Appraisal quality and loan characteristics: evidence from Newcomb–Benford Law

Abstract Leading digits in mortgage collateral value estimates are expected to approximate a logarithmic distribution, consistent with the Newcomb–Benford Law (NBL), when such values are modeled as geometric sequences or random samples drawn from heterogeneous price distributions. Using representative US datasets, we document substantial discrepancies between the observed and expected distributions of leading digits in appraisal values. The magnitude of this deviation increases with loan-to-value ratios and interest rates, while it declines with higher credit scores and safer credit classifications. We also find a systematic underrepresentation of high digits (e.g., 8 and 9) and overrepresentation of low digits (e.g., 0 and 1) in the second leading positions, and that this pattern becomes more pronounced with greater ex-ante loan risk. These findings suggest that nonconformance with NBL may stem from upward bias in appraised values, particularly in riskier lending environments.