ECON 7331 ECONOMETRIC THEORY Tutorial 4 Questions
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ECON 7331 ECONOMETRIC THEORY
Tutorial 4 Questions
(for 26 August 2021)
1. Consider the linear model
y = B1 ı + B2 x + u
where y e Rn , E[∈lX] = 0, and V [Elx] = σ I2n . Write explicitly:
a. P1 y
b. M1 y
2. Consider the linear regression
y = B1 ı + X2 B2 + u
where ı is an n-vector of 1s, and X2 is an n x (k - 1) matrix of observations on the remaining regressors. Show, using the FWL Theorem, that the OLS estimators B1 and B2 can be written as
/ 、 /0(n) X、_ 1 /Xı\21 y、
where, as usual, M1 is the matrix that takes deviations from the sample mean.
3. Show FWL Theorem holds in a model
y = X1 B1 + X2 B2 + u
using R. (please set the seed to 89 when generating vectors).
Hint: For OLS regress y on X1 and X2 . For FWL, regress y on X1 , X2 on X1 and use residuals.
2022-08-29