\begin{tabular}{lc}
\toprule
Quantity & Value \\
\midrule
Within-cell variance of $\ln SP$ & 0.224 \\
Within-cell variance of $\ln AV$ & 0.167 \\
Within-cell covariance & 0.147 \\
Within-cell correlation & 0.759 \\
Forward slope $\hat\beta_{F}$ (Cheng FE) & 0.656 \\
Inverse reverse slope $1/\hat\beta_{R}$ (Kochin--Parks) & 1.137 \\
Noise share $\lambda$ rationalising $\beta = 1$ & 0.344 \\
Implied transaction-noise s.d.\ for $\beta = 1$ (log points) & 0.277 \\
Clapp IV $\hat\beta_{IV}$ & 0.917 \\
Noise share $\lambda$ implied by $\hat\beta_{IV}$ & 0.285 \\
Implied transaction-noise s.d.\ under $\hat\beta_{IV}$ (log points) & 0.252 \\
First stage: coefficient on $Z$ (s.e.) & 0.509 (0.010) \\
First stage: cluster-robust $F$ & 2,418 \\
First stage: $R^2$ & 0.587 \\
Share of sales with $Z = -1$ / $Z = +1$ & 0.244 / 0.263 \\
\bottomrule
\end{tabular}