Semi‐parametric estimation of non‐separable models: a minimum distance from independence approach

Abstract

Abstract. This paper focuses on nonseparable structural models of the form Y = m(X, U, α 0 ) with U ⊥ X and in which the structural parameter α 0 contains both finite dimensional (θ 0 ) and infinite dimensional (h 0 ) unknown components.Our proposal is to estimate α 0 by a minimum distance from independence (MDI) criterion. We show that: (i) our estimator of h 0 is consistent and obtain rates of convergence; (ii) the estimator of θ 0 is √ n consistent and asymptotically normally distributed.

Point-identification in multivariate nonseparable triangular models

“…To conclude this section, we also want to stress again that Theorem 1 and its absolutely continuous counterpart from the appendix are not constructive identification results in the sense that they do not provide us with the function m. They just provide the identified set I which we prove to contain a single element m, just as the univariate result Torgovitsky (2015a) and d 'Haultfoeuille & Février (2015). There are ways to estimate the function m semi-parametrically like Komunjer & Santos (2010) or Torgovitsky ( 2016), but a fully nonparametric approach is still lacking. This is especially important to keep in mind in the following section where we show identification of the Hedonic model in multiple markets and identification of the BLP-model without index restrictions.…”

Minimum Integrated Distance Estimation in Simultaneous Equation Models

“…The estimator studied in this paper is also related to other alternative methods. For instance, Komunjer and Santos (2010) develop a semiparametric estimator for invertible nonseparable models with scalar latent variables and an infinite dimensional component. Santos (2011) proposes an M-estimator under the assumption that the model is strictly monotonic in the scalar error term and derives its corresponding asymptotic properties.…”