I'm trying to construct summary variables for proportion of time spent in different employment statuses over an individual's working life (e.g. % of time spent unemployed between ages 18-21).
My data has missing values which I would like to impute. The problem is proportions are mutually dependent: if an individual spends at least 90% of the time unemployed, they can spend no more than 10% of the time in any other employment status. Imputation of one value (e.g. time in unemployment) influences the range of values another incomplete variable can take (e.g. time in work).
Does anyone know the best way to impute data in this situation? I've tried using Brendan Halpin's method of imputing the raw month-by-month statuses first (link here), before creating summary variables. But, I have some individuals with no status data whatsoever, and this method cannot handle that as far as I am aware.
Another approach might be to naively impute each variable (% time in unemployment, etc) and then divide by the sum of all of them, thus constraining to 1. Are there any drawbacks to this or other approaches I should consider?
I should also add, in imputing the data, I don't want to throw away the information I already have which gives a lower bound to the value to be imputed. For instance, I may have data for 50% of the months I want to derive a summary variable from. If an individuals was unemployed for 75% of this time, then I know that the true value for % time spent unemployment must be at least 37.5% (.5 * 0.75).