Remarks on the Young‐Balk‐Mehrhoff‐Dikhanov Elementary Price Index
研究一种新提出的基本价格指数（YBMD指数）的公理性质，通过模拟比较其与常用指数在偏误和均方误差上的表现，发现该指数在特定条件下更优。
ABSTRACT Common elementary price indices include Dutot, Carli, and Jevons, while less‐known ones include Carruthers‐Sellwood‐Ward‐Dalén (CSWD) and harmonic indices. Recently, a new elementary index, the Dikhanov index, has been proposed, previously introduced independently by Allyn Young, Bert Balk, and Jens Mehrhoff. This paper presents the axiomatic properties of the Young‐Balk‐Mehrhoff‐Dikhanov (YBMD) index and compares it with population elementary indices under log‐normal price assumptions. Using simulations, biases, and Mean Squared Errors (MSEs) of sample indices are analyzed. Results show that the YBMD index is asymptotically unbiased, with bias and MSE decreasing as price correlations between periods increase. Notably, the study identifies scenarios where the sample YBMD index exhibits lower bias and MSE than the sample CSWD and Jevons indices, highlighting its potential advantages in practical applications.