What are the main imputation methods that can be used to deal with top censored panel income data if a big proportion (about 40%) is censored?
You deal with a highly skewed censored distribution which makes it really hard to get good estimates. The key question is what information is available to model the skewed income distribution (you don't say anything on that).
There is quite some literature on the issue of imputing top incomes. E.g. "Measuring inequality using censored data: a multiple‐imputation approach to estimation and inference" by Stephen P. Jenkins Richard V. Burkhauser Shuaizhang Feng Jeff Larrimore. The abstract kind of nails the problem:
To measure income inequality with right‐censored (top‐coded) data, we propose multiple‐imputation methods for estimation and inference. Censored observations are multiply imputed using draws from a flexible parametric model fitted to the censored distribution, yielding a partially synthetic data set from which point and variance estimates can be derived using complete‐data methods and appropriate combination formulae. The methods are illustrated using US Current Population Survey data and the generalized beta of the second kind distribution as the imputation model. With Current Population Survey internal data, we find few statistically significant differences in income inequality for pairs of years between 1995 and 2004. We also show that using Current Population Survey public use data with cell mean imputations may lead to incorrect inferences. Multiply‐imputed public use data provide an intermediate solution.
Also see "Recent Trends in Top Income Shares in the United States: Reconciling Estimates from March CPS and IRS Tax Return Data" to get an idea how to model a censored right-skewed income distribution in a proper way.