Statistical Analysis: Marginal Effects

Marginal effects reported

  • Compute for all models with conditional mean functions
  • Compute at means and at specified points
  • Compute at specified strata
  • List estimates and standard errors

Dummy variables

Discrete choice models distinguish between dummy variables and continuous variables. For a dummy variable, the effect is computed as the difference in the estimated probabilities with the dummy variable equal to one and zero and other variables at their means. For continuous variables, the effect is the derivative.

Example

The following shows the computation for an ordered probit model for labor supply. There are three outcomes, not working, part time and full time. The marginal effects are computed for a dummy variable, KIDS for whether there are kids in the home and two continuous variables.

+----------------------------------------------------+
| Marginal effects for ordered probability model     |
| M.E.s for dummy variables are Pr[y|x=1]-Pr[y|x=0]  |
| Names for dummy variables are marked by *.         |
+----------------------------------------------------+
+---------+--------------+----------------+--------+--------+---------+
|Variable | Coefficient  | Standard Error |b/St.Er.|P[|Z|>z]|Mean of X|
+---------+--------------+----------------+--------+--------+---------+
          These are the effects on Prob[Y=00] at means.
 Constant     .0000000000 ........(Fixed Parameter)........
 *KIDS        .1090877836   .26203295E-01    4.163   .0000  .68400000
 WFED     -.2708901544E-02  .78310729E-02    -.346   .7294  8.6080000
 FAMINC   -.3140480482E-02  .22504152E-02   -1.396   .1629  23.062540
          These are the effects on Prob[Y=01] at means.
 Constant     .0000000000 ........(Fixed Parameter)........
 *KIDS     .9273212165E-03  .53844616E-02     .172   .8633  .68400000
 WFED      .6214395868E-04  .22051118E-03     .282   .7781  8.6080000
 FAMINC    .7204465950E-04  .15694855E-03     .459   .6462  23.062540
          These are the effects on Prob[Y=02] at means.
 Constant     .0000000000 ........(Fixed Parameter)........
 *KIDS       -.1100151048   .81754048E-01   -1.346   .1784  .68400000
 WFED      .2646757585E-02  .77700308E-02     .341   .7334  8.6080000
 FAMINC    .3068435823E-02  .22937500E-02    1.338   .1810  23.062540
 (Note: E+nn or E-nn means multiply by 10 to + or -nn power.)

+-------------------------------------------------------------------
| Summary of Marginal Effects for Ordered Probability Model (probit)
+-------------------------------------------------------------------
Variable|    Y=00    Y=01    Y=02    Y=03    Y=04    Y=05    Y=06   
--------------------------------------------------------------------
ONE         .0000   .0000   .0000
*KIDS       .1091   .0009  -.1100
WFED       -.0027   .0001   .0026
FAMINC     -.0031   .0001   .0031