Herding Behavior among Residential Developers

Abstract

We investigate whether US real estate developers display herding in their building permit seeking behavior. We measure herding over the period 1988 through 2011 by applying to permit issuances measures previously used in studies of stock herding. We find evidence of herding at levels comparable to those found in studies involving common-stock trading. Developer herding is also stronger in up markets, than in down markets. This is consistent with up market buoyancy constraining the availability of reliable, independent information, which reinforces the tendency to follow the behavior of others.

Appendices

Appendix 1

By Bayes’ Rule, since

$$ {\displaystyle \begin{array}{l}\mathit{\Pr}\left(V=1|{S}_{1A}=1\right)=\mathit{\Pr}\left({S}_{1A}=1\cap V=1\right)/\mathit{\Pr}\left({S}_{1A}=1\right)\\ {}=\frac{\mathit{\Pr}\left({S}_{1A}=1|V=1\right)\mathit{\Pr}\left(V=1\right)}{\mathit{\Pr}\left({S}_{1A}=1|V=1\right)\mathit{\Pr}\left(V=1\right)+\Pr \left({S}_{1A}=1|V=0\right)\mathit{\Pr}\left(V=0\right)}\\ {}=\frac{\phi_1p}{\phi_1p+\left(1-{\phi}_1\right)\left(1-p\right)},\end{array}} $$

we have

$$ {\displaystyle \begin{array}{l}{R}_{1A}\left({\left.{S}_{1A}\right|}_{S_{1A}=1}\right)=E\left(V|{S}_{1A}=1\right)-C\\ {}=\Pr \left(V=1|{S}_{1A}=1\right)-C\\ {}=\frac{\phi_1p}{\phi_1p+\left(1-{\phi}_1\right)\left(1-p\right)}-C.\end{array}} $$

Appendix 2

By Bayes’ Rule, because

$$ {\displaystyle \begin{array}{l}\mathit{\Pr}\left({S}_{1A}=1\cap {S}_{2B}=0\right)\\ {}=\Pr \left({S}_{1A}=1\cap {S}_{2B}=0|V=1\right)\mathit{\Pr}\left(V=1\right)\\ {}\kern0.48em +\Pr \left({S}_{1A}=1\cap {S}_{2B}=0|V=0\right)\mathit{\Pr}\left(V=0\right)\\ {}={\phi}_1\left(1-{\phi}_2\right)p+{\phi}_2\left(1-{\phi}_1\right)\left(1-p\right),\end{array}} $$

we have

$$ {\displaystyle \begin{array}{l}{R}_{2B}\left({\left.{S}_{1A},{S}_{2B}\right|}_{S_{1A}=1\cap {S}_{2B}=0}\right)=\rho \left[E\left(V|{S}_{1A}=1\cap {S}_{2B}=0\right)-C\right]\\ {}=\rho \left[\frac{\mathit{\Pr}\left({S}_{1A}=1\cap {S}_{2B}=0|V=1\right)\mathit{\Pr}\left(V=1\right)}{\mathit{\Pr}\left({S}_{1A}=1\cap {S}_{2B}=0\right)}-C\right]\\ {}=\frac{\rho {\phi}_1\left(1-{\phi}_2\right)p}{\phi_1\left(1-{\phi}_2\right)p+{\phi}_2\left(1-{\phi}_1\right)\left(1-p\right)}-\rho C.\end{array}} $$

Appendix 3

By Bayes’ Rule, because

$$ {\displaystyle \begin{array}{l}\mathit{\Pr}\left({S}_{1A}=0\cap {S}_{2B}=1\right)\\ {}=\Pr \left({S}_{1A}=0\cap {S}_{2B}=1|V=1\right)\mathit{\Pr}\left(V=1\right)\\ {}\kern0.6em +\Pr \left({S}_{1A}=0\cap {S}_{2B}=1|V=0\right)\mathit{\Pr}\left(V=0\right)\\ {}=\left(1-{\phi}_1\right){\phi}_2p+{\phi}_1\left(1-{\phi}_2\right)\left(1-p\right),\end{array}} $$

we can obtain

$$ {\displaystyle \begin{array}{l}{R}_{2B}\left({\left.{S}_{1A},{S}_{2B}\right|}_{S_{1A}=0\cap {S}_{2B}=1}\right)=\rho \left[E\left(V|{S}_{1A}=0\cap {S}_{2B}=1\right)-C\right]\\ {}=\rho \left[\frac{\mathit{\Pr}\left({S}_{1A}=0\cap {S}_{2B}=1|V=1\right)\mathit{\Pr}\left(V=1\right)}{\mathit{\Pr}\left({S}_{1A}=0\cap {S}_{2B}=1\right)}-C\right]\\ {}=\frac{\rho \left(1-{\phi}_1\right){\phi}_2p}{\left(1-{\phi}_1\right){\phi}_2p+{\phi}_1\left(1-{\phi}_2\right)\left(1-p\right)}-\rho C.\end{array}} $$