Instrumental variables

Question 1

What is the probability limit (PLIM)?

Answer 1

The variance of the distribution of the estimates… more samples means less variance

Question 2

How does measurement error impact a correct variable z?

Answer 2

Yi=B0+B1zi+v
the measurement error is xi=zi+w
Yi=B0+B1(xi-w)+v
=B0+B1xi+u (where u=v-B1w)

Question 3

How does measurement error impact the explanatory variable?

Answer 3

The coefficients will be biased towards zero and standard errors, t/f-tests are invalid

Question 4

How do we solve the issue of correlation between an explanatory variable and the disturbance term?

Answer 4

By using an instrumental variable: they are used to shock an endogenous independent variable that has a subsequent impact on y

Question 5

What are the three conditions for an instrumental variable?

Answer 5

1) Correlated with the variable it is instrumenting
2) Uncorrelated with the disturbance term in the regression equation
3) Must not be in the regression equation already

Question 6

How do we test if we need to use the IV or not?

Answer 6

We use the Durbin-Wu-Hausman test.
Null hypothesis: explanatory variable is uncorrelated with the error term… if true, OLS/IV are consistent.