Margins for a specific change in the independent variables

[Hans Huber]

Hello there,
my name is Hans Huber an I'm currently doing my Master in Applied Economics final thesis. I'm using probit models to predict and understand defaults (dependent variable = 1 or 0) in a specific data set. To interpret the coefficients of the probit models I'm using margins commands, but as I understand those commands give me the probability of success in the dependent variables for changes in 1 unit in the independent variables... With that being said I'm looking for a way to use the margins command for changes of X units in the independent variables, because I'm looking for no linear effects.

So, for know I'm using this command: margins, dydx(*) ; and as I understand that gives me the probability of success for changes in 1% in the independent variable and I'm looking for a way to calculate the probability of success in the dependent variable for changes of 5% (for example) in the independent variable

Hope my english and my question are understandable.

Than you very much,
Hans Huber

[Clyde Schechter]

I understand that gives me the probability of success for changes in 1% in the independent variable

Incorrect. It gives you the difference in probability of success for differences (or changes) of 1 unit in the independent variable. Moreover, since the probit link is non-linear, this difference (also called the marginal effect) is different depending on the "starting point" of the 1 unit difference in X. What -margins, dydx()- will give you is an average marginal effect, averaged over the joint distribution in the data set of all the independent variables.

If that is the statistic you want, but you want to talk differences associated with a 1% difference (or change) in the independent variable, you need the semi-elasticity: -margins, dyex()-.

Whether we are dealing with the semi-elasticity or the marginal effect, if you want to get differences associated with a 5 unit (marginal effect) or 5% (semi-elasticity) difference in X, then the simplest way to do that is to redo the probit model and re-scale X.

gen X5 = X/5 // 1 UNIT DIFFERENCE IN X5 = 5 UNIT DIFFERENCE IN X
probit ...X5... // X5, NOT X
margins, dydx(X) // OR dyex(X) IF YOU WANT SEMI-ELASTICITY