[Gretl-users] problem with tsls in Monte Carlo simulation

First of all I wish a happy new year 2017. My problem is the following: Given the simultaneous system of equations withe the endegenous variables p and e, the exegenous variable A and the error terms u and v. * p = 1.5 + 0.5e + u * e = 2.5 + 0.5p -0.4A + v Say that we have β1 = 1.5, β2= 0.5 in (1) and α1 = 2.5, α2 = 0.5, α3 = -0.4 I want to estimate the parameter of e in the first equation p = 1.5 + 0.5e + u performing a Monte Carlo simulation. First I want to show that the OLS-estimation produces a bias in the estimation of e (see the script below). For u,v and A I create the following variables: series u = normal(0,1) series v = normal(0,1) series A = normal(0,1) Then I take the reduced form equations from the structurel form (1)/(2) to produce the endegenous variables p and e: series p = (2.75 - 0.2*A + 0.5*v + u)/0.75 series e = (3.25 - 0.4*A + 0.5*u + v)/0.75 The formulas are the result oft he following general (reduced) formulas: p = (β1 + α1* β2 + α3* β2*A + u + β2*v) / (1 – α2* β2) e = (α1 + α2* β1 + α3*A + v + α2*u) / (1 – α2* β2) Taking 500 times a sample of size N=50 and executing the OLS-regression p against e in (1) I collect the 500 estimated parameters in the variables koeff_beta1 and koeff_beta2. The frequency distribution for the coefficients of variable "e" looks very good! The mean value is „0.76283“ and „0.26283“ is nearly the expected bias of β2= 0.5 ( with an appropriate mathematical formula I calculated the bias and he gives me the value of 0.266 !!!). So all seems good. But when I perform an TSLS or IV-estimation (see below) of (1), using the external variable A as an instrument for e (what is allowed), I get for the estimated α2 the mean value „0.16681“ (instead of expected roughly 0.5). The test-statistic of chi-quadrat is 92024.584, that means no normality in the frequency distribution of α2 !!!! I got this (bad) result, when I changed the command „ols p const e“ to „tsls p const e ; const A“ or alternatively: ols e const A series e_dach = $yhat ols p const e_dach scalar koeff_beta2[t] = $coeff(e_dach) ------------------- gives the same result Is something wrong with the tsls – command or am I wrong using A as an instrument for e ? Here is my script: nulldata 500 series koeff_beta1 = 0 series koeff_beta2 = 0 set seed 16577899 smpl 1 50 #series A = 2 loop for (t=1; t<=500; t++) --quiet series u = normal(0,1) series v = normal(0,1) series A = normal(0,1) series p = (2.75 - 0.2*A + 0.5*v + u)/0.75 series e = (3.25 - 0.4*A + 0.5*u + v)/0.75 #tsls p const e ; const A alternative tsls !!!!!!!!! goes wrong ols p const e koeff_beta1[t] = $coeff(const) koeff_beta2[t] = $coeff(e) endloop smpl full Greetings Jürgen Malitte