nulldata 1000
set seed 16577899
scalar umf_sample = 1000
series a = 0
matrix tab_beta = a
loop for (t=1; t<= umf_sample; t++) --quiet
    smpl 1 20
    res = normal(0,1)
    matrix m_Quadratmeter = {40,55,28,81,107,130,74.5,96,63,46,37.5,150,87,30,65,70,92,49,83,105}
    series Quadratmeter = m_Quadratmeter
    series Miete = 9.33 + 9.18*Quadratmeter + res
    ols Miete const Quadratmeter    --quiet
    scalar beta = $coeff(Quadratmeter)
    smpl 1 umf_sample
    tab_beta[t:t,1] = beta
endloop
series a = tab_beta
printf "Schätzer beta = %.6f ", mean(a)

Try it with umf_sample (=Sample size) = 20, 100, 500 and you will see, that beta (the beta coefficient) will be nearer to the value 9.18.

I construct the variable Miete with residuals and values of m_Quadratmeter. The residuals (variable res) are constructed with the command normal(0,1). Therefore they have mean 0 and std-error 1.

All 20 (100, 500) beta-values are saved in a tab_beta with size 20 (100,500). At end the mean ist calculated. The higher

the sample_size, the more precise is the variable a (in aspect of the value 9.18 !!!). That is what you want !!!

Dear all,

I have been having some troubles computing a Monte Carlo simulation.

I am a student, so please don't be too horrified by my short experience :)

The problem is the following:

I am requested to perform a MC simulation on a lagged-dependent variable model with autocorrelated residuals. The estimator for the lagged-dependent variable, the only regressor, should be inconsistent and biased.

My concern is that decreasing the sample size the bias decreases, and I guess that that's just wrong.

(I also tried using robust std errors, and nothing changes!)

here's the code I used:

nulldata 200
setobs --time-series

scalar n=$nobs

scalar beta1=0.8
scalar rho=0.4

smpl 1 1
series u=0
series y=0

smpl 2 200
series e=randgen(N,0,1)
series u=rho*u(-1)+e
series y=beta1*y(-1)+u

ols y y(-1) --simple

loop 5000 --progressive --quiet

series e=randgen(N,0,1)
series u=rho*u(-1)+e
series y=beta1*y(-1)+u

ols y y(-1)

scalar beta1hat= $coeff(y_1)
scalar s1= $stderr(y_1)
scalar bias=$coeff(y_1)-beta1
genr LB = beta1hat - critical(t,$df,0.025)*s1
genr UB = beta1hat + critical(t,$df,0.025)*s1
print beta1 beta1hat bias LB UB

endloop

smpl 50 --random --replace

loop 5000 --progressive --quiet

series e=randgen(N,0,1)
series u=rho*u(-1)+e
series y=beta1*y(-1)+u

ols y y(-1)

scalar beta1hat= $coeff(y_1)
scalar s1= $stderr(y_1)
scalar bias=$coeff(y_1)-beta1
genr LB = beta1hat - critical(t,$df,0.025)*s1
genr UB = beta1hat + critical(t,$df,0.025)*s1
print beta1 beta1hat bias LB UB

endloop

Thank you so much