemma 3.2, and noting:

$$ J_{sta} = \left[ \max \left( 0, \sum_{t=1}^{T'} z_{it} + \sum_{t=1}^{T'} x_{it} - T' \right), \min \left( \sum_{t=1}^{T'} z_{it}, \sum_{t=1}^{T'} x_{it} \right) \right] \cap \mathbb{N} \text{ and} $$

$$ J_{dyn} = \left[ \max \left( 0, 2 \sum_{t=1}^{T} y_{it} - T + 1 - y_1 - y_T \right), \sum_{t=1}^{T} y_{it} - 1 - y_1 y_T \right] \cap \mathbb{N}, $$

the likelihood of a trajectory $(z, x)$ in the static model will be the same as the likelihood of a trajectory $y$ in the dynamic model if and only if the following sets are equal:
$$ \left\{ \left( \left( \sum_{t=1}^{T'} x_{it} \right) \left( \sum_{t=1}^{T'} z_{it} - j \right), j - \sum_{t=1}^{T'} x_{it} z_{it} \right) \right\}_{j \in J_{\text{sta}}} \\ \left\{ \left( \left( \sum_{t=1}^{T} y_{it} - 1 \right) \left( \sum_{t=1}^{T} y_{it} - j - y_1 - y_T \right), j - \sum_{t=2}^{T} y_{it} y_{it-1} \right) \right\}_{j \in J_{\text{dyn}}} $$

First we show (1.) by summing all the terms in both sets and using Vandermonde's identity:

$$ \sum_{j=\max(0,2\sum_t y_{it}-T+1-y_1-y_T)}^{\sum_t y_{it}-1-y_1y_T} \binom{\sum_t y_{it}-1}{j} \binom{T-\sum_t y_{it}-1}{\sum_t y_{it}-j-y_1-y_T} = \binom{T-2}{\sum_t y_{it}-1} $$

and

$$ \min \left( \sum_{t=1}^{T'} z_{it}, \sum_{t=1}^{T'} x_{it} \right) \sum_{j=\max(0, \sum_{t=1}^{T'} z_{it} + \sum_{t=1}^{T'} x_{it} - T')} \binom{\sum_{t=1}^{T'} x_{it}}{j} \binom{T' - \sum_{t=1}^{T'} x_{it}}{\sum_{t=1}^{T'} z_{it} - j} = \binom{T'}{\sum_{t=1}^{T'} z_{it}} $$

Thus, assuming that we want a general relationship between $T$ and $T'$ which should be independent from the trajectories $y$ and $(z, x)$, for one part $T' = T - 2$ and for the other part,

$$ \sum_{t=1}^{T-2} z_{it} = \sum_{t=2}^{T-1} y_{it} \quad \text{or} \quad \sum_{t=1}^{T-2} z_{it} = T - 2 - \sum_{t=2}^{T-1} y_{it} $$

Second, we consider the case of the uninformative trajectories (end of 2.):

* If $\sum_{t=2}^{T-1} y_{it} = 1$ and $y_{i1} = y_{iT} = 0$ then the equality of the likelihoods implies that $\sum_{t=1}^{T-2} z_{it} \in \{1, T-3\}$ and the likelihood of the static model does not depend on $\delta$ if and only if $x$ is constant.

* If $\sum_{t=2}^{T-1} y_{it} = T - 3$ and $y_{i1} = y_{iT} = 1$ then the equality of the likelihoods implies that $\sum_{t=1}^{T-2} z_{it} \in \{1, T-3\}$ and the likelihood of the static model does not depend on $\delta$ if and only if $x$ is constant.

Third, the show the rest of (2.). Note first, that we only need to prove the result for $\sum_{t=1}^{T-2} z_{it} = \sum_{t=2}^{T-1} y_{it}$ and $(y_1, y_T) \in \{(0,0), (1,0)\}$. Indeed, considering a logistic model with two binary variables $U$ and $V$ and unobserved heterogeneity $\gamma_i$,
$$ \mathbb{P}(U = u | V = v, \gamma_i) = \frac{e^{u(\delta v + \gamma_i)}}{1 + e^{\delta v + \gamma_i}} = \frac{e^{(1-u)(\delta(1-v) - \delta - \gamma_i)}}{1 + e^{\delta(1-v) - \delta - \gamma_i}} $$

Therefore, since conditioning makes the unobserved heterogeneity disappear, for a dynamic model, the conditional likelihoods of the trajectories $y = (y_1, y_2, \dots, y_T)$ and $(1-y) = (1-y_1, 1-y_2, \dots, 1-y_T)$ will be the same, and likewise, for a static model, the conditional likelihoods of the trajectories $(z, x) = ((z_1, x_1), \dots, (z_{T'}, x_{T'}))$ and $(1-z, 1-x) = ((1-z_1, 1-x_1), \dots, (1-z_{T'}, 1-x_{T'}))$ will also be the same.

