# The null hypothesis tested is: E [Z’i vi] = 0

Since using IV when it is not necessary worsens our estimates, we would like to test whether the variables that worry us are indeed endogenous. This problem is addressed by the **Hausman test for endogeneity**, where the null hypothesis is . Thus, rejecting the null hypothesis indicates the existence of endogeneity and the need for instrumental variables.

## Use ivreg2 without small to obtain large-sample test statistic.) .

### the Durbin–Watson statistic is a test statistic ..

Note the difference in the null hypotheses if there aretwo or more endogenous regressors: the AP test will fail to reject if aparticular endogenous regressor is unidentified, whereas theAnderson/Cragg-Donald/Kleibergen-Paap tests of underidentification will fail toreject if of the endogenous regressors is unidentified.

### Implicit Nulls & Alternatives of Hypothesis ..

The Angrist-Pischke (AP) first-stage chi-squared and F statistics are tests ofunderidentification and weak identification, respectively, of individualendogenous regressors.

## to ensure that a Wald test for a null hypothesis is invariant to ..

. Also known as the . The Sargan test is based on the observation that the residuals should be uncorrelated with the set of exogenous variables if the instruments are truly exogenous. The Sargan test statistic can be calculated as TR² (the number of observations multiplied by the coefficient of determination) from the OLS regression of the residuals (from IV estimation) onto the set of exogenous variables.

## Enter the value of the test statistic in the box below ..

indicates that 2SLS is preferred over OLS at 5% level of significance. In this case, the null hypothesis of no measurement error is rejected. Hence, the instrumental variable estimator is required for this example due to the presence of measurement error.

## Do you reject the null hypothesis?

The version of this test that is robust to heteroskedasticity in the errors isHansen's J statistic; under the assumption of conditional homoskedasticity,Sargan's statistic becomes Hansen's J (see Hayashi (2000), p.