Moments of Simulated Variables: Mean (in a linearised model)

Quick question for the Dynare team as I may have missed this in the documentation or somewhere on this forum: Take an off-the-shelf basic log-linearised RBC model, declare model(linear), and then run stock_simul (with periods=0 to get the theoretical moments). The first moments of the variables are all zero. So far so good.

Then, change the option in stoch_simul to something like periods=200. The means are quite significantly different from zero. Even changing this to some extremely long period such as periods=5000 does not seem to bring the means close to zero.

I could imagine that in a nonlinear model there could be some issues with Jensen’s Inequality causing some of the means to be different from zero. But I’m struggling to rationalise this for the case of a linearised model.

Is there an explanation for this? Thanks!

Any shock in the RBC model is going to cause persistent deviations from the mean. With random shocks draws from simulations, these deviations will not perfectly average to 0 even in somewhat large simulations.

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