How can I apply a Pareto tail to a truncated distribution?

Question

Many income surveys (especially older ones) truncate key variables, such as household income, at some arbitrary point, to protect confidentiality. This point changes over time. This reduces inequality measures associated with the variable. I am interested in fitting a Pareto tail to the truncated distribution, replacing truncated values with imputed values to mimic the actual distribution. What's the best way to do this?

Answer 1

The following paper describes a couple of approaches for imputing right censored data in the same domain (i.e. topcoded wage data). They use a truncated normal distribution and describe a single imputation model assuming homoscedasticity, and a multiple imputation model assuming heterscedasticity. Also a second paper of interest, where a generalized beta distribution is assumed, might be closer to what you want.

• Multiple Imputation Approaches for Right-Censored Wages in the German IAB-Employment Register
• Measuring Inequality Using Censored Data: A Multiple Imputation Approach