Describe the consequences of estimating an equation by OLS in the presence of an endogenous regressor. How can you overcome these obstacles? Present an alternative estimator and state its properties

What will be an ideal response?

Answer: In the case of an endogenous regressor, there is correlation between the variable and the error term. In this case, the OLS estimator is inconsistent. To get a consistent estimator in this situation, instrumental variable techniques, such as TSLS, should be used. If one or more valid instruments can be found, meaning that the instrument must be relevant and exogenous, then a consistent estimator can be derived. The relevance of instruments can be tested using the rule of thumb (a first-stage F-statistic of more than 10 in the TSLS estimator). The exogeneity of the instruments can be tested using the J-statistic. The test requires that there is at least one more instrument than endogenous regressors, i.e., that the equation is overidentified. In large samples the sampling distribution of the TSLS estimator is approximately normal, so that statistical inference can proceed as usual using the t-statistic, confidence intervals, or joint hypothesis tests involving the F-statistic. However, inference based on these statistics will be misleading in the case where instruments are not valid.