Interpreting probit marginal effects

[Fathima Salih]

I have a question about how to interpret the marginal effects in a probit model that I hope someone can help me with. Take a model that looks at school dropout (dependent variable =1 if dropped out, 0 otherwise) and household asset loss (independent variable ranging from 0 to 1, indicating the proportion of assets lost in the past year due to earthquake).

 . probit dropout assetloss

dropout       Coef.   Std. Err.      z    P>z     [95% Conf.    Interval]
        
assetloss     .491884   .0888692     5.53    0.000     .3177036    .6660644
_cons   -1.493199   .0399956   -37.33    0.000    -1.571589    -1.414809

margins, dydx(assetloss) predict(pr) post 

Average marginal effects    Number of obs     =    2,879
Model VCE    : OIM

Expression   : Pr(enrolled), predict(pr)
dy/dx w.r.t. : assetloss

        
Delta-method
dy/dx   Std. Err.      z    P>z     [95% Conf.    Interval]      
assetloss    .0736991   .0134485     5.48    0.000     .0473406    .1000576

Is it correct to interpret the marginal effects as follows: As asset losses increased by 100 per cent, the average marginal effect on the probability of dropping out of school increased by 0.073 percentage points?

[Maarten Buis]

It is not the average marginal effect on the probability of dropping out of school that increased but it is the probability of dropping out of school that (on average) increased. Moreover, it did not increase by 0.074 percentage points, but by 7.3 percentage points; a probability is a number between 0 and 1, and you can turn it into percentages by multiplying it by a 100.

[Fathima Salih]

Many thanks Maarten.

[Richard Williams]

Marginal effects for continuous variables can be difficult to interpret or can be misinterpreted. See

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

Excerpt: "MEMs for continuous variables measure the instantaneous rate of change, which may or may not be close to the effect on P(Y=1) of a one unit increase in Xk."

Personally, with continuous independent variables, I like to use Royston's MCP command, available from SSC:

https://www.stata-journal.com/articl...article=gr0056

I summarize some highlights of the command at

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