Question

3. Consider the following model:

health = Bo + ß1age + β2weight + β3height + β4male + ß5work + β6 exercise + u1

where health is some quantitative measure of the person's health; age, weight, height, male are the person's characteristics; work is weekly hours worked; and exercise is the hours of exercise per week.

a) Should you be concerned about exercise being correlated with u1? Explain your answer.

b) Suppose you can collect data on two additional variables, disthome and distwork, the distances from home and from work to the nearest gym. Discuss whether these are likely to be uncorrelated with u1 .

c) Now assume that disthome and distwork are indeed uncorrelated with u1. Write down the reduced form for exercise. State the conditions under which the parameters of the equation above are identified.

d) How can the identification assumption in part in letter c) be tested?

Answer 1

A) exercise can be correlated with the u1 as in the regression model income is not taken. If a person has more income then he will be able to purchase the gadgets required to exercise and also if income is low then he can't join a gym club as well. So obviously the omitted variables bias is occurring here which leads to the problem of endogeneity.

B) obviously disthome and distwork from gym is not correlated with the other factors such as income or willingness to exercise or other unobservable genetic features of health. So this two variables will not cause the endogenous variables regression problem. They are uncorrelated with u1.

C) the RF will be health= b0+b1*age +b2*weight+b3*height+b4*disthome +b5*male +b6* exercise+b7*work+b8* distwork+v1

And if health and exercise are jointly determined variables then again exercise will be function of health and other exogenous variables. Then the rank condition must be satisfied. Which can be calculated from the data and the parameters given.

D) first check the order condition then check the rank condition. That is no of excluded exogenous variables in a equation greater than eq to no of inclufei endogenous variables in a equation given the structural form in the a part of the question. The equation is given in the question. Here health and exercise can be seen as endogenous variables. Other variable are exogenous.