Instrumental variables - Inference of IV

5 important questions on Instrumental variables - Inference of IV

What is the null hypothesis and how do we test it?

The null hypothesis means H0: Bj=0 and we test it with the t statistic, which we use the t statistic for.

Under the MLR1-MLR6, what can be said in regards to the t distribution for the standardised estimators?

The estimate parameter divided by standard error of Bj can be correlated to the t distribution with degrees of freedom.

How do we test the one-sided alternative hypothesis H1: Bj > 0 and what do these values mean?

Under H1, we expect t value to be positive. We reject H0 if t > c, for some critical value c (one-tailed test).
The critical value c is chosen such that the probability of rejecting H0 when it is true equals some given significance level. (5 % level test, 95th percentile of the appropriate t distribution)
  • Higher grades + faster learning
  • Never study anything twice
  • 100% sure, 100% understanding
Discover Study Smart

When do you reject two-sided alternatives and what's different for the critical value?

The t-statistic is now absolute and if the significance level is e.g. 5 %, the 97.5th percentile of the t distribution will be taken.

What formula is used for testing other hypothesis about Bj?

We can test H0: Bj=a(j) against a one- or two-sided alternative using the alternative (centralized) t statistic 

The question on the page originate from the summary of the following study material:

  • A unique study and practice tool
  • Never study anything twice again
  • Get the grades you hope for
  • 100% sure, 100% understanding
Remember faster, study better. Scientifically proven.
Trustpilot Logo