# Random Walk and Infinitely Many Steady States

Hi.

I am studying the behavior of an oil exporting economy where the source of shocks - oil price follows a random walk process without drift. Because of this, my model has infinitely many steady states. Here I can provide Dynare with a single steady state in the “steady_state_model block” and set “nocheck” option. As far as I know, the approximation will become worse the further away I get from the given initial steady state. However, points far from the steady state are also important in my estimation.

Can Dynare handle this issue as it log linearizes only around the given steady state.

Thanks,
Ruslan

Dear Ruslan,

I don’t think you need the nocheck option. This option is necessary only if you have a drift in your random walk, i.e. something like:

a_t = \alpha + a_{t-1} + \varepsilon_t

in which case there is no steady state at all (that’s why we use the nocheck option). In your situation you only have to choose one steady state among an infinity, so what you provide in the steady_state_model block must be a steady state (i.e. solve the static equations of your model).

The point where you do the approximation should not matter, because I suppose that in your model, whatever the arbitrary choice you do on the non stationary variable (a), you have the same slopes (given by the evaluations of the Jacobian at the steady state). You can check that by looking at the reduced form returned by the stoch_simul command for different values of the unit root variable’s steady state.

That said, it is always true that if you deviate a lot from the steady state, the approximation will be less accurate and this will affect your estimation. This a general issue, not specific to the unit root in your model.

Best,
Stéphane.