# Demand Estimation in the Presence of Revenue Management

Xavier d'Haultfoeuille, Philippe Février, Lionel Wilner

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Direction des Études et Synthèses Économiques

G 2012 / 13

Demand Estimation in the Presence of
Revenue Management

Xavier D'HAULTFOEUILLE, Philippe FÉVRIER et
Lionel WILNER

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 2012 / 13

Demand Estimation in the Presence of Revenue
Management

Xavier D'HAULTFOEUILLE* - Philippe FÉVRIER** -
Lionel WILNER***

OCTOBRE 2012

Les auteurs remercient Jean-Jacques BECKER, Éric DUBOIS, Johan HOMBERT, Claire LELARGE, Laurent LINNEMER, Corinne PROST et Michael VISSER pour leurs suggestions, et les participants aux séminaires INSEE-DEEE et CREST-LEI pour leurs commentaires. Ils remercient également la SNCF et iDTGV pour leur avoir donné accès aux données.

<footnote>* CREST-LMI
15, bd Gabriel Péri - 92245 MALAKOFF CEDEX</footnote>

<footnote>** CREST-LEI
15, bd Gabriel Péri - 92245 MALAKOFF CEDEX</footnote>

<footnote>*** Département des Études Économiques - Division Marchés et Entreprises
Timbre G230 - 15, bd Gabriel Péri - BP 100 - 92244 MALAKOFF CEDEX</footnote>
# Demand Estimation in the Presence of Revenue Management

## Abstract

Yield management has become a standard tool in several industries to increase the profits of firms facing demand uncertainty or consumers heterogeneity. But this technique also raises econometric problems in the estimation of demand models. Quantity-based management, in particular, is the source of both an endogeneity and a right-censoring problem. Disposing of macro data only and ignoring these issues leads to an aggregation bias. We develop a structural model of demand in the presence of quantity-based management. We show that the price elasticity is identified in this model provided that (i) we observe two subpopulations that face different prices but are not separated in the yield management policy, (ii) the highest prices and quantities sold at these prices are observed, (iii) the highest prices vary with time or across markets. We apply our method to the French railroad industry, using disaggregated data on trips between Paris and big cities on the period 2007-2009. Our estimates of the price-elasticity are consistent with a rather responsive demand, from 1.7 to 2 in economy class and from 1.3 to 1.5 in business class.

**Keywords:** revenue management, demand estimation, price-elasticity, railways transportation.

## Estimation de la demande en présence de revenue management

### Résumé

Le *revenue management* est devenu un outil standard de plusieurs industries, augmentant le profit des firmes faisant face à une demande incertaine ou des consommateurs hétérogènes. Mais cette technique soulève également des problèmes économétriques dans l'estimation de modèles de demande. Un *revenue management* basé sur les quantités, en particulier, est source à la fois d'endogénéité et de censure à droite. Utiliser des données agrégées en ignorant ces problèmes conduit à un biais d'agrégation. Nous développons un modèle structurel de demande en présence d'un tel *revenue management*. Nous montrons que l'élasticité-prix est identifiée dès lors (i) qu'il existe deux sous-populations qui payent des prix différents mais ne sont pas distinguées par le *revenue management*, (ii) que les prix les plus élevés et quantités vendues correspondantes sont observés et (iii) que les prix les plus élevés varient dans le temps ou entre marchés. Nous appliquons notre méthode au transport ferroviaire en France, en utilisant des données détaillées sur les trajets entre Paris et plusieurs grandes villes sur la période 2007-2009. Nos estimations suggèrent une demande plutôt réactive, l'élasticité-prix se situant entre 1,7 et 2 en deuxième classe et entre 1,3 et 1,5 en première classe.

**Mots-clés :** revenue management, modèles structurels de demande, élasticité-prix, transport ferroviaire.

**Classification JEL :** C25, D12, R40.
# 1 Introduction

This paper proposes to estimate a structural model of demand in the presence of yield management. Talluri and van Ryzin (2005) define revenue management as a set of techniques devoted to the maximization of revenues. It typically involves demand-management decisions: structural decisions (related to the selling format, bundling issues, etc.), price decisions and quantity decisions. Price decisions refer to the (possibly dynamic) optimal pricing strategy. Quantity decisions may involve rationing schemes.

Yield management is only adopted by firms and industries selling perishable products and has been used by airlines, railways, hotel and rental car industries, telecommunications, and in the e-business. The e-commerce is a growing industry and firms resort increasingly to yield management techniques. We focus here on the railroad industry adopting quantity-based yield management with a pricing scheme of the following form: several fare classes are defined, in which the price is fixed. The question is to allocate a number of tickets (a booking limit or a quota) to each fare class.

Quantity-based management raises several issues in terms of demand estimation. First, the usual simultaneity issue in the formation of demand cannot be ignored: the price may vary because the opening and closing of fare classes adjust to current demand fluctuations. For this reason, endogeneity arises. Second, quotas are fixed by firms for every fare class. As a result, only the minimum of this quota and of the demand at that price can be obtained from data of purchases in every fare class. These quantities do not correspond to the actual demand at that price, which causes a right-censoring problem. Some of these issues have already been studied in the literature, especially the censoring issue (Swan (1990), Lee (1990) and Stefanescu (2012)).

Our contribution is (i) to provide a model of consumer behavior in the presence of quantity-based management; (ii) to explain under which conditions the price-elasticity of demand is identified in the data; (iii) to estimate our model of demand on prices and purchases available for every yield class of French trains resorting to such revenue management.

We propose to micro-found the demand thanks to a simple structural model that relies on individual decisions of purchases made by strategic and forward-looking consumers. The revenue management literature has devoted little attention to the micro-foundation of the demand. We assume that the flow of consumers' arrivals on the market follows a Poisson process. This Poisson process is nonhomogeneous so that the instantaneous
probability of an arrival is allowed to vary over time. The revenue management literature has already resorted to such processes for consumers' arrivals, at least since Beckmann and Bobkowski (1958). Lee (1990) and Gallego and van Ryzin (1994), among others, also assumed homogeneous or non-homogeneous Poisson processes. As a result, different consumers indexed by their time of arrival are on the market and may purchase or not, the outcome depending on their valuation. Depending on this date, consumers draw their valuation for the good from a Pareto distribution. Contrary to theoretical models in the yield management literature (Littlewood (1972), Brumelle and McGill (1993)), we do not impose that more price-sensitive consumers come first, which is a more general approach. Consumers who buy are those for which the valuation is higher than the corresponding fare. This last part, including a rational choice made by strategic and forward-looking agents, has received less attention from the literature, apart from the recent papers of Talluri and van Ryzin (2004, 2008), Ratliff et al. (2008) and Haensel et al. (2011).

We consider the case of the French railroad industry where such a quantity-based yield management is actually used. We estimate structural preferences for destinations and the price-elasticity of demand in this industry.

We obtain a rather high price-elasticity, which tends to suggest that the population is very responsive to price changes. The elasticity is found to be between 1.3 and 1.5 in the business class, and between 1.7 and 2 in the economy class. These results are high but still in the range of the estimates presented in the previous literature (see for instance Jevons et al. (2005), Oum et al. (1992), Rolle (1997), Wardman (1997, 2006) and Wardman et al. (2007) among others). On French data, Sauvant (2002) finds a price-elasticity of about 0.7.

In comparison with most of these papers in the transportation literature, the main advantage of this study stems from the very detailed level of information. Most studies cited above rely on macro data, and the authors cannot correct for the endogeneity bias. This bias is increased by the aggregation of data. Moreover, the aggregation itself is responsible for spurious price variations coming from changes in quantities sold and not in prices. On the contrary, using detailed data enables us to identify the price-effect and to control for the endogeneity problem as well.

Studying such revenue management practices may be of some interest in the construc-
tion of consumer price indices (CPI). Indeed, goods that are exposed to intertemporal
variation (including promotions, increasing or decreasing price patterns) have already
received attention from statisticians in charge of these indices. Facing dynamic price
patterns, consumers may react and try to buy in advance or later, which could imply
to make further price listings and to weight every price accordingly, in relation with
corresponding purchases – usually unobserved.

Section 2 is devoted to the yield management. We present our model in Section 3.
We discuss identification issues in Section 4. In Section 5, we present an application to
the railroad industry. Section 6 concludes.

2 Yield management practices

Historically, revenue management was first used by American airlines after the adop-
tion of the Airline Deregulation Act in 1978. Companies were then allowed to change
their prices, the schedules and the service without the approval of the regulator, namely
the U.S. Civil Aviation Board. In Europe and notably in France, this practice has also
been widely used over the last years. Such techniques are not restricted to airways:
railways have also been resorting to them, as well as hotel and rental car industries,
telecommunications, etc.

Firms may use several types of yield management techniques to price discriminate
among their customers. The two main practices are price-based and quantity-based
revenue management.

Price-based yield management is mainly used in the retailing industry and involves
promotions, discounts and sales as instruments for dynamic pricing. “E-tailers” may
resort to dynamic pricing and to adjustments based on real-time information.<fnref n="1" /> Finally,
consumer-packages goods promotions in the retailing industry are a form of price-based
management. Such practices are related to the stockpiling behavior of (at least some)
consumers (see for instance Hendel and Nevo (2011)) and relate to intertemporal price
discrimination models. They are typically devoted to durable or storable products, and
may result in periods of regular prices followed by occasional sales.