Now, assume that $T-3 \ge \sum_{t=2}^{T-1} y_{it} \ge 1$ and $T-2 \ge \sum_{t=1}^{T} y_{it} \ge 2$ and $\sum_{t=1}^{T-2} z_{it} = \sum_{t=2}^{T-1} y_{it}$. The only conditions we need concern $\sum_{t=1}^{T-2} x_{it}$ and $\sum_{t=1}^{T-2} x_{it}z_{it}$.

1. Trajectories such that $(y_1, y_T) = (1, 0)$.

Considering the coefficient of the term of highest degree in each set gives:

$$ \left( \min \left( \sum_{t=1}^{T-2} x_{it}, \sum_{t=1}^{T-2} z_{it} \right) \right) \left( \sum_{t=1}^{T-2} z_{it} - \min \left( \sum_{t=1}^{T-2} z_{it}, \sum_{t=1}^{T-2} x_{it} \right) \right) = 1 $$

If $\sum_{t=1}^{T-2} z_{it} < \sum_{t=1}^{T-2} x_{it}$, then $\sum_{t=1}^{T-2} z_{it} = 0$ which is impossible, so we deduce that $\sum_{t=1}^{T-2} x_{it} \le \sum_{t=1}^{T-2} z_{it}$. Then we have either, $T - \sum_{t=1}^{T-2} x_{it} = \sum_{t=1}^{T-2} z_{it} - \sum_{t=1}^{T-2} x_{it}$ or $\sum_{t=1}^{T-2} z_{it} = \sum_{t=1}^{T-2} x_{it}$. The first choice is impossible because $\sum_{t=1}^{T-2} z_{it} < T - 2$ and then $\sum_{t=1}^{T-2} x_{it} = \sum_{t=1}^{T-2} y_{it}$.

Now considering the highest degree in both sets, we have: $\sum_{t=1}^{T-2} z_{it} - \sum_{t=1}^{T-2} x_{it}z_{it} = \sum_{t=1}^{T} y_{it} - 1 - \sum_{t=2}^{T} y_{it}y_{it-1}$ and therefore, $\sum_{t=1}^{T-2} x_{it}z_{it} = \sum_{t=2}^{T} y_{it}y_{it-1}$.

2. Trajectories such that $(y_1, y_T) = (0, 0)$.

We consider the terms of lowest degree and therefore distinguish between:

$$ 2 \sum_{t=1}^{T} y_{it} - T + 1 - y_1 - y_T < 0, = 0, \text{ and } > 0 $$
• $2 \sum_{t=1}^{T} y_{it} - T + 1 < 0$

We have $\sum_{t=1}^{T-2} z_{it} < T - 1 - \sum_{t=1}^{T-2} z_{it}$ and $\sum_{t=1}^{T} y_{it} - 1 = \sum_{t=1}^{T-2} z_{it} - 1$.

The equality of the number of terms in each likelihood gives:

$$ \min \left( \sum_{t=1}^{T-2} z_{it} + 1, \sum_{t=1}^{T-2} x_{it} + 1, T - 1 - \sum_{t=1}^{T-2} x_{it}, T - 1 - \sum_{t=1}^{T-2} z_{it} \right) = \sum_{t=1}^{T-2} z_{it}. $$

Because $\sum_{t=1}^{T-2} z_{it} < \sum_{t=1}^{T-2} z_{it} + 1 \le T - 1 - \sum_{t=1}^{T-2} z_{it}$, the equality of the likelihoods implies $\sum_{t=1}^{T-2} x_{it} + 1 = \sum_{t=1}^{T-2} z_{it}$ or $T - 1 - \sum_{t=1}^{T-2} x_{it} = \sum_{t=1}^{T-2} z_{it}$.

