Monte Carlo simulation problem

Hello! i am a new beginner of Gauss. I hope to do a monte carlo simulation with regression y= xB + error, and x are two a random variables from correlated bi-variate normal distribution.  It's any one know how to write the codes? Thank you!

1 Answer


You can use the function, rndMVn to take draws from the multivariate normal distribution and if you only want parameter estimates, you can use the slash operator '/' to compute least squares estimates. Something like this would work for a model with a zero intercept:

beta_true = { 1.2, -0.5 };

//Covariance between 'x1' and 'x2'
cov = {   1 0.6,
        0.6 1 };

//Mean of 'x1' and 'x2'
mu = { 0, 0 };

//Number of rows per draw of 'x'
r = 100;

//Number of iterations of Monte Carlo simulation
iters = 1e5;

//Pre-allocate vector to contain
//parameter estimates for all iterations
beta_hat = zeros(iters, 2);

for i(1, iters, 1);
    //Take draws from multivariate normal distribution
    //parameterized by 'mu' and 'cov' from above
    x = rndMVn(r, mu, cov);
    //Create error term: err ~ N(0, 1)
    err = rndn(r, 1);
    //Create simulated 'y'
    y = x * beta_true + err;
    //Estimate beta_1 and beta_2
    //Notice transpose operator
    beta_hat[i,.] = (y / x)';

After that you could draw a histogram of the estimated values of each estimated parameter:

//Draw histogram of beta_1
plotHistP(beta_hat[.,1], 30);

//Add histogram of beta_2 to plot
plotAddHistP(beta_hat[.,2], 30);

or calculate descriptive statistics, like this:

call dstatmt("", beta_hat);

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