The Impact of Differential Measurement Error in House Price Indices

Introduction

House price indices are essential tools in real estate analysis, mortgage modeling, and decision-making. These indices provide a standardized way to track changes in home values over time, helping homeowners, lenders, and policymakers gauge market trends and forecast future price movements. However, a recent study by Darren Hayunga, R. Kelley Pace, Shuang Zhu, and Raffaella Calabrese (2024) has uncovered a critical issue: differential measurement error within these indices. This type of error can significantly distort house price estimates, impacting the accuracy of mortgage and housing market models.

In a previous article, I emphasized the need for systematic analysis of the errors produced by mark-to-market (i.e., HPI-based) models. This new research aligns with that idea and echoes similar conclusions, particularly around the importance of building price-tier-specific HPIs and the advantage of hedonic models and automated valuation models (AVMs) over mark-to-market approaches.

This article summarizes the key findings of the study and examines its broader implications for real estate professionals, mortgage lenders, and policymakers.

Key Concepts and Findings

What is Differential Measurement Error? 

Differential measurement error occurs when errors in estimating house prices are correlated with other variables in the model, such as the value of the home itself. Unlike random or non-differential measurement error, which does not introduce systematic bias, differential measurement errors skew the relationships being modeled, leading to biased results.

The study found that commonly used house price indices, such as the S&P CoreLogic Case-Shiller (SPCCS) and the Federal Housing Finance Agency (FHFA) index, frequently suffer from differential measurement error. These errors are not random; instead, they tend to vary based on house prices, often underrepresenting price appreciation for high-priced homes and overrepresenting it for lower-priced homes.

While differential measurement error is sometimes confused with heteroskedasticity, the two are distinct. Heteroskedasticity refers to variability in the size of errors depending on the level of an independent variable but without systematic bias. In contrast, differential measurement error both changes in magnitude and introduces bias by distorting the true relationship between variables. Where heteroskedasticity affects the precision of estimates, differential measurement error affects the reliability of the estimates themselves.

Bias in House Price Indices

The study examined nearly 600,000 home transactions in the Dallas-Fort Worth (DFW) Metroplex and found significant measurement errors in both the SPCCS and FHFA indices. In some cases, the errors were as large as 30% of actual transaction prices. Specifically, the indices tended to underestimate price appreciation for homes in the highest price deciles while overestimating appreciation for homes in the lower deciles.

Impact on Mortgage Models

These measurement errors have serious consequences for mortgage models, which often rely on house price indices to calculate loan-to-value (LTV) ratios, a key factor in assessing a borrower’s risk of default or prepayment. The study revealed that the errors in house price indices could lead to biased LTV ratios, resulting in misleading assessments of both borrower creditworthiness and loan risk.
For instance, homes owned by borrowers with high credit scores often appreciate faster than indicated by price indices, meaning mortgage models may undervalue these properties and underestimate the associated risks. Conversely, for lower-value homes, the measurement errors may lead to overestimated risks.

Implications for Real Estate and Mortgage Professionals

Inaccurate Price Predictions Affect Lending Decisions

Mortgage lenders and GSEs like Fannie Mae and Freddie Mac may make misinformed lending decisions by relying on house price indices affected by differential measurement errors. These errors could lead to less favorable loan terms for high-credit borrowers whose homes appreciate faster than predicted while overestimating the risk in loans to lower-income borrowers.

Measurement Error Can Skew Real Estate Market Analyses

Real estate professionals use price indices to track market trends and advise clients on buying, selling, or refinancing. Differential measurement error can distort these analyses, leading to inaccurate market assessments. This problem is especially acute for homeowners in high-value or low-value segments, where the bias in the indices is most pronounced.

Model Biases Could Lead to Policy Missteps

Policymakers depend on accurate housing data to design programs that address issues like housing affordability, mortgage assistance, and economic stability. If the house price indices they use suffer from differential measurement error, it could result in misguided policies that fail to address the needs of homeowners across various price tiers.

Recommendations for Addressing Measurement Error

Internal Validation Studies

Researchers and decision-makers should conduct internal validation studies to estimate and correct bias in house price indices, similar to those used in the study. This approach could reduce the impact of differential measurement error on house price models.

Hedonic Pricing Models

 The study found that hedonic models, which estimate house prices based on property characteristics (e.g., size, age, location), are effective at reducing the impact of measurement error. Incorporating these models into mortgage risk assessments could lead to more accurate valuations and better loan underwriting decisions.

Avoiding Strong Non-Linear Transformations

Non-linear transformations of house price data can magnify the effects of measurement error. Avoiding these transformations can reduce sensitivity to errors and improve model reliability.

Use Price-Tier Specific Indices

GSEs and other users of house price data should adopt price-tier-specific indices wherever possible. These indices account for the different price levels in a housing market and can help mitigate bias in predictions for high-value and low-value homes.

Read more: Hybrid models the best of both worlds

Conclusion

The presence of differential measurement error in house price indices presents a significant challenge for real estate professionals, mortgage lenders, and policymakers. This error introduces bias into models that depend on these indices, leading to flawed assessments of home values, loan risks, and overall market conditions. By implementing the strategies outlined above, stakeholders can mitigate the effects of these errors and base their decisions on more accurate, reliable data. Addressing these challenges is critical for improving the predictive power of mortgage models and fostering more informed real estate practices and policies.

Written by Franklin Carroll. September 16, 2024

Franklin Carroll is Kukun's VP of Modelling and Analytics; After finishing his studies at the University of Chicago, he worked at Fannie Mae where he helped build Collateral Underwriter, roll out the Value Verify initiative, and specialized in collateral related and credit related policy.