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An example: unbiased and consistent estimate

This document outlines a method to obtain unbiased and consistent estimates of regression coefficients in a linear regression framework. Using a simulated dataset with a specified number of observations (n=10,000) and sampling times (T=30), the model incorporates two independent variables and noise. The process utilizes ordinary least squares (OLS) estimation to derive the coefficients, specifically beta1 and beta2. Finally, the average estimated values of these coefficients are printed, providing insight into the accuracy and reliability of the estimation process.

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An example: unbiased and consistent estimate

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  1. An example: unbiased and consistent estimate

  2. new; • format /m1 /rd 9,3; • T=30; @ the number of observations@ • n=10000; @ the number of sampling times@ • beta1=1; beta2=2.0; • Beta_e=zeros(n,2); • x1=1*Rndn(T,1); • x2=2*Rndn(T,1); • X=x1~x2;

  3. i=1; • do until i>n; • @ Data Gerneration Process: Y=beta1*X1+beta2*X2+e@ • e=Rndn(T,1); • Y=beta1*x1+beta2*x2+e;

  4. @ Parameter Estimation Process: Y=beta1*X1+beta2*x2+u @ • Beta_e[i,.]=olsqr(Y,X)'; • i=i+1; • endo; • print " the average value of the beta1 estimates"; • print meanc(Beta_e[.,1]); • print " the average value of the beta2 estimates"; • print meanc(Beta_e[.,2]);

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