In the booming field of real estate analysis, we rely on data to make critical decisions. Whether we're building an Automated Valuation Model (AVM) to instantly price homes or conducting a deep dive into local market trends, we're utilizing modeling. But beneath the surface of the standard regression equation lies a crucial distinction: are we performing statistical modeling or econometric modeling?
While the two disciplines employ
the same mathematical tools, their objectives are fundamentally distinct. Statistical
modeling is concerned with prediction—finding the best mathematical model
that fits a given dataset. Econometric modeling, by contrast, is concerned with
causality—using
economic theory to understand why a variable matters and to quantify its specific
economic impact.
This post will demystify this
difference, demonstrating how we move from simply running a correlation (a
statistical exercise) to rigorously estimating the actual, defensible economic
value of property characteristics (a robust econometric analysis). By focusing
on the real estate market, we'll show that in high-volume valuation
environments, we aren't just using statistics; we're using statistics as the
engine for a comprehensive, theory-driven econometric analysis.
Statistical Modeling vs.
Econometric Modeling
The
primary difference between statistical and econometric modeling lies in their purposes and theoretical foundations. Think of statistics as
the toolset and econometrics as
the specialized application of that toolset to economic
questions.
(Click on the image to enlarge)
Statistical
Modeling: The Foundational Toolset
Statistical
modeling is a broad discipline focused on establishing a mathematical
relationship between variables within a given dataset.
· Focus on Description and Prediction: The
primary aim is to describe how changes in independent variables relate
to changes in the dependent variable and to predict the value of the
dependent variable for new data points.
· A-Theoretical: A
statistical model is not inherently constrained by an underlying theory. We
could statistically model the relationship between the number of times a
particular word appears in a book and the book's sale price—it's just a
correlation, not an economic explanation.
· Real Estate Analysis: When
we use a regression equation to estimate a sale price solely by
minimizing the error between the predicted and actual price, we are engaged in
statistical modeling. Our goal is the most accurate prediction possible,
regardless of whether the coefficients make perfect economic sense.
Econometric
Modeling: The Economic Application
Econometric
modeling is the application of statistical methods (the
"metrics") to economic data (the "econo-") to give
empirical content to economic theories and measure the effects of economic
phenomena.
· Focus on Causality and Theory:
Econometricians start with an economic theory (e.g., in real estate, the
Hedonic Price Theory states that a home's price is determined by the
demand for its individual, measurable characteristics). The model's purpose is
to test this theory and quantify the causal impact of the
characteristics.
· The Why and What If: An
econometric model seeks to answer the "why"—why does
the price change?—and the "what if"—what if we change a
policy or an input?
· Real Estate Analysis: We
use a model to estimate the economic impact of a specific variable,
such as the marginal contribution to value of an extra bedroom, which is
a pure application of econometrics. When we leverage the model's coefficients
to analyze the housing market's supply, demand, or policy impacts, we're
performing econometric analysis.
We are using statistical
modeling tools (such as OLS regression, R-squared calculations, and specific coding
methods for categorical variables) to perform an econometric analysis of
the real estate market. The moment we frame the problem as assessing the
economic value of housing characteristics or testing a market hypothesis, we've
moved into econometrics.
The
Econometric Modeling Process in Automated Valuation
Our six-step process effectively
demonstrates the transition from a purely statistical exercise to a rigorous econometric
analysis suitable for a high-volume automated valuation
modeling (AVM) environment.
· Hypothesis
Formation (Economic Theory): This step is the crux of econometrics. It anchors the model in the Hedonic Price
Model, stating that price is a function of structural and neighborhood characteristics and the time of sale, leading to an economic
assertion that guides the statistical model specification.
· Data
Collection and Preparation (Statistical/Data Science): This is the data science engine.
The crucial part is transforming real-world, non-numeric data (like the town's
name) into quantifiable variables. Methods such as dummy coding,
effect
coding, and one-hot coding are statistical techniques
used in econometrics to create a fixed-effects model, enabling the estimation of a specific, non-linear economic premium for being in one town relative to a
baseline town.
· Model
Specification (Econometric/Statistical): Choosing Ordinary Least Squares (OLS)
regression is a statistical decision based on the desired
properties of the estimator. However, selecting which independent
variables to include (e.g., log(Land Area), log(Living Area), Age, Bathrooms, etc.) is an econometric decision based on the hedonic theory and domain knowledge of factors that influence property value.
· Estimation
(Statistical Computation): The mechanical process of running the software to find
the coefficients that minimize the Sum of Squared Residuals (SSR) is a statistical
calculation.
· Evaluation
(Statistical/Econometric Validation): Statistical metrics, such as the p-value and R-squared (R2),
assess the model's goodness-of-fit and the significance of variables. Econometric
validation involves ensuring the estimated coefficients (e.g.,
the value of an extra bedroom) are plausible and interpretable within the context of
the housing market. Sales ratio analysis (the predicted price to sale
price) is a critical valuation-specific metric for real-world
applications.
· Assumption
Testing (Econometric Rigor): This involves validating the model to ensure it produces Best Linear
Unbiased Estimators (BLUE). Testing for assumptions such as homoscedasticity
(constant variance of errors) and addressing autocorrelation
(especially in time-series data) are vital econometric steps to ensure that the
coefficients are reliable for policy testing and causal inference, not just
prediction.
· Application
(Econometric Output): The
application is the final economic utility of the process. The top-down
(mass appraisal) and bottom-up (individual valuation) uses demonstrate
that the model is no longer just a statistical exercise; it's an economic tool
for mass valuation and financial analysis.
Conclusion
We've established that the
distinction between statistical and econometric modeling is one of purpose,
not just tools. While data preparation, model building, and metric evaluation
are powered by statistical tools (such as OLS, R-squared, and
dummy coding), the entire valuation exercise is guided by econometric
principles.
In the real estate market, this
distinction is everything. A purely statistical model might offer a robust
price prediction, but it lacks the theoretical foundation necessary for
rigorous testing and market defensibility. The econometric approach, starting
with the Hedonic Price Model and validated through stringent assumption testing
(for BLUE properties), ensures that the coefficients we generate aren't just numbers—they
are credible,
quantifiable measures of economic value.
Ultimately, whether we are
generating system-wide values (top-down) or creating a valuation grid for a
series of subject properties (bottom-up), we are applying the results of a
robust econometric model. By embracing this approach, we move beyond simple
data fitting to truly understand, quantify, and explain the complex economic
forces that determine home prices.
