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I am running a Heckman Probit. Both steps assume normal errors of the latent variable, correct? My data is from a survey and a lot of variables are strongly skewed, so I am worried whether this assumption holds. Is there any test I can use? The sample is 10 000, does it help? Also, can I make the errors closer to normal by transforming the data in some way? Say, taking logs?

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The distribution of the explanatory variable is immaterial for the distribution of the residuals. Since this is at its core a probit model with some additional bells and whistles the residuals that your model cares about cannot be observed, so you can forget about checking these directly. It is easier to think about this assumption as an assumption on the functional form of the relationship between the probability and the explanatory variables and (graphically) check these.

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    $\begingroup$ Thanks! How do I check it graphically? Do you suggest plotting actual dependent variable vs predicted for the variable of interest at mean of other controls? $\endgroup$
    – user41196
    Commented Mar 2, 2014 at 16:01

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