A comparison of bias approximations for the two-stage.
Abstract. We consider the bias of the 2SLS estimator in the linear instrumental variables regression with one endogenous regressor only. By using asymptotic expansion techniques we approximate 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments.
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Abstract. 2SLS is by far the most-used estimator for the simultaneous equation problem. However, it is now well-recognized that 2SLS can exhibit substantial finite sample (second-order) bias when the model is over-identified and the first stage partial R2 is low.
Michael R. Roberts, Toni M. Whited, in Handbook of the Economics of Finance, 2013. 2.3 Identifying and Discussing the Endogeneity Problem. Before discussing how to address endogeneity problems, we want to emphasize a more practical matter.A necessary first step in any empirical corporate finance study focused on disentangling alternative hypotheses or identifying causal effects is identifying.
If we are interested in bias, we take the expectation on both sides of the equation, when we are interested in consistency we take the probability limit instead. Now both and are random, so simply taking expectations will not get us anywhere unless we make some assumptions about the expected value of nonlinear combinations of the two.
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