Identification and estimation of local average derivatives in non-separable models without monotonicity
Stefan Hoderlein and
Econometrics Journal, 2009, vol. 12, issue 1, 1-25
In many structural economic models there are no good arguments for additive separability of the error. Recently, this motivated intensive research on non-separable structures. For instance, in Hoderlein and Mammen (2007) a non-separable model in the single equation case was considered, and it was established that in the absence of the frequently employed monotonicity assumption local average structural derivatives (LASD) are still identified. In this paper, we introduce an estimator for the LASD. The estimator we propose is based on local polynomial fitting of conditional quantiles. We derive its large sample distribution through a Bahadur representation, and give some related results, e.g. about the asymptotic behaviour of the quantile process. Moreover, we generalize the concept of LASD to include endogeneity of regressors and discuss the case of a multivariate dependent variable. We also consider identification of structured non-separable models, including single index and additive models. We discuss specification testing, as well as testing for endogeneity and for the impact of unobserved heterogeneity. We also show that fixed censoring can easily be addressed in this framework. Finally, we apply some of the concepts to demand analysis using British Consumer Data. Copyright The Author(s). Journal compilation Royal Economic Society 2009
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