ECON6300/7320/8300 Advanced Microeconometrics Bootstrap
Christiern Rose 1University of Queensland
Practical 7 April 2019
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Introduction
This class will review:
Bootstrap without asymptotic refinement
Bootstrap with asymptotic refinement Clustered bootstrap
Residual bootstrap
We begin with a demonstration using the data from Microeconometrics using STATA chapter 3 (Health and insurance data)
We move on to a Monte-Carlo based practical.
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Practical
In this practical you will conduct a Monte-Carlo experiment to assess the distribution of the OLS estimator under endogeneity.
The data generating process is:
yi = βxi + ui i = 1, …, N
α1zi +α2ui +vi x i = α 12 + α 2 2 + 1
ui ∼ N(0,1),zi ∼ N(0,1),vi ∼ N(0,1)
Note: We scale xi by α12 +α2 +1 so that xi ∼ N(0,1). Consequently, we can vary α1, α2 without changing the
marginal distribution of xi , though clearly we change it’s joint distribution with zi , ui , vi .
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Practical
1. For which value(s) of α1 , α2 does E[ui |xi ] = 0? For which
value(s) does E[ui |zi ] = 0?
2. Write a program to generate the data, compute the OLS
and 2SLS estimators of β, and store them as scalars. Togeneratethedata,useN=500,β=1and
α1 =α2 =0.5.
For the 2SLS estimator, use zi as the instrument.
3. Conduct a Monte-Carlo experiment with 1000 replications
in order to obtain the distributions of βOLS and β2SLS.
4. Summarize βOLS and β2SLS and produce a histogram of their distributions. What do you conclude about the estimators?
5. Repeat 2-4 setting α1 = 0.5, α2 = 0. Explain why your results change.
6. Repeat 2-4 setting α1 = 0, α2 = 0.5. Explain why your results change.
7. Repeat 2-4 using N = 10, 000. Explain why your results change.
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