# Temporary subsidization of an import price shock

Hello everyone,

In my model, I want to analyze the effects of temporary fiscal measures in response to an import price shock.

The import price (`P_i`) is exogenously given and is increased by a shock (`e_i`):

``````log(P_i)=(1-rho) * log(steady_state(P_i (-1)))+rho * log(P_i (-1))+e_i
``````

A portion of this price increase is intended to be offset by the government through subsidies, so that the effective costs (`C_eff`) for the import of I for the firms are as follows:

``````C_eff=P_i * I+sub * steady_state(I) * (steady_state(P_i) - P_i)
``````

`sub` indicates the proportion of the cost increase that is subsidized by the government. However, the subsidies are only intended to be temporary from period 0 to 3. Therefore, I defined the variable `sub` as follows (`kappa` is just a scaling factor):

``````sub=(e_i+e_i(-1)+e_i(-2)+e_i(-3))/kappa
``````

When I perform a stochastic simulation, changing sub has no effect on `C_eff` (with `order=2`). Is this because a change in `sub` has no effect in the steady state? However, with a deviation of P_i from steadystate, sub should have an effect on the effective cost.

Unfortunately, I couldn’t find anything about this issue in the forum so far, perhaps I haven’t found the right term for the topic. I would therefore also appreciate hints to appropriate threads.

Thank you in advance for your support.

How exactly do you conduct your simulation, i.e. which experiment/sequence of shocks are you conducting? It seems at second order there should indeed be an interaction effect.

Thank you, I found my mistake in the simulation.