Imputing the mean of a heteroskedastic log-normal missing variable: A unified approach to ratio imputation

In official economic statistics, the goal of surveys is often to estimate the mean or the total of a heteroskedastic log-normal variable. For this purpose, ratio imputation has been often used to treat missing values. However, there are three competing ratio estimators in the literature: ordinary least squares (OLS); ratio of means (RoM); and mean of ratios(MoR). It is not quite obvious which of the estimators is best, thus leading to a gap between theory and practice. The objective of this article is to fill in this gap by unifying ratio imputation models and by proposing a novel estimation strategy for selecting a ratio imputation model based on the magnitude of heteroskedasticity. The proposed method estimates the magnitude of heteroskedasticity under the framework of weighted least squares (WLS). Using the 135,000 simulated datasets that cover different parameter settings, the results in the Monte Carlo simulation give a strong support for the proposed method. If the estimated magnitude of heteroskedasticity is moderate, RoM should be used. If the estimated magnitude is severe, MoR should be used. If the estimated magnitude is mild, either OLS or RoM may be used.