Question

In a study of the effectiveness of cardiac catheterization, McClellan, McNeil and New- house (1994) used as an instrumental variable the difference between (a) the distance to the nearest hospital and (b) the distance to the nearest hospital performing cardiac catheterization. The data consists of a sample of elderly patients who had an acute my- ocardial infarction (heart attack) in 1987. Each patient either received a cardiac catheter or an alternative treatment. “Effectiveness” could be measured many ways, but suppose they considered the number of months the patient lived after the heart attack.

(i) What is the first stage regression? (That is, what are the dependent variable and the regressor(s) in this regression?)

(ii) What is the second stage regression?

Answer 1

(i)

Let y denote the number of months the patient lived after the heart attack.

Let x = 1 if patient received a cardiac catheter and x = 0 if patient received an alternative treatment.

The instrumental variable (z) is the difference between the distance to the nearest hospital and the distance to the nearest hospital performing cardiac catheterization.

In the first stage regression, the endogenous variable is regressed on all exogenous and instrument variables.

Thus, the dependent variable in first stage regression is x and the regressors is z. As, x is a categorical variable with 2 levels, we define the first stage regression in the form of logistics regression.

The first stage regression is,

If p < 0.5, we assume x = 0 and if p 0.5, we assume x = 1

(ii)

In the second stage regression,  the dependent variable is y and the regressor is the x (which is determined by the 1st stage regression).