- If $T - 1 - \sum_{t=1}^{T-2} x_{it} = \sum_{t=1}^{T-2} z_{it}$, the equality of the terms with the smallest index in each likelihood implies that:

$$ \sum_{t=1}^{T-2} x_{it}z_{it} = \sum_{t=2}^{T} y_{it}y_{it-1} + 1 $$

and

$$ T - 1 - \sum_{t=2}^{T-1} y_{it} = \left( T - 1 - \sum_{t=2}^{T-1} y_{it} \right) $$

Because we exclude $\sum_{t=2}^{T-1} y_{it} = 1$ (uninformative trajectory), we deduce $2 \sum_{t=2}^{T-1} y_{it} = T - 2$.

- If $\sum_{t=1}^{T-2} x_{it} + 1 = \sum_{t=1}^{T-2} z_{it}$, we deduce that $\sum_{t=1}^{T-2} z_{it}x_{it} = \sum_{t=2}^{T} y_{it}y_{it-1}$

• $2 \sum_{t=1}^{T} y_{it} - T + 1 = 0$

We have $\sum_{t=1}^{T-2} z_{it} = \frac{T-1}{2}$, and the number of terms in the likelihood of the dynamic model is equal to $\frac{T-1}{2}$. The equality of the number of terms implies $\sum_{t=1}^{T-2} x_{it} + 1 \ge \frac{T-1}{2}$ and $T - 1 - \sum_{t=1}^{T-2} x_{it} \ge \frac{T-1}{2}$, and we deduce that $\sum_{t=1}^{T-2} x_{it} \in \{\frac{T-1}{2}, \frac{T-3}{2}\}$.

- If $\sum_{t=1}^{T-2} x_{it} = \frac{T-1}{2}$, the equality of the terms with the smallest index in the two likelihoods implies that $\frac{T-1}{2} = 1$, and next $T = 3$ which is absurd.

- If $\sum_{t=1}^{T-2} x_{it} = \frac{T-3}{2}$, the likelihoods are the same if and only if $\sum_{t=1}^{T-2} z_{it}x_{it} = \sum_{t=2}^{T} y_{it}y_{it-1}$.

• $2 \sum_{t=1}^{T} y_{it} - T + 1 > 0$

We have $\sum_{t=1}^{T-2} z_{it} > T - 1 - \sum_{t=1}^{T-2} z_{it}$, the number of terms in each likelihood is
$$ \min(\sum_{t=1}^{T-2} z_{it} + 1, \sum_{t=1}^{T-2} x_{it} + 1, T-1 - \sum_{t=1}^{T-2} x_{it}, T-1 - \sum_{t=1}^{T-2} z_{it}) \text{ and } T-1 - \sum_{t=1}^{T-2} z_{it}. $$

$$ \text{So, } \sum_{t=1}^{T-2} x_{it} + \sum_{t=1}^{T-2} z_{it} - T + 2 \ge 0 \text{ and } \sum_{t=1}^{T-2} z_{it} \ge \sum_{t=1}^{T-2} x_{it}. $$

The equality of the terms with the smallest index in each likelihood implies that

$$ \sum_{t=1}^{T-2} x_{it} + \sum_{t=1}^{T-2} z_{it} - T + 2 - \sum_{t=1}^{T-2} x_{it}z_{it} = 2 \sum_{t=1}^{T} y_{it} - T + 1 - \sum_{t=2}^{T} y_{it}y_{it-1} $$

and

$$ \left( \frac{\sum_{t=1}^{T-2} x_{it}}{\sum_{t=1}^{T-2} x_{it} + \sum_{t=1}^{T-2} z_{it} - T + 2} \right) = \left( \frac{\sum_{t=1}^{T} y_{it} - 1}{2 \sum_{t=1}^{T} y_{it} - T + 1} \right) $$

or equivalently

$$ \sum_{t=1}^{T-2} x_{it} + 1 - \sum_{t=1}^{T-2} x_{it}z_{it} = \sum_{t=1}^{T} y_{it} - \sum_{t=2}^{T} y_{it}y_{it-1} $$

and

$$ \left( \frac{\sum_{t=1}^{T-2} x_{it}}{T - 2 - \sum_{t=1}^{T-2} z_{it}} \right) = \left( \frac{\sum_{t=1}^{T} y_{it} - 1}{T - 2 - \sum_{t=1}^{T-2} z_{it}} \right) $$

