| Theophile Azomahou, BETA, Universite Louis Pasteur |
| Semiparametric Estimation of Models with Spatially Dependent Unbalanced Panel Data |
| Session: C-10-19 Tuesday 15 August 2000 by Azomahou, Theophile |
| Edge effects structure is a methodological issue which may affect severely statistical inference in spatial processes. In a regression framework, when a spatial lag of the response variable is used as additional regressor, edge effects lead to mis-specification of the functional form. The resulting model contains then only part of the spatial influences. Therefore, it is revelant to have robust estimators for such mis-specification. This study provides theoretical and empirical advances on this topic. New insights are provided on the computation of the so-called "connectivity relation". While the balanced nature of a panel allows us to consider a fixed weighting scheme over time, unbalanced samples induce time varying spatial influences. I define two patterns of spatial dependence. Observations pertaining to the same group are characterized by a within-group spatial dependence, and groups are linked via a between spatial structure. It is shown that, under some conditions, the between dependence involves a weaker weighting structure than the within dependence. The resulting weights matrix is then included in a partially linear model, with unknown functional form that is expressed in terms of spatial process. I propose a two-stage semiparametric generalized method of moments type estimation procedure based on the kernel method. First, relying on an over identified model, a best instrumental variable estimator is computed, the residuals of which are used in a second stage to construct the GMM estimator. The performance of the kernel estimator depends on the strength of the dependence between observations and requires the computation of potentially T by N(N-1) spatial covariates. A "within" version of these estimators is also suggested and their asymptotic distribution stated. This framework is applied to a lattice sample from the French network of residential water distribution. The data represent an unbalanced panel of about a thousand households over a half year collection frequency from 1994 to 1997. Estimation results and tests clearly support the proposed approach. |