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Discussion Paper

Joint Distribution Theory for Some Statistics Based on LIML and TSLS

In the context of a single linear structural equation under classical assumptions, we derive the joint conditional density of the LIML endogenous coefficient estimator, and the usual characteristic root arising from the LIML procedure, given the OLS estimates of the reduced form coefficients for the excluded exogenous variables. This provides the joint distributions for various combinations of the statistics commonly used for inference in this model, and is hence an important stepping stone in the analysis of these procedures.