Automatic removing of trends

Stationarizing a non-linear model by hand is a tedious process that is better done by the computer.

Computing the equilibrium growth rates of a balanced growth model is complicated and will not be attempted here. We limit ourselves to replace non-stationary variables by their stationary counterpart as specified by the user.

First case: exogenous nonstationary process

$\begin{eqnarray*} y_t &=& A_t k_{t-1}^\alpha\\ A_t &=& (1+g_t)A_{t-1}\\ g_t &=& \rho\, g_{t-1}+e_t \end{eqnarray*}$

Assuming that $y_t$ and $k_t$ have common trend $A_t$ , the stationarizing procedure calls for dividing first and second equation by $A_t$ . The second equation becomes meaningless and corresponds to the fact that $A_t$ doesn't belong to the stationary model.

== Second case: endogenous nonstationary process {{{$!latex \begin{eqnarray*} P_t\,C_t &= W_t\, L_t\\ P_t &= (1+\pi_t) P_{t-1}\\ r_t &= \rho_1 (\pi_t - \bar \pi) \end{eqnarray*} }}} In this case as well, the second equation becomes meaningless after stationarizing the model.