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In a linear dynamic model with heteroscedastic errors, we compare some aspects of ordinary least squares and least absolute error estimation. After deriving the properties of the estimators and the Wald, Lagrange multiplier and Likelihood ratio tests under a local alternative, we derive the Hausman test comparing the estimators. From this, and the equivalent generalized method of moment tests, we obtain as special cases tests for specification and symmetry based on the signs of the residuals from ordinary least squares. We also show that in the presence of heteroscedasticity, asymmetry can affect the estimates of all the parameters, not just the constant term.


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