Are the assumptions the same for OLS-PCSE?

[Vegard Tjorhom]

Hi,

I wonder if the assumptions for OLS-PCSE are the same as for OLS?

And I have been running some of the tests now: Some of them - like ovtest - is not available for OLS-PCSE. Is it okay to run a .ovtest for OLS, and apply it on an OLS-PCSE-model?

Best, Vegard

[li yi]

What is the stata command of OLS-PCSE?

[Carlo Lazzaro]

Vegard and Li:
1) the Stata command for OLS_PCSE is -xtpcse-;
2) the best way to check for misspecification of the functional form of the regressand in -xt- linear regression commands is to replicate -linktest- by hand, as in the following toy-example:

. webuse grunfeld

. xtset company year, yearly

Panel variable: company (strongly balanced)
 Time variable: year, 1935 to 1954
         Delta: 1 year

. xtpcse invest mvalue kstock, correlation(ar1)
note: estimates of rho outside [-1,1] bounded to be in the range [-1,1].

Prais–Winsten regression, correlated panels corrected standard errors (PCSEs)

Group variable:   company                       Number of obs     =        200
Time variable:    year                          Number of groups  =         10
Panels:           correlated (balanced)         Obs per group:
Autocorrelation:  common AR(1)                                min =         20
                                                              avg =         20
                                                              max =         20
Estimated covariances      =        55          R-squared         =     0.5468
Estimated autocorrelations =         1          Wald chi2(2)      =      93.71
Estimated coefficients     =         3          Prob > chi2       =     0.0000

------------------------------------------------------------------------------
             |           Panel-corrected
      invest | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      mvalue |   .0950157   .0129934     7.31   0.000     .0695492    .1204822
      kstock |    .306005   .0603718     5.07   0.000     .1876784    .4243317
       _cons |  -39.12569   30.50355    -1.28   0.200    -98.91154    20.66016
-------------+----------------------------------------------------------------
         rho |   .9059774
------------------------------------------------------------------------------

. predict fitted, xb

. gen sq_fitted=fitted^2

. xtpcse invest fitted sq_fitted , correlation(ar1)
note: estimates of rho outside [-1,1] bounded to be in the range [-1,1].

Prais–Winsten regression, correlated panels corrected standard errors (PCSEs)

Group variable:   company                       Number of obs     =        200
Time variable:    year                          Number of groups  =         10
Panels:           correlated (balanced)         Obs per group:
Autocorrelation:  common AR(1)                                min =         20
                                                              avg =         20
                                                              max =         20
Estimated covariances      =        55          R-squared         =     0.6168
Estimated autocorrelations =         1          Wald chi2(2)      =     156.12
Estimated coefficients     =         3          Prob > chi2       =     0.0000

------------------------------------------------------------------------------
             |           Panel-corrected
      invest | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      fitted |   .3282114   .1810327     1.81   0.070    -.0266062    .6830291
   sq_fitted |   .0006834   .0001607     4.25   0.000     .0003684    .0009984
       _cons |   53.43712     26.897     1.99   0.047     .7199566    106.1543
-------------+----------------------------------------------------------------
         rho |   .9097158
------------------------------------------------------------------------------

. test sq_fitted=0

 ( 1)  sq_fitted = 0

           chi2(  1) =   18.08
         Prob > chi2 =    0.0000


.

Given the statistical significance of the -test- outcome, there's evidence of model misspecification.