Statistics and Its Interface

Volume 1 (2008)

Number 2

Convergency and divergency of functional coefficient weak instrumental variables models

Pages: 333 – 346

DOI: http://dx.doi.org/10.4310/SII.2008.v1.n2.a11

Authors

Zongwu Cai (Department of Mathematics & Statistics, University of North Carolina at Charlotte, N.C., U.S.A.)

Henong Li (Department of Mathematics & Statistics, University of North Carolina at Charlotte, N.C., U.S.A.)

Abstract

In this paper, we consider a functional coefficient model under weak instrument assumptions as in Staiger and Stock (1997) and Hahn and Kuersteiner (2002). Under this functional coefficient representation, models are linear in endogenous components with coefficients governed by unknown functions of the predetermined exogenous variables.We propose a two-step estimation procedure to estimate the coefficient functions. We investigate how the limiting distribution of the proposed nonparametric estimator changes as the degree of weakness of instruments varies. As a result, our new theoretical findings are that the possible convergency of the proposed nonparametric estimator can be attained only for the nearly weak case and the rate of convergence for the nonparametric estimator for coefficient functions of endogenous variables is slower than the conventional rate. But the nonparametric estimator for coefficient functions of endogenous variables is divergent for both the weak and nearly non-identified cases. A Monte Carlo simulation is conducted to illustrate the finite sample performance of the resulting estimator and results support these theoretical findings.

Keywords

discontinuity, divergence, endogeneity, functional coefficient model, local linear fitting, simultaneous equations, weak instrumental variables

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