Question

(Stock and Watson #12.7) In an instrumental variable regression model with one regressor, X iand two instruments, 1Z 1i and Z 2i the value of the J-statistic is:

a) Related to the covariance matrix of the instruments
b) Calculated as the ratio of the variance of the instruments to the variance of the error term
c) A measure of the joint significance of the instruments
d) Unrelated to the quality of the instruments used in the regression

Answer 1

The J-statistic in an instrumental variable regression model assesses the joint significance of the instruments, indicating their validity and relevance to the model, but not necessarily their quality beyond statistical significance.

Step-by-step explanation:

In an instrumental variable regression model with one regressor, X and two instruments, Z1 and Z2, the value of the J-statistic is primarily a measure of the joint significance of the instruments. This means it assesses whether the instruments are valid, i.e., whether they are correlated with the endogenous regressor X and uncorrelated with the error term. Despite the intricacies of the calculation, it's critical to recognize that a significant J-statistic suggests that the instruments are relevant and the model is correctly specified. However, it does not directly comment on the quality of the instruments beyond their statistical significance. Therefore, the correct answer is that the J-statistic is a measure of the joint significance of the instruments. The J-statistic is related to the performance of the instruments in the context of an instrumental variable regression analysis.