Testing the difference of margins interaction coefficients

[Elias Markstedt]

Hi Statalisters,

I would like to test the difference between interaction coefficients produced by the -margins- command and report that test in a marginsplot using Stata 13 (i.e. visualizing the difference as well as reporting a test in the same graph). I have used the suggested -test- postestimation command, but in many cases the Wald tests leave me with significant results where the confidence intervals calculated by -margins- are overlapping quite a bit.

The following code snippet illustrates what I have been trying to do using an example dataset.

use http://www.stata-press.com/data/r13/nlswork, clear

xtset idcode year
qui xtreg ln_wage i.year##union, fe vce(cl idcode)
margins i.year##union if union==1 & (year==83 | year==85), post
test _b[83.year#1.union]=_b[85.year#1.union]
mat p=r(p)
local p: di %4.2f p[1,1]
marginsplot, note("Test of difference: p=`p'")

This is the output from -margins- and -test-:

. margins i.year##union if union==1 & (year==83 | year==85), post

Predictive margins    Number of obs   =    922
Model VCE    : Robust

Expression   : Linear prediction, predict()

        
Delta-method
Margin   Std. Err.      z    P>z     [95% Conf.    Interval]
        
year 
83     1.871275   .0137086   136.50    0.000     1.844407    1.898143
85     1.905756   .0132669   143.65    0.000     1.879754    1.931759
             
1.union    1.891021   .0108374   174.49    0.000      1.86978    1.912262
             
year#union 
83 1     1.871275   .0137086   136.50    0.000     1.844407    1.898143
85 1     1.905756   .0132669   143.65    0.000     1.879754    1.931759
        

. test _b[83.year#1.union]=_b[85.year#1.union]

( 1)  83bn.year#1.union - 85.year#1.union = 0

chi2(  1) =    4.57
Prob > chi2 =    0.0325

In the example above the upper bound for the year-union interaction for 1983 (1.90) is overlapping the lower bound for 1985 (1.88) while the Wald test is significant at the 95 percent level.

Any suggestions on how to reproduce the nonsignificant difference (according to the current -margins- setup)?

Thank you in advance!
Elias Markstedt