Suppose You Regress a Time-Series of Appraisal-Based Index Periodic Returns $r_{t}^{*}=\alpha+\beta_{0} r_{M t}+\beta_{1} r_{M t-1}+\beta_{2} r_{M,t t-2}+\beta_{3} r_{M,t t-3}+\varepsilon_{t}$

Essay

Suppose you regress a time-series of appraisal-based index periodic returns onto both contemporaneous and lagged securities market returns that do not suffer from lagging or measurement errors. That is, you perform the following regression, where rM,t is the accurate market return in period t and r*t is the appraisal-based real estate return in period t:

$r_{t}^{*}=\alpha+\beta_{0} r_{M t}+\beta_{1} r_{M t-1}+\beta_{2} r_{M,t t-2}+\beta_{3} r_{M,t t-3}+\varepsilon_{t}$

The resulting contemporaneous and lagged beta values are:


$\begin{array}{l}\hat {B}_{0}=0.12 \\ \hat {B}_{1}=0.20 \\ \hat {B}_{2}=0.15 \\ \hat {B}_{3}=0.02\end{array}$


What is your best estimate of the true long-run beta between real estate and the securities market index?