\section{Publication selection and robustness}
\label{sec:selection}

\subsection{Publication selection}

Figure~\ref{fig:funnel} shows funnel plots for the six most-estimated families and Table~\ref{tab:pubsel} the diagnostics for all
\nPubTested{} families with at least ten estimates: the Egger test, the PET and PEESE intercepts, and, where at least thirty
estimates are available, a three-step selection model. Funnel asymmetry is common: the Egger test is significant in
\nEggerSig{} of \nPubTested{} families. Under such heterogeneity, however, asymmetry is not evidence of publication selection
alone, because precision is correlated with sample size, country, data type and specification, all of which shift the effect
itself; the dependence of multiple estimates on the same study also inflates the test. The PET--PEESE intercepts are reported as
sensitivity analyses rather than as corrected estimates: for the structural core (living-area elasticity, bathrooms, age, garage)
they remain of the same sign and order of magnitude as the random-effects means, which is reassuring; for several amenity premiums
the PET intercept is smaller or of opposite sign to the random-effects mean, which is what one would expect if the
less-precise estimates of small samples are more often reported when they are large and positive (the swimming pool and the
renovation premium are examples). The selection models converge in most families but produce implausible values in a few
(for instance for water proximity), which is a known failure mode of step-function models under extreme heterogeneity and is
reported rather than hidden. The working-paper indicator in the meta-regressions is insignificant in every family, so the
published literature does not differ detectably from the grey literature that was retrievable.

\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{fig10_funnel_plots.pdf}
\caption{Funnel plots for the six most-estimated characteristic--family combinations (vertical line: fixed-effect mean; dashed
lines: pseudo 95 percent limits).}
\label{fig:funnel}
\end{figure}

{\setlength{\tabcolsep}{3pt}\tiny\input{tables/tab09_publication_selection_long}}

\subsection{Robustness}

Table~\ref{tab:robustness} compares, for every pooled family with at least ten studies, the REML estimate from metafor with the
independent Python implementation (which agree to four decimals), the three-level estimate, the range of leave-one-study-out
estimates, the Bayesian posterior mean with its credible interval and the PET--PEESE value. The Bayesian hierarchical model,
fitted on study-level aggregated effects with weakly informative priors, reproduces the frequentist means with wider intervals;
all chains converge (maximum $\hat R$ \maxRhat, minimum effective sample size \minEss). Leave-one-study-out ranges are narrow for
the structural core and wide for the amenity premiums with fewer than ten studies, which identifies the families whose pooled
value depends on one or two studies. Further sensitivity analyses in the replication material, not tabulated here, confirm that
restricting the sample to high-confidence extractions, to journal articles, or to transaction prices, and trimming the one
percent most extreme harmonised values, change the pooled means of the structural characteristics by less than their
cluster-robust standard errors. The retrieved and non-retrieved stage-one studies cannot be compared on estimates, but they can
be compared on metadata: the retrieved set over-represents recent years, open-access journals and conference papers, and
under-represents the older North American journal literature, which is the main threat to the representativeness of the
synthesis and is discussed in Section~\ref{sec:limitations}.

{\setlength{\tabcolsep}{3pt}\tiny\input{tables/tab10_robustness_long}}