options crt;  ? 10e5
in lucas;
freq a;
smpl 29,65;
y1 = log(n/pop);
y2 = log(ql*n/rgnp);
y3 = log(hw);
y4 = log(hw/ql);
x2 = log(rgnp/pop);
x3 = log(ql);
smpl 30,65;
x1 = log(pgnp/pgnp(-1));
x4 = log(rgnp/rgnp(-1));
y5 = log(hw/hw(-1));

title 'Exercise 5, part (a)';
regopt(lmlags=2) ;  ? turn on Breusch-Godfrey LM AR test
olsq y3 c y3(-1) x1 x2 x3 y2(-1) x4 y1(-1);  ? (10.41)
  resy3 = @res;
  copy @dhalt dm3a; ? note:  "Durbin's h alternative" = "Durbin's m"
  copy @lmar2 bg3a;
olsq y1 c y3(-1) x1 x2 x3 y2(-1) x4 y1(-1);  ? (10.42)
  resy1 = @res;
  copy @dhalt dm1a;  ? same as @lmar1, by the way
  copy @lmar2 bg1a;
regopt(lmlags=0);  ? turn off automatic B-G tests
?  Note:  the Durbin-Watson is not completely inappropriate for
?  testing for serial correlation with lagged dependent variables.
?  Although it is biased towards 2 (and its P-value is biased towards 1),
?  it usually has more power than Durbin's h and Durbin's m (h alternative).
?  So it can sometimes still detect serial correlation when h and m do
?  not find it.  However, it is still true that a large DW (and large
?  P-value) do not mean that one should conclude that rho=0.

title "Exercise 5, part (b) - Durbin's m";  ? use " when title contains ' .
smpl 31,65;
olsq(silent) resy3 c y3(-1) x1 x2 x3 y2(-1) x4 y1(-1) resy3(-1);
   set dm3 = @t(9);
   print dm3,dm3a;
   cdf dm3;
olsq(silent) resy1 c y3(-1) x1 x2 x3 y2(-1) x4 y1(-1) resy1(-1);
   set dm1 = @t(9);
   print dm1,dm1a;
   cdf dm1;

title 'Exercise 5, part (c) - Breusch-Godfrey LM AR test';
smpl 32,65;
olsq(silent) resy3 c y3(-1) x1 x2 x3 y2(-1) x4 y1(-1) resy3(-1) resy3(-2);
   ? use ANALYZ to compute F-test and chi-squared test
   frml r1 resy3(-1); frml r2 resy3(-2);
   analyz r1 r2;
   print @wald bg3a;
olsq(silent) resy1 c y3(-1) x1 x2 x3 y2(-1) x4 y1(-1) resy1(-1) resy1(-2);
   frml r1 resy1(-1); frml r2 resy1(-2);
   analyz r1 r2;
   print @wald bg1a;

title 'Exercise 5, part (d) - Breusch-Godfrey LM in 2SLS';
smpl 30,65;
list ivs c x1-x4 y1(-1) y2(-1) y3(-1);
2sls(inst=ivs) y1 c y3 y3(-1) x1 y1(-1);
   copy @res res1;
2sls(inst=ivs) y2 c y4 y2(-1) x4;
   copy @res res2;
2sls(inst=ivs) U c x1 y5 U(-1);
   copy @res res3;
smpl 31,65;
list iv2 ivs ivs(-1);  ? ivs(-1) applies lags to all the variables in ivs
2sls(inst=iv2) res1 res1(-1) c y3 y3(-1) x1 y1(-1);
   cdf @t(1);
2sls(inst=iv2) res2 res1(-1) c y4 y2(-1) x4;
   cdf @t(1);
2sls(inst=iv2) res3 res1(-1) c x1 y5 U(-1);
   cdf @t(1);