Ai and Norton Formula: marginal effects

[Jade Li]

Dear Statausers,

I want to use the formula suggested by Ai and Norton as in their paper "Computing interaction effects and standard errors in logit and probit models".

I applied this code:

xtprobit  depvar indepvar, vce(cluster inds)

the this code:

inteff depvar indepvar

But I am getting this error:

last estimates not found
r(301);

end of do-file

r(301);

Can anyone help, please? I data example is required I am happy to provide it.

[Rich Goldstein]

as far as I know, inteff only works after -probit- and -logit-; you did not use either of those so -inteff- won't work,, actually, you can view the ado file and see this for yourself - -inteff- cannot be used after -xtprobit-

[Maarten Buis]

inteff only works after logit or probit. It does not work after xtprobit. That makes sense; the random effects make it a harder problem. The easiest solution is to estimate your model with xtlogit and interpret the odds ratios and the interaction as a ratio of odds ratios.

[Jade Li]

Thank you, Rich. That is true...

[Jade Li]

Dear Maarten Buis, Thank you for your answer. Could you please provide a link to Stata code that I can use to implement your advice? In fact, xtlogit would work better for me since I am using panel data and I want to use fixed effects of all French firms in the data.

[Maarten Buis]

There is no code, you just add the or option and start interpreting. Here is an example:

. webuse union, clear
(NLS Women 14-24 in 1968)

.
. // make sure that the value 0 in year is meaningful
. tab year

  Interview |
       year |      Freq.     Percent        Cum.
------------+-----------------------------------
         70 |      1,658        6.33        6.33
         71 |      1,793        6.84       13.17
         72 |      1,958        7.47       20.65
         73 |      2,057        7.85       28.50
         77 |      2,670       10.19       38.69
         78 |      1,993        7.61       46.29
         80 |      2,028        7.74       54.03
         82 |      2,408        9.19       63.23
         83 |      2,194        8.37       71.60
         85 |      2,488        9.50       81.10
         87 |      2,536        9.68       90.77
         88 |      2,417        9.23      100.00
------------+-----------------------------------
      Total |     26,200      100.00

. replace year = year - 80
(26,200 real changes made)

.
. // estimate the model
. xtlogit union age grade i.not_smsa south##c.year, fe or
note: multiple positive outcomes within groups encountered.
note: 2,744 groups (14,165 obs) omitted because of all positive or
      all negative outcomes.

Iteration 0:   log likelihood = -4516.5881  
Iteration 1:   log likelihood = -4510.8906  
Iteration 2:   log likelihood =  -4510.888  
Iteration 3:   log likelihood =  -4510.888  

Conditional fixed-effects logistic regression        Number of obs    = 12,035
Group variable: idcode                               Number of groups =  1,690

                                                     Obs per group:
                                                                  min =      2
                                                                  avg =    7.1
                                                                  max =     12

                                                     LR chi2(6)       =  78.60
Log likelihood = -4510.888                           Prob > chi2      = 0.0000

------------------------------------------------------------------------------
       union | Odds ratio   Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   1.073686   .1031314     0.74   0.459      .889439    1.296099
       grade |   1.085034   .0454709     1.95   0.051     .9994743    1.177917
  1.not_smsa |   1.022736   .1157518     0.20   0.843     .8192672    1.276736
     1.south |    .475493   .0596215    -5.93   0.000     .3718887    .6079605
        year |   .9383002   .0908037    -0.66   0.510     .7761882     1.13427
             |
south#c.year |
          1  |   1.026765   .0085443     3.17   0.002     1.010155    1.043649
------------------------------------------------------------------------------

So being in the south decreases the odds of being in a union by a factor of 0.48 or (0.48-1)*100%=-52% if the interview took place in 1980 (as you can see I centered year on 80). For every year later that the interview took place the odds ratio of south increases (becomes less negative) by a factor of 1.03 or (1.03-1)*100%=3%.

[Jade Li]

Thank you very much!