(b) A researcher is interested in the effect of military service on human capita

Question

(b) A researcher is interested in the effect of military service on human capital. He collects data from a random sample of 4000 workers aged 40 and runs the regression y_i = beta_0 + beta_1 x_i + u_i, where y_i indicates the worker's annual earning and x_i is a binary variable that takes value 1 if the individual i served in the military and 0 otherwise. (i) Explain why OLS estimates are likely to be unreliable. In particular, think of which variables might be omitted from the regression. Are these valiables potentially correlated with x? (ii) During the Vietnam war there was a round of enrolment to military service based on a random lottery. Explain how the lottery can be used as an instrument to estimate the effect of military service on earnings.

Explanation / Answer

Solution:

i) According to the information given, the bias created due to ommitted variables will be the major apprehension here. In other words, running a regression for a worker's annual earnings on military service will have too many omitted variables. If there is any variable which is correlated with the serving in the military and that variable which is correlated with serving in the military and that variable is also affecting the annual earnings, then it will lead to occurrence of bias in the estimates.
For example, some military personnel are reservists which mean they may have both civilian and military careers. Motivation and teamwork propensity are some reasons people join the military which may also impact career earnings. In other words, the persons who found it more difficult to get job in some other field than military might get enrolled in military. It will affect the estimates by creating downward bias.

ii) According to the information given, the two-stage least squares method can be used in order to estimate the effect of serving in the military by making of the birth date, where the birth date can be used as an instrumental variable. The draft can be seen as a random sampling which was chosen independently, so that the impact on annual earnings due to military services possibly is captured by an instrumental variable lottery. With the relevance of a draft, the decision to join the military is no longer correlated with individual decisions and characteristics for military service. However, it is xpected that the relevance condition should be satisfied because a person's date of birth would be correlated with serving in the military or not.
On the other hand, if the exogeneity condition is to be validated, then there will be requirement of the assumption that the effect on earnings, due to birth date, is only because of the presence of the lottery resolves the issue of whether to serve or not.

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