RDP 2011-04: Assessing Some Models of the Impact of Financial Stress Upon Business Cycles Equation

\begin{array}{l} \ln l_{t} = \ln Q_{t} + \ln R_{K N, t} . \\ \ln l_{t} - \ln \bar{l} = \ln Q_{t} - \ln \bar{Q} + \ln R_{K N, t} - \ln {\bar{R}}_{K N} . \\ \ln l_{t} = {\tilde{q}}_{t} + {\tilde{k}}_{t} - {\tilde{n}}_{t} + \ln {\bar{R}}_{K N} . \\ ∴ l_{t} = \exp ({\tilde{q}}_{t} + {\tilde{k}}_{t} - {\tilde{n}}_{t} + \ln (\frac{\bar{K}}{\bar{N}})) . \end{array}