Estimating Indices in the Presence of Seller Reservation Prices

This paper documents the potential bias induced in an index of asset prices when sellers use reservation rules that may include some component of private value. We develop a model in which the seller's asking price is determined by private valuation while the buyer's bid price is determined by the market valuation, and a transaction takes place only if the bid is higher than the ask. Therefore, the trading volume and the observed transaction prices are both affected by the ratio of seller's private valuation to the market valuation, which is called the seller reserve ratio. The higher the seller reserve ratio, the lower is the trading volume and the larger is the difference between the market valuations estimated using observed prices and the actual market valuations. To address the estimation problem posed by the bias, we propose a three-step econometric procedure. We first estimate the index using observed prices. We next use residuals from the first step and observed trading volume to estimate the latent series of seller reserve ratio and the unconditional population variance of pricing errors. We then use these estimates in step two to correct for the bias in the index based on observed prices in either a hedonic regression or a repeat sale regression. We call the unbiased index a reserve-conditional index. Simulations show that this remedy effectively mitigates the bias, and the reserve-conditional indices are more accurate than traditional hedonic and repeat sale indices. We apply this technique to Los Angele