In contrast, quantity-based management relies on the optimal allocation of capacity
to different classes of demand that are called yield classes or fare classes. A unique
price is assigned to each fare class. The firms’ strategy consists in defining “protection
levels”, that is, amounts of capacity to reserve for a particular fare class (or set of fare

<footnote n="1">¹They also practice behavior-based price discrimination or customer recognition, the price being a function of purchase history. Such techniques may be based on e-tracking with the help of cookies (see Fudenberg and Villas-Boas (2006) for a survey of those practices).</footnote>
classes). These protection levels can be viewed as class-specific quotas. Usually, quantity-
based management implies that prices keep increasing over time, with the cheapest prices
corresponding to the lowest fare class.<fnref n="1" /> Such a quantity-based management is typically
applied to perishable goods; a seat in a plane or a train is perishable in the sense that it
has no value after departure.

Note that if quantity-based management consists in rationing with a limiting-supply
mechanism, price-based management may achieve the same objective by increasing prices,
which reduces sales. As a result, these two forms of yield management are not neces-
sarily conflicting; firms often use both of them. For instance, airlines may resort to
advance-purchase discounts, which is a price-management practice, and moreover limit
this number of discount seats, which is a quantity-based management.<fnref n="2" />

Static models of quantity-based management have been developed over the last
decades. They rely on several assumptions and determine the optimal quotas *ex-ante*
in every fare class. First, demands for different classes are independent. Second, and
more importantly, demands are assumed to arrive in the order of increasing prices of the
fare classes, which rules out overlapping intervals of demands. Third, these demands do
not depend on the capacity controls, and especially on the availability of other classes.
Fourth, group bookings are ruled out. Finally, firms are assumed to be risk-neutral,
which is a rather reasonable assumption since such decisions repeat for numerous goods
sold repeatedly over time. The most famous and earliest model is the model proposed by
(Littlewood (1972)) also known as “Littlewood’s rule”. The extension of this rule to *K*
classes was provided by Brumelle and McGill (1993). An approximation of this rule to *K*
classes widely used in practice was provided by Belobaba (1989) and is called Expected
Marginal Seat Revenue (EMSR).

Contrary to previous static models, dynamic models of pricing under revenue man-
agement (Gallego and van Ryzin (1994), Feng and Gallego (1995), Feng and Xiao (2000)
and McAfee and te Velde (2008)) do not posit that the number of seats allocated in each
fare class is fixed *ex-ante*. They determine the optimal stopping times for every fare class,
that is, the best moments for a monopoly to close the current yield class and to open the
next one. In the rest of the paper, we focus on demand only. An interesting extension
would consist in estimating both a supply and demand model, where the supply part

<footnote n="1">¹As a result, intertemporal price discrimination arises since according to the time of arrival on the market, the same good may be proposed at different prices.</footnote>

<footnote n="2">²The literature devoted to advance-purchase discounts includes for instance Shugan and Xie (2000), Shugan and Xie (2005), Möller and Watanabe (2010) and Nocke and Peitz (2007).</footnote>
would come from theoretical times of fare classes closing/opening.

## 3 Model

In this section we present a structural model of demand in presence of a quantity-based management with K yield classes (or fare classes). This model of demand relies on consumers' individual decisions of purchase. In the following, we consider the railroad industry and goods will correspond to destinations; note that the same model could be applied to markets where such a quantity-based management is at stake.

First, we need Assumption 1 that simply recognizes the need of observing several subpopulations submitted to the same yield management rule.

**Assumption 1 (Goods).** In every yield class (or fare class), at least two different goods are proposed to the customers, and the yield management is the same regardless of the good.

Note that either consumers may choose between distinct goods or distinct groups of consumers may be offered the same good. Typically, different goods may encompass different destinations but also different types of passengers. In the case of airways (resp. railways), Assumption 1 is likely to be verified when either two destinations are offered by the same flight (resp. train) or when different prices are offered to consumers according to some observable characteristics like age (student or elderly fares) or marital status (families fares) for instance. Indeed, it is reasonable to think that these different goods obey the same booking procedure, even though an optimal booking policy would consist in fixing quotas for every type. If several destinations are desired by a train before its terminal, the protection levels (and the corresponding quotas) may be decided “uniformly” at the train level and not at the destination level, which is what Assumption 1 requires. In other words, quotas are supposed to apply to the whole yield class, which may be filled up either with customers for one or the other destination, as long as the total number of tickets does not exceed the quota.

In the rest of the paper, we consider two destinations $d \in (a, b)$ with $a$ being the terminal and $b$ the intermediate stop. Importantly, we do not allow consumers to choose their destination (see infra). By fare, we mean a couple $(p_{ak}, p_{bk})$ in the fare class $k$. To be more precise, the yield management puts the following constraint on the price pattern: for all trains $T$, $\exists t_1 = 0 < t_2 < \dots < t_K < t_{K+1} = \bar{t}$ such that

$$p_d(t) = p_{dk} \quad \forall t \in [t_k; t_{k+1}), \forall k = 1, \dots, K, \quad \forall d$$
such that once $q_k$ tickets have been sold, the $k^{th}$ fare class closes and the $k + 1^{th}$ fare class opens at $t = t_{k+1}$. Times $t_k$ when fare classes close are thus endogenous.

Second, for the sake of flexibility, we assume that consumers' arrivals $N_{dT}(t)$ for the destination $d$ of train $T$ follow a non-homogeneous Poisson process with parameter $\lambda_{dT}(t)$ on a fixed time interval $[0; \bar{t}]$. $\bar{t}$ corresponds to the delay between the opening of the booking and the train's departure. Arrivals refer to consumers showing up online or at a ticket office to purchase a ticket. Nothing guarantees that the distribution of the number of arrivals $N_{dT}(t)$ is constant over time: in contrast, peaks of arrivals are likely to be observed when the booking starts, or at the end of the selling period and this is why we choose a nonhomogeneous Poisson process.<fnref n="1" /> The number of arrivals may also be increasing or decreasing over time. Non-homogeneous Poisson processes are characterized by the following relation:

**Assumption 2 (Consumers' arrivals).**

$$ \lim_{dt \to 0} \frac{\mathbb{P}(N_{dT}(t+dt) - N_{dT}(t) = 1)}{dt} = \lambda_{dT}(t). \qquad (1) $$

Third, we assume that this population is constituted of heterogeneous consumers differing in their valuation for the trip and that these valuations are distributed according to a Pareto on $[\underline{v}_T(t); +\infty)$:

**Assumption 3 (Heterogeneity of valuations).** For all destinations,

$$ F_T(v|t) = 1 - \left( \frac{v}{\underline{v}_T(t)} \right)^{-\epsilon}. \qquad (2) $$

Assumption 3 imposes for consumers to have the same constant price-elasticity since $\epsilon_T(p|t) = \frac{pf_T(p|t)}{1-F_T(p|t)} = \epsilon$, regardless of their time of arrival. The distribution of valuations is assumed here to be independent from $d$, which is rather well-suited to a population who does not choose the destination. More generally, we think that the choice of the destination is not too much an issue here: many travels are constrained (not only in the business class) and we make this assumption. In other words, we do not allow consumers to choose among destinations but assume rather that travelers have an obligation, either professional or personal, such that they must go to some given destination provided that they can afford it. Finally, for reasons that will be developed in Section 5, it would not be possible to estimate a significant proportion of distance-specific price-elasticities.

<footnote n="1">¹The Poisson assumption for consumers' arrivals is standard in the revenue management literature, as documented by Talluri and van Ryzin (2004).</footnote>
However, consumers' expected valuation may evolve over time according to the lowest valuation $\underline{v}_T(t)$ of the sub-population arriving at $t$. The behavior of $\underline{v}_T(t)$ with $t$ gives some information about the correlation between valuations and time of arrival. In a context of intertemporal pricing, the knowledge of this parameter is crucial: indeed, an increasing pattern of prices over time is a best response to valuations increasing over time, which is the case if $\underline{v}_T(t)$ is nondecreasing. This corresponds to a situation where low valuation consumers arrive earlier in the market. Otherwise, a uniform price should be observed (see for instance Choné et al. (2012)).

Conditional on a time arrival $t \ge t_K$, that is after the opening of the last class, the probability that a consumer buys equals:

$$ \mathbb{P}(v \ge p_d(t)|t \ge t_K) = \mathbb{P}(v \ge p_d(t)|p_d(t) = p_{dK}) = 1 - F(p_{dK}|t) = \underline{v}_T^\epsilon(t) p_{dK}^{-\epsilon}. \quad (3) $$

At this point, another assumption is required: we need some separability between $d$ and $t$. In other words, the consumers' arrival process must be separable between a train-specific component and a destination-specific component:

**Assumption 4** (Separability - 1).

$$ \lambda_{dT}(t) = \xi_d \nu_T(t). \quad (4) $$

Then the number of consumers arriving between $t_k$ and $t_{k+1}$ $\forall k = 1, \dots, K_T$ and who are ready to buy a ticket to destination $d$ – that is, the instantaneous demand $D_{dkT}$ for class $k$ and for destination $d$ in the train $T$ – follows a Poisson distribution since it is the counting process of the Poisson process for arrivals:

$$ \lim_{dt \to 0} \frac{\mathbb{P}(D_{dkT}(t+dt) - D_{dkT}(t) = 1)}{dt} = \xi_d \nu_T(t) \underline{v}_T^\epsilon(t) p_{dk}^{-\epsilon} \quad \forall d, \forall t \in [t_k; t_{k+1}). \quad (5) $$

This expression corresponds to the product of the instantaneous probability of arrival (1) and of the probability of purchase conditional on arrival (3). If $\theta = (\epsilon, \xi, \nu_T, \underline{v}_T)$ is the vector of structural parameters, one obtains easily Proposition 1.

