options double crt nwidth=17,signif=9;
name glr 'LR and Wald tests for random effects and serial correlation';
?   LR and Wald versions of the LM tests.
?    by Clint Cummins 9/04

?  Data Source: Grunfeld (1958)
?  Description: Panel Data, 10 U.S. firms over 20 years, 1935-1954.
?  Variables:
doc FN 'Firm Number';
doc YR 'Year 1935-1954';
doc I 'Annual real gross investment';
doc F 'Real value of the firm (shares outstanding)';
doc K 'Real value of the capital stock';
list vars FN YR I F K;
const n,10 t,20 ystart,1935;
set nt=n*t;
smpl 1,nt;
read(file='grunfeld.txt') vars;

freq(panel,n=n,t=t,id=FN,time=YR,start=ystart) a;

panel(rei) i c f k;
set logl_0 = @loglt;
set logl_mu = @loglrei;
set W_mu = @TREI(4)**2;  print W_mu;

ar1 i c f k;
set logl_rho = @logl;
set W_rho = @T(4)**2;  print W_rho;

ar1(rei) i c f k;
set logl_murho = @logl;
set W_rhoS = @T(4)**2;
set W_muS = @T(5)**2;
frml erho rho;
frml erhoi rho_i;
analyz erho erhoi;
set W_murho = @WALD;
print W_mu W_muS W_rho W_rhoS W_murho;

? Benchmark
?
?             LR statistic     p-value
? LR_mu     193.090781907    .000000000
? LR_mu*      2.251032295    .133525302
? LR_rho    303.019854961    .000000000
? LR_rho*   112.180105348    .000000000
? LR_murho  305.270887256    .000000000
?
? Logl_0      -1191.802360368
? Logl_mu     -1095.256969414
? Logl_rho    -1040.292432887 
? Logl_murho  -1039.166916740 
?
?           Wald statistic     p-value
? W_mu       50.566219034    .000000000
? W_mu*      40.739012709    .000000000
? W_rho    1264.589760379    .000000000
? W_rho*    131.242837089    .000000000
? W_murho   239.175118327    .000000000

print logl_0 logl_mu logl_rho logl_murho;

title 'LR test for individual random effects';
set LR_mu  = 2*(logl_mu - logl_0);
set LR_muS = 2*(logl_murho - logl_rho);  ? modified version
cdf(chisq,df=1) LR_mu %LR_mu;
cdf(chisq,df=1) LR_muS %LR_muS;
print LR_mu LR_muS %LR_mu %LR_muS;

title 'LR test for serial correlation';
set LR_rho  = 2*(logl_rho - logl_0);
set LR_rhoS = 2*(logl_murho - logl_mu);  ? modified version
cdf(chisq,df=1) LR_rho %LR_rho;
cdf(chisq,df=1) LR_rhoS %LR_rhoS;
print LR_rho LR_rhoS %LR_rho %LR_rhoS;

title 'joint test for individual random effects and serial correlation';
set LR_murho = 2*(logl_murho - logl_0);
cdf(chisq,df=2) LR_murho %LR_murho;
print LR_murho %LR_murho;

?  Note:  the one-sided test for individual random effects
?  is not computed, because in TSP's implementation, RHO_I, the
?  intraclass correlation coefficient can be (slightly) negative.