Instrumental variable estimation based on grouped data

Abstract

* We would like to thank Tom Wansbeek, Ton Steerneman, Eric Zivot and anonymous referees for helpful comments. ABSTRACTThe paper considers the estimation of the coefficients of a single equation in the presence of dummy intruments. We derive pseudo ML and GMM estimators based on moment restrictions induced either by the structural form or by the reduced form of the model.The performance of the estimators is evaluated for the non-Gaussian case. We allow for heteroscedasticity. The asymptotic distributions are based on parameter sequences where the number of instruments increases at the same rate as the sample size. Relaxing the usual Gaussian assumption is shown to affect the normal asymptotic distributions. As a result also recently suggested new specification tests for the validity of instruments depend on Gaussianity. Monte Carlo simulations confirm the accuracy of the asymptotic approach.

Instrumental variable estimation with heteroskedasticity and many instruments

“…The inconsistency of LIML was pointed out by Bekker and van der Ploeg (2005) and Chao and Swanson (2004) in special cases. We give a characterization of the inconsistency here, showing the precise restriction on the heteroskedasticity that would be needed for LIML to be consistent.…”

Asymptotic Distribution of Jive in a Heteroskedastic Iv Regression With Many Instruments

“…Bekker and van der Ploeg (2005), Ackerberg and Devereux (2009), Chao and Swanson (2006), and Hausman et al (2007)). The main objective of this paper is to develop asymptotic theory for the JIV estimators in a setting that includes the many instrument sequence of Kunitomo (1980), Morimune (1983), and Bekker (1994) and the many weak instrument sequence of Chao and Swanson (2005).…”

Asymptotics of Diagonal Elements of Projection Matrices Under Many Instruments/Regressors

“…In the well known case of grouped data (Bekker and van der Ploeg, 2005), if the group sizes are not equal, the diagonal of the instrument projection matrix is generally asymptotically heterogeneous. Let us assume that all observations are split into l groups and proceed by brute force.…”

“…A well-known example in the literature is the case of grouped data (Bekker and van der Ploeg, 2005) where the instruments are indicator variables. The instrument design in this example is deterministic and hence does not fit in our IID framework.…”

“…It is important to know the circumstances under which an asymptotically balanced design may or may not occur, on the one hand, and how much distortion a failure of this property may create, on the other. 2 One well-known example encountered in previous literature is the case of grouped data (Bekker and van der Ploeg, 2005) where the instruments are indicator variables. If group sizes are equal, it is known that the diagonal of the instrument projection matrix is asymptotically homogeneous (e.g., van Hasselt, 2010), and is asymptotically heterogeneous otherwise.…”