5. Endogeneity and instrumental variables

When is zero conditional mean assumption violated?

if X_i and e_i have non-zero covariance - Cov(X_i,e_i) =/ 0

or

If Z_i is ommited - Cov(X_i,Z_i) =/ 0

• X_i is endogenous

• Result, E(β₁hat) =/ β₁ - OLS estimator is biased

What are sources of endogeneity?

• Omitted variables - Cov(X_i,Z_i) =/ 0

• measurement error - Cov(X_i*,v_i) =/ 0

• Autocorrelation - Cov(Y_t-1,e_t) =/ 0

• Simultaneity - Cov(X_i,e_i) =/ 0

What is simultaneity?

aka reverse causality

Y_i a function of X_i and vide verse

Examples:

demand estimation

relationship btw good institutions and econ growth

Effect of policing on crime

What does endogeneity mean for the OLS estimator?

OLS estimate will be biased

How do we proceed?

some way to “break” the correlation btw the endogenous regressor (X_i) and the error term (e_i)

isolating the part of the variation in X_i that is uncorrelated with e_i

What assumptions do instrumental variables satisfy?

1. Instrument relevance

   • we require that the instrument is highly correlated with X_i

   • It is relevant for explaining variation in X_i -allows us to pin down Z ans X

2. Instrument exogeneity

   • we require that the instrument is uncorrelated with e_i

   • it is exogenous in the equation Y_i

IF these 2 are right we can use it

How do we use an instrumental variable to identify β₁?

What does an instrumental variable Z_i satisfy?

• relevance: Cov(Z_i, X_i) =/ 0

• exogeneity: Cov(Z_i, e_i) = 0

How do we demystify the instrumental variable of β₁?

What is the difference btw standard errors for IV vs OLS?

How can we obtain β₁^IV in practice?

What is a structural model?

What is first stage?

What is reduced form

What is second stage?

What does two-stage least squares look like graphically?

What is the 1st stage of two-stage least squares?

What is the 2nd stage of two-stage least squares?

How do you use two-stage least squares if we have more variables

What happens if our instrument is poor?

What is the Durbin-Wu Hausman test for endogeneity?

What are the uses of IV in applied economics papers?

build some intuition on instruments

• i.e. what is/has been a convincing use of IV