Because we exclude $\sum_{t=2}^{T-1} y_{it} = T - 2$, we deduce $\sum_{t=1}^{T-2} x_{it} = \sum_{t=1}^{T} y_{it} - 1$ and

$$ \sum_{t=1}^{T-2} z_{it}x_{it} = \sum_{t=2}^{T} y_{it}y_{it-1} $$

The necessary conditions given above are trivially sufficient using the closed forms of the conditional likelihoods.
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CŒURE<br>Profitabilité de l'investissement productif et transmission des chocs financiers</td></tr><tr><td>G 9202</td><td>J. OLIVEIRA-MARTINS, J. TOUJAS-BERNATE</td><td>G 9411 J. BOURDIEU - B. COLIN-SEDILLOT<br>Les théories sur la structure optimal du capital : quelques points de repère</td></tr><tr><td></td><td></td><td>G 9311 J. BOURDIEU - B. COLIN-SEDILLOT<br>Les décisions de financement des entreprises</td></tr></table>

<table><tr><td>G 9312</td><td>L. BLOCH - B. CŒURÉ<br>Q de Tobin marginal et transmission des chocs financiers</td></tr><tr><td>G 9313</td><td>Equipes Amadeus (INSEE), Banque de France, Métric (DP)<br>Presentation des propriétés des principaux modèles macroéconomiques du Service Public</td></tr><tr><td>G 9314</td><td>B. CREPON - E. DUGUET<br>Research &amp; Development, competition and innovation</td></tr><tr><td>G 9315</td><td>B. DORMONT<br>Quelle est l'influence du coût du travail sur l'emploi ?</td></tr><tr><td>G 9316</td><td>D. BLANCHET - C. BROUSSE<br>Deux études sur l'âge de la retraite</td></tr><tr><td>G 9317</td><td>D. BLANCHET<br>Répartition du travail dans une population hétérogène : deux notes</td></tr><tr><td>G 9318</td><td>D. EYSSARTIER - N. PONTY<br>AMADEUS - an annual macro-economic model for the medium and long term</td></tr><tr><td>G 9319</td><td>G. CETTE - Ph. CUNÉO - D. EYSSARTIER - J. GAUTIÉ<br>Les effets sur l'emploi d'un abaissement du coût du travail des jeunes</td></tr><tr><td>G 9401</td><td>D. BLANCHET<br>Les structures par âge importent-elles ?</td></tr><tr><td>G 9402</td><td>J. GAUTIÉ<br>Le chômage des jeunes en France : problème de formation ou phénomène de file d'attente ?<br>Quelques éléments du débat</td></tr><tr><td>G 9403</td><td>P. QUIRION<br>Les déchets en France : éléments statistiques et économiques</td></tr><tr><td>G 9404</td><td>D. LADIRAY - M. GRUN-REHOMME<br>Lissage par moyennes mobiles - Le problème des extrémités de série</td></tr><tr><td>G 9405</td><td>V. MAILLARD<br>Theorie et pratique de la correction des effets de jours ouvrables</td></tr><tr><td>G 9406</td><td>F. ROSENWALD<br>La décision d'investir</td></tr><tr><td>G 9407</td><td>S. JACOBZONE<br>Les apports de l'économie industrielle pour définir la stratégie économique de l'hôpital public</td></tr><tr><td>G 9408</td><td>L. BLOCH, J. BOURDIEU, B. COLIN-SEDILLOT, G. LONGUEVILLE<br>Du défaut de paiement au dépôt de bilan : les banquiers face aux PME en difficulté</td></tr><tr><td>G 9409</td><td>D. EYSSARTIER, P. MAIRE<br>Impacts macro-économiques de mesures d'aide au logement - quelques éléments d'évaluation</td></tr><tr><td>G 9410</td><td>F. ROSENWALD<br>Suivi conjoncturel de l'investissement</td></tr><tr><td>G 9411</td><td>C. DEFEUILLE - Ph. QUIRION<br>Les déchets d'emballages ménagers : une analyse économique des politiques française et allemande</td></tr></table>

