Marc Ivaldi

Comparing Fourier and Translog Specifications of Multiproduct Technology: Evidence from an Incomplete Panel of French Farmers

Selecting a functional form for a cost or profit function in applied production analysis is a crucial step in assessing the characteristics of a technology. The present study highlights differences in the description of a technology which are induced by fitting a Fourier or a translog cost functions. On average, both forms provide similar information on the technology. However, estimation results and statistical tests tend to favour the Fourier specification. This is mainly because many trigonometric terms appear to be significant in our application. Accordingly, our results show that the Fourier cost function is able to represent a broader range of technological structures than the translog. The paper presents an application to the case of an incomplete panel of French farmers. In the process, three technical issues are addressed: the missing data problem, the choice of the order of approximation and the conditions ensuring asymptotic normality of Fourier parameters estimates. Coauthors are Norbert Ladoux, Herve Ossard, and Michel Simioni. Copyright 1996 by John Wiley & Sons, Ltd.

Stochastic Frontiers and Asymmetric Information Models

This article is an attempt to shed light on the specification and identification of inefficiency in stochastic frontiers. We consider the case of a regulated firm or industry. Applying a simple principal-agent framework that accounts for informational asymmetries to this context, we derive the associated production and cost frontiers. Noticeably this approach yields a decomposition of inefficiency into two components: The first component is a pure random term while the second component depends on the unobservable actions taken by the agent (the firm). This result provides a theoretical foundation to the usual specification applied in the literature on stochastic frontiers. An application to a panel data set of French urban transport networks serves as an illustration.

Sobolev Estimation of Approximate Regressions

This paper focuses on the estimation of an approximated function and its derivatives. Let us assume that the data-generating process can be described by a family of regression models null, where a is a multi-index of differentiation such that D α null(x i ) is the αth derivative of null( x ) with respect to x i . The estimated model is characterized by a family D α f(X i |θ), where D α f(X i |θ) is the αth derivative of f(x i ,|θ) and θ is an unknown parameter. The model is in general misspecified; that is, there is no θ such that D α f(X i |6) is equal to D α null(X i ). Three different problems are discussed. First, the asymptotic behavior of the seemingly unrelated regression estimator of θ is shown to achieve the best approximation, in the Sobolev norm sense, of null by an element of (f(X i |θ)|θ e Θ). Second, in the case of polynomial approximations, the expected derivatives of the limit of the estimated regression and of the true regression are proved to be equal if and only if the set of explanatory variables has a normal distribution. Third, different sets of α are introduced, and the different limits of estimated regressions characterized by these sets are proved to be equal if and only if the explanatory variables have a normal distribution. This result leads to a specification test.