# Terminology: Moment matching and SMM

I’ve been reading Ruge-Murcia (2012) paper where the author defines the SMM estimation for DSGE models. Also I’ve seen papers where there’s performed moment matching by minimizing (to zero most of the times) the norm between simulated moments and empirical moments, but do not mention that this procedure is actually SMM.

In my work I’m doing the same procedure of minimizing (hopefully to zero) the norm of simulated and empirical moments, nonetheless I’m a bit confused in if this is actually SMM, since i just make the minimization and that’s it. Then,

1. is it safe to say (academically speaking) that just minimizing the norm of the diff. between simulated and empirical moments is SMM? And if not what “would it take” for that minimization to be an actual SMM?

2. Also in the Ruge-Murcia paper the minimization is performed to the sum of squares of the diff. (different to my “norm” approach"), but in the case that my model has a perfect fit with empirical moments, the estimators would be the same (I think), then I’d have the same Ruge-Murcia estimator?

3. Is there any kind of test or something that I should perform to my estimators (using the method I described was using) in order to assess the results I’m getting?

Another thing worth mentioning is that the paper I’m referring to calls the procedure just “calibration” not “estimation”. Is there any difference in this case?

Thanks.

Calibration usually refers to rather loosely picking parameter values by matching some moments, without caring much about the statistical properties. Also, it typically implies having as many moments as parameters.

SMM is more narrowly defined as a particular estimation technique that allows finding parameters and provides you with information on the statistical distribution of the parameters.

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Thanks! Also I was wondering, since in practice -at least solely at the moment of obtaining our estimates/calibration- the procedure both in SMM and moment-matching is practically the same (minimizing simulated and empirical moments distance), if I’ve performed moment-matching alone so far, what would it take for it to be a proper SMM?

You would compute the optimal weighting matrix and then minimize the distance. But for the just identified case that is not really needed. Any matrix will work.

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Thanks! May you refer me to some literature on how to compute an optimal weighting matrix and study statistical properties of estimators? I get most of Ruge-Murcia but some documented example would help me a lot.

The standard reference is
https://www.jstor.org/stable/2951768

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