1. Consider the following linear model: y=Bo+ B1x1 + B2x2 + U₂ where x₁ is exogenous and x2 is endogenous, i.e., Cov(x2, u) ‡ 0. a) Suppose there is a variable, z. Write down the required assumptions for z to be a valid instrument. Which of these assumptions can be tested in the sample? [5 marks] b) Suppose we want to estimate the model by 2SLS. State the first stage regression and the second stage regression that you need to run. Are the estimated standard errors in the second stage correct? Explain. [5 marks] c) State the reduced form regression. Explain how would you obtain the 2SLS estimates from the reduced form and first stage regressions.