<table><tr><td>G 9412</td><td>J. BOURDIEU - B. CŒURÉ - B. COLIN-SEDILLOT<br>Investissement, incertitude et irréversibilité<br>Quelques développements récents de la théorie de l'investissement</td></tr><tr><td>G 9413</td><td>B. DORMONT - M. PAUCHET<br>L'évaluation de l'élasticité emploi-salaire dépend-elle des structures de qualification ?</td></tr><tr><td>G 9414</td><td>I. KABLA<br>Le Choix de breveter une invention</td></tr><tr><td>G 9501</td><td>J. BOURDIEU - B. CŒURÉ - B. SEDILLOT<br>Irreversible Investment and Uncertainty : When is there a Value of Waiting ?</td></tr><tr><td>G 9502</td><td>L. BLOCH - B. CŒURÉ<br>Imperfections du marché du crédit, investissement des entreprises et cycle économique</td></tr><tr><td>G 9503</td><td>D. GOUX - E. MAURIN<br>Les transformations de la demande de travail par qualification en France<br>Une étude sur la période 1970-1993</td></tr><tr><td>G 9504</td><td>N. GREENAN<br>Technologie, changement organisationnel, qualifications et emploi : une étude empirique sur l'industrie manufacturière</td></tr><tr><td>G 9505</td><td>D. GOUX - E. MAURIN<br>Persistance des hiérarchies sectorielles de salaires : un réexamen sur données françaises</td></tr><tr><td>G 9505 Bis</td><td>D. GOUX - E. MAURIN<br>Persistance of inter-industry wages differentials: a reexamination on matched worker-firm panel data</td></tr><tr><td>G 9506</td><td>S. JACOBZONE<br>Les liens entre RMI et chômage, une mise en perspective<br>NON PARU - article (sorti dans Economie et Prévision n°122 (1996) - pages 95 à 113</td></tr><tr><td>G 9507</td><td>G. CETTE - S. MAHFOUZ<br>Le partage primaire du revenu<br>Constat descriptif sur longue période</td></tr><tr><td>G 9601</td><td>Banque de France - CEPREMAP - Direction de la Prévision - Erasme - INSEE - OFCE<br>Structures et propriétés de cinq modèles macro-économiques français</td></tr><tr><td>G 9602</td><td>Rapport d'activité de la DESE de l'année 1995</td></tr><tr><td>G 9603</td><td>J. BOURDIEU - A. DRAZNIEKS<br>L'octroi de crédit aux PME : une analyse à partir d'informations bancaires</td></tr><tr><td>G 9604</td><td>A. TOPIOL-BENSAÎD<br>Les implantations japonaises en France</td></tr><tr><td>G 9605</td><td>P. GENIER - S. JACOBZONE<br>Comportements de prévention, consommation d'alcool et tabagie : peut-on parler d'une gestion globale du capital santé ?<br>Une modélisation microéconométrique empirique</td></tr><tr><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 9607</td><td>N. GREENAN - D. GUELLEC<br>La théorie coopérative de la firme</td></tr></table>
<table>
  <tbody>
    <tr>
      <td>G 9608</td>
      <td>N. GREENAN - D. GUELLEC<br>Technological innovation and employment<br>reallocation</td>
      <td>G 9714</td>
      <td>F. LEQUILLER<br>Does the French Consumer Price Index Over-<br>state Inflation?</td>
      <td>G 9808</td>
      <td>A. Mourougane<br>Can a Conservative Governor Conduct an Ac-<br>comodative Monetary Policy?</td>
      <td>G 9913</td>
      <td>Division « Redistribution et Politiques Sociales »<br>Le modèle de microsimulation dynamique<br>DESTINIE</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>
      <td>G 9715</td>
      <td>X. BONNET<br>Peut-on mettre en évidence les rigidités à la<br>baisse des salaires nominaux ?<br>Une étude sur quelques grands pays de l'OCDE</td>
      <td>G 9809</td>
      <td>X. BONNET - E. DUBOIS - L. FAUVET<br>Asymétrie des inflations relatives et menus costs<br>: tests sur l'inflation française</td>
      <td>G 9914</td>
      <td>E. DUGUET<br>Macro-commandes SAS pour l'économétrie des<br>panels et des variables qualitatives</td>
    </tr>
    <tr>
      <td>G 9610</td>
      <td>S. DUCHENE - G. FORGEOT - A. JACQUOT<br>Analyse des évolutions récentes de la producti-<br>vité apparente du travail</td>
