Using state level data, a researcher wishes to examine the relationship between the median rent paid (RENT)

Question:

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 \$$1000).$ The percentage of the state population living in an urban area (PCTURBAN) is used as an additional control. Use the results in Table 10.3 to answer the following questions.

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

b. Two instruments are considered: median family income (FAMINC in $\$ 1000$ ) and a regional dummy variable REG4. 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 OLS. 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 OLS 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 column (5) are regressed upon the variables shown. What information is contained in these results?

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