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  • Fixed Effects Interpretation of Independent Categorical Variable

    Suppose we are interested in knowing whether longer experience in a white collar job has any effect on wages. Suppose, for the purposes of this example, that work experience as a white collar is a categorical variable.

    bcuse keane, clear
    xtset id year
    xtreg lwage i.expwc, fe


    My question relates to the interpretation of this effect. Some have answered this question by saying that the interpretation of categorical variables is the same as in the case of OLS -- i.e. compared to those who do not have experience (the reference category) those who have one year of experience earn 0.2 more.

    The alternative is to say that the effect of a change in work experience (say from 0 to 1) makes that individual earn 0.2 more.

    If it is the latter case, how is one to interpret the reference category?

    a) Is it that those who have changed their work experience are earning 0.2 more than they were earning when they had no work experience b) Is is that, compared to those who (assuming it's possible) have changed and now they have no work experience (say a move from 2 years to 0 years), those who have now one year (moving from 0-1) earn 0.2 more?










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    Some have answered this question by saying that the interpretation of categorical variables is the same as in the case of OLS -- i.e. compared to those who do not have experience (the reference category) those who have one year of experience earn 0.2 more.
    No, that is completely wrong. The fixed-effects regression is a purely within-panel estimator. It says nothing whatsoever about comparisons between people. It refers only to what happens within an individual person over time. The contrast between people with different levels of the independent variable is not estimated in any way by the fixed effects estimator and it has no necessary relationship to the within-person results.

    The alternative is to say that the effect of a change in work experience (say from 0 to 1) makes that individual earn 0.2 more.
    Well, this is closer, but you are using causal language here. You don't tell us about your data collection and study design, but if this is observational data, then you cannot draw any causal inference.

    The interpretation of the reference category cannot be ascertained from what you show here. It depends on how the categorical variable was created. For example, it may be that it was created by imposing 8 cutpoints on a continuous variable, and coding the resulting 9 intervals with numbers 0 through 8. The reference category, 0, corresponds to any amount of experience in that lowest interval. But there are many other ways of creating a variable like this. The generalization is that the reference category is whatever the value 0 means, unless somewhere you have designated some other value as the base category for expwc with an -fvset- command.

    The interpretation of the coefficient of 1.expwc is simply that the expected value of lnwage for a person is 0.2 higher when his/her experience falls into category 1 than when it falls into category 0. Since lnwage is, I assume, the natural logarithm of actual wage, this could also be said as the expected value of a person's wage associated with experience in the 1 category is approximately 1.22 (= exp(0.2)) times as high as when that person was in category 0.




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