      <td>G 9716</td>
      <td>N. IUNG - F. RUPPRECHT<br>Productivité de la recherche et rendements<br>d'échelle dans le secteur pharmaceutique<br>français</td>
      <td>G 9810</td>
      <td>E. DUGUET - N. IUNG<br>Sales and Advertising with Spillovers at the firm<br>level: Estimation of a Dynamic Structural Model<br>on Panel Data</td>
      <td>G 9915</td>
      <td>R. DUHAUTOIS<br>Evolution des flux d'emplois en France entre<br>1990 et 1996 : une étude empirique à partir du<br>fichier des bénéfices réels normaux (BRN)</td>
    </tr>
    <tr>
      <td>G 9611</td>
      <td>X. BONNET - S. MAHFOUZ<br>The influence of different specifications of<br>wages-prices spirals on the measure of the<br>NAIRU : the case of France</td>
      <td>G 9717</td>
      <td>E. DUGUET - I. KABLA<br>Appropriation strategy and the motivations to use<br>the patent system in France - An econometric<br>analysis at the firm level</td>
      <td>G 9811</td>
      <td>J.P. BERTHIER<br>Congestion urbaine : un modèle de trafic de<br>pointe à courbe débit-vitesse et demande<br>élastique</td>
      <td>G 9916</td>
      <td>J.Y. FOURNIER<br>Extraction du cycle des affaires : la méthode de<br>Baxter et King</td>
    </tr>
    <tr>
      <td>G 9612</td>
      <td>PH. COUR - E. DUBOIS, S. MAHFOUZ,<br>J. PISANI-FERRY<br>The cost of fiscal retrenchment revisited: how<br>strong is the evidence ?</td>
      <td>G 9718</td>
      <td>L.P. PELÉ - P. RALLE<br>Âge de la retraite : les aspects incitatifs du ré-<br>gime général</td>
      <td>G 9812</td>
      <td>C. PRIGENT<br>La part des salaires dans la valeur ajoutée : une<br>approche macroéconomique</td>
      <td>G 9917</td>
      <td>B. CRÉPON - R. DESPLATZ - J. MAIRESSE<br>Estimating price cost margins, scale economies<br>and workers' bargaining power at the firm level</td>
    </tr>
    <tr>
      <td>G 9613</td>
      <td>A. JACQUOT<br>Les flexions des taux d'activité sont-elles seule-<br>ment conjoncturelles ?</td>
      <td>G 9719</td>
      <td>ZHANG Yingxiang - SONG Xueqing<br>Lexique macroéconomique français-chinois,<br>chinois-français</td>
      <td>G 9813</td>
      <td>A.Th. AERTS<br>L'évolution de la part des salaires dans la valeur<br>ajoutée en France reflète-t-elle les évolutions<br>individuelles sur la période 1979-1994 ?</td>
      <td>G 9918</td>
      <td>Ch. GIANELLA - Ph. LAGARDE<br>Productivity of hours in the aggregate production<br>function: an evaluation on a panel of French<br>firms from the manufacturing sector</td>
    </tr>
    <tr>
      <td>G 9614</td>
      <td>ZHANG Yingxiang - SONG Xueqing<br>Lexique macroéconomique Français-Chinois</td>
      <td>G 9720</td>
      <td>M. HOUBEBINE - J.L. SCHNEIDER<br>Mesurer l'influence de la fiscalité sur la locali-<br>sation des entreprises</td>
      <td>G 9814</td>
      <td>B. SALANIÉ<br>Guide pratique des séries non-stationnaires</td>
      <td>G 9919</td>
      <td>S. AUDRIC - P. GIVORD - C. PROST<br>Evolution de l'emploi et des coûts par quali-<br>fication entre 1982 et 1996</td>
    </tr>
    <tr>
      <td>G 9701</td>
      <td>J.L. SCHNEIDER<br>La taxe professionnelle : éléments de cadrage<br>économique</td>
      <td>G 9721</td>
      <td>A. Mourougane<br>Crédibilité, indépendance et politique monétaire<br>Une revue de la littérature</td>
      <td>G 9901</td>
      <td>S. DUCHÈNE - A. JACQUOT<br>Une croissance plus riche en emplois depuis le<br>début de la décennie ? Une analyse en compa-<br>raison internationale</td>
      <td>G 2000/1</td>
      <td>R. MAHIEU<br>Les déterminants des dépenses de santé : une<br>approche macroéconomique</td>
    </tr>
    <tr>
      <td>G 9702</td>
      <td>J.L. SCHNEIDER<br>Transition et stabilité politique d'un système<br>redistributif</td>
