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The delta method/bootstrap method is used to obtain the standard error of marginal effect in case of limited dependent variable model (like tobit model). I have seen these being applied for the continuous variables, but my question is whether these can be also applied for categorical variables (say with 4 categories) or binary variables (say only with two categories). Please suggest academic papers if it is relevant to the question.

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Take a look at the formulas on page 324 of Tamás Bartus' "Estimation of Marginal Effects Using Margeff" from Stata Journal. The formulas and explanations are not Stata-specific.

Stata now handles these calculations using the margins command.

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