Write a code that separately runs the first stage regression

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Reference no: EM132473246

Assignment -

Instructions - In what follows, the 'full' model considers x1 and x2, while the truncated model refers to a specification that only uses x1.Z1, Z2, Z3 and Z4 will be candidates for instrumental variables.

This is the Var-Cov matrix that I used for simulating the data:

Correlations	Const	x1	x2	Z1	Z2	Z3	Z4	eps
Const	1	0	0	0	0	0	0	0
x1	0	1	0.12	0.5	0	0.2	0.01	0.6
x2	0	0.12	1	0.4	0	0	0.001	0.02
Z1	0	0.5	0.4	1	0.6	0	0	0.6
Z2	0	0	0	0	1	0.4	0	0
Z3	0	0.2	0	0	0.4	1	0	0
Z4	0	0.01	0.001	0	0	0	1	0
eps	0	0.6	0.02	0.6	0	0	0	1

Here are the "true coefficients" I used to generate y4 and y5:

y4 = 0.48 + 1.18*x[1] + 0.72*x[2] + eps

y5 = 0.48 + 2.2*x[1] + 1.74*x[2] + 0.4*eps

Question - IV for starters

Compare the estimates of the full OLS model and the IV Regression. -Why are the estimated coefficients different?

Looking at the Var-Cov Matrix, what bias would you expect for x1 and what bias for x2?, calculate! (Hint: the X - matrix for calculating the bias consists of x1 and x2., i.e. you can disregard the z's and the constant for this calculation. E(X,u) is given by the "eps" - column)

Which of the X Variables is endogenous with y (e.g.asimultaneityproblem)?

You have 4 candidates that you can use as an instrumental variable for X1, but

- One is itself endogenous.

- One is a weak instrument

- One is irrelevant and

- Only one is valid.

Which is which?

Now try instrumenting for x2!

Before you go ahead, consider for each z if you can or cannot use it as instrument. Explain, why not, or, if you can, explain what the assumptions would be and explain the exclusion restriction.

Refer to the "IV-assumptions" in the Angristbook or on the slides for your argument.

Independent of your answer in the previous points: consider using Z4 as an instrument for X2:

- Do 2SLS, describe which steps you have to take?

- Write a code that separately runs the first stage and the second stage regression.

- Which of the two assumptions can you test? Is it satisfied?

- Rehash the MM-IV Estimator that we saw in class.

- What variables will you include in the Z matrix?

- Write a code that directly implements the estimator in matrix notation.

- Now interpret the coefficient estimates that you got In the direct IV and In the 2SLS.

- Share any thoughts, questions or confusion on this exercise. (Hint: it's likely that the final estimation result is not satisfactory - maybe you can see why, but don't worry if you cannot.)

Reference no: EM132473246

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