Affiliations: [a] Tokyo University of Foreign Studies, Tokyo, Japan | [b] Seikei University, Tokyo, Japan | [c] National Statistics Center, Japan
Correspondence:
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Corresponding author: Masayoshi Takahashi, Tokyo University of Foreign Studies, 3-11-1 Asahi-cho, Fuchu-Shi, Tokyo 1838534, Japan. Tel.: +81 42 330 5158; E-mail:mtakahashi@tufs.ac.jp
Abstract: 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.
Keywords: Ratio imputation, missing value, log-normal, heteroskedasticity, regression through the origin, mean of ratios, ratio of means
