I have some Matlab code on using Monte Carlo Simulation and then OLS regression to estimate some coefficients. How is it possible to do this in Python?
see screenshot of code, or below
Define the true DGP parameters and distributions
% Set the parameters in the model
b1 = 5;
b2 = -2;
% The variance of the error term
sigma2 = 2;
% The sample length. We will play with three different sample sizes and see how this affects the results
N = [100 500 1000];
% The number of simulations
S = 1000;
Generate x data
% Generate the x values as draws from the multivariate normal distributions
% This is the correlation structure between the x's
Sigma = [0.7 0.4;
0.4 0.3];
% Simple way of drawing random numbers from the multivariate normal distribution
x = chol(Sigma)'*randn(2,max(N));
% Make the x1 and x2 variables
x1 = x(1,:)';
x2 = x(2,:)';
Monte Carlo simulation 1
y = b1*x1 + e is the true model
We will now simulate data from this model and then use OLS to estimate two versions of the model:
y = b1mc*x1 + e and
y = b1mc_2*x1 + b2*x2 + e
% Always good practive to allocate empty output before loops
b1mc = nan(S, numel(N));
b1mc_2 = nan(S, numel(N));
% Simple counter to use when allocating results into b1mc below
cnt = 1;
for n = N % Loop over the different sample sizes N
for s = 1 : S
% generate random errors
u = randn(n,1)*sqrt(sigma2);
% simulate the process
y = b1*x1(1:n) + u;
% Estimate coefficients by OLS (easy in Matlab) and save
b1mc(s,cnt) = x1(1:n)\y;
tmp = [x1(1:n) x2(1:n)]\y;
b1mc_2(s,cnt) = tmp(1); % Only save the first parameter
end
cnt = cnt + 1;
end
