Margins for unbalanced panel giving inaccurate estimates

[Jeremy Lim]

I found that margins gives an inaccurate estimate after xtreg, fe on an unbalanced panel, but it works fine if the panel is balanced. Does anyone know why? Here is an example in Stata 17:

*1. Create unbalanced panel
webuse nlswork.dta, clear
drop if year>69 | hours==.
xtset idcode year
drop if year==69 & L.year==.
tab year

*2. Test margins for unbalanced panel
xtreg hours year, fe
margins, by(year)
bysort year: su hours

*3. Create balanced panel
xtset idcode year
drop if year==68 & F.year==.

*4. Test margins for balanced panel
xtreg hours year, fe
margins, by(year)
bysort year: su hours

Below is an excerpt from the output for margins on unbalanced panel, which does not tally with summary means.

. margins, by(year)

Predictive margins                                       Number of obs = 2,224
Model VCE: Conventional

Expression: Linear prediction, predict()
Over:       year

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
        year |
         68  |   37.54182   .1774929   211.51   0.000     37.19394     37.8897
         69  |    38.1724   .2313402   165.01   0.000     37.71899    38.62582
------------------------------------------------------------------------------

. bysort year: su hours

------------------------------------------------------------------------------------------------
-> year = 68

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
       hours |      1,374    37.35007    9.303987          1         84

------------------------------------------------------------------------------------------------
-> year = 69

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
       hours |        850    38.48235    7.161952          2         70

[William Lisowski]

*1. Create unbalanced panel
webuse nlswork.dta, clear
drop if year>69 | hours==.
xtset idcode year
drop if year==69 & L.year==.
tab year

*2. Test margins for unbalanced panel
xtreg hours year, fe
predict hhat
margins, by(year)
bysort year: su hours hhat

. predict hhat
(option xb assumed; fitted values)

. margins, by(year)

Predictive margins                                       Number of obs = 2,224
Model VCE: Conventional

Expression: Linear prediction, predict()
Over:       year

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
        year |
         68  |   37.54182   .1774929   211.51   0.000     37.19394     37.8897
         69  |    38.1724   .2313402   165.01   0.000     37.71899    38.62582
------------------------------------------------------------------------------

. bysort year: su hours hhat

------------------------------------------------------------------------------------------------
-> year = 68

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
       hours |      1,374    37.35007    9.303987          1         84
        hhat |      1,374    37.54182           0   37.54182   37.54182

------------------------------------------------------------------------------------------------
-> year = 69

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
       hours |        850    38.48235    7.161952          2         70
        hhat |        850    38.17241           0   38.17241   38.17241


.

[Jeremy Lim]

Dear William, thank you very much for your response. Perhaps I can put the question a little differently - why is the estimate for hhat (37.54182) different from the actual mean (37.35007) when the panel is unbalanced, but not when it is balanced? Thank you!

[William Lisowski]

The short answer is, because mathematics.

There's no reason to expect the means of the predictions to equal the means of the data within separate subgroups in general. The math works out that way in balanced panels. I'm sure my linear models textbooks provide a more complete answer, but I'm about 50 years away from them so I can't do better than that.

Note that even with the unbalanced panel, the mean of the predictions is equal to the mean of the data across the entire population.

. margins

Predictive margins                                       Number of obs = 2,224
Model VCE: Conventional

Expression: Linear prediction, predict()

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   37.78282   .1336238   282.76   0.000     37.52093    38.04472
------------------------------------------------------------------------------

. su hours hhat

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
       hours |      2,224    37.78282    8.564909          1         84
        hhat |      2,224    37.78282    .3064868   37.54182   38.17241

[Jeremy Lim]

Hi William, thank you so much, that helps to clear things up.