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I am trying to interpret the coefficients on the year dummies in an ordered probit regression. My data is a panel with 20 years. I have included 19 year dummies with the exclusion of the first year. This enables me to interpret the coefficients of each dummy in relation to the year that was dropped. Now I have to include a variable which has the same value in each year across the panel. WHen I run my oprobit on stata it automatically drops one of the year dummies due to collinearity. How do I interpret the remaining coefficients on the year dummies?

As an additional note the focus of the study is on trends in the coefficients of the time dummies. So if two year dummies are dropped can the remaining dummies be interpreted in relation to the ones that were dropped and if so, what is the interpretation?

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I am not sure your dummy coefficients have any clean interpretation at all any more, although of course they are OK to be used for predictive purposes. There's a formal interpretation of he coefficient showing whatever's left after accounting for all other variables, but identification does make things complicated, as you don't have a well-defined reference category anymore.

If you know the functional form of the trend (linear, quadratic, changepoint), you'd be better off adding that trend directly to your explanatory variables.

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