Incorporating Oil Prices in DSGE


I’m working with a DSGE model that incorporates oil prices, and wanted to ask specifically about how to deal with structural shifts in observed data. Though there was volatility in oil prices through the 2000s, there has been a clear shift from one steady state to a new (though perhaps temporary) steady-state over the past year or two.

My questions are:
Can a log-linearized DSGE model understand steady-state transitions in observed variables? I would assume “no” since the log-linearized stochastic model essentially assumes a single steady state.

-If so, what’s the intuition behind this?

-If not, is it more theoretically justifiable given the current state of the market to leave oil prices out as an observed variable and accept the loss in information, or include oil prices and accept the increased noise/unpredictability? Is there another way the data can be worked with to make it easier to incorporate observed variables with steady-state transitions?


What you seem to have in mind is estimating a regime-switching model, which you cannot do in Dynare (but in Junior Maih’s RISE toolbox)

Regarding shifts in steady state in Dynare: you seem to have a model in mind where a shift in oil prices shifts the approximation point (in constrast to models with balanced growth paths where you can simply detrend by the unit root variable). For simulation purposes, you could simply specify oil prices as a unit root process. For short horizons you will be close to the original approximation point so there is no problem. With estimation, things become tricky (unless you detrend oil prices to make the BGP in your model hold). You might also want to look at [Using dummy variables in dynare)

Thank you for your response Johannes. I am not trying to estimate a regime-switching model, the model was built before the oil price crash (it is based on Medina and Soto 2007, which was built for Chile) and is not designed to attempt to estimate regime-switching effects. I will try to be more precise in framing my thoughts and questions but it is not a subject I am particularly comfortable with yet so I apologize if I am still not clear in what I’m asking.

What I’m interested in is what kind of effect a structural break will have on what is, as you pointed out, essentially a BGP model. The model is log-linearized around a steady-state of zero for each variable, and all of the observed variables are similarly detrended to be log-deviations around the mean zero steady-state.

From my understanding of how these models function, there is an assumption of a single, constant steady-state for the duration of the data. A deterministic, linearized model can model transitions between steady-states, but a log-linearized model cannot (even if it is deterministic). So then, what effect does incorporating a data series that has a clear structural break have on the estimation results, even if it’s detrended?

I believe I am using a first-order approximation, so from the post you linked it would seem like certainty equivalence saves me from the problem of exceptionally large shocks. The question then becomes “is this a unit root process?” In the source data it is, but detrending the data should remove the unit root process, I believe. Based on this, the data series shouldn’t introduce any inherent approximation error within the scope of the log-linearized model. On the other hand, it seems to me like the information loss from detrending away from the unit root process will necessarily change the information space the model has available for estimation, creating a divergence between the data generating process the model sees and the true data generating process. This thereby produces results that aren’t necessarily comparable with the real world without further corrections - i.e. this is not problematic in time series econometrics because structural breaks are easy to explicitly correct for, but it does not seem to be something DSGEs are equipped to handle.

Under these conditions, how valid are my results likely to be? Am I likely to get more stable or objectively “better” results by not incorporating observed data series with structural breaks that the model cannot appropriately account for?

I am confused for several reasons.
You cannot estimate a determinstic model in Dynare. It does not matter whether you do linearization or loglinearization. Both will have a hard time with permanent shifts away from the approximation point.
What do you mean with

This is only because you assume that you can model the break independently from everything else. If you think this is the case, you can clean the data from the structural break before bringing it to the model.

The unit root in the model allows you to model permanent shifts away from the steady state in the context of simulation (structural break). It does typically not deal with unit roots in the data, which are handled by detrending both the model and the data by this unit root.

I apologize for the confusion, I am not attempting to estimate a deterministic model. I will try to greatly simplify my question.

If I detrend the model and the data by the unit root process, what kind of inaccuracy does that introduce to my model if I can’t explicitly incorporate corrections or controls for any permanent structural breaks in the data?

I am not sure how you will remove the unit root in the data. But in principle, Dynare can solve perfect foresight models up to any accuracy. As now Taylor approximation is involved, there is no problem.