Uploaded November 2013 | Updated September 2026, 2 hours ago

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This video provides an example of Monte Carlo Simulation, using Ordinary Least Squares Estimators.

Check out oxbridge-tutor.co.uk/undergraduate-econometrics-course for course materials, and information regarding updates on each of the courses.

The Matlab code used in this simulation is shown below.

clear; close all; clc;



%Define the population parameters

alpha=1;

beta=1;



% Sample size n

n=10000;



% Number of samples m

m=1000;



% Store the estimated beta in a vector

beta_hat=zeros(m,1);





for i=1:m



%Generate independent variable randomly

x=4*randn(n,1);



%Generate errors in the population

e=randn(n,1);





%Generate the dependent variable

y=alpha+beta*x+e;



%Generate the LS estimates of alpha and beta using matrix formulation



X=[ones(n,1) x];



beta_hatvec=(inv((X'*X)))*X'*y;



% Pull out only the second component - the estimate of beta



beta_hat(i)=beta_hatvec(2);

end





zoom=0.8;

% Draw a histogram of the result

FigHandle = figure('Position', [750, 300, 1049*zoom, 895*zoom]);

hist(beta_hat,20)

xlabel('Beta hat')

ylabel('Frequency') Check out ben-lambert.com/econometrics-course-problem-sets-and-data for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: ben-lambert.com/bayesian Accompanying this series, there will be a book: amazon.co.uk/gp/product/1473916364/ref=pe_3140701_247401851_em_1p_0_ti