**Proposition 1.** Under Assumptions 1-4, the demand at date $t \ge t_k$ in fare class $k$ of train $T$ for destination $d$ follows a Poisson distribution:

$$ D_{dkT}(t)|t_k, p_{dkT}; \theta \sim \mathcal{P} \left( \xi_d p_{dkT}^{-\epsilon} \int_{t_k}^{t} \nu_T(u) \underline{v}_T^{\epsilon}(u) du \right) \quad \forall d, \forall t \in [t_k; t_{k+1}). \quad (6) $$

Noting the class-train specific effect $A_{kT}(t) = \int_{t_k}^{t} \nu_T(u) \underline{v}_T^{\epsilon}(u) du$, we have:

$$ D_{dkT}(t)|t_k, p_{dkT}; \theta \sim \mathcal{P} \left( \xi_d p_{dkT}^{-\epsilon} A_{kT}(t) \right) \quad \forall d, \forall t \in [t_k; t_{k+1}). \quad (7) $$
# 4 Identification

The price-elasticity of demand is a crucial parameter of interest, both for economists and firms, since it impacts directly the optimal tarification. The econometrician interested in estimating this parameter has thus to wonder whether the price-sensitivity is identified in the data. In our setting, the identification of the demand's response to prices raises two non standard issues, in addition to the well-known endogeneity problem in the estimation of demand models. First, because of quantity-based management and the class-specific quotas, the demand (dependent variable) is not exactly observed, but right-censored. Second, in such a setting, the identification of the price-elasticity of demand is far from being guaranteed since exogenous variation in prices is required to identify this parameter, but prices are constant within fare classes.

## 4.1 Endogeneity

In demand models, prices are suspected to be endogenous for at least two reasons. First, the price is expected to be positively correlated to unobserved determinants of demand, like quality for instance. Second, there might be a simultaneity bias due to the fact that prices are set contemporaneously to the formation of the demand.

In this quantity-based management setting, these two problems are likely to occur. The supply should react to a higher demand by closing quickly the first fare classes with a low price in order to charge a higher price. As a result, prices and idiosyncratic shocks of demand must be positively correlated. In airlines or railways, prices are higher in rush hours because the demand is higher. Even if the adjustment is not dynamic, the fixation of the quotas must somehow be based on past demand: contrary to the econometrician, the supply knows unobserved components of its demand and fixes quotas accordingly. As a result, a positive correlation between prices and unobserved components of demand is very likely and may be responsible for an upward (resp. downward) bias of the price-effect (resp. the price-elasticity).

In the rest of the paper, we will document empirical evidence in favor of the existence of such endogeneity and try to quantify the corresponding bias.

## 4.2 Right-censoring

As already mentioned, this form of quantity-based management is responsible for a right-censoring problem of the dependent variable: the true demand is partly observed.
To make this point clear, consider here<fnref n="1" /> the total demand as a function of prices $D(p)$ that would have been realized if a single price had been proposed (as opposed to the previous demand $D_k(t)$ in every fare class defined for $t \in [t_k; t_{k+1})$), and noting $n_j$ the number of tickets purchased in fare class $j$, we know only from the data that

$$D(p_k) \geq \sum_{j=k}^{K} n_j. \qquad (8)$$

Indeed, if consumers purchase at price $p_j > p_k$, we know for sure that they would have purchased also at price $p_k$. We cannot say more about $D(p_k)$ since the reverse is not true.

If $b_k$ is the booking limit (the quota), the econometrician only observes the number of tickets purchased $n_k$ in class $k$. Since $n_k = \min(D_k(t_{k+1}), b_k)$, this constitutes a lower bound of the demand $D_k(t_{k+1})$. Without further assumption on consumers' behavior, the true demand cannot be recovered. However, it is worth mentioning that the demand in the highest fare class is exactly observed in the case where the capacity constraint is not binding, that is, when the booking is not full. To be more precise, in the highest fare class reached ($k = K$) and in the event when the train is not full we do know that:

$$D_K(\bar{t}) = n_K. \qquad (9)$$

As a result, we avoid the right-censoring issue by focusing on this highest fare class reached, in cases where the train is not full. Note that such an estimation based on Equation (9) makes use neither of the data on full trains nor on data about lower fare classes, which is an important caveat. However, the use of the information contained in the other fare classes would necessarily cost some further assumption about the way the booking is filled-up.

## 4.3 Identification of the price-elasticity

Restricting our attention to class $K_T$ (there is some variation in the highest fare class reached), we will consider $t = \bar{t}$ for which $D_{dKT}(\bar{t}) = n_{dKT}$ and note the train effect in the last class reached $A_T = A_{KT}(\bar{t}) = \int_{t_{KT}}^{\bar{t}} \nu_T(u) \underline{v}_T^\epsilon(u) du$, which gives:

$$D_{dKT}(\bar{t})|_{t_K, p_{dKT}}; \theta \sim \mathcal{P}(\xi_d p_{dKT}^{-\epsilon} A_T). \qquad (10)$$

Hence $A_T$ plays the role of a train fixed-effect. We could think of estimating the fixed-effect Poisson model (10) by maximum likelihood. This would provide a consistent

<footnote n="1">¹In this subsection, subscripts $d$ and $T$ are removed for the sake of clarity.</footnote>
estimate for $(\epsilon, \xi)$ (Lancaster (2000)), but not for the train-specific effect $A_T$ since there are only as many observations per train as the number of distinct destinations. For the estimate to be consistent however, the number of observations for every train should tend to infinity. It could be tempting to parameterize the fixed-effect as some function of trains' characteristics (schedule for instance). However, this would not solve the endogeneity issue coming from the potential correlation between the price and the fixed-effect $A_T$, which could lead to underestimate the price-elasticity (in absolute) as soon as $A_T$ is present.

As a result, to avoid the endogeneity issue, we get rid of the train fixed-effect and more generally of every component that is not destination-specific, by conditioning on $n_{aKT} + n_{bKT}$, the sum of tickets sold in class K, as soon as Assumption 1 is verified and at least destinations a and b are available for a route r:

**Proposition 2.** Under Assumptions 1-4, one has:

$$n_{aKT}|(n_{aKT} + n_{bKT} = n) \sim \mathcal{B}(n, \mu). \qquad (11)$$

*Proof.* We use the fact that a random variable following a Poisson distribution ($n_{aK}$), conditional on the sum of several independent Poissons ($n_{aKT}$ and $n_{bKT}$), follows a binomial distribution with parameters $n$ and $\mu$, where $\mu$ satisfies:

$$\mu = \frac{A_T \xi_a p_{aKT}^{-\epsilon}}{A_T \xi_a p_{aKT}^{-\epsilon} + A_T \xi_b p_{bKT}^{-\epsilon}} = \frac{1}{1 + e^{\Delta \log \xi - \epsilon \Delta \log p_{KT}}}. \qquad (12)$$

and using the notation $\Delta X = X_b - X_a$ for some covariate $X$. $\square$

This method had already been used by Ridder et al. (1994). Note that Proposition 2 only holds for trains that are not full, for which by definition, the number of purchases observed in the last fare class $K_T$ is inferior to the capacity of the train minus the sum of purchases in previous fare classes.

This model can be estimated simply by MLE.<fnref n="1" /> The likelihood of an observation ($n_{aKT} = k, n_{aKT} + n_{bKT} = n$) has to be maximized with respect to $\theta = (\epsilon, \xi)$ and writes:

$$\mathbb{P}(n_{aKT} = k | (n_{aKT} + n_{bKT} = n)) = \binom{k}{n} \mu^k (1 - \mu)^{(n-k)}. \qquad (13)$$

Since the fixed-effect disappears from the likelihood, there is no more correlation between price and any other component of the demand, which solves the endogeneity

<footnote n="1">¹Note that the estimation can also be done thanks to a simple logit model on reshaped data ($\forall i = 1, \dots, n_{aKT} + n_{bKT}$ define $Y_{iKT} = 1[i < n_{aKT}]$).</footnote>
problem. However, the estimation based on Equations (12) and (13) depends on the
ratios of prices between destinations *a* and *b*, for a given train, in the last class reached
$\Delta \log p_{KT}$. As a result, the identification of the price-effect requires both variation in
the ratio $\frac{p_{bKT}}{p_{aKT}}$ (thus variation in *K*) and that this ratio be not 1: it cannot be obtained
in the case where $p_{aKT} = p_{bKT}$. In other words, at least two points of the demand
curve are needed in order to recover the shape of the demand curve, controlling for route
effects. Note also the key role of Assumption 1: the variation required is necessarily
obtained thanks to the existence of several subpopulations (here, going to destination *a*
or to destination *b*).

The identification of $\xi_d$ stems directly from variations of ratios of tickets sold within a train route and between destinations. In particular, the normalization $\xi_b = 1$ is required for every route. The coefficient $\xi_a$ gives information about the odds ratio of average demands for destinations *a* and *b* controlling for price effects.

To sum up, only the parameters $\epsilon$ for the price-sensitivity and $\xi_a$ accounting for
relative preferences for destinations are identified. In Appendix A, we explain why it
is not possible to recover more; in particular, even the observation of times of purchase
combined with further separability assumptions between train and time effects would not
enable us to identify the behavior of the demand over time.

