\section{Meta-analytical econometric framework}
\label{sec:framework}

Let $y_{ij}$ be the $j$-th harmonised estimate from study $i$ within a given characteristic and effect-size family, with sampling
variance $v_{ij}$. The random-effects model
\begin{equation}
y_{ij}=\mu+u_i+e_{ij},\qquad u_i\sim N(0,\tau^2),\qquad e_{ij}\sim N(0,v_{ij}),
\label{eq:re}
\end{equation}
is estimated by restricted maximum likelihood \citep{viechtbauer2010conducting}; the paper reports the pooled estimate, its
standard error and confidence interval, the 95 percent prediction interval for a new study, $\tau^2$, $I^2$, the number of
independent studies $k$ and of estimates $n$. Because most studies contribute several estimates, the primary inference comes from
the three-level model
\begin{equation}
y_{ij}=\mu+u_i+w_{ij}+e_{ij},\qquad u_i\sim N(0,\sigma^2_{study}),\qquad w_{ij}\sim N(0,\sigma^2_{model}),
\label{eq:ml}
\end{equation}
with estimates nested in studies \citep{cheung2014modeling}, and from cluster-robust variance estimation with the CR2
small-sample correction and Satterthwaite degrees of freedom \citep{hedges2010robust,pustejovsky2022meta}, which does not rely on the
correctness of the assumed dependence structure. Moderator analysis extends \eqref{eq:ml} with study- and model-level
covariates: the midpoint of the transaction period (not the publication year), a spatial-estimator indicator, a machine-learning
indicator, a working-paper indicator, the log sample size, a rent indicator, an apartment indicator, a non-US indicator and the
presence of time and location fixed effects. Publication selection is examined with funnel plots, the Egger regression test
\citep{egger1997bias}, the PET-PEESE procedure \citep{stanley2014meta} on families with at least twenty estimates and a
step-function selection model \citep{vevea1995general} on families with at least thirty, without applying any correction
mechanically. A Bayesian hierarchical model with weakly informative priors (normal on the mean, half-Cauchy on $\tau$) is fitted
by Gibbs sampling with slice updates on study-level aggregated effects, with $\hat R$ and effective sample sizes reported.
Finally, random forests and gradient boosting with study-grouped cross-validation are used to search for non-linear moderators;
their results are exploratory \citep{mullainathan2017machine,athey2019machine}. All models are run in R (metafor, clubSandwich)
and independently re-implemented in Python; Table~\ref{tab:robustness} reports both.