elasticity calculation with a factor variable regression

[Liu Qiang]

hi dear all statalisters,
I now face a problem in getting the elasticity after running a logit model. To put it more understandable, I use this code as an example:

sysuse auto.dta,clear
logit foreign turn length weight c.price#i.rep78
margins, eyex(*)

then there's an error information:
factor variables not allowed in option eyex()
how could I overcome this problem?
Thanks in advance.

[Marcos Almeida]

Just as a side note: I fail to understand why adding an interaction term between price and rep78, and not adding the so-called "main effects".

That being said, you may type:

margins, eyex( turn length weight  price )

[FernandoRios]

In addition to Marcos helpful comments
you cannot calculate elasticities with respect to a categorical variable, because the numerator is not correctly defined. You could calculate Semi-elasticities with respect to the categorical variable.
Best

[Liu Qiang]

Just as a side note: I fail to understand why adding an interaction term between price and rep78, and not adding the so-called "main effects".

That being said, you may type:

margins, eyex( turn length weight price )

Dear Marcos, thank you for your explanation. Because in my paper, I want to change the cross-sectional data into a semi-panel data. i.e, I want to investigate the effect of price on the possibility of being a foreign car would change over time or not so I generate an interaction variable=price*in which year it was produced for example. Have I made a mistake?

[Marcos Almeida]

Theoretically, I see no problem in using the interaction term, but I believe it should come with the predictors as well,

Just adding an extra # will provide the predictors plus the interaction term.

[Liu Qiang]

Theoretically, I see no problem in using the interaction term, but I believe it should come with the predictors as well,

Just adding an extra # will provide the predictors plus the interaction term.

thank you for your kind reminder. But how could I get the elasticity for each interaction term then?

[Marcos Almeida]

You can easily have the answer for the question in #6, I mean, "why not".

You just need to type:

. sysuse auto
(1978 Automobile Data)

. logit foreign turn length weight c.price##i.rep78

note: 1.rep78 != 0 predicts failure perfectly
      1.rep78 dropped and 2 obs not used

note: 2.rep78 != 0 predicts failure perfectly
      2.rep78 dropped and 8 obs not used

note: 5.rep78 omitted because of collinearity
note: 2.rep78#c.price omitted because of collinearity
note: 5.rep78#c.price omitted because of collinearity
Iteration 0:   log likelihood = -38.411464  
Iteration 1:   log likelihood = -14.747241  
Iteration 2:   log likelihood = -11.766559  
Iteration 3:   log likelihood = -11.015015  
Iteration 4:   log likelihood = -10.945121  
Iteration 5:   log likelihood = -10.944407  
Iteration 6:   log likelihood = -10.944406  

Logistic regression                             Number of obs     =         59
                                                LR chi2(8)        =      54.93
                                                Prob > chi2       =     0.0000
Log likelihood = -10.944406                     Pseudo R2         =     0.7151

-------------------------------------------------------------------------------
      foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
         turn |  -.4981345   .4036253    -1.23   0.217    -1.289226    .2929566
       length |   .0328362   .1129737     0.29   0.771    -.1885882    .2542606
       weight |  -.0044512   .0035285    -1.26   0.207     -.011367    .0024645
        price |   .0019742   .0012189     1.62   0.105    -.0004147    .0043631
              |
        rep78 |
           1  |          0  (empty)
           2  |          0  (empty)
           3  |   4.447291   5.735345     0.78   0.438    -6.793777    15.68836
           4  |  -.5519409   7.950418    -0.07   0.945    -16.13447    15.03059
           5  |          0  (omitted)
              |
rep78#c.price |
           1  |          0  (empty)
           2  |          0  (empty)
           3  |  -.0012724   .0012456    -1.02   0.307    -.0037137    .0011688
           4  |  -.0001351   .0015902    -0.08   0.932    -.0032518    .0029816
           5  |          0  (omitted)
              |
        _cons |   14.12164   19.74753     0.72   0.475    -24.58281     52.8261
-------------------------------------------------------------------------------

. margins, eyex( turn length weight  price )

Average marginal effects                        Number of obs     =         59
Model VCE    : OIM

