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I am trying to compare the coefficients of two panel data regressions with the same dependent variable. What I am aiming at is the following:

    y1 = c + β x
    y2 = c + β x

In Stata

    xtreg y1 x i.z
    xtreg y2 x i.z

I want to check whether the βs are significantly different.

With two regular regressions I would use something like the following code in Stata to test a cross-equation restriction:

    sureg (y1 x ) (y2 x )
    lincom [y1]x - [y2]x

However Stata is explaining that this is not possible when I try to use xtreg.

I have searched a lot of different sites. However I do not have a clue, it only made me more confused. Hopefully you guys can help.

edit

I am using a Fixed effect models

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  • $\begingroup$ You should probably amend your xtreg code with the , fe option. $\endgroup$ – Dimitriy V. Masterov Jul 24 '14 at 17:59
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There's a user-written panel version of the random effects SUR estimator that you can obtain with ssc install xtsur. I am assuming you are using a RE estimator since that is the default with xtreg. The "add a constant" part is a bit of a hack, and I can't quite tell if it is in fact a bad idea.

Here's an toy example of what this would look like:

. webuse nlswork
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. gen constant=1

. xtsur (ln_wage constant age) (hours constant age)
(running multi-step estimates...)

Calculating multi-step estimates...
Iteration   1 : relative difference =  .00761817
Iteration   2 : relative difference =  6.278e-11


Seemingly unrelated regression (SUR) in panel data set

One-way random effect estimation:
------------------------------------------------------------------------------
Number of Group variable:   15                  Number of obs      =     28443
Panel variable: idcode                          Number of eqn      =         2
Time variable : year                            Number of panels   =        15

Random effects u_i ~ Gaussian
corr(u_i, e_it)    = 0 (assumed)
Panel type         : unbalanced

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ln_wage      |
    constant |   1.091836   .0125271    87.16   0.000     1.067283    1.116388
         age |   .0192946   .0002957    65.26   0.000     .0187151     .019874
-------------+----------------------------------------------------------------
hours        |
    constant |   37.04146   .2495206   148.45   0.000     36.55241    37.53052
         age |  -.0271416   .0071549    -3.79   0.000    -.0411649   -.0131183
-------------+----------------------------------------------------------------
     sigma_u |   see e(sigma_u)
     sigma_e |   see e(sigma_e)
------------------------------------------------------------------------------
Dependent variables:   ln_wage hours 
Independent variables: age 
------------------------------------------------------------------------------

. test [ln_wage]age=[hours]age

 ( 1)  [ln_wage]age - [hours]age = 0

           chi2(  1) =   42.51
         Prob > chi2 =    0.0000

lincom would also work here:

. lincom [ln_wage]age - [hours]age

 ( 1)  [ln_wage]age - [hours]age = 0

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   .0464362   .0071221     6.52   0.000     .0324772    .0603951
------------------------------------------------------------------------------

The coefficients match the output of xtreg pretty closely in this case, though they won't be identical:

. xtreg ln_wage age, re

Random-effects GLS regression                   Number of obs      =     28510
Group variable: idcode                          Number of groups   =      4710

R-sq:  within  = 0.1026                         Obs per group: min =         1
       between = 0.0877                                        avg =       6.1
       overall = 0.0774                                        max =        15

                                                Wald chi2(1)       =   3140.35
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0185667   .0003313    56.04   0.000     .0179174    .0192161
       _cons |   1.120439   .0112038   100.01   0.000      1.09848    1.142398
-------------+----------------------------------------------------------------
     sigma_u |  .36972456
     sigma_e |  .30349389
         rho |  .59743613   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xtreg hours age, re

Random-effects GLS regression                   Number of obs      =     28443
Group variable: idcode                          Number of groups   =      4709

R-sq:  within  = 0.0005                         Obs per group: min =         1
       between = 0.0007                                        avg =       6.0
       overall = 0.0002                                        max =        15

                                                Wald chi2(1)       =      7.81
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0052

------------------------------------------------------------------------------
       hours |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0240426   .0086031    -2.79   0.005    -.0409043   -.0071809
       _cons |   36.97867   .2717048   136.10   0.000     36.44613     37.5112
-------------+----------------------------------------------------------------
     sigma_u |  6.4129132
     sigma_e |  8.2312259
         rho |  .37771867   (fraction of variance due to u_i)
------------------------------------------------------------------------------
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  • $\begingroup$ Hi Dimitriy, thank you for you answer. I am using a Fixed effect model it this answer this applicable? $\endgroup$ – vincent Jul 24 '14 at 15:43
  • $\begingroup$ @vincent I don't believe this will work. $\endgroup$ – Dimitriy V. Masterov Jul 24 '14 at 17:58
  • $\begingroup$ For fixed effects, I believe you can maybe use the approach in this SJ paper by J. Lloyd Blackwell. It's a bit more involved since it involves reshapeing your data extensively. $\endgroup$ – Dimitriy V. Masterov Jul 24 '14 at 18:10
  • $\begingroup$ @Dimitry, thank you for the trouble but unfortunately this does not work for my data. $\endgroup$ – vincent Jul 27 '14 at 20:36
  • $\begingroup$ @vincent You might try this question on Statalist. $\endgroup$ – Dimitriy V. Masterov Jul 28 '14 at 18:05

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