Question

1. Your right-hand-side variable is likely correlated with some unobservable characteristics of the people in your sample which are important for explaining your left-hand-side variable. You have two potential instruments that you believe might be correlated with your RHS variable but not with the unobservables.
   1. What test could you perform to determine if instrumental variables are necessary for consistent estimates? What is the intuition behind this test?
   2. What test could you use to check the assumption that your instruments are uncorrelated with the unobservables? Give an intuitive explanation of this test
   3. Assuming that the test in a. says that you need to do IV and that the test in b. fails to reject that your instruments are exogenous, will your estimates be biased? How might you know how badly biased?

Answer 1

a) here we could check Convergence in square mean.

  

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* we can use CHI SQUARE TEST FOR GOODNESS OF FIT. in the test collected data are classified into different categories or groups according to one or more attributes

(b) Here we can apply

(1) WILCOXON MATCHED PAIR SIGNED RANK TEST : This test account the information of signs as well as of magnitude of differences.

(2) KOLMOGOROV SMIRNOV TWO SAMPLE TEST : This test is based on the comparison of empirical (sample) cumulative distributions functions from the sample data as the proportion of the number of sample observations less than or equal to some number to the number of observation

(c) Normally if the expected value of the estimator does not equal to the true value of parameter, then the estimator is said to be biased estimator that is E(T)≠θ

the amount of biasness is given by :

IF