The Robustness of the Higher-Order 2SLS and General k-Class Bias Approximations to Non-Normal Disturbances
نویسندگان
چکیده
In a seminal paper Nagar (1959) obtained rst and second moment approximations for the k-class of estimators in a general static simultaneous equation model under the assumption that the structural disturbances were i.i.d and normally distributed.Later Mikhail (1972) obtained a higher-order bias approximation for 2SLS under the same assumptions as Nagar while Iglesias and Phillips (2010) obtained the higher order approximation for the general k-class of estimators. These approximations show that the higher order biases can be important especially in highly overidenti ed cases. In this paper we show that Mikhails higher order bias approximation for 2SLS continues to be valid under symmetric, but not necessarily normal, disturbances with an arbtrary degree of kurtosis but not when the disturbances are asymmetric. A modi ed approximation for the 2SLS bias is then obtained which includes the case of asymmetric disturbances. The results are then extended to the general k class of estimators.
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