Estimating Logistic Regressions with Two Stage Least Squares
8 Pages Posted: 7 Feb 2018 Last revised: 1 Jun 2018
Date Written: January 29, 2018
I develop an algorithm to estimate a flexible binary regression model with endogeneity by repeatedly solving a two-stage least squares problem; the algorithm is numerically stable and guaranteed to converge regardless of starting value. The method is numerically stable even when a successful outcome is rare because it has a uniformly small condition number, unlike Newton methods with maximum likelihood estimation whose condition number is unbounded across potential parameter values. The instrumental variable method does not require choosing a special regressor or making assumptions on the first stage relationship between covariates and instruments other than a rank restriction to ensure the instruments are relevant enough.
Keywords: logistic regression, nonlinear instrumental variables
JEL Classification: C25, C26
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