Generalized marginal effects

Effects when other variables change along with the focal variable

A marginal effect usually holds the other variables in the model constant. But some variables change along with the focal variable: college graduates, for example, tend to have higher wages and more prestigious jobs than those without a degree. The cochange() option lets those variables change too. The table then reports two marginal effects of the focal variable: the usual one, and one labeled with co-change in which the co-change variables change too. metest can be used to test the difference between the two.

The example uses the data and the full model of the nested models example (Example 6.2 of Mize, Doan, and Long 2019): a logit of being very happy on a college degree, wages, occupational prestige, and controls.

use "https://tdmize.github.io/data/data/gss_cme", clear
(gss_cme.dta | GSS 1972 - 2016 Weighted | 2018-07-10)
drop if year < 2000
(38,116 observations deleted)
drop if employed != 1
(9,556 observations deleted)
drop if missing(vhappy, college, wages, occprest, age, married, parent, woman, conserv, reltrad)
(5,578 observations deleted)

. 
quietly logit vhappy i.college c.wages c.occprest i.married i.parent i.woman ///
              i.conserv i.reltrad i.year c.age##c.age, vce(robust)
estimates store m4

Co-change variables at chosen values

start() and end() set the values the co-change variables change from and to. Here wages and occupational prestige change from their average among those without a college degree to their average among college graduates.

quietly summarize wages if college == 0 & e(sample)
local w0 : display %5.2f r(mean)
quietly summarize wages if college == 1 & e(sample)
local w1 : display %5.2f r(mean)
quietly summarize occprest if college == 0 & e(sample)
local p0 : display %5.2f r(mean)
quietly summarize occprest if college == 1 & e(sample)
local p1 : display %5.2f r(mean)
. 
mecompare i.college, models(m4) cochange(wages occprest) ///
    start(wages=`w0' occprest=`p0') end(wages=`w1' occprest=`p1')
Predicting: Pr(vhappy)

Marginal effects (N_m4=9216)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
college                          |                                       
    College Deg - No Col Deg     |                                       
                              m4 |     1      0.019      0.012      0.103
---------------------------------+---------------------------------------
college with co-change           |                                       
                              m4 |     2      0.063      0.011      0.000


NOTE: college with co-change: college 0 to 1; wages 13.60 to 24.88; occprest 40.51 to 54.68.

Row 1 is the usual marginal effect of a college degree, with wages and occupational prestige held at their observed values. Row 2 is the effect of a college degree when wages and occupational prestige also change; the note under the table lists each change. Use metest to test the difference between the two:

metest 2 - 1
                                 |  estimate         se     pvalue 
---------------------------------+--------------------------------
              cochange - college |     0.044      0.006      0.000

Example 6.2 asks how the effect of a college degree changes when wages and occupational prestige are added to the model. cochange() asks a different question within one model: what the effect of a college degree is when wages and occupational prestige change along with it.

Co-change variables changed by an amount

Without start() and end(), co-change variables change as focal variables do (see amount()). Here wages and occupational prestige each increase by a standard deviation along with the degree:

mecompare i.college, models(m4) cochange(wages occprest) amount(sd)
Predicting: Pr(vhappy)

Marginal effects (N_m4=9216)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
college                          |                                       
    College Deg - No Col Deg     |                                       
                              m4 |     1      0.019      0.012      0.103
---------------------------------+---------------------------------------
college with co-change           |                                       
                              m4 |     2      0.067      0.010      0.000


NOTE: college with co-change: college 0 to 1; wages + SD (centered); occprest + SD (centered).

A nominal focal or co-change variable with three or more categories needs the two levels it changes between in start() and end(), e.g. start(race=1) end(race=2). The options page and the help file list what cochange() cannot be combined with.

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