One way to test whether investors amplify the effect of an exogenous increase in mortgage credit suppy on house prices would be to estimate a “Graham-style” regression for the boom:

\[ \begin{align} \Delta \log P_{z,t} = \alpha_{c,t} &+ X_{z,t}'\Gamma \\ &+ \beta \Delta \log M_{z,t} \\ &+ \delta_1(\Delta \log M_{z,t} \times \Delta InvShare_{z,t}) + \epsilon_{z,t} \end{align} \]

I could try to instrument for mortgage credit growth using the Favara-Imbs credit shock, which is potentially better than Graham’s non-GSE instrument. To be completely water tight, I would also have to instrument for the investor share. Graham instruments for the investor share with its own lagged value, which is unsatisfactory (especially in the boom, if investors have strongly extrapolative expectations).