Multiple imputation for demographic hazard models with left-censored predictor variables

A common problem when using panel data is that an individual’s history is incompletely known at the first wave. We show that multiple imputation, the method commonly used for data that are missing due to non-response, may also be used to impute these data that are “missing by design.” Our application is to a woman’s duration of fulltime employment as a predictor of her risk of first birth. We multiply-impute employment status two years earlier to “incomplete” cases for which employment status is observed only in the most recent year. We then pool these “completed” cases with the “complete” cases to derive regression estimates for the full sample. Relative to not being fulltime employed, having been fulltime-employed for two or more years is a positive and statistically significant predictor of childbearing whereas having just entered fulltime employment is not. The fulltime-employment duration parameter variances are about one third lower in the multiply-imputed sample than in the complete-data sample, and only in the multiply-imputed sample does the employment-duration coefficient attain statistical significance