THE EQUIVALENCE OF HAUSMAN AND LAGRANGE MULTIPLIER TESTS OF INDEPENDENCE BETWEEN DISTURBANCE AND A SUBSET OF STOCHASTIC REGRESSORS
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This note shows that the Hausman test and Lagrange Multiplier tests of independence between the disturbance term and a subset of stochastic regressors in a regression equation are algebraically equivalent if they are evaluated at the 2SLS estimates of parameters. 1985.