Welfare analysis using nonseparable models

This paper proposes a framework to model empirically welfare effects that are associated with a price change in a population of heterogeneous consumers. Individual demands are characterized by a nonseparable model which is nonparametric in the regressors, as well as monotonic in unobserved heterogeneity. In this setup, we first provide and discuss conditions under which the heterogeneous welfare effects are identified, and establish constructive identification. We then propose a sample counterpart estimator, and analyze its large sample properties. For both identification and estimation, we distinguish between the cases when regressors are exogenous and when they are endogenous. Finally, we apply all concepts to measuring the heterogeneous effect of a chance of gasoline price using US consumer data and find very substantial differences in individual effects.

Saturation spaces for regularization methods in inverse problems

The aim of this article is to characterize the saturation spaces that appear in inverse problems. Such spaces are defined for a regularization method and the rate of convergence of the estimation part of the inverse problem depends on their definition. Here we prove that it is possible to define these spaces as regularity spaces, independent of the choice of the approximation method. Moreover, this intrinsec definition enables us to provide minimax rate of convergence under such assumptionsLinear inverse problems, regularization methods, structural econometrics

A unified approach to solve ill-posed inverse problems in econometrics

We consider the general issue of estimating a nonparametric function x from the inverse problem r = Tx given estimates of the function r and of the linear transform T. Two typical examples include the estimation of a probability density function fromdata contaminated by a noise whose distribution is unknown (blind deconvolution) and the nonparametric instrumental regression. We provide a unified framework based on Hilbert scales that synthesizes most of existing results in the econometric literature and also covers new relevant structural models. Results are given on the rate of convergence of the estimator of x as well as of its derivatives.inverse problem, Hilbert scale, deconvolution, instrumental variable, nonparametric regression

Accuracy of areal interpolation methods for count data

The combination of several socio-economic data bases originating from different administrative sources collected on several different partitions of a geographic zone of interest into administrative units induces the so called areal interpolation problem. This problem is that of allocating the data from a set of source spatial units to a set of target spatial units. A particular case of that problem is the re-allocation to a single target partition which is a regular grid. At the European level for example, the EU directive 'INSPIRE', or INfrastructure for SPatial InfoRmation, encourages the states to provide socio-economic data on a common grid to facilitate economic studies across states. In the literature, there are three main types of such techniques: proportional weighting schemes, smoothing techniques and regression based interpolation. We propose a stochastic model based on Poisson point patterns to study the statistical accuracy of these techniques for regular grid targets in the case of count data. The error depends on the nature of the target variable and its correlation with the auxiliary variable. For simplicity, we restrict attention to proportional weighting schemes and Poisson regression based methods. Our conclusion is that there is no technique which always dominates

Iterative regularization in nonparametric instrumental regression

We consider the nonparametric regression model with an additive error that is correlated with the explanatory variables. We suppose the existence of instrumental variables that are considered in this model for the identification and the estimation of the regression function. The nonparametric estimation by instrumental variables is an ill-posed linear inverse problem with an unknown but estimable operator. We provide a new estimator of the regression function using an iterative regularization method (the Landweber-Fridman method). The optimal number of iterations and the convergence of the mean square error of the resulting estimator are derived under both mild and severe degrees of ill-posedness. A Monte-Carlo exercise shows the impact of some parameters on the estimator and concludes on the reasonable finite sample performance of the new estimator.nonparametric estimation, instrumental variable, ill-posed inverse problem, iterative method, estimation by projection

Iterative Regularization in Nonparametric Instrumental Regression

We consider the nonparametric regression model with an additive error that is correlated with the explanatory variables. We suppose the existence of instrumental variables that are considered in this model for the identification and the estimation of the regression function. The nonparametric estimation by instrumental variables is an illposed linear inverse problem with an unknown but estimable operator. We provide a new estimator of the regression function using an iterative regularization method (the Landweber-Fridman method). The optimal number of iterations and the convergence of the mean square error of the resulting estimator are derived under both mild and severe degrees of ill-posedness. A Monte-Carlo exercise shows the impact of some parameters on the estimator and concludes on the reasonable finite sample performance of the new estimator.Nonparametric estimation; Instrumental variable; Ill-posed inverse problem

Semiparametric transformation model with endogeneity: a control function approach

We consider a semiparametric transformation model, in which the regression function has an additive nonparametric structure and the transformation of the response is\ud assumed to belong to some parametric family. We suppose that endogeneity is present\ud in the explanatory variables. Using a control function approach, we show that the pro-\ud posed model is identified under suitable assumptions, and propose a profile likelihood\ud estimation method for the transformation. The proposed estimator is shown to be\ud asymptotically normal under certain regularity conditions. A small simulation study\ud shows that the estimator behaves well in practice