marginal effect of probit model, margins, dydx(*) atmeans or margins, dydx(*) post?

[Alice Yang]

Hello,

As indicated in the title, I'm running a probit regression model, with dependent variables an indicator variable (disclose, =1 if the firm discloses and =0 if the firm doesn't disclose) and independent variable is a continuous variable (leverage). I wonder when calculating the marginal effect for my variable of interest, leverage, should I use margins, dydx(*) atmeans or margins, dydx(*) post? The two gives different results.

If use dydx(*) atmeans

------------------------------------------------------------------------------------
                   |            Delta-method
                   |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
           leverage|  -.2389898    .070307     3.40   0.001     .1011905    .3767891

If use dydx(*) post

------------------------------------------------------------------------------------
                   |            Delta-method
                   |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
           leverage|  -.2820114    .070307     3.40   0.001     .1011905    .3767891

Moreover, if I want to interpret this result, is it correct to say an increase of 1-unit in leverage decreases the probability of disclosure by 0.239, holding all else constant?

Thanks a lot for any suggestion!

[FernandoRios]

Hi Alice
Both are correct, but both are giving you numbers that apply to different "representative" estimations
When you say "atmeans" you are estimating the effect for the "average" person or unit. If that is what you are interested in, go ahead

When you do not say at means, you are estimating the average effects across all units. Again, is this what you are interested in ? if so, use this one.

Which one is correct will depend strongly of what you want to show.
F

[Alice Yang]

Hi Fernando,

Thanks for your quick reply! I think estimating the average effects across all units is more proper for me. If I want to go with this one, how can I organize the interpretation? Is it correct to say an increase of 1-unit in leverage on average decreases the probability of disclosure by 0.282, holding all else constant?

Thanks.

[FernandoRios]

Yep. but you need to add the words "on average"

[Alice Yang]

Thanks!

[Richard Williams]

Alice, your wording seems to imply that you think atmeans and post are mutually exclusive options. They aren't. If you dropped post from the command where you used it, or added it to the command where you used atmeans, the results of each command would be the same, The post option posts margins and their VCE as estimation results which can be handy if, say, you want to use a command like esttab to format the results, but it has no effect on the results themselves.

Is it correct to say an increase of 1-unit in leverage on average decreases the probability of disclosure by 0.282, holding all else constant?

No, not really. Marginal effects for continuous variables measure the instantaneous rate of change. They are popular in some disciplines (e.g. Economics) because they often provide a good approximation to the amount of change in Y that will be produced by a 1-unit change in Xk. But then again, they often do not. For more, see

https://www3.nd.edu/~rwilliam/xsoc73994/Margins02.pdf

For continuous independent variables, I often like to use Royston's mcp command. See

https://www3.nd.edu/~rwilliam/xsoc73994/Margins03.pdf

For more on the different types of marginal effects, see

https://www3.nd.edu/~rwilliam/xsoc73994/Margins01.pdf

[Alice Yang]

Hi Richard,

Thanks for your documents, and mcp is very useful.