Margins command returning "not estimable"

[Lea Bart]

Hello!

I am looking for help regarding the margins command. I am running xtreg using state-year panel data and I want to test for different effects for states with high and low birthrates using interaction terms, but when I run the margins command I'm getting a result that is "not estimable." I am trying to estimate margins using the following code:

xtreg birthrate c.simelig##i.highbirthrate i.year c1year-c8year [aweight=populationmean],
fe vce(cluster fips)
margins, dydx(simelig) at(highbirthrate=(0 1))

Note: c1year-c8year are census region time interactions to account for region specific trends.

In the above case, xtreg returns the following output:

note: 1.highbirthrate omitted because of collinearity
Fixed-effects (within) regression               Number of obs      =       714
Group variable: fips                            Number of groups   =        51

R-sq:  within  = 0.9509                         Obs per group: min =        14
       between = 0.3664                                        avg =      14.0
       overall = 0.0326                                        max =        14

                                                F(23,50)           =    280.65
corr(u_i, Xb)  = -0.3530                        Prob > F           =    0.0000

                                     (Std. Err. adjusted for 51 clusters in fips)
---------------------------------------------------------------------------------
                |               Robust
      birthrate |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        simelig |   .0281689   .0224591     1.25   0.216    -.0169417    .0732794
1.highbirthrate |          0  (omitted)
                |
  highbirthrate#|
      c.simelig |
             1  |  -.1151857   .0282641    -4.08   0.000    -.1719558   -.0584157
                |
           year |
          1991  |  -1.326654   .2133969    -6.22   0.000    -1.755274   -.8980335
          1992  |  -1.981944   .3023724    -6.55   0.000    -2.589277   -1.374612
          1993  |  -2.707751   .4849461    -5.58   0.000    -3.681794   -1.733708
          1994  |  -4.855094   .6516258    -7.45   0.000    -6.163923   -3.546265
          1995  |  -7.590643   .9927567    -7.65   0.000    -9.584654   -5.596633
          1996  |  -9.993006   1.182542    -8.45   0.000    -12.36821   -7.617801
          1997  |  -11.91885   1.455844    -8.19   0.000      -14.843   -8.994706
          1998  |  -13.71345    1.58068    -8.68   0.000    -16.88833   -10.53856
          1999  |  -15.06773   1.789333    -8.42   0.000    -18.66171   -11.47374
          2000  |  -18.01335   1.937266    -9.30   0.000    -21.90446   -14.12224
          2001  |  -19.85275   2.057514    -9.65   0.000    -23.98539   -15.72011
          2002  |  -21.28267   2.169835    -9.81   0.000    -25.64091   -16.92443
          2003  |  -21.94815   2.259343    -9.71   0.000    -26.48617   -17.41013
                |
         c1year |   .6410636   .2012706     3.19   0.002     .2367998    1.045327
         c2year |   .5668106   .2027973     2.79   0.007     .1594802     .974141
         c3year |   .5823073   .2162658     2.69   0.010     .1479247     1.01669
         c4year |   .9935927   .1900171     5.23   0.000     .6119321    1.375253
         c5year |   .3884749   .1967836     1.97   0.054    -.0067765    .7837263
         c6year |   .3084339   .2081009     1.48   0.145    -.1095491    .7264169
         c7year |   .6459406   .2272479     2.84   0.006     .1894997    1.102382
         c8year |   .7960811   .2041904     3.90   0.000     .3859526     1.20621
          _cons |   39.29763   .4062755    96.73   0.000      38.4816    40.11366
----------------+----------------------------------------------------------------
        sigma_u |  12.173588
        sigma_e |  1.4760461
            rho |  .98551147   (fraction of variance due to u_i)
---------------------------------------------------------------------------------

And the margins command returns the following:

Average marginal effects                          Number of obs   =        714
Model VCE    : Robust

Expression   : Linear prediction, predict()
dy/dx w.r.t. : simelig

1._at        : highbirthrate   =           0

2._at        : highbirthrate   =           1

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
simelig      |
         _at |
          1  |          .  (not estimable)
          2  |          .  (not estimable)
------------------------------------------------------------------------------

In trying to identify the problem I played around with a few other configuration of the model. The following also returns "not estimable:"

xtreg birthrate c.simelig##i.highbirthrate i.year c1year-c8year, fe vce(cluster fips)
margins, dydx(simelig) at(highbirthrate=(0 1))

If I don't weight or cluster the margins command works just fine, and the following code returns normal results:

xtreg birthrate c.simelig##i.highbirthrate i.year c1year-c8year
margins, dydx(simelig) at(highbirthrate=(0 1))

Meanwhile, this returns an error that says "aweight not allowed:"

xtreg birthrate c.simelig##i.highbirthrate i.year c1year-c8year [aweight=populationmean]
margins, dydx(simelig) at(highbirthrate=(0 1))

Does anyone have any thoughts as to why I'm not getting estimates for the original code? Any help would be much appreciated.

Thanks,
Lea

[William Lisowski]

Welcome to Statalist!

The note at the top of your xtreg output tells us that xtreg was unable to estimate an effect for highbirthrate==1, and I expect that this failure is the cause of the problems in margins. I expect that were you to try

margins, dydx(simelig) at(highbirthrate=0)

you would not get the error message.

You are running a fixed effects model, and I assume that highbirthrate is constant within each state, so I expect that is the source of the collinearity. You shouldn't include variables in a fixed effect model that are constant within the panels.

[Lea Bart]

Thanks for the quick response!

I tried the code you posted, but I'm still getting the same problem:

Average marginal effects                          Number of obs   =        714
Model VCE    : Robust

Expression   : Linear prediction, predict()
dy/dx w.r.t. : simelig
at           : highbirthrate   =           0

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     simelig |          .  (not estimable)
------------------------------------------------------------------------------

highbirthrate is constant within each state - it's coded as 1 if the state is above the national mean and 0 if it's below the national mean. I understand the reason highbirthrate alone is omitted for collinearity, but the interaction between highbirthrate and simelig seems fine. I would like Stata to add the coefficients (and calculate standard errors) on simelig and the simelig-highbirthrate interaction for me for when highbirthrate=1 and when highbirthrate=0. Since the simelig-highbirthrate interaction isn't omitted I don't understand why the margins command isn't giving a result.

[William Lisowski]

Ah yes, I see that I didn't look closely enough at your output. My assertion still stands, however.

When you write

c.simelig##i.highbirthrate

it is equivalent to the full factorial interaction

c.simelig i.highbirthrate c.simelig#i.highbirthrate

For your purposes, I think you should only include

c.simelig#i.highbirthrate

rather than the full factorial interaction.

Try that in your original formulation and see if it gives you what you want. Anyone following this thread is welcome to jump in with a better explanation!

[Richard Williams]

This thread -- in particular Jeff Pitblado's comments -- may be relevant.

http://www.statalist.org/forums/foru...fe-and-margins

I think William is on the right track although I suspect you also want to include c.simeliq, i.e.

c.simelig c.simelig#i.highbirthrate

i.e. do NOT include the main effect of birthrate but do include the main effect of simeliq.

[Lea Bart]

Thank you! Everything worked out using

 c.simelig c.simelig#i.highbirthrate

Thanks again,
Lea