options crt;  ? 8e8
?  Note: enter version of TSP below, to reduce the number of
?  AR1 commands required.  If you have TSP 4.4 dated after
?  June 1998, enter the version as 4.5 .
?  
set version = 4.5;
in qual;
freq n;
smpl 1,54;
print ly1-ly5 lpr1-lpr5 ladr1-ladr5 lqual;
smpl 30,32;
print ladr1-ladr5;  ? (a)

smpl 2,54;
dot 1-5;
  olsq ly. c ly.(-1) lpr. ladr. lqual dmr pjf pnd;  ? (b.1)
  frml elast1 lreout. = ladr./(1-ly.(-1));
  frml elast2 lrequal. = lqual/(1-ly.(-1));
  analyz elast1 elast2;  ? (b.2)
enddot;

smpl 2,54;  ? AR1 will drop the first obs. properly
dot 1-5;
  if (version >= 4.5); then;
    ar1 ly. c ly.(-1) lpr. ladr. lqual dmr pjf pnd;  ? (c)
  else; do;
   ? Since there can be multiple local optima when there is a lagged
   ? dependent variable with AR(1), use HILU first to find the best one,
   ? and then use CORC to iterate to a precise solution.
   ? Note that this is automated in TSP 4.5 and later
    ar1(method=hilu) ly. c ly.(-1) lpr. ladr. lqual dmr pjf pnd;  ? (c)
    ar1(method=corc,rstart=@rho) ly. c ly.(-1) lpr. ladr. lqual dmr pjf pnd;
  enddo;
enddot;

title 'Exercise 8, part (d) - Cross-section het and AR(1) / Kmenta';
smpl 3,54;
const N,5;  ? 5 individuals (regions in Canada)
set T=@NOB;  ? specify number of individuals and time periods
list ydep ly;        ? put dependent variable name here
list Xs lylag lpr ladr lquals dmrs pjfs pnds;  ? put RHS variable names here
                     ? (do not include C;
                     ? C will be inserted automatically as CC)
?
?  Stack data so to that Proc Ar1het can be used.
mmake(vert) mly ly1-ly5;
mmake(vert) mlylag ly1(-1) ly2(-1) ly3(-1) ly4(-1) ly5(-1);
mmake(vert) mlpr lpr1-lpr5;
mmake(vert) mladr ladr1-ladr5;
dot lqual dmr pjf pnd;
  mmake(vert) m. . . . . . ;
enddot;
set nt = N*T;
smpl 1,nt;
dot ly lylag lpr ladr;
  unmake m. . ;
enddot;
dot lqual dmr pjf pnd;
  unmake m. .s ;
enddot;
?
ar1het;  ? call the Proc defined below

title 'Exercise 8, part (e) - same as (d) but drop obs. with zeros';
smpl 3,29 35,54;  ? drop obs. with zeros (also from lags)
set T=@NOB;
? Perform same stacking operations as in (d), but in this smaller sample
mmake(vert) mly ly1-ly5;
mmake(vert) mlylag ly1(-1) ly2(-1) ly3(-1) ly4(-1) ly5(-1);
mmake(vert) mlpr lpr1-lpr5;
mmake(vert) mladr ladr1-ladr5;
dot lqual dmr pjf pnd;
  mmake(vert) m. . . . . . ;
enddot;
set nt = N*T;
smpl 1,nt;
dot ly lylag lpr ladr;
  unmake m. . ;
enddot;
dot lqual dmr pjf pnd;
  unmake m. .s ;
enddot;
?
ar1het;  ? call the Proc defined below

?---------------------------------------------------
? Code from  ar1het.tsp  on TSP Examples web page
?
? Estimate the "Cross-sectionally Heteroskedastic and Timewise
? Autoregressive Model" on p.618-620 of Kmenta's "Elements of Econometrics",
? (1986).  We'll do the balanced case just to make it easier, but it
? could also be done for the unbalanced case.
?  by Clint Cummins  11/21/97  (code should run fine on TSP 4.3 or 4.4)
?
? Example of call:
?const N,5 T,160;  ? specify number of individuals and time periods
?list ydep y1;        ? put dependent variable name here
?list Xs x1 x2 x3;  ? put RHS variable names here (do not include C;
?                     ? C will be inserted automatically as CC)
?ar1het;  ? call the Proc defined below
?---------------------------------------------------
Proc ar1het;
  local y x cXs cc e id time i rho rtomr2 tmk s2u s2ui;
  supres smpl;
  ? save the y and X data in matrices, so that we may overwrite
  ? them in this Proc, and then restore them at the end.
  select 1;
  mmake y ydep;
  mmake x Xs;
  list cXs cc Xs;
  cc = 1;
  title 'OLS on original data';
  olsq(silent) ydep cXs;
  e = @res;
  trend id 0;
  id = 1 + int(id/t);  ? id = 1 for first T obs, 2 for second T, etc.
  trend(period=T) time;
  do i=1,n;  ? loop over individuals, creating y*, X*
    select (id=i) & (time>1);
    corr(noprint) e e(-1);  ? (12.26 B)
    set rho = @corr(2,1);
    ? overwrite the original y,X data with y*,X*  (12.27)
    dot ydep cXs;
      genr(static) . = . - rho*.(-1);
    enddot;
    set rtomr2 = sqrt(1-rho**2);
    select (id=i) & (time=1);
    dot ydep cXs;
      genr . = rtomr2* . ;
    enddot;
  enddo;
  select 1;
  ? run regression on rho-transformed data
  title 'GLS on rho-transformed data';
  olsq(silent) ydep cXs;
  ? compute residual variances (s2u) for each individual
  set tmk = T - @NCOEF;
  s2u = 0;
  do i=1,n;
    select id=i;
    mat s2ui = (@res'@res)/tmk;
    s2u = s2ui;
  enddo;
  ? create y**, X**
  select 1;
  dot ydep cXs;
    genr . = . / s2u ;
  enddot;
  title 'GLS on s2u- and rho-transformed data';
  olsq ydep cXs;
  title 'Alternative SEs for GLS, with degree of freedom adjustment';
  mat vcov = @vcov*((@nob-@ncoef)/(@nob-@ncoef-n*2));  ? rho & sig for each N
  tstats(names=@rnms) @coef vcov;
  ? restore original data
  unmake y ydep;
  unmake x Xs;
endproc;