Short version:
Is there a post-estimation structural break test for DSGE models for checking the stability of the estimated parameters? Or all structural break tests should be done outside of the DSGE model pre-estimation? Not sure though if structural breaks in one or more variables even always cause problems for DSGE model estimation.
Long version:
I have a variance structural break in my data for real GDP per capita y_t (which is statistically confirmed by a CUSUM square test using the following AR(1) model: y_t = \alpha + \beta y_{t-1} + \epsilon_t).
So my plan has been to divide the sample into a post-structural break (low variance) and a pre-structural break (high variance) sub-samples. Indeed a structural program was implemented by the government at the point of the break.
However, through experimentation, I have also realized that the structural variance break is not detected in a 5-variable VAR model (i.e., for each equation, including y_t) but detected in a 2-variable VAR model.
Since the DSGE model includes even more variables and it is also essentially a VARMA model, my guess is that a structural variance break in y_t may still be okay for estimation. But not sure if my guess is correct.
Let me side-step the issue: it is never a good idea to approach economics from a purely statistical perspective. With statistical tests there is always the issue of not detecting a break although it is there. You are saying that there is outside evidence for a break in the form of a “structural program”. If that program was large, you may want to model a break regardless of what the tests say.
Regarding tests, you could of course do model_comparison between a model allowing or a break and one without. But that is cumbersome.
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From a technical perspective the answer is yes, of course you can estimate your model using data that features a structural break.
But I think you might also be asking a question about whether other people (like potential reviewers) will have an issue with it, and this this depends on what exactly the research you are conducting deals with. The secular decline in US output growth is pretty well documented. I would search for recently published articles that estimate DSGE models and see what they do.
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hmmm, it seems it depends. I mean some people divide the sample to account for the break in the mid-1980s, others do not. But I think SW did.
Hi Prof. Pfeifer, may I make further inquiries about this statement "it is never a good idea to approach economics from a purely statistical perspective."
I guess an example will be the case when one is just playing around with the data, and then by chance, he/she spots a structural break that maybe does not link to any economic phenomenon or event at the time of the break, but purely statistical.
But if he/she starts to investigate, maybe based on the history of the economy, and then perhaps he finds something major around the time the structural break is found to have occurred in the data, then I guess it is gradually shifting away from being a purely statistical observation, right? Maybe, now partly statistical. Not sure though how to call the other part.
But I think I see that a couple of times. Like a researcher would say, “Hey, why is I_t less volatile than Y_t for this economy. This contradicts economic theory. I am going to try to explain this anomaly”. So as before, it kinda started out as a purely statistical observation in the data (i.e., comparing variances), but it can gradually shift away from being purely statistical, right? Is this a better approach to macroeconomics or economics in general?
I am essentially saying that most often theory should come before measurement. There are cases where you start from a statistical fact and then explore the economics behind it.
But your case was different. You essentially stated above that there are reasons to think there is a structural break in the data, but statistical tests do not consistently spot it (AR1 vs. VAR). In that case, you need to keep in mind that tests have a certain size and power embedded. Thus, when in doubt with respect to the test and there is economic outside evidence to rely on, go with the economic evidence.
Take the papers on the great moderation. They started with a statistical fact, but then found economic interpretations. I doubt that literature would have taken off without any explanation for the break.
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