Consider the regression model yi = β1 + β2x2i + β3x3i + ei where x2, is endogenous. Two potential instruments. zi and Z'2 t are available. Open this data set in Gretl and estimate the model using 2SLS with both instruments.
(a) Enter the sum of squared errors (SSE) of the 2SLS regression in the box below (rounded to 3 decimal places).
Conduct a Sargan test for instrument validity.
To get full marks for this question you will need to estimate the appropriate auxiliary regression equation and construct the test statistic 'manually'.
(b) In the box below, enter the estimate of the intercept term in the auxiliary regression (rounded to 3 decimal places).
(c) In the box below, enter the le of the auxiliary regression (rounded to 3 decimal places).
(d) Enter the value of the test statistic in the box below (rounded to 3 decimal places).
(e) Enter the critical value corresponding to a 1% significance level in the box below (rounded to 3 decimal places).
(f) Do you reject the null hypothesis?