1\section{Publication selection and robustness}2\label{sec:selection}34\subsection{Publication selection}56Figure~\ref{fig:funnel} shows funnel plots for the six most-estimated families and Table~\ref{tab:pubsel} the diagnostics for all7\nPubTested{} families with at least ten estimates: the Egger test, the PET and PEESE intercepts, and, where at least thirty8estimates are available, a three-step selection model. Funnel asymmetry is common: the Egger test is significant in9\nEggerSig{} of \nPubTested{} families. Under such heterogeneity, however, asymmetry is not evidence of publication selection10alone, because precision is correlated with sample size, country, data type and specification, all of which shift the effect11itself; the dependence of multiple estimates on the same study also inflates the test. The PET--PEESE intercepts are reported as12sensitivity analyses rather than as corrected estimates: for the structural core (living-area elasticity, bathrooms, age, garage)13they remain of the same sign and order of magnitude as the random-effects means, which is reassuring; for several amenity premiums14the PET intercept is smaller or of opposite sign to the random-effects mean, which is what one would expect if the15less-precise estimates of small samples are more often reported when they are large and positive (the swimming pool and the16renovation premium are examples). The selection models converge in most families but produce implausible values in a few17(for instance for water proximity), which is a known failure mode of step-function models under extreme heterogeneity and is18reported rather than hidden. The working-paper indicator in the meta-regressions is insignificant in every family, so the19published literature does not differ detectably from the grey literature that was retrievable.2021\begin{figure}[H]22\centering23\includegraphics[width=\textwidth]{fig10_funnel_plots.pdf}24\caption{Funnel plots for the six most-estimated characteristic--family combinations (vertical line: fixed-effect mean; dashed25lines: pseudo 95 percent limits).}26\label{fig:funnel}27\end{figure}2829{\setlength{\tabcolsep}{3pt}\tiny\input{tables/tab09_publication_selection_long}}3031\subsection{Robustness}3233Table~\ref{tab:robustness} compares, for every pooled family with at least ten studies, the REML estimate from metafor with the34independent Python implementation (which agree to four decimals), the three-level estimate, the range of leave-one-study-out35estimates, the Bayesian posterior mean with its credible interval and the PET--PEESE value. The Bayesian hierarchical model,36fitted on study-level aggregated effects with weakly informative priors, reproduces the frequentist means with wider intervals;37all chains converge (maximum $\hat R$ \maxRhat, minimum effective sample size \minEss). Leave-one-study-out ranges are narrow for38the structural core and wide for the amenity premiums with fewer than ten studies, which identifies the families whose pooled39value depends on one or two studies. Further sensitivity analyses in the replication material, not tabulated here, confirm that40restricting the sample to high-confidence extractions, to journal articles, or to transaction prices, and trimming the one41percent most extreme harmonised values, change the pooled means of the structural characteristics by less than their42cluster-robust standard errors. The retrieved and non-retrieved stage-one studies cannot be compared on estimates, but they can43be compared on metadata: the retrieved set over-represents recent years, open-access journals and conference papers, and44under-represents the older North American journal literature, which is the main threat to the representativeness of the45synthesis and is discussed in Section~\ref{sec:limitations}.4647{\setlength{\tabcolsep}{3pt}\tiny\input{tables/tab10_robustness_long}}48