Using your computer software, and the 50 observations on savings (y), income (x), and averaged income (z) in savings.dat,

(a) Estimate a least squares regression of savings on income.

(b) Estimate the relation between savings and income (x) using the instrumental variables estimator, with instrument z, using econometric software designed for instrumental variables, or two-stage least squares, estimation.

(c) Using the steps outlined in Section 10.4.1, carry out the Hausman test (via an artificial regression) for the existence of correlation between x and the random disturbance e.

(d) Use two least squares regressions to obtain the IVestimates in part (b). Compare the estimates, standard errors, and t-statistics to those in part

(b) and comment on the differences.