Using state level data, a researcher wishes to examine the relationship between the median rent paid (RENT) as a function of median house values (MDHOUSE in

$1,000). The percentage of the state population living in an urban area (PCTURBAN)

is used as an additional control.

(a) The least squares estimates of the model are in column (1). Why might we be concerned that MEDHOUSE, the median price of houses, is endogenous in this regression?

(b) Four instruments are considered: median family income (FAMINC in $1,000)
and region of the country (REG1, REG2, REG3). Using the models in columns (2) and (3), test if the instruments are weak.

(c) In column (4) the least squares residuals (VHAT) from the regression in column (2) are added as a regressor to the basic regression. The estimates are obtained using least squares. What is the usefulness of this regression? What does it indicate about the results in (1)?

(d) In column (5) are IV/2SLS estimates using the instruments listed in part (b). What differences do you observe between these results and the least squares results in column (1)? Note that the estimates (though not the standard errors) are the same in columns (4) and (5). Is this a mistake? Explain.

(e) In column (6) the residuals from the estimation in (5) are regressed upon the variables shown. What information is contained in these results?

(1) (2) (3) (4) (5) (6) RENT MDHOUSE MDHOUSE RENT RENT EHAT C 125.9 -18.67 7.225 120.7 120.7 -62.85 (14.19) (12.00) (8.936) (12.43) (15.71) (26.95) PCTURBAN 0.525 0.182 0.616 0.0815 0.0815 -0.283 (0.249) (0.115) (0.131) (0.244) (0.305) (0.258) MDHOUSE 1.521 2.240 2.240 (0.228) (0.268) (0.339) FAMINC 2.731 4.448 (0.682) (1.532) REG2 -5.095 -6.768 (4.122) (9.262) REG3 -1.778 4.847 (4.073) REG4 13.41 (4.048) (9.151) -18.77 (9.096) VHAT -1.589 (0.398) N R SSE 50 50 50 0.669 0.691 0.317 20259.6 3767.6 8322.2 50 0.754 15054.0 50 50 0.599 0.226 24565.7 19019.9 Standard errors in parentheses