Finally, interesting extensions would consist in positing a model on the outside option
for railroad passengers (like taking the car, the plane, etc.) and to allow for a choice across
destinations.

# 5 Application

## 5.1 Data

We use French data from iDTGV where a quantity-based management close to the
one described in Section 3 is used.

We observe trains from October 2007 to February 2009. The destinations fall into
six train routes *r*: (i) from Paris to Mulhouse through Strasbourg; (ii) from Paris to
Perpignan through Nîmes or Montpellier; (iii) from Paris to Bayonne, Biarritz, Saint-
Jean-de-Luz and Hendaye through Bordeaux; (iv) from Paris to Toulouse through Bor-
deaux; (v) from Paris to Toulon, Saint Raphaël, Cannes and Nice through Marseille; (vi)
from Paris to Marseille through Aix-en-Provence or Avignon. A train *T* has a schedule
(day and hour of departure), a terminal and a direction (from Paris or to Paris). We
aggregate Nîmes and Montpellier into Nîmes/Montpellier; Aix-en-Provence and Avignon into Aix/Avignon; Toulon, Saint Raphaël, Cannes and Nice into Côte d'Azur; Bayonne, Biarritz, Saint-Jean-de-Luz and Hendaye into Côte basque, because for all those sets of close destinations, the fares are identical: for instance, it does not cost more to go to Montpellier than to Nîmes. As a result, once this aggregation has been made, all trains have two destinations: their final stop *a* and an intermediate stop *b*. Some trains are scheduled during a “rush hour”, periods with peaks of demand such as Friday and Sunday nights, holidays and public holidays, etc. In this case, prices are set according to a price scale very similar to the one for regular hours, with the same fare classes, except that prices are uniformly higher.

A train systematically offers a business class and an economy class. We observe several fare classes within both the business class and the economy class. The number of fare classes differs in the business and in the economy class. For instance, prices run from 19 to 76.9 euros for a Paris-Bordeaux trip in economy class and in regular hours; they run from 39 to 104.9 euros for the same trip in rush hours.

To sum up, for each train $T$, we observe some features of $T$ in both business and economy class: its schedule, terminal (which will be confounded with the route $r$), direction (from or to Paris) and stops $d$, as well as the sets of prices and tickets in each fare class $\{(p_{dT}, n_{dT})\} \forall d \in (a, b)$ and $\forall k \in [1; K_T]$ where $K_T$ is the last class reached in train $T$.<fnref n="1" />

<figure><img src="image_2.png" /><figcaption>Figure 1: Number of purchases per train in economy class (density)</figcaption></figure>

Figure 1 gives a nonparametric estimation of the density of trains’ filling-up. The

<footnote n="1">¹By “train”, we mean from now and by convenience either the business class or the economy class.</footnote>
value of exact frequencies (on the y-axis) has been removed. In economy class, the event “full train” is frequent: in that case, the capacity constraint of the train is binding, and 350 seats are occupied. It also frequently occurs that in economy class trains are filled up at about 83% of their capacity.

19% of the total variation in the number of tickets sold comes from the heterogeneity between destinations, a major determinant of demand in the railroad industry. But fundamentally, most of the residual variance of demand is due to train effects. We believe that unobserved factors like weather conditions, local events, (national) holidays are widely responsible for the formation of demand. As a result, railroad companies respond to such a behavior with a different pricing: when they expect a high demand during some specific week-end for a given destination, they should fix smaller quotas in the lowest classes, as an optimal firm would do.

Table 1 shows how the demand for railroad transportation is divided into several services. The service from Paris to Marseille is the most popular. Interestingly, passengers for the intermediate stop Aix-en-Provence/Avignon take the train to Marseille rather than the train to Côte d'Azur: as a result, trains to Côte d'Azur are most of the time filled up with passengers going to Côte d'Azur, and less often with passengers for Aix-en-Provence or Avignon.<fnref n="1" /> On the contrary, the service Paris-Mulhouse is used more by passengers for Strasbourg, the intermediate stop. The same phenomenon occurs on the train route to Perpignan through Nîmes-Montpellier. We do not see major differences between the business and the economy classes in this respect, except in the case of Bordeaux, for which the demand in business is relatively lower.

<table><caption>Table 1: Number of purchases per train by destinations</caption><thead><tr><th rowspan="3">to</th><th rowspan="3">via</th><th colspan="6">Business class</th><th colspan="6">Economy class</th><th colspan="2">Total</th></tr><tr><th rowspan="2">Total</th><th colspan="3">Terminal</th><th colspan="2">Stop</th><th colspan="3">Terminal</th><th colspan="2">Stop</th><th rowspan="2">mean</th><th rowspan="2">std</th></tr><tr><th>mean</th><th>mean</th><th>std</th><th>mean</th><th>std</th><th>mean</th><th>mean</th><th>mean</th><th>std</th><th>mean</th><th>std</th></tr></thead><tbody><tr><td>Côte basque</td><td>Bordeaux</td><td>80</td><td>53</td><td>22</td><td>27</td><td>16</td><td>248</td><td>141</td><td>70</td><td>107</td><td>53</td><td>328</td><td></td></tr><tr><td>Marseille</td><td>Aix/Avignon</td><td>159</td><td>93</td><td>18</td><td>66</td><td>14</td><td>307</td><td>187</td><td>27</td><td>120</td><td>25</td><td>466</td><td></td></tr><tr><td>Mulhouse</td><td>Strasbourg</td><td>74</td><td>22</td><td>8</td><td>52</td><td>14</td><td>195</td><td>49</td><td>16</td><td>146</td><td>30</td><td>269</td><td></td></tr><tr><td>Côte d'Azur</td><td>Aix/Avignon</td><td>141</td><td>113</td><td>28</td><td>28</td><td>16</td><td>254</td><td>206</td><td>51</td><td>48</td><td>24</td><td>395</td><td></td></tr><tr><td>Perpignan</td><td>Nîmes/Montpellier</td><td>125</td><td>49</td><td>22</td><td>76</td><td>14</td><td>286</td><td>78</td><td>28</td><td>208</td><td>40</td><td>411</td><td></td></tr><tr><td>Toulouse</td><td>Bordeaux</td><td>86</td><td>48</td><td>13</td><td>38</td><td>13</td><td>284</td><td>174</td><td>38</td><td>110</td><td>40</td><td>370</td><td></td></tr></tbody></table>

Prices and fare classes are fixed at a national level but the quotas of fare classes may vary for each train, depending on the level of the demand. As already explained,

<footnote n="1">¹Both trains run on the same route, thus none of them is faster than the other.</footnote>
quantity-based revenue management consists in allocating booking limits to every fare class. Importantly, these quotas are determined for each class at the train level and thus apply to the sum of tickets over all destinations. For instance, quotas are set for the fare classes of the train Paris-Côte Basque on March, 30th 2008, and not for every trip Paris-Bordeaux, Paris-Biarritz, Paris-Bayonne, Paris-Hendaye, Bordeaux-Hendaye, etc. As a result, at least two options (destinations) follow the same yield management rule and thus Assumption 1 is verified.

Note that quotas may or not be reached. For instance, if a train goes from Paris to Nice by Marseille, the quota of class *k* depends not only on the demand for Marseille, but also on the demand for Nice. A quota of 100 tickets may be reached with 80 tickets for Marseille and 20 for Nice, and *vice-versa*. Quotas may not be reached if the total demand for Marseille and Nice does not exceed 100 people. In the case where the quota for class *k* has been reached, class *k* + 1 opens to booking and tickets are available at the new price $p_{k+1}$. The process goes on until the train leaves: either the train is not filled up, or there is an excess demand, in which case the train's capacity constraint is binding. The so-called *duplex* trains – with two stages – may carry up to 545 passengers, 197 in the business class and 348 in the economy class. In practice, the capacity constraint is sometimes reached in economy, but almost never in business.

<figure><img src="image_3.png" /><figcaption>Figure 2: Variation in relative prices between terminal and intermediate stop for the last fare class</figcaption></figure>

It is helpful to have a rough idea of the “optimality” of yield management. To that purpose, we compute the correlation between the number of tickets sold in low fare classes
and the number of tickets sold in high classes. On Paris-Toulouse and Paris-Hendaye for instance, this correlation amounts to -0.69 when we compare purchases in the first three classes with those in the last three classes. This negative sign is consistent with a correct revenue management practice. Indeed, to maximize revenues when the demand is high, and thus when high classes are reached, it is necessary to close low classes quickly. The strongly negative correlation that we observe indicates that it is actually the kind of strategy that is adopted here by railroad companies. In other words, when a large number of tickets with a high price has been sold, it generally means that few tickets were sold with a low price. This statistics is also consistent with the presence of endogeneity and especially a positive correlation between prices and unobserved components of demand. Indeed, a correct management of fare classes moves prices in the same direction as unobserved components of demand (higher prices when the demand is higher).

Finally, Figure 2 provides information on the variation of $\Delta \log p_K$, that is, the only source of variation that enables the econometrician to identify the price-elasticity. On both the business and the economy classes, this covariate exhibits enough variation to be able to infer the price-effect.

Note however that for all trains to Marseille-Aix/Avignon and to Mulhouse-Strasbourg, we have no variation in the relative prices for destinations A and B (in both cases, prices are always identical for destinations A and B: $\log p_{aK} = \log p_{bK}$). As a result, it would not be possible to estimate a separate model for each of the six routes and therefore to assume that price-sensitivity is route-specific, since at least two of these route-dependent price elasticities would not be identified in the data. This is the reason why we estimate our model under the assumption that the price-elasticity is the same for all routes.

