Re: [Gretl-users] HOW TO CORRECT FOR HETEROSCEDASTICITY WHEN DEALING WITH NON POSITIVE NUMBERS IN EVIEWS

On Sat, 10 Oct 2015, Clive Nicholas wrote: On 9 October 2015 at 18:24, Allin Cottrell <cottrell(a)wfu.edu&gt; wrote: > > [...] > > For the record, then, let's point out that the two basic approaches to > >> heteroskedasticity in gretl -- namely, switching to "robust" standard >> errors, or switching from OLS to GLS via the "hsk" command -- do not >> require taking logs of negative numbers. The following script >> illustrates. >> The series y and x contain both positive and negative values, and the >> data-generating process is heteroskedastic by construction. >> >> <hansl> >> nulldata 50 >> set seed 3711 >> series x = normal() >> # generate heteroskedastic y >> series y = -1 + 3*x + normal()*x >> # verify we have negative values in both y and x >> print y x --byobs >> # run OLS >> ols y 0 x >> # try robust standard errors: no problem >> ols y 0 x --robust >> # try GLS: again, no problem >> hsk y 0 x >> </hansl> >> >> In this case the "hsk" command produces a closer approximation to the >> true >> x-slope of 3.0 (2.997, versus 3.098 from OLS), although obviously one >> would >> have to replicate the example a large number of times to verify that (as >> theory says) the hsk estimates are more efficient, given >> heteroskedasticity. >> > > [...] >> > > Very interesting things happen when you keep increasing the simulation > sample size by factors of 10. > > At N=500, the OLS estimate is closer to the true value of X (3.01) than > the > GLS estimate (3.06). At N=5000, they were pretty much identical, yet > further away from X than before (2.97). At N=50000, they both tended back > to the true value at 2.99. > > As Arthur Atkinson without his washboard would have said, "How queer!" > Actually (sorry, but) not really so interesting, or queer. The sample size is basically irrelevant. What matters is how many replications you run at a given sample size. Consider the following: <hansl> nulldata 50 set seed 3711 series x = normal() # generate heteroskedastic y series y = -1 + 3*x + normal()*x # verify we have negative values in both y and x print y x --byobs # run OLS ols y 0 x # try robust standard errors: no problem ols y 0 x --robust # try GLS: again, no problem hsk y 0 x scalar N=5000 matrix B1 = zeros(N, 2) loop i=1..N -q series y = -1 + 3*x + normal()*x ols y 0 x --quiet B1[i,1] = $coeff[2] hsk y 0 x --quiet B1[i,2] = $coeff[2] endloop eval meanc(B1) eval sdc(B1) </hansl> This produces (the tail of the output): ? eval meanc(B1) 3.0002 2.9993 ? eval sdc(B1) 0.26747 0.19028 Since heteroskedasticity does not bias the coefficient estimates it is unsurprising that the means of both columns are very close to 3.0 (the known "true" slope). But heteroskedasticity makes OLS inefficient compared to GLS, and that is amply confirmed by the substantially larger standard deviation of the estimated slopes under OLS (column 1 of matrix B1) relative to GLS (column 2). (Reckoned worth replying since this sort of thing shows off the ease of doing Monte Carlo in hansl.) Allin Cottrell _______________________________________________ Gretl-users mailing list Gretl-users(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-users