Jean-Pierre Florens

Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization

Inverse problems can be described as functional equations where the value of the function is known or easily estimable but the argument is unknown. Many problems in econometrics can be stated in the form of inverse problems where the argument itself is a function. For example, consider a nonlinear regression where the functional form is the object of interest. One can readily estimate the conditional expectation of the dependent variable given a vector of instruments. From this estimate, one would like to recover the unknown functional form. This chapter provides an introduction to the estimation of the solution to inverse problems. It focuses mainly on integral equations of the first kind. Solving these equations is particularly challenging as the solution does not necessarily exist, may not be unique, and is not continuous. As a result, a regularized (or smoothed) solution needs to be implemented. We review different regularization methods and study the properties of the estimator. Integral equations of the first kind appear, for example, in the generalized method of moments when the number of moment conditions is infinite, and in the nonparametric estimation of instrumental variable regressions. In the last section of this chapter, we investigate integral equations of the second kind, whose solutions may not be unique but are continuous. Such equations arise when additive models and measurement error models are estimated nonparametrically.

Entry and Competition in the Postal Market: Foundations for the Construction of Entry Scenarios

This paper presents a model of entry and imperfect competition, which is inspired by the product differentiation literature and incorporates facts pertaining to the postal sector. There are two operators: incumbent and potential entrant. The entrant offers only one of the products (commercial mail) with a specific technology and delivers only to part of the addressees (located in low cost areas). Its degree of coverage is viewed as a quality attribute; it affects demand and hence market share. The incumbent faces a USO while the entrant is an unregulated profit maximizing firm. To illustrate the potential applications of our approach, we provide some numerical simulations of entry scenarios.

Specification and inference in linear models

Abstract In the framework of I.I.D. sampling, a general class of linear models is analyzed. Incidental parameters are shown to naturally arise in this class of models. More fundamentally, special attention is paid to the high dimensionality of the parameter space. The objective of the paper is to offer a strategy for progressively specifying a model within that class of linear models. By so doing, we aim at displaying the precise role of each assumption, at offering alternatives to unnecessarily restrictive specifications, and, thereby, at improving the robustness of the inference procedures we discuss. Decompositions of the inference process are obtained through a systematic use of (Bayesian) cuts. Maximum Likelihood Estimation and Bayesian Inference are discussed. An objective of the progressive specification is to preserve the computational tractability and the interpretability of the procedures we develop by relying on known properties of the usual multivariate regression model.

Additive Nonparametric Instrumental Regressions: A Guide to Implementation

Abstract We present a review on the implementation of regularization methods for the estimation of additive nonparametric regression models with instrumental variables. We consider various versions of Tikhonov, Landweber-Fridman and Sieve (Petrov-Galerkin) regularization. We review data-driven techniques for the sequential choice of the smoothing and the regularization parameters. Through Monte Carlo simulations, we discuss the finite sample properties of each regularization method for different smoothness properties of the regression function. Finally, we present an application to the estimation of the Engel curve for food in a sample of rural households in Pakistan, where a partially linear specification is described that allows one to embed other exogenous covariates.

Duration Models and Point Processes

This survey is devoted to the statistical analysis of duration models and point processes. The first section introduces specific concepts and definitions for single-spell duration models. Section two is devoted to the presentation of conditional duration models which incorporate the effects of explanatory variables. Competing risks models are presented in the third section. The fourth section is concerned with statistical inference, with a special emphasis on non- and semi- parametric estimation of single-spell duration models. Section 5 sets forth the main definitions for point and counting processes. Section 6 presents important elementary examples of point processes, namely Poisson, Markov and semi-Markov processes. The last section presents a general semi-parametric framework for studying point processes with explanatory variables.

A Panel Data Analysis of Inefficiency and Heterogeneity in the Postal Sector

This compilation of original papers selected from the 19th Conference on Postal and Delivery Economics and authored by an international cast of economists, lawyers, regulators and industry practitioners addresses perhaps the most significant problem that has ever faced the postal sector – electronic competition from information and communication technologies. This has increased significantly over the last few years with a consequent serious drop in mail volume.

Structural time series modeling: a Bayesian approach

Alternative progressive strategies for specification of linear dynamic models are presented. The main theme is that specification is basically concerned with endowing the pure incidental case-i.e., the case of different moment for each observations-with progressively more structure. Linearity and exogeneity are successively introduced in that spirit, first at a global level, then at a sequential level. This latter case is also shown to provide fuller possibilities for specification by means of the concepts of innovation and noncausality. This analysis along with the prior specification is conducted within the limits imposed by the possibility of concluding the analysis with computable posterior distributions on the parameters of interest.