does anyone know where would go the mark-up shock in the recursive form of the Philips curve such as it is described in SGU(2005) ?
I am trying to do a welfare analysis, and I would like to use estimated shocks from models approximated of first order to calibrate my shocks, but I cannot find a way to get the mark-up shock to produce identical IRFs in both form approximated to the first order ?
Could anyone help ?
Markup shocks make the exponent on prices in the FOC for price setting time-varying. This renders a recursive representation impossible and is the reason you only see markup shocks in linearized papers. I would recommend having a look at Justiniano/Primiceri/Tambalotti (2013) who are the only ones I know to consider welfare with markup shocks.
Thank you very much for the reference, that’s a quite interesting one. I haven’t found anything really satisfying myself ( some authors replace it by a dividend shock on first profits…).
I have a related question, my issue is related to the empirical moments obtained when computing conditional welfare which are returned as NaN. I would like to check that most of the policy instruments have a reasonable volatility over my grid and therefore, I need well defined moments for each points on the grid.
Are those moments computed by the Stoch_simul(…, periods=1000) command the conditional variance ?
I am assuming that those are not well defined due to the conditioning set but extending the number of periods to 100000 and burning the first 10000 but that didn’t help, I still got NaN and only the the theorical moments (those returned by the stoch_simul command without the number of periods defined) are well defined. Shouldn’t the two approaches converge to the same moments ? Am I missing something?
I am searching for a way to obtained those unconditional moments without having to run twice Stoch_simul for each point on the grid (one to get the conditional welfare and one for the unconditional moments for this particular set of parameters). Pruning could also help but that might make the measure of welfare problematic (I haven’t found any discussion of welfare ordering and pruning in the literature…).
I am also a bit puzzled about the policy rules computed with moments returned as NaN. Does it make sense with a second order approximation?
Could someone provide help ?
Andreasen (2013) in the EER discusses the issue as well and uses a fixed cost shock to the same effect.
This is most probably an issue with pruning and explosive simulations. That would explain why only only the theoretical moments are well-defined. Pruning should be fine for welfare. See Kim/Kim/Schaumburg/Sims (2008).
You should only need to run stoch_simul once for every parameter draw as all moments should be computed in one run (unless you are trying to mix simulated and theoretical moments)
what do you reckon to be the most convenient way to log linearize by hand an equation with time varying exponents, not only in the case of a markup shock as in Justiniano et al. (2013), but also for example in the case of a time varying intertemporal elasticity of substitution in the Euler equation?
Thanks a lot
What do you consider a
Something like the Uhlig tricks? I personally always go for a first order Taylor approximation.
Yes, I did it with a first order Taylor expansion too. However, since the derivative with respect to an exponent needs to be multiplied by the log of the base, the effect of the shock changes sign according to whether the ss value of the variable in the base is greater or smaller than one (or it cancels out if it is one). That makes me wonder if it makes sense to consider a shock to an exponent.
Why is that a problem? If you raise a number smaller than 1 to a power, it will become smaller, if it’s bigger than 1 it will increase, if it’s equal to 1, there is no effect.