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A Natural Robustification of the Ordinary Instrumental Variables Estimator

Tuesday, March 4, 2014 - 11:00
Ruben Zamar, Professor, UBC Department of Statistics
Statistics Seminar
Room 4192, Earth Sciences Building (2207 Main Mall)

Speaker:  Ruben Zamar

Instrumental variables estimators are designed to provide consistent parameter estimates for linear regression models when some covariates are correlated with the error term. We propose a new robust instrumental variables estimator (RIV) which is a natural robustification of the ordinary instrumental variables estimator (OIV). Specifically, we construct RIV using a robust multivariate location and scatter S-estimator to robustify the solution of the estimating equations that define OIV.
RIV is computationally inexpensive and readily available for applications through the R-library riv. It has attractive robustness and asymptotic properties, including:

- high resilience to outliers,
- bounded inuence function,
- consistency under weak distributional assumptions,
- asymptotic normality under mild regularity conditions, and
- equivariance.

We further endow RIV with an iterative algorithm which allows for the estimation of models with endogenous continuous covariates and exogenous dummy covariates. We study the performance of RIV when the data contains outliers using an extensive Monte Carlo simulation study and by applying it to a limited-access dataset from the Framingham Heart Study-Cohort to estimate the effect of long-term systolic blood pressure on left atrial size.

Key words: Endogenous covariate; instrumental variable; robust estimation; S-estimator.

Joint work with

-Gaby Cohen (Statistics, UBC) and
-Hernan Ortiz-Molina (Sauder School of Business, UBC)