\section{Additional tables and experiment register}
\label{app:extra}

\paragraph{Experiment register.} Each experiment was pre-registered with the following hypothesis before it was run; the outcome
column records whether the stored results support it.
\begin{enumerate}[label=E\arabic*.]
\item Baseline: unique equilibrium, durations of a few months, urgency discount of a few percent, positive between-type dispersion,
decreasing population hazard. Supported (Tables~\ref{tab:baseline}--\ref{tab:types}, Figures~\ref{fig:equilibrium}, \ref{fig:survival}).
\item Urgency gradient: monotone schedules, attenuation $|\bar p'|<|V'|$, steeper when arrivals fall. Supported (Figures~\ref{fig:urgency_price}--\ref{fig:urgency_hazard}).
\item Arrival collapse: lower prices and tightness, longer durations, more inventory, wider discount; GE exceeds PE; $\Gamma$ changes sign. Supported (Table~\ref{tab:compstat}, Figure~\ref{fig:discount}).
\item Financing: screen equivalent to $A$; mortgage deals need better matches; three-term gap; $\Delta_b$ rising in urgency. Supported except that mortgage deals need better matches only for urgent sellers (selection term negative for patient sellers), and the extension is inadmissible for $\phi_m\le0.6$ (Table~\ref{tab:financing}).
\item Bargaining power: hump-shaped welfare near the Hosios value; heterogeneity shifts the optimum. Supported for the hump; the optimum is at 0.55 for both economies, so the heterogeneity shift is not detectable (Table~\ref{tab:welfare}).
\item Matching versus approval: distinct signatures in the extension. Supported (Table~\ref{tab:match_vs_approval}).
\item Entry: monotone residual, amplification, entry costs. Supported (Tables~\ref{tab:entry}, \ref{tab:uniqueness_draws}).
\item Heterogeneity: dispersion rises with the spread of $F$ and when liquidity falls. Supported (Table~\ref{tab:heterogeneity}).
\item Dynamics: impact fall of the index, inventory build-up, slow volume; composition transitory; sign depends on $G$. Supported, with the qualification that prices adjust fully on impact (Table~\ref{tab:dynamics}).
\item Selection: small composition term, sign governed by $h_GM$. Supported (Table~\ref{tab:selection}).
\item Posted prices: pickier sellers, between-type dispersion only, gradient preserved. Supported (Table~\ref{tab:protocols}).
\item Sensitivity and convergence: signs robust, objects converge, Monte Carlo agrees. Supported (Tables~\ref{tab:sensitivity}--\ref{tab:distributions}, Appendix~\ref{app:computation}).
\end{enumerate}

\begin{table}[H]
\centering
\caption{Qualification screen $\phi$ in the baseline (model-generated, general equilibrium)}
\label{tab:screen}
\footnotesize
\input{tables/tab04a_qualification_screen}
\end{table}

\begin{table}[H]
\centering
\caption{Financing extension: approval delay (model-generated)}
\label{tab:fin_delay}
\footnotesize
\resizebox{\textwidth}{!}{\input{tables/tab04c_financing_delay}}
\end{table}

\begin{table}[H]
\centering
\caption{Financing extension: bargaining power and the delay-bargaining term (model-generated)}
\label{tab:fin_beta}
\footnotesize
\resizebox{\textwidth}{!}{\input{tables/tab04d_financing_bargaining}}
\end{table}

\begin{table}[H]
\centering
\caption{Entry and search costs (model-generated, general equilibrium)}
\label{tab:entry}
\footnotesize
\resizebox{\textwidth}{!}{\input{tables/tab07e_entry_costs}}
\end{table}

\begin{table}[H]
\centering
\caption{Uniqueness check: number of roots of the free-entry residual in 60 random parameter draws (model-generated)}
\label{tab:uniqueness_draws}
\footnotesize
\input{tables/tab07f_uniqueness}
\end{table}

\begin{table}[H]
\centering
\caption{Dispersion decomposition as a function of the seller's bargaining share (model-generated)}
\label{tab:disp_beta}
\footnotesize
\input{tables/tab05b_dispersion_beta}
\end{table}

\begin{table}[H]
\centering
\caption{Planner's steady-state flow optimum versus the decentralised equilibrium (model-generated)}
\label{tab:planner}
\footnotesize
\resizebox{\textwidth}{!}{\input{tables/tab08b_planner}}
\end{table}

\begin{table}[H]
\centering
\caption{One-at-a-time sensitivity of baseline moments (model-generated)}
\label{tab:sensitivity}
\scriptsize
\input{tables/tab07_sensitivity}
\end{table}

\begin{table}[H]
\centering
\caption{Alternative match-value distributions at the baseline parameters (model-generated)}
\label{tab:distributions}
\footnotesize
\resizebox{\textwidth}{!}{\input{tables/tab07b_distributions}}
\end{table}