BST169: Course Work Project
Students should work individually to prepare a study of the following investigation. Every student should submit an electronic copy of the report and the R script file via Learning Central.
The project report should contain no more than 2,000 words (not includ- ing titles, appendices, formulas, tables and/or graphs). All pages, equations, tables and figures should be numbered. Tables and figures should be given proper captions and comments of explanation when necessary.
Topic 1 Suppose our true model is:
yi = α0 + α1x1i + α2x2i + eiexp(x1i),
where ei ∼ N(0,0.012) and the data generating processes of x1 and x2 are as follow,
x1i = γz1i + z2i + u1i, x2i = ωu1i + u2i.
z1 and z2 are exogenous variables generated from some distribution of your choice. u1i and u2i are zero mean random noises. Suppose you cannot observe x2i and have to estimate the equation below.
yi =β0 +β1x1i +εi, i=1,2,…,N. (1)
• Please investigate the following issues with different sample sizes and support your arguments with both algebraic proof and Monte Carlo ex- periment results.
1. If one estiamte α1 through (1) with OLS, what are the finite sample and asymptotic bias? How will the value of ω affect the bias?
2. One could include z1i as an instrument to estimate (1) by 2SLS or 3SLS. What is the finite sample bias of 2SLS? How will the value of γ affect the performance of the 2SLS/3SLS estimators?
3. One could also include z2i along with z1i to perform 2SLS/3SLS. For different estimators, which estimator has the least bias and which estimator is the most efficient?
• Given the data “pbpiv.csv”, which estimator will you use to estimate (1)? Why? Does your chosen estimator follow normal distribution? How can you verify it?
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