spb/wp9_uqo

1\begin{table}[htbp]\centering2\caption{Decomposition of the explained variance of log list prices (percentage points of $R^2$)}3\label{tab:shapley}4\begin{threeparttable}5\begin{tabular}{lccc}6\toprule7Block & Sequential & Shapley & Owen (grouped) \\8\midrule9\multicolumn{4}{l}{\emph{All residential} ($N=142,121$, $R^2=0.776$)} \\10\quad Structure & 43.6 & 33.0 & 34.0 \\11\quad Dwelling type and ownership & 1.6 & 7.5 & 7.3 \\12\quad Province & 14.3 & 8.9 & --- \\13\quad Neighbourhood (FSA) & 18.1 & 28.2 & 36.3\tnote{a} \\14\addlinespace15\multicolumn{4}{l}{\emph{Houses} ($N=83,524$, $R^2=0.769$)} \\16\quad Structure & 46.7 & 31.8 & 33.8 \\17\quad Dwelling type and ownership & 0.3 & 0.9 & 1.0 \\18\quad Province & 13.5 & 10.8 & --- \\19\quad Neighbourhood (FSA) & 16.5 & 33.5 & 42.2\tnote{a} \\20\addlinespace\bottomrule21\end{tabular}22\begin{tablenotes}\footnotesize23\item Notes: \emph{Sequential} is the increment in $R^2$ when the block is added in the order structure $\to$ type/ownership $\to$ province $\to$ FSA. \emph{Shapley} averages the increment over all $4!$ orderings of the four blocks \citep{israeli2007shapley,gromping2007estimators}. \emph{Owen} treats province and FSA as a single location group and averages over the $3!$ orderings of the three groups \citep{huettner2012axiomatic}. Province dummies are nested in the FSA effects, so the province block adds nothing once FSA effects are present.24\item[a] Location group (province $+$ FSA).25\end{tablenotes}26\end{threeparttable}27\end{table}28