In this exercise, you are the data scientist for an hospital. The director of the data division wants to know which factors determine expenditure on medical services. The dataset is an extract (that is, a cross section) of patients, over the age of 65 years, who have been treated at this hospital.

LMEDEXP=-2.0543+0.1086PRIVATEINSURANCE+0.4389TOTCHR + 0.2012AGE-0.0013AGE2+0.0455FEMALE +0.0411LINCOME

(se) (2.1853) (0.0377) (0.0137) (0.057063) (0.000370) (0.036741) (0.019860)

R^2=0.1804

where medexpi denotes the dollar amount of out-of-pocket medical expenditure for individual i (out-of-pocket expenditure means expenditure paid directly by the patient); private insurancei is a dummy variable that takes the value of 1 if individual i has private insurance and zero otherwise; totchri is the total number of chronic conditions that individual i is diagnosed with; agei is age in years; femalei is a dummy variable that takes the value of 1 if individual i is a female and zero otherwise; and incomei denotes income.

1. Interpret the estimated coefficients. Do the results corroborate your expectations (in terms of sign and statistical significance)?

2. What assumptions of the classical linear regression model are likely to be violated? Discuss what the problem might be. Also, what are the properties of the OLS estimator in this case in terms of unbiasedness and consistency?

3. Consider an instrument called ssiratioi, which denotes the ratio of an individuals social security income over individual income from all sources. High values indicate a significant income constraint, i.e. most income comes from social security services. Justify the reason behind which ssiratioi is likely to be a relevant instrument. What is the expected sign of the correlation between the instrument and the endogenous regressor?