Expression   : Pr(foreign), predict()
ey/ex w.r.t. : turn length weight price

------------------------------------------------------------------------------
             |            Delta-method
             |      ey/ex   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        turn |   -13.3061   10.81663    -1.23   0.219    -34.50631    7.894107
      length |   4.175763   14.36291     0.29   0.771    -23.97502    32.32655
      weight |  -9.705913   7.721956    -1.26   0.209    -24.84067    5.428842
       price |   4.053252    2.70474     1.50   0.134     -1.24794    9.354445
------------------------------------------------------------------------------

. margins, eyex( turn length weight  price rep78)
factor variables not allowed in option eyex()
r(198);

. margins, eyex( turn length weight  price#rep78)
invalid eyex() option;
levels of interactions not allowed
r(198);

. margins, eyex( turn length#weight  price)
invalid eyex() option;
levels of interactions not allowed
r(198);

Hopefully that helps.

[Liu Qiang]

You can easily have the answer for the question in #6, I mean, "why not".

You just need to type:

. sysuse auto
(1978 Automobile Data)

. logit foreign turn length weight c.price##i.rep78

note: 1.rep78 != 0 predicts failure perfectly
1.rep78 dropped and 2 obs not used

note: 2.rep78 != 0 predicts failure perfectly
2.rep78 dropped and 8 obs not used

note: 5.rep78 omitted because of collinearity
note: 2.rep78#c.price omitted because of collinearity
note: 5.rep78#c.price omitted because of collinearity
Iteration 0: log likelihood = -38.411464
Iteration 1: log likelihood = -14.747241
Iteration 2: log likelihood = -11.766559
Iteration 3: log likelihood = -11.015015
Iteration 4: log likelihood = -10.945121
Iteration 5: log likelihood = -10.944407
Iteration 6: log likelihood = -10.944406

Logistic regression Number of obs = 59
LR chi2(8) = 54.93
Prob > chi2 = 0.0000
Log likelihood = -10.944406 Pseudo R2 = 0.7151

-------------------------------------------------------------------------------
foreign | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
turn | -.4981345 .4036253 -1.23 0.217 -1.289226 .2929566
length | .0328362 .1129737 0.29 0.771 -.1885882 .2542606
weight | -.0044512 .0035285 -1.26 0.207 -.011367 .0024645
price | .0019742 .0012189 1.62 0.105 -.0004147 .0043631
|
rep78 |
1 | 0 (empty)
2 | 0 (empty)
3 | 4.447291 5.735345 0.78 0.438 -6.793777 15.68836
4 | -.5519409 7.950418 -0.07 0.945 -16.13447 15.03059
5 | 0 (omitted)
|
rep78#c.price |
1 | 0 (empty)
2 | 0 (empty)
3 | -.0012724 .0012456 -1.02 0.307 -.0037137 .0011688
4 | -.0001351 .0015902 -0.08 0.932 -.0032518 .0029816
5 | 0 (omitted)
|
_cons | 14.12164 19.74753 0.72 0.475 -24.58281 52.8261
-------------------------------------------------------------------------------

. margins, eyex( turn length weight price )

Average marginal effects Number of obs = 59
Model VCE : OIM

Expression : Pr(foreign), predict()
ey/ex w.r.t. : turn length weight price

------------------------------------------------------------------------------
| Delta-method
| ey/ex Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
turn | -13.3061 10.81663 -1.23 0.219 -34.50631 7.894107
length | 4.175763 14.36291 0.29 0.771 -23.97502 32.32655
weight | -9.705913 7.721956 -1.26 0.209 -24.84067 5.428842
price | 4.053252 2.70474 1.50 0.134 -1.24794 9.354445
------------------------------------------------------------------------------

. margins, eyex( turn length weight price rep78)
factor variables not allowed in option eyex()
r(198);

. margins, eyex( turn length weight price#rep78)
invalid eyex() option;
levels of interactions not allowed
r(198);

. margins, eyex( turn length#weight price)
invalid eyex() option;
levels of interactions not allowed
r(198);

Hopefully that helps.

thanks! I understand what's wrong now. I have made a mistake.