      <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<br>sectorielles</td>
      <td>G 9902</td>
      <td>Ch. COLIN<br>Modélisation des carrières dans Destinie</td>
      <td>G 2000/2</td>
      <td>C. ALLARD-PRIGENT - H. GUILMEAU -<br>A. QUINET<br>The real exchange rate as the relative price of<br>nontrables in terms of tradables: theoretical<br>investigation and empirical study on French data</td>
    </tr>
    <tr>
      <td>G 9703</td>
      <td>D. GOUX - E. MAURIN<br>Train or Pay: Does it Reduce Inequalities to En-<br>courage Firms to Train their Workers?</td>
      <td>G 9723</td>
      <td>P. AUGERAUD - J.E. CHAPRON<br>Using Business Accounts for Compiling National<br>Accounts: the French Experience</td>
      <td>G 9904</td>
      <td>Ch. COLIN<br>Evolution de la dispersion des salaires : un essai<br>de prospective par microsimulation</td>
      <td>G 2000/3</td>
      <td>J.-Y. FOURNIER<br>L'approximation du filtre passe-bande proposée<br>par Christiano et Fitzgerald</td>
    </tr>
    <tr>
      <td>G 9704</td>
      <td>P. GENIER<br>Deux contributions sur dépendance et équité</td>
      <td>G 9724</td>
      <td>P. AUGERAUD<br>Les comptes d'entreprise par activités - Le pas-<br>sage aux comptes - De la comptabilité<br>d'entreprise à la comptabilité nationale - A<br>paraitre</td>
      <td>G 9905</td>
      <td>B. CREPON - N. IUNG<br>Innovation, emploi et performances</td>
      <td>G 2000/4</td>
      <td>Bilan des activités de la DESE - 1999</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>
      <td>G 9801</td>
      <td>H. MICHAUDON - C. PRIGENT<br>Présentation du modèle AMADEUS</td>
      <td>G 9907</td>
      <td>B. CREPON - Ch. GIANELLA<br>Wages inequalities in France 1969-1992<br>An application of quantile regression techniques</td>
      <td>G 2000/5</td>
      <td>B. CREPON - F. ROSENWALD<br>Investissement et contraintes de financement : le<br>poids du cycle<br>Une estimation sur données françaises</td>
    </tr>
    <tr>
      <td>G 9706</td>
      <td>M. HOUBEBINE - A. TOPIOL-BENSAÏD<br>Les entreprises internationales en France : une<br>analyse à partir de données individuelles</td>
      <td>G 9802</td>
      <td>J. ACCARDO<br>Une étude de comptabilité générationnelle<br>pour la France en 1996</td>
      <td>G 9908</td>
      <td>C. BONNET - R. MAHIEU<br>Microsimulation techniques applied to inter-<br>generational transfers - Pensions in a dynamic<br>framework: the case of France</td>
      <td>G 2000/6</td>
      <td>A. FLIPO<br>Les comportements matrimoniaux de fait</td>
    </tr>
    <tr>
      <td>G 9707</td>
      <td>M. HOUBEBINE<br>Polarisation des activités et spécialisation des<br>départements en France</td>
      <td>G 9803</td>
      <td>X. BONNET - S. DUCHÈNE<br>Apports et limites de la modélisation<br>« Real Business Cycles »</td>
      <td>G 9909</td>
      <td>F. ROSENWALD<br>L'impact des contraintes financières dans la dé-<br>cision d'investissement</td>
      <td>G 2000/7</td>
      <td>R. MAHIEU - B. SÉDILLOT<br>Microsimulations of the retirement decision: a<br>supply side approach</td>
    </tr>
    <tr>
      <td>G 9708</td>
      <td>E. DUGUET - N. GREENAN<br>Le biais technologique : une analyse sur don-<br>nées individuelles</td>
      <td>G 9804</td>
      <td>C. BARLET - C. DUGUET -<br>D. ENCAOUA - J. PRADEL<br>The Commercial Success of Innovations<br>An econometric analysis at the firm level in<br>French manufacturing</td>
      <td>G 9910</td>
      <td>Bilan des activités de la DESE - 1998<br>J.P. ZOYEM<br>Contrat d'insertion et sortie du RMI<br>Evaluation des effets d'une politique sociale</td>
      <td>G 2000/8</td>
      <td>C. AUDENIS - C. PROST<br>Déficit conjoncturel : une prise en compte des<br>conjonctures passées</td>
    </tr>
    <tr>
