Hi,

I can solve the model in dynare but I need your help for the following problem: How does one derive a log-linearized expression for a forward-looking variable around the steady-state? For example, the price dividend ratio can be defined as

\frac{P_t}{D_t} = E_t [M_{t,t+1}\frac{D_{t+1}}{D_t}(1+ \frac{P_{t+1}}{D_{t+1}})]

The goal is to derive the relation between \frac{P_{t+1}}{D_{t+}} and shocks at t+1, assuming that at t the system is in steady state so \frac{P_t}{D_t} is the steady state value C.

If we ignore the expectation and log-linearize it, I get

\log C = m_{t,t+1} + \Delta D_{t+1} + \log(1+\frac{P_{t+1}}{D_{t+1}})

and clearly one can solve \frac{P_{t+1}}{D_{t+1}} analytically (assuming that m and \Delta D are known functions of shocks).

But, isn’t ignoring expectation imposing that the equality hold **state by state**, instead of on average?

Please advise, thanks!