## 5.2 Results

Table 2 provides the results from the estimation of the binomial model of demand summarized by Equations (11) and (12). The estimated price-elasticity $\hat{\epsilon}$ in economy class is close to 2 while it is about 1.4 in business class. The estimations of tastes for destinations have the following interpretation: they suggest that the demand for the terminal Côte d'Azur is much higher than the demand for the intermediate stop Aix-en-Provence/Avignon. On the contrary, the demand for Mulhouse or Perpignan, two terminals, is lower than the demand for the intermediate stops, respectively Strasbourg and Nîmes/Montpellier. In economy class, these ratios can be ordered as follows from the lowest to the highest: Perpignan/Nîmes-Montpellier, Mulhouse/Strasbourg, Côte Basque/Bordeaux, Marseille/Aix-Avignon, Toulouse/Bordeaux and Côte d'Azur/Aix-
Avignon.

It may be interesting to add some further structure on preferences for destinations log ξ at the cost of specifying a multiplicative model. For instance, log ξ could be some function of the distance and the time of the trip, as well as of the arrival<fnref n="1" /> city’s population measured in millions of inhabitants. We form therefore the ratio of the distance (resp. the time) between Paris and the intermediate stop on the one hand, and the distance (resp. the time) between Paris and the last stop on the other hand. We proceed similarly for the corresponding ratios of population. In the same vein, we have a proxy for the intensity of the substitution with airlines by considering the daily number of Air France flights for a given destination.

<table><caption>Table 2: Binomial model of demand
Equation (11)</caption><thead><tr><th></th><th>Business class</th><th>Economy class</th></tr></thead><tbody><tr><td>log (price)</td><td>-1.441<sup>***</sup><br>(0.219)</td><td>-1.994<sup>***</sup><br>(0.125)</td></tr><tr><td>Côte Basque</td><td>-0.066<sup>***</sup><br>(0.033)</td><td>-0.610<sup>***</sup><br>(0.023)</td></tr><tr><td>Marseille</td><td>0.248<sup>***</sup><br>(0.033)</td><td>0.008<br>(0.021)</td></tr><tr><td>Mulhouse</td><td>-1.085<sup>***</sup><br>(0.038)</td><td>-1.444<sup>***</sup><br>(0.021)</td></tr><tr><td>Côte d'Azur</td><td>1.145<sup>***</sup><br>(0.031)</td><td>0.844<sup>***</sup><br>(0.020)</td></tr><tr><td>Perpignan</td><td>-0.663<sup>***</sup><br>(0.036)</td><td>-1.457<sup>***</sup><br>(0.019)</td></tr><tr><td>Toulouse</td><td>0.185<sup>***</sup><br>(0.027)</td><td>0.511<sup>***</sup><br>(0.018)</td></tr><tr><td>N</td><td>4,413</td><td>5,595</td></tr></tbody></table>

N: number of (non full) trains with Paris being either the departure or the terminal.

In business class, the average odds ratio of demands for Mulhouse (terminal) wrt Strasbourg (intermediate stop) is $e^{-1.085} \approx 0.34$; the price-elasticity is 1.441.

**Assumption 5 (Structure).**

$$ \log \xi = \alpha_0 + \alpha_1 \log(\text{distance}) + \alpha_2 \log(\text{time}) + \alpha_3 \log(\text{population}) + \alpha_4 \log(\text{airline}). \quad (14) $$

Table 3 provides results of the estimation under Assumption 5. The estimated price-elasticities are still higher, between 1.61 and 2.66. The effects of distance, travel time and

<footnote n="1">¹the departure being Paris</footnote>
population all have the same expected and positive sign, which indicates that demand is higher *ceteris paribus* for a destination that is further away, longer to serve and larger. The effect of distance may account for the substitution with the car: as distance increases, choosing the car becomes less a plausible outside option. Substitution with airlines should go the opposite way, since as the distance increases, choosing the airplane is more likely.

<table><caption>Table 3: Binomial model - Equation (11) with Assumption 5</caption><thead><tr><th></th><th>Business class</th><th>Economy class</th></tr></thead><tbody><tr><td>log(price)</td><td>-1.607<sup>***</sup><br>(0.207)</td><td>-2.663<sup>***</sup><br>(0.121)</td></tr><tr><td>Constant</td><td>0.962<sup>***</sup><br>(0.036)</td><td>0.827<sup>***</sup><br>(0.002)</td></tr><tr><td>Distance</td><td>1.618<sup>***</sup><br>(0.297)</td><td>3.472<sup>***</sup><br>(0.192)</td></tr><tr><td>Time</td><td>1.744<sup>***</sup><br>(0.147)</td><td>1.094<sup>***</sup><br>(0.089)</td></tr><tr><td>Population</td><td>0.690<sup>***</sup><br>(0.015)</td><td>0.662<sup>***</sup><br>(0.009)</td></tr><tr><td>Airline</td><td>-0.173<sup>***</sup><br>(0.031)</td><td>0.377<sup>***</sup><br>(0.021)</td></tr><tr><td>N</td><td>4,413</td><td>5,595</td></tr></tbody></table>

N: number of (non full) trains with Paris being either the departure or the terminal.

In business class, the price-elasticity is 1.607.

Distance in kilometers, time in minutes, population in millions inhabitants, airline in number of daily flights.

To check how much is gained with a nonparametric approach for the train fixed-effect, we also estimate a model based on Equation (10) where the effect $A_T$ is some function of the time of departure (month $m$ and day $d$) and of the type of period $p$ (normal or rush hour):

$$D_{dKT} \sim \mathcal{P}(A_0 \xi_d p_{dKT}^{-\epsilon} e^{\delta_m \mathbb{1}_m + \delta_d \mathbb{1}_d + \delta_p \mathbb{1}_p}). \quad (15)$$

However, as explained above, this approach is valid only if the endogeneity issue can be ignored and provides a consistent estimation only if there is no correlation between the price and unobserved demand effects once month/day/period effects have been controlled for. Results are shown in Table 4. They are rather conform to the intuition. The demand is higher in December, July, August and May, i.e. during holidays or public holidays. *Ceteris paribus*, the demand is higher during rush hour and week-ends. Marseille is the most frequented route, followed by Côte d'Azur, Perpignan (maybe because of the intermediate stop Nîmes/Montpellier), Toulouse, Côte basque and Mulhouse. Finally,
<table><caption>Table 4: Poisson model of demand - Equation (15)</caption><thead><tr><th></th><th>Business class</th><th>Economy class</th></tr></thead><tbody><tr><td>Intercept</td><td>8.335<sup>***</sup><br>(0.078)</td><td>10.003<sup>***</sup><br>(0.042)</td></tr><tr><td>log (price)</td><td>-1.496<sup>***</sup><br>(0.017)</td><td>-1.708<sup>***</sup><br>(0.010)</td></tr><tr><td>Côte basque</td><td>-0.144<sup>***</sup><br>(0.017)</td><td>-0.313<sup>***</sup><br>(0.011)</td></tr><tr><td>Marseille</td><td>+0.984<sup>***</sup><br>(0.014)</td><td>+0.935<sup>***</sup><br>(0.010)</td></tr><tr><td>Mulhouse</td><td>-0.326<sup>***</sup><br>(0.018)</td><td>-0.344<sup>***</sup><br>(0.011)</td></tr><tr><td>Côte d'Azur</td><td>+0.753<sup>***</sup><br>(0.015)</td><td>+0.831<sup>***</sup><br>(0.010)</td></tr><tr><td>Perpignan</td><td>+0.645<sup>***</sup><br>(0.018)</td><td>+0.789<sup>***</sup><br>(0.009)</td></tr><tr><td>Toulouse</td><td>ref.</td><td>ref.</td></tr><tr><td>normal</td><td>-0.479<sup>***</sup><br>(0.019)</td><td>-0.482<sup>***</sup><br>(0.010)</td></tr><tr><td>rush hour</td><td>ref.</td><td>ref.</td></tr><tr><td>Monday</td><td>-0.343<sup>***</sup><br>(0.015)</td><td>-0.444<sup>***</sup><br>(0.009)</td></tr><tr><td>Tuesday</td><td>-0.156<sup>***</sup><br>(0.023)</td><td>-0.317<sup>***</sup><br>(0.013)</td></tr><tr><td>Wednesday</td><td>-0.074<sup>***</sup><br>(0.023)</td><td>-0.222<sup>***</sup><br>(0.013)</td></tr><tr><td>Thursday</td><td>0.021<br>(0.023)</td><td>-0.033<sup>***</sup><br>(0.013)</td></tr><tr><td>Friday</td><td>-0.086<sup>***</sup><br>(0.014)</td><td>-0.169<sup>***</sup><br>(0.008)</td></tr><tr><td>Saturday</td><td>-0.146<sup>***</sup><br>(0.019)</td><td>0.059<sup>***</sup><br>(0.011)</td></tr><tr><td>Sunday</td><td>ref.</td><td>ref.</td></tr><tr><td>January</td><td>-0.224<sup>***</sup><br>(0.019)</td><td>-0.455<sup>***</sup><br>(0.010)</td></tr><tr><td>February</td><td>-0.062<sup>***</sup><br>(0.019)</td><td>-0.374<sup>***</sup><br>(0.010)</td></tr><tr><td>March</td><td>-0.204<sup>***</sup><br>(0.019)</td><td>-0.476<sup>***</sup><br>(0.011)</td></tr><tr><td>April</td><td>0.052<sup>**</sup><br>(0.021)</td><td>-0.163<sup>***</sup><br>(0.012)</td></tr><tr><td>May</td><td>0.019<br>(0.022)</td><td>0.011<br>(0.011)</td></tr><tr><td>June</td><td>0.061<sup>***</sup><br>(0.021)</td><td>-0.030<sup>***</sup><br>(0.011)</td></tr><tr><td>July</td><td>0.094<sup>***</sup><br>(0.021)</td><td>0.023<sup>**</sup><br>(0.011)</td></tr><tr><td>August</td><td>0.180<sup>***</sup><br>(0.019)</td><td>-0.001<sup>***</sup><br>(0.011)</td></tr><tr><td>September</td><td>-0.259<sup>***</sup><br>(0.021)</td><td>-0.174<sup>***</sup><br>(0.011)</td></tr><tr><td>October</td><td>-0.244<sup>***</sup><br>(0.021)</td><td>-0.558<sup>***</sup><br>(0.012)</td></tr><tr><td>November</td><td>-0.195<sup>***</sup><br>(0.022)</td><td>-0.435<sup>***</sup><br>(0.012)</td></tr><tr><td>December</td><td>ref.</td><td>ref.</td></tr><tr><td>N</td><td>8,840</td><td>11,112</td></tr></tbody></table>

N : destination-(non full) trains.

