Re: [amelia] "Partially missing data" problem

Dear Amelia-listers, I have the following, probably atypical, missing data problem. My variable of interest is "hourly earnings," which I calculate by dividing "annual earnings" by "annual hours worked." The data set I am using (the March supplement of the Current Population Survey) has the first variable over 1960-2005. It also has the variables "total weeks worked" and "usual hours of work per week" in each year over 1960-2005, so "annual hours worked" can be obtained by multiplying these two variables. The problem is that while from 1977 on these variables are measured in integers (i.e, as the exact number of weeks and hours worked, in integers), over 1960-1976 they are measured in interval scales. Hence, for 1960-1976 the data may be considered as "partially missing." I am thinking of using Amelia II to do multiple imputation of these partially missing values, using the data for 1977-1978 as the basis for the imputation. These are my questions: (a) Prima facie, is this a sensible idea? If the answer to (a) is yes: (b) Would it be better to impute each of the two variables ("total weeks worked" and "usual hours of work") separately, and then multiply them to obtain "total weeks worked," or to directly impute the latter variable? (My intuition is that the first method should be preferred, but I do not have a clear reason to give as to why this would be the case.)

(c) Should I treat the observations in each interval of the variable I am imputing as a separate imputation problem, in which the boundaries of the interval provide the boundaries for the imputed values? (This would assure that each person gets imputed a value that is fully consistent with his or her value as measured by the interval scale, but it would require me to do as many imputations as intervals; moreover, for some intervals there may be insufficient observations in 1977-78.) Or should I impute all values at once, and include the variable measured in an interval scale "on the right"? (The problem of this is that the imputed values may be inconsistent with the values measured in the interval scale).

I would appreciate any help a lot. All best, Pablo Mitnik