*
* Example 19.6 from page 585
*
open data tablef5-1[1].txt
calendar(q) 1950
data(format=prn,org=columns) 1950:1 2000:4 year qtr realgdp realcons realinvs realgovt realdpi $
  cpi_u m1 tbilrate unemp pop infl realint
*
set logc = log(realcons)
set logy = log(realgdp)
set delc = logc-logc{1}
set dely = logy-logy{1}
*
linreg logc
# constant logc{1 2} logy{0 1 2}
compute rss0=%rss,ndf0=%ndf
*
* This model tends to have multiple local minima for the sum of squared
* residuals, so getting good guess values is important. This takes the roots of
* the unrestricted own lags to start the lambda's. (If the roots are complex,
* we act as if the lag 2 coefficient is zero and use the remaining root).
*
nonlin mu b0 tau1 lambda2 tau2
compute mu=%beta(1),b0=%beta(4)
compute discrim=%beta(2)**2-4*%beta(3)
compute roots=%polyroots(%eqnlagpoly(0,logc))
if %rows(roots)==2
   compute lambda1=roots(1),lambda2=roots(2)
else
   compute lambda1=-%beta(2),lambda2=0.0
endif
compute tau1=lambda1,tau2=lambda2

frml comfac logc = mu+(tau1+lambda2)*logc{1}-(tau1*lambda2)*logc{2}+b0*logy-b0*(tau1+tau2)*logy{1}+b0*tau1*tau2*logy{2}
nlls(frml=comfac)
compute rss1=%rss
nonlin mu b0 tau1 tau2 lambda2=tau2
nlls(frml=comfac)
compute rss2=%rss
*
* Do the tests of the restrictions. The second test statistic in the text (1st
* printing) is missing the /2
*
cdf(title="Test of One Common Factor vs Zero") ftest (rss1-rss0)/(rss0/ndf0) 1 ndf0
cdf(title="Test of Two Common Factors vs Zero") ftest (rss2-rss0)/2/(rss0/ndf0) 2 ndf0