The average demand in business class a Sunday of December on rush hour is $e^{8.335 p^{-1.496}}$.
all these effects encompassed by $\delta$ are found to be very similar in both the business and the economy classes, and the average demand is higher in economy. According to these estimates, the price-elasticity tends to be about 1.50 (resp. 1.71) in business (resp. economy) class. In comparison with the previous estimation, especially in economy where the estimated elasticity was close to 2, this lower price-elasticity in absolute is consistent with the presence of some endogeneity that introduces a downward bias towards zero. The seemingly small magnitude of this bias, in particular in the business class, would tend to suggest that controlling for month, day and period (rush hours/regular schedule) effects treats much of the endogeneity problem.

For further robustness checks, it can be tempting to modify slightly Equation (15) and to replace $\epsilon$ with $\epsilon_{dT}$ in order to recover a distribution of price-elasticities across destinations, months, days or types of period. This experiment is provided by Table 5. The more constrained the demand is, as is the case during holidays, public holidays or week-ends, the less price-sensitive it is, which is rather intuitive. Overall, the price-sensitivity is low on Sundays, rush hours and in December. Moreover, the demand is almost always more price-sensitive in economy than in business class. Finally, the population of customers going to Toulouse is rather less price-sensitive than the one going to Marseille or Mulhouse for instance, which could be explained by the fact that the trip to Toulouse is long (about 5 hours, because of the absence of a high-speed rails) and that the population resorting to the train is very specific and has no other outside option.

Finally, to quantify more precisely the endogeneity bias in a reduced-form approach, it is interesting to perform the following regressions which correspond to a log-log estimation of the demand:

$$ \log D(p_{dKT}) = -\epsilon \log p_{dKT} + \delta_T + \zeta_{dr} + \eta_{dKT}. \quad (16) $$

and its corresponding first-difference equation:

$$ \Delta \log D(p_{KT}) = -\epsilon \Delta \log p_{KT} + \Delta \zeta_r + \Delta \eta_{KT}. \quad (17) $$

Note that this reduced-form approach can also be seen as a robustness check with respect to the previous structural model. Equation (16) measures a reduced-form price-elasticity where the train-effect has been parameterized while Equation (17) is the corresponding estimation in first difference (model within). For the reasons exposed in Section 4.1, Equation (16) suffers from an endogeneity bias because the train component $\delta_T$ is correlated to $p_{dKT}$ while Equation (17) should not suffer from such a bias.<fnref n="1" />

<footnote n="1">¹The analogue in the structural approach was the comparison between Equations (10) and (15).</footnote>
<table><caption>Table 5: Robustness checks on the price-elasticity $\epsilon$</caption><thead><tr><th></th><th>Business class</th><th>Economy class</th></tr></thead><tbody><tr><td>€ Côte basque</td><td>1.445<sup>***</sup><br>(0.039)</td><td>1.188<sup>***</sup><br>(0.027)</td></tr><tr><td>€ Marseille</td><td>1.738<sup>***</sup><br>(0.028)</td><td>2.136<sup>***</sup><br>(0.017)</td></tr><tr><td>€ Mulhouse</td><td>1.743<sup>***</sup><br>(0.052)</td><td>1.441<sup>***</sup><br>(0.029)</td></tr><tr><td>€ Côte d'Azur</td><td>1.297<sup>***</sup><br>(0.029)</td><td>1.564<sup>***</sup><br>(0.016)</td></tr><tr><td>€ Perpignan</td><td>1.569<sup>***</sup><br>(0.049)</td><td>1.797<sup>***</sup><br>(0.017)</td></tr><tr><td>€ Toulouse</td><td>1.068<sup>***</sup><br>(0.054)</td><td>0.962<sup>***</sup><br>(0.043)</td></tr><tr><td>€ Monday</td><td>1.814<sup>***</sup><br>(0.044)</td><td>2.212<sup>***</sup><br>(0.025)</td></tr><tr><td>€ Tuesday</td><td>2.064<sup>***</sup><br>(0.044)</td><td>1.939<sup>***</sup><br>(0.023)</td></tr><tr><td>€ Wednesday</td><td>1.940<sup>***</sup><br>(0.043)</td><td>2.203<sup>***</sup><br>(0.022)</td></tr><tr><td>€ Thursday</td><td>1.934<sup>***</sup><br>(0.042)</td><td>2.225<sup>***</sup><br>(0.021)</td></tr><tr><td>€ Friday</td><td>1.517<sup>***</sup><br>(0.042)</td><td>2.060<sup>***</sup><br>(0.026)</td></tr><tr><td>€ Saturday</td><td>0.998<sup>***</sup><br>(0.039)</td><td>1.050<sup>***</sup><br>(0.020)</td></tr><tr><td>€ Sunday</td><td>0.855<sup>***</sup><br>(0.033)</td><td>0.785<sup>***</sup><br>(0.022)</td></tr><tr><td>€ normal</td><td>1.928<sup>***</sup><br>(0.024)</td><td>2.006<sup>***</sup><br>(0.012)</td></tr><tr><td>€ rush hour</td><td>1.145<sup>***</sup><br>(0.022)</td><td>1.335<sup>***</sup><br>(0.014)</td></tr><tr><td>€ January</td><td>2.085<sup>***</sup><br>(0.042)</td><td>2.219<sup>***</sup><br>(0.022)</td></tr><tr><td>€ February</td><td>1.543<sup>***</sup><br>(0.043)</td><td>2.184<sup>***</sup><br>(0.024)</td></tr><tr><td>€ March</td><td>1.486<sup>***</sup><br>(0.051)</td><td>1.396<sup>***</sup><br>(0.031)</td></tr><tr><td>€ April</td><td>1.726<sup>***</sup><br>(0.050)</td><td>1.461<sup>***</sup><br>(0.033)</td></tr><tr><td>€ May</td><td>1.093<sup>***</sup><br>(0.055)</td><td>1.783<sup>***</sup><br>(0.027)</td></tr><tr><td>€ June</td><td>2.312<sup>***</sup><br>(0.058)</td><td>2.767<sup>***</sup><br>(0.030)</td></tr><tr><td>€ July</td><td>1.687<sup>***</sup><br>(0.060)</td><td>0.311<sup>***</sup><br>(0.037)</td></tr><tr><td>€ August</td><td>0.990<sup>***</sup><br>(0.050)</td><td>0.667<sup>***</sup><br>(0.033)</td></tr><tr><td>€ September</td><td>2.290<sup>***</sup><br>(0.067)</td><td>2.968<sup>***</sup><br>(0.033)</td></tr><tr><td>€ October</td><td>1.603<sup>***</sup><br>(0.050)</td><td>1.938<sup>***</sup><br>(0.027)</td></tr><tr><td>€ November</td><td>0.909<sup>***</sup><br>(0.057)</td><td>1.570<sup>***</sup><br>(0.031)</td></tr><tr><td>€ December</td><td>0.558<sup>***</sup><br>(0.048)</td><td>0.493<sup>***</sup><br>(0.024)</td></tr><tr><td>route effects</td><td>Yes</td><td>Yes</td></tr><tr><td>month effects</td><td>Yes</td><td>Yes</td></tr><tr><td>day effects</td><td>Yes</td><td>Yes</td></tr><tr><td>period effects</td><td>Yes</td><td>Yes</td></tr><tr><td>N</td><td>8,840</td><td>11,112</td></tr></tbody></table>

N : destination-(non full) trains.

Benchmark: Table 4/Equation (15).

Panels separated by two lines correspond to different regressions.

