An Analysis of the Relationship between Price and Variance for Homogeneous Housing Stock

This study examines the structure of price variance for homogeneous residential housing stock, where homogeneous is defined as economically equivalent, not necessarily physically identical. Assessed values, obtained from ad valorem tax rolls, are used as the basis for identifying properties considered to be economically equivalent. From these data an investigation of the distribution of sale price and variance for housing in selected value ranges is conducted. Subsequently, ANOVA is performed to determine the composition of variance through time and across cities within one metropolitan housing market. In line with conventional wisdom, we find that variance increases with price over the entire data set. The increase, however, is not constant nor does it exhibit a simple proportional relationship to price. Variance increases at an increasing rate in the lower to mid-price ranges and continues to increase but at a decreasing rate in the upper price ranges. From this it was determined that the functional relationship between price and variance is best approximated by a quadratic function in the lower to mid-price ranges and a cubic function when higher price properties are included. ANOVA results indicate that variance is significantly different through time and across location. The interactive term was also significant. The findings of this study would appear to have implications for fee appraisers, assessors, investors, and mortgage lenders.