Linear Probability Model on unbalanced panel with dummy dependent variable

[Laura Roncaglia]

Dear all,

I am new to Stata. I am analyzing a dataframe made on a survey. The survey is conducted every two years and it is about complementary pension; my answer is about the commands that I should use to run a simple LPM (without effect) and a LPM with fixed effect. I also run a probit model without effect and a probit with random effect, but I was interested also on LPM.


I used the xtset command to create the panel df:

xtset id year

where id is the individual variable and year is time variable. The dependent variable is a dummy (pension) which takes value 1 if the individual has a complementary pension form and 0 otherwise.

I read on the website and I suppose that the following commands should be right:

regress pension i.sex age sqage i.area i.instruction, robust

xtreg pension i.sex age sqage i.area i.instruction, fe vce(cluster id)

probit pension i.sex age sqage i.area i.instruction

xtprobit pension i.sex age sqage i.area i.instruction, re

and the mfx compute command to get the marginal effects

My answer regard mostly the command for the LPM: I know I can't change the nature of pension in factor and use regress or xtreg and so I am not sure the these commands give me the right results when the dependent variable is binary but coded as numeric in stata.

Thanks in advance

[Nick Cox]

Cross-posted http://stackoverflow.com/questions/4...ndent-variable

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[Clyde Schechter]

I'm not really sure what you are asking. But I'll make some general comments.

The command -regress pension i.sex age sqage i.area i.instruction, robust- correctly codes a linear probability model. The coefficients you get are estimators of the absolute difference in the probability of having a complementary pension associated with a unit increase in the value of the corresponding predictor variable. The -xtreg- version of the command does this also, while accommodating repeated observations within individual id and providing an estimate of the effects of the predictor variables over time within person.

The main objections people have to linear probability models is that heteroscedasticity is almost invariably present, and the fact that the model can potentially predict probabilities that are not between 0 and 1 if sufficiently extreme values of the predictor variables are used. The latter problem may or may not arise in your data. Even if it does, it doesn't necessarily compromise the usefulness of the coefficients as estimators of effects. The former compromises the standard errors and p-values, but is adequately dealt with by using the robust variance estimator (as you have done). So I think these linear probabilitiy models are reasonable.

All of that said, I'm guessing that the variable sqage is age squared (age*age). If so, you would be better off using factor variable notation to deal with it:

regress pension i.sex c.age##c.age  i.area i.instruction, robust

If you are using current Stata, then use the -margins- command (which has replaced the older -mfx-) to calculate your marginal effects. You can also use -marginsplot- after -margins- to make helpful graphs. If you are using an older version of Stata, you are asked to tell us that in your post so we don't give you advice you can't apply.

[Laura Roncaglia]

Thank you very much Clyde Schechter; your answer is completely satisfying.