$\epsilon_{DT}$ instead of $\epsilon$ (1.496 in business class, 1.708 in economy class).
<table><caption>Table 6: Reduced-form evidence on the endogeneity bias - Equations (16) and (17)</caption><thead><tr><th rowspan="2"></th><th colspan="2">Business class</th><th colspan="2">Economy class</th></tr><tr><th>level</th><th>first difference</th><th>level</th><th>first difference</th></tr></thead><tbody><tr><td>log (price)</td><td>-1.013<sup>***</sup><br>(0.051)</td><td>-1.302<sup>***</sup><br>(0.427)</td><td>-1.300<sup>***</sup><br>(0.058)</td><td>-1.734<sup>***</sup><br>(0.324)</td></tr><tr><td>model within</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>route effects</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>month effects</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td></tr><tr><td>day effects</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td></tr><tr><td>period effects</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td></tr><tr><td>R<sup>2</sup></td><td>0.10</td><td>0.32</td><td>0.08</td><td>0.54</td></tr><tr><td>N</td><td>7,210</td><td>2,790</td><td>8,840</td><td>3,950</td></tr></tbody></table>

Table 6 shows the results: one can see that the endogeneity bias may be responsible of a downward attenuation of about -0.29 to -0.43 of the price-elasticity. Moreover, this reduced-form estimation leads to estimates that are close to the previous ones, such that a range of price-elasticities can be [1.3; 1.5] (resp. [1.7; 2]) in business (resp. in economy) class. Note that Equation (17) provides a reduced-form estimation of the price-elasticity of demand that is perhaps more reliable in the presence of yield management.

## 5.3 Aggregating data

The estimation of demand (and thus of the price-elasticity) at a macro level is somehow problematic because aggregation leads to an attenuation bias that biases estimates towards zero. To illustrate, we aggregate our micro data and estimate corresponding price-elasticities. For instance, we propose to aggregate data over fare classes at the train level, and thus to consider an average price for every train. Then we regress the logarithm of total purchases on the logarithm of this average price. Formally, let $D_{dT}$ be the total demand for destination $d$ in the train $T$: $D_{dT} = \sum_{k=1}^{K_T} n_{dkT}$ and the average price $\bar{p}_{dT}$ is given by:

$$ \bar{p}_{dT} = \frac{\sum_{k=1}^{K_T} n_{dkT} p_{dkT}}{\sum_{k=1}^{K_T} n_{dkT}}. $$

We could get rid of the train fixed-effect by considering the regression in differences as soon as at least two destinations $a$ and $b$ are available (Assumption 1):

$$ \Delta \log D_T = -\epsilon \Delta \log \bar{p}_T + \Delta \log \xi_r + \delta_t + \Delta \eta_T, \quad (18) $$
where log($\xi_{dr}$) accounts for a destination-specific component if $d \in (a, b)$ and $r$ is some train route. Results are given in Table 7. The estimated price-elasticity of 0.67 is reminding about Sauvant (2002) who found a value close to 0.7. However, the demand would be more responsive to prices in business than in economy, which is rather counter-intuitive.

Similarly, we can aggregate data at the train level:

$$D_T = \sum_d \sum_{k=1}^{K_T} n_{dkT},$$

define an average price:

$$\bar{p}_T = \frac{\sum_d \sum_{k=1}^{K_T} n_{dk} p_{dkT}}{\sum_d \sum_{k=1}^{K_T} n_{dk}},$$

and perform identical regressions by controlling for the day of departure (model train):

$$\log D_T = -\epsilon \log \bar{p}_T + \delta_t + \eta_T, \quad (19)$$

Finally, the most aggregated approach (a time series approach) consists in aggregating these demands at a weekly or monthly level, either by train route or at the national level. Results show the existence of the attenuation bias. We conclude that the time series approach measures rather a covariation of quantities with prices than the microeconomic parameter of interest, the price-elasticity.

<table><caption>Table 7: Estimated price-elasticity from aggregated data - Equations (18) and (19)</caption><thead><tr><th></th><th>Business class</th><th>Economy class</th></tr></thead><tbody><tr><td>model within</td><td>1.61<sup>***</sup><br>(0.11)</td><td>0.67<sup>***</sup><br>(0.10)</td></tr><tr><td>model train</td><td>0.22<sup>***</sup><br>(0.02)</td><td>0.24<sup>***</sup><br>(0.02)</td></tr><tr><td>model week (by route)</td><td>0.56<sup>***</sup><br>(0.23)</td><td>0.23<br>(0.15)</td></tr><tr><td>model month (by route)</td><td>1.41<sup>**</sup><br>(0.59)</td><td>0.70<sup>**</sup><br>(0.31)</td></tr><tr><td>model week (France)</td><td>0.76<sup>***</sup><br>(0.18)</td><td>-0.06<br>(0.12)</td></tr><tr><td>model month (France)</td><td>1.64<sup>***</sup><br>(0.51)</td><td>0.42<br>(0.40)</td></tr></tbody></table>

The opposite of the log-price coefficient is reported for each model.

Refer to the text for an explanation of each model.
## 5.4 Discussion

The literature devoted to the transportation industry provides several estimations of the price-elasticity. Most studies rely on aggregated data (see for instance the meta-analysis by Jevons et al. (2005) and several papers like Wardman (1997), Wardman (2006) and Wardman et al. (2007)). The elasticities that were obtained by these authors, in the meta-analysis and in their econometric study as well, belong to [1.3; 2.2]. On German data, using a market-share approach, Ivaldi and Vibes (2005) find an elasticity close to the lowest part of this range, about 1.3. On Swiss data, Rolle (1997) has a price-elasticity of 1.5. His paper is focused on rather short travels and he is noticing that the elasticity tends to increase with distance, which could explain our higher elasticities in the French case since distances are longer. Other papers point out a lower elasticity, like the survey by Oum et al. (1992) presenting elasticities varying between 0.1 and 1.5. Similarly, Sauvant (2002) finds a price-elasticity of 0.7 on French data.

The difference between our results and those from studies relying on aggregated data comes precisely from the fact that we dispose of very disaggregated data. We already mentioned in Section 5.3 that the approach based on aggregated data leads to bias towards zero the estimated price-elasticities. In presence of such quantity-based management, disposing of very fine data at the fare class level seems necessary to identify the price-sensitivity.

Finally, our results may even provide lower bounds for the price-elasticity of demand. Indeed, the estimation relies on tickets bought in the highest fare class, which must correspond to less price sensitive consumers. Otherwise, we argued that it is hard to rationalize an increasing pattern over time. Though our model assumes the price-elasticity is constant, it is likely that more eager consumers come first. As a result, the price-elasticity should be lower in the highest class and higher in the lowest classes. More generally, if the true demand were observed in each of the *K* fare classes, we would be able to estimate $\forall k = 1, ..., K$ the collection of price-elasticities $\epsilon_k$. In this paper, we provide an estimation of $\epsilon_K$ only, and perhaps the lowest – though already high.

## 6 Conclusion

The use of very fine data enables us to estimate the price-elasticity in the French railroad industry and structural parameters of a model of demand in presence of quantity-based revenue management. We explained how this form of yield management creates two econometric issues: a standard endogeneity problem and a non-standard right-censoring
problem in demand models. In particular, disposing of aggregated data in presence
of such a pricing seems not enough to recover the true price effect. We provided a
simple solution to overcome both problems and estimated a structural binomial model
of demand. Railroad passengers are found to be rather responsive to prices since this
price-elasticity varies from 1.3 – 1.5 in business class to 1.7 – 2 in economy class.
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# A Appendix: times of purchase

In our model, it is not possible to disentangle what is due to a higher flow of arrivals, namely a strong potential demand, from what is due to large valuations. Generally speaking, a high demand can come either from a large market size and low individual propensions of purchase, or from a small market size and high individual propensions of purchase. In other words, $v_T(t)$ and $\nu_T(t)$ cannot be simultaneously identified: only the product $\nu_T(\cdot) v_T^\epsilon(\cdot)$ can be recovered.

Moreover, we face an incidental parameters problem since $\nu_T(\cdot)$ depends on the train. To be more precise, we need some further separability assumption between time and train effects in the product of arrivals' flow and consumers' minimum valuations (to get rid of the incidental parameters problem):

**Assumption 6 (Separability - 2).**

$$ \nu_T(\cdot) v_T^\epsilon(\cdot) = f(T) h(\cdot). \qquad (20) $$

Furthermore, we also need to observe the individual times of purchase. In that case, one could recover the function of time $h(\cdot)$ that gives information about how the demand behaves over time. This is a crucial issue since it indicates among others, whether the demand is more eager at the beginning or not. Such a behavior is encompassed by the effect $A_{KT}(t) = \int_{t_K}^t \nu_T(u) v_T^\epsilon(u) du = f(T) \int_{t_K}^t h(u) du = f(T)H(t)$.

The behavior of $h(\cdot)$ is interesting from a microeconomic point of view. It is hard to rationalize the optimality of this quantity-based yield management practice if $h(\cdot)$ were some decreasing function over time; uniform pricing would then be optimal. On the contrary, when $h(\cdot)$ is nondecreasing over time, then some nondecreasing price pattern is optimal.