      <td>G 9709</td>
      <td>J.L. BRILLET<br>Analyzing a small French ECM Model</td>
      <td>G 9805</td>
      <td>P. CAHUC - Ch. GIANELLA -<br>D. GOUX - A. ZILBERBERG<br>Equalizing Wage Differences and Bargaining<br>Power - Evidence form a Panel of French Firms</td>
      <td>G 9911</td>
      <td>Ch. COLIN - FI. LEGROS - R. MAHIEU<br>Bilans contributifs comparés des régimes de<br>retraite du secteur privé et de la fonction<br>publique</td>
      <td>G 2000/9</td>
      <td>R. MAHIEU - B. SÉDILLOT<br>Equivalent patrimonial de la rente et souscription<br>de retraite complémentaire</td>
    </tr>
    <tr>
      <td>G 9710</td>
      <td>J.L. BRILLET<br>Formalizing the transition process : scenarios for<br>capital accumulation</td>
      <td>G 9806</td>
      <td>J. ACCARDO - M. JLASSI<br>La productivité globale des facteurs entre 1975<br>et 1996</td>
      <td>G 9912</td>
      <td>G. LAROQUE - B. SALANIÉ<br>Une décomposition du non-emploi en France</td>
      <td>G 2000/10</td>
      <td>R. DUHAUTOIS<br>Ralentissement de l'investissement : petites ou<br>grandes entreprises ? industrie ou tertiaire ?</td>
    </tr>
    <tr>
      <td>G 9711</td>
      <td>G. FORGEOT - J. GAUTIÉ<br>Insertion professionnelle des jeunes et proces-<br>sus de déclassement</td>
      <td>G 9807</td>
      <td>J. ACCARDO - M. JLASSI<br>La productivité globale des facteurs entre 1975<br>et 1996</td>
      <td>G 9912</td>
      <td>B. SALANIÉ<br>Une maquette analytique de long terme du<br>marché du travail</td>
      <td>G 2000/11</td>
      <td>G. LAROQUE - B. SALANIÉ<br>Temps partiel féminin et incitations financières à<br>l'emploi</td>
    </tr>
    <tr>
      <td>G 9712</td>
      <td>E. DUBOIS<br>High Real Interest Rates: the Consequence of a<br>Saving Investment Disequilibrium or of an in-<br>sufficient Credibility of Monetary Authorities?</td>
      <td>G 9808</td>
      <td>J. ACCARDO - M. JLASSI<br>La productivité globale des facteurs entre 1975<br>et 1996</td>
      <td>G 9912</td>
      <td>Ch. GIANELLA<br>Une estimation de l'élasticité de l'emploi peu<br>qualifié à son coût</td>
      <td>G 2000/12</td>
      <td>Ch. GIANELLA<br>Local unemployment and wages</td>
    </tr>
    <tr>
      <td>G 9713</td>
      <td>Bilan des activités de la Direction des Etudes<br>et Synthèses Economiques - 1996</td>
      <td>G 9809</td>
      <td>Bilan des activités de la Direction des Etudes et<br>Synthèses Economiques - 1997</td>
      <td>Bis</td>
      <td></td>
      <td>G 2000/13</td>
      <td>B. CREPON - Th. HECKEL<br>- Informatisation en France : une évaluation à<br>partir de données individuelles</td>
    </tr>
  </tbody>
</table>
- 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 profonde-t-elle aussi aux non-diplômés ?

G2001/03 I. BRAUN-LEMAIRE
Evolution 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
Evaluation 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
- Rétroposition des séries de FBCF et calcul du capital fixe en SEC-95 dans les comptes nationaux français

- Rétroposition 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? Microeconomic 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
Âge, 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 Techologies, 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 a1974

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 Economiques - 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. DUÉE
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 réinterprétation 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'économètre 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-prix des consommations énergétiques des ménages

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

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