L11 - (PL) Endogeneity and IV Estimator

Question 1

What does a basic linear regression look like?

Answer 1

• y is the dependent variable,
• x is an explanatory variable or regressor,
• u is the error term or disturbance –> assumed obe normally distributed
• β’s are unknown parameters of interest to be estimated.

OLS estimator become inconsistent if the explanatory variable and the errors aren’t independent of each other –> OLS estimator can no longer be given a causal interpretation (marginal effect on Y as a exogenous change on X)

Question 2

Difference between Exogenous and Endogenous variables?

Answer 2

• Exogenous variable is determined outside the model and is imposed on the model ==> not correlated with the error term.
• The endogenous variable is determined by the model ==> correlated with the error term.

Question 3

Sources of Endogeneity?

Answer 3

• Omitted Variables
  
  • E(y|x,q) –> conditional expectation of interest (can be written as a linear function of parameter x and q)
    
    • if q is unobserved (part of the error term), and correlated to x –> x is therefore correlated to the error term and, therefore, endogenous
• Measurement Error
• Simultaneity

Question 4

How does endogeneity affect our coefficient estimates?

Answer 4

• Example if we want to estimate the returns to exogenous changes in schooling with a normal linear regression
  
  • u is thought to be correlated with educatoin because of other factors, for example omitted ability, quality of education and family background.

Question 5

What is the Instrumental Variable (IV) approach to dealing with endogeneity?

Answer 5

• General solution to find only the exogenous variation in x

Question 6

What are the properities of instrument z?

Answer 6

• z doesnt directly affect y, only indirectly through x
• We must sub the x_k formula including the instrument into our equation of interest (y = …)

Question 7

What is the IV Estimator?

Answer 7

• Both the indirect and direct effect included

Question 8

What is the efficiency of the IV Estimator?

Answer 8

Question 9

What is the Order Condition for the IV estimator?

Answer 9

• THe number of instruments must be at least equal to or greater than the number of independent endogenous components
  
  • If equal –> model is said to be just identified
  • If greater –> model is said to overidentified

Question 10

When do you use Two-Stage Least Squares?

Answer 10

• Most efficient estimator for IV when you have more than one variable
• OMITTED VARIABLES CAN ALSO BE TIME VARIANT

Question 11

What does 2SLS estimator help you decide?

Answer 11

Question 12

What are the stages of the 2SLS?

Answer 12