Since $\forall t \ge t_K$ one has $D_{dkT}(t)|_{t_K} \sim \mathcal{P}(f(T) \xi_d p_{dKT}^{-\epsilon} H(t))$, one can use the same method as previously:

$$ D_{dkT}(t)|D_{dkT}(t) + D_{dkT}(t') \sim \mathcal{B} \left( D_{dkT}(t) + D_{dkT}(t'), \frac{1}{1 + \frac{H(t')}{H(t)}} \right). $$

**Proposition 3.** If times of purchase are observed, and under Assumption 1-6, the function $h(\cdot)$ is identified nonparametrically up to a scale over $[\inf_T t_{K_T}; \bar{t}]$.
Proof. From the data and

$$D_{dkT}(t)|D_{dkT}(t) + D_{dkT}(t') \sim \mathcal{B} \left( D_{dkT}(t) + D_{dkT}(t'), \frac{1}{1 + \frac{H(t')}{H(t)}} \right),$$

the ratio $\frac{H(t')}{H(t)}$ is identified. By fixing $t$ and making $t'$ vary, one identifies $H(t')$ up to a scale over $[\inf_T t_{K_T}; \bar{t}]$. As a result, its derivative $h(.)$ is identified up to a scale. $\square$

Note yet that some model of supply derived from the quantity-based management would add further constraints on the model, and this supplementary structure might help in achieving some functional identification of these two forces.
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    <td>G 9300</td>
    <td>B. CREPON et E. DUGUET<br>Research and development, competition and innovation: an application of pseudo maximum likelihood methods to Poisson models with heterogeneity</td>
    <td>G 9318</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>
    <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 9104</td>
    <td>H. ROUSSE<br>Le modèle AMADEUS - Troisième partie - Le commerce extérieur et l'environnement international</td>
    <td>G 9301</td>
    <td>J. TOUJAS-BERNATE<br>Commerce international et concurrence impartie : développements récents et implications pour la politique commerciale</td>
    <td>G 9319</td>
    <td>D. BLANCHET<br>Les structures par âge importent-elles ?</td>
    <td>G 9505<br>Bis</td>
    <td>D. GOUX - E. MAURIN<br>Persistence of inter-industry wages differentials: a reexamination on matched worker-firm panel data</td>
  </tr>
  <tr>
    <td>G 9105</td>
    <td>H. ROUSSE<br>Effets de demande et d'offre dans les résultats du commerce extérieur manufacturé de la France au cours des deux dernières décennies</td>
    <td>G 9302</td>
    <td>Ch. CASES<br>Durées de chômage et comportements d'offre de travail : une revue de la littérature</td>
    <td>G 9400</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>
    <td>G 9506</td>
    <td>S. JACOBZONE<br>Les liens entre RMI et chômage, une mise en perspective<br>NON PARU - article sorti dans Économie et Prévision n° 122 (1996) - pages 95 à 113</td>
  </tr>
  <tr>
    <td>G 9106</td>
    <td>B. CREPON<br>Innovation, taille et concentration : causalités et dynamiques</td>
    <td>G 9303</td>
    <td>H. ERKEL-ROUSSE<br>Union économique et monétaire : le débat économique</td>
    <td>G 9401</td>
    <td>P. QUIRION<br>Les déchets en France : éléments statistiques et économiques</td>
    <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 9107</td>
    <td>B. AMABLE et D. GUELLEC<br>Un panorama des théories de la croissance endogène</td>
    <td>G 9304</td>
    <td>N. GREENAN - D. GUELLEC / G. BROUSSAUDIER - L. MIOTTI<br>Innovation organisationnelle, dynamisme technologique et performances des entreprises</td>
    <td>G 9402</td>
    <td>D. LADIRAY - M. GRUN-REHOMME<br>Lissage par moyennes mobiles - Le problème des extrémités de série</td>
    <td>G 9601</td>
    <td>Banque de France - CEPREMAP - Direction de la Prévision - Érasme - INSEE - OFCE<br>Structures et propriétés de cinq modèles macroéconomiques français</td>
  </tr>
  <tr>
    <td>G 9108</td>
    <td>M. GLAUDE et M. MOUTARDIER<br>Une évaluation du coût direct de l'enfant de 1979 à 1989</td>
    <td>G 9305</td>
    <td>P. JAILLARD<br>Le traité de Maastricht : présentation juridique et historique</td>
    <td>G 9403</td>
    <td>V. MAILLARD<br>Theorie et pratique de la correction des effets de jours ouvrables</td>
    <td>G 9602</td>
    <td>Rapport d'activité de la DESE de l'année 1995</td>
  </tr>
  <tr>
    <td>G 9109</td>
    <td>P. RALLE et alii<br>France - Allemagne : performances économiques comparées</td>
    <td>G 9306</td>
    <td>J.L. BRILLET<br>Micro-DMS : présentation et propriétés</td>
    <td>G 9404</td>
    <td>F. ROSENWALD<br>La décision d'investir</td>
    <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 9110</td>
    <td>J.L. BRILLET<br>Micro-DMS<br>NON PARU</td>
    <td>G 9307</td>
    <td>J.L. BRILLET<br>Micro-DMS - variantes : les tableaux</td>
    <td>G 9405</td>
    <td>S. JACOBZONE<br>Les apports de l'économie industrielle pour définir la stratégie économique de l'hôpital public</td>
    <td>G 9604</td>
    <td>A. TOPIOL-BENSAÏD<br>Les implantations japonaises en France</td>
  </tr>
  <tr>
    <td>G 9111</td>
    <td>A. MAGNIER<br>Effets accélérateur et multiplicateur en France depuis 1970 : quelques résultats empiriques</td>
    <td>G 9308</td>
    <td>S. JACOBZONE<br>Les grands réseaux publics français dans une perspective européenne</td>
    <td>G 9406</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>
    <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 9112</td>
    <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 9407</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 9408</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 9410</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>N. GREENAN - D. GUELLEC<br>La théorie coopérative de la firme</td>
  </tr>
</table>
<table>
  <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 9807</td>
    <td>Bilan des activités de la Direction des Études et<br/>Synthèses Économiques - 1997</td>
    <td>Bis</td>
    <td>Une estimation de l'élasticité de l'emploi peu<br/>qualifié à son coût</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 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 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 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 9611</td>
    <td>X. BONNET - S. MAHFOUZ<br/>The influence of different specifications of wages-<br/>prices spirals on the measure of the NAIRU: the<br/>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 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/>Évolution 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 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 régime<br/>général</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 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 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 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 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 firms<br/>from the manufacturing sector</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 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/>Évolution de l'emploi et des coûts par quali-<br/>fication entre 1982 et 1996</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 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 2000/01</td>
    <td>R. MAHIEU<br/>Les déterminants des dépenses de santé : une<br/>approche macroéconomique</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 9902</td>
    <td>Ch. COLIN<br/>Modélisation des carrières dans Destinie</td>
    <td>G 2000/02</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 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 9903</td>
    <td>Ch. COLIN<br/>Évolution de la dispersion des salaires : un essai<br/>de prospective par microsimulation</td>
    <td>G 2000/03</td>
    <td>J.-Y. FOURNIER<br/>L'approximation du filtre passe-bande proposée<br/>par Christiano et Fitzgerald</td>
  </tr>
  <tr>
    <td>G 9705</td>
    <td>E. DUGUET - N. IUNG<br/>R &amp; 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 9904</td>
    <td>B. CREPON - N. IUNG<br/>Innovation, emploi et performances</td>
    <td>G 2000/04</td>
    <td>Bilan des activités de la DESE - 1999</td>
  </tr>
  <tr>
    <td>G 9706</td>
    <td>M. HOUBEBINE - A. TOPIOL-BENSAÎD<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 9905</td>
    <td>B. CREPON - Ch. GIANELLA<br/>Wages inequalities in France 1969-1992<br/>An application of quantile regression techniques</td>
    <td>G 2000/05</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 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 9906</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 2000/06</td>
    <td>A. FLIPO<br/>Les comportements matrimoniaux de fait</td>
  </tr>
  <tr>
    <td>G 9708</td>
    <td>E. DUGUET - N. GREENAN<br/>Le biais technologique : une analyse sur données<br/>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 9907</td>
    <td>F. ROSENWALD<br/>L'impact des contraintes financières dans la dé-<br/>cision d'investissement</td>
    <td>G 2000/07</td>
    <td>R. MAHIEU - B. SÉDILLOT<br/>Microsimulations of the retirement decision: a<br/>supply side approach</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 9908</td>
    <td>Bilan des activités de la DESE - 1998</td>
    <td>G 2000/08</td>
    <td>C. AUDENIS - C. PROST<br/>Déficit conjoncturel : une prise en compte des<br/>conjonctures passées</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 et<br/>1996</td>
    <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>
    <td>G 2000/09</td>
    <td>R. MAHIEU - B. SÉDILLOT<br/>Équivalent patrimonial de la rente et souscription<br/>de retraite complémentaire</td>
  </tr>
  <tr>
    <td>G 9711</td>
    <td>G. FORGEOT - J. GAUTIÉ<br/>Insertion professionnelle des jeunes et processus<br/>de déclassement</td>
    <td>G 9807</td>
    <td>G. LAROQUE - B. SALANIÉ<br/>Une décomposition du non-emploi en France</td>
    <td>G 9910</td>
    <td>Ch. COLIN - FI. LEGROS - R. MAHIEU<br/>Bilans contributifs comparés des régimes de<br/>retraite du secteur privé et de la fonction publique</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 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>G. LAROQUE - B. SALANIÉ<br/>Une maquette analytique de long terme du<br/>marché du travail</td>
    <td>G 9911</td>
    <td>G. LAROQUE - B. SALANIÉ<br/>Une décomposition du non-emploi en France</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 9713</td>
    <td>Bilan des activités de la Direction des Études<br/>et Synthèses Économiques - 1996</td>
    <td>G 9809</td>
    <td>Ch. GIANELLA<br/>La productivité globale des facteurs entre 1975 et<br/>1996</td>
    <td>G 9912</td>
    <td>B. SALANIÉ<br/>Une maquette analytique de long terme du<br/>marché du travail</td>
    <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 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'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 macroéconométrique pour la zone euro

G2011/16 R. AEBERHARDT - I. BUONO - H. FADINGER Learning, Incomplete Contracts and Export Dynamics: theory and Evidence from 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. MAUROUX Le crédit d'impôt dédié au développement durable : une évaluation économétrique

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