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ECONOMETRICS AND BUSINESS STATISTICS

APPLIED ECONOMETRICS

Tutorial 5

Exercise 1 In this exercise we will investigate which factors determine expenditure on medical ser- vices . The dataset (on Moodle) is an extract from the Medical Expenditure Panel Survey (“medi- cal survey.xlsx”) and contains individuals over the age of 65 years . We consider the following model:

log (medexpi ) = α+β1 ×private insurancei +β2 ×totchri +β3 ×agei +β4 ×agei(2)+β5 ×femalei +β6 ×log (incomei )+ui ; where

❼ 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);

❼ private insurancei is a dummy variable that takes the value of 1 if individual i has private

insurance and zero otherwise;

❼ totchri is the total number of chronic conditions that individual i is diagnosed with; ❼ agei is age in years;

❼ femalei is a dummy variable that takes the value of 1 if individual i is a female and zero otherwise; ❼ incomei denotes income.

1. Estimate the model above using OLS. Provide a detailed interpretation for each estimated coeﬃ- cient. 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 individual’s social secu- rity 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? Estimate the model above using the 2SLS (IV) estimator. Treat all other variables as exogenous. Do the results corroborate your expectations (in terms of sign and statistical signiﬁcance)?

4. Consider an additional instrument, lowincomei , which is a qualitative indicator of low-income status. Justify why this variable may be a relevant instrument. Estimate the model above using the 2SLS (IV) estimator with both instruments. Do the results corroborate your expectations (in terms of sign and statistical signiﬁcance)? What is the main diﬀerence between these results and those in question 3?

5. Test for exogeneity vs. endogeneity using the Hausman-Wu test. What is your conclusion?

6. Test for weak instruments using the F-test. What is your conclusion?

7. Test for the validity of your instruments. What is your conclusion? Is the IV estimator consistent?

Exercise 2 Consider the following demand and supply model:

Demand: Qt = α0 + α1 Pt + α2 It + u1t, α 1 < 0, α2 > 0

Supply: Qt = β0 + β1 Pt + β2 Pt − 1 + u2t, β 1 > 0, β2 > 0

Qt(d) = Qt(s)

1. Derive the reduced form equations.

2. Deduce the structural form parameters from the reduced form equations.

3. Is the supply function identiﬁed? The demand function? What about the system as a whole?

Exercise 3 One way of writing a Cobb-Douglas production function and its ﬁrst- order conditions for proﬁt maximization is:

ln(Kt ) = α2 + ln(Pt ) + ln(Yt ) - ln(Rt ) + e2t (2)

ln(Lt ) = α3 + ln(Pt ) + ln(Yt ) - ln(Wt ) + e3t (3)

Equation (1) above deﬁnes the production function. Equations (2) and (3) come from the assump- tion that each ﬁrm is maximizing proﬁts. At period t the ﬁrm faces costs Pt (price), Rt (interest rate) and Wt (wages). Given these costs, we assume that the ﬁrm chooses input levels Lt (Labour) and Kt (capital) and output Yt so as to maximize proﬁts. The existence of the errors means the ﬁrms are maximizing proﬁts “on average”, rather than “exactly” .

Given that Yt , Kt and Lt are simultaneously determined by equations (1), (2) and (3), and Pt , Rt and Wt are determined from outside, it seems appropriate to treat the three equations as a simultaneous system where Yt , Kt and Lt are the endogenous variables and Pt , Rt and Wt are the exogenous variables.

(a) Determine whether the production function (1), the capital function (2) and the labour function (3) are identiﬁed or not.

(b) Show that the reduced form equation for Yt (known in economics as a supply function) can

be written as

ln(Yt ) = π1 + π2 ln ╱ _ + π3 ln ╱ _ + υt ,