Imputation and Price Indexes: Theory and Evidence from the International Price Program

The goal of this paper is to theoretically and empirically demonstrate the consequences of different imputation methods, using recent data from the International Price Program. We suppose that prices are missing due to random or erratic reporting. We consider three different imputation methods: carry-forward, which just assumes that the missing price is the same as in the previous period; cell-mean, which imputes the missing price using either the short-term or long-term index for related commodities; and linear interpolation, which uses the last and next observations for the item to linearly interpolate. Certain hybrid techniques, combining either carry-forward or cell-mean with linear interpolation, are also considered. Our conclusions are: (1) Some imputation is better than no imputation; (2) the short term cell-mean introduces some "noise" into the price index: (3) linear interpolation results in less fluctuation of prices than the true series: (4) combining either carry-forward or cell-mean with linear interpolation gives similar results.