*
* Dougherty, Introduction to Econometrics, 4th ed
* Example from Section 12.3
* Fitting a model with AR(1) correction
*
open data demand.xls
calendar(a) 1959:1
data(format=xls,org=columns) 1959:01 2003:01 adm book busi clot date dent doc dpi flow food furn gas gaso $
 hous legl mags mass opht padm pbook pbusi pclot pdent pdoc pflow pfood pfurn pgas pgaso phous plegl $
 pmags pmass pop popht prelg ptele ptob ptoys ptpe relg tele time tob toys tpe
*
set lghous   = log(hous)
set lgdpi    = log(dpi)
set lgprhous = log(100.0*phous/ptpe)
*
* By NLLS
*
nonlin rho b1 b2 b3
frml ar1frml = rho*lghous{1}+b1*(1-rho)+b2*(lgdpi-rho*lgdpi{1})+b3*(lgprhous-rho*lgprhous{1})
nlls(frml=ar1frml) lghous
*
* By AR1
*
ar1 lghous
# constant lgdpi lgprhous
*
* The published results don't appear to be correct. With the estimated rho fed
* into AR1, we can reproduce the results in the book, but it's clearly a worse fit.
*
ar1(rho=.719102) lghous
# constant lgdpi lgprhous