 # Tips with tricky calibration approach

I’m working with a model with around 50 relevant exogenous variables (i.e. excluding AR processes, “made-up” variables from other endos., etc.), and about 35 parameters, I mention this so you know approximately the size of the model.

Most of the parameters are chosen with prior assumptions or past literature, what I’m left with is about 17 parameter values that I want to calibrate with moment-matching. I already have the calibration for 3 of then through an analytic ss (exogenizing ss target for variables and endogenizing parameter values such that those targets are met).

With the other 14 parameters I want that my model matches second-moments such as standard deviations, correlations and autocorrelations. I already have a routine for doing this, but so far I have not had luck matching those data moments, tried different initial parametrizations and the furthest I got is a norm of the errors vector of around 0.03, but with the biggest relative deviation of theoretical moment from data moment of 100%, which is huge.

Thus, I would be very grateful if you may give me some advice on how to choose those initial guesses for the numeric solver, and also if it would be advisable to try something else, like dropping some of the moments to match or change of strategy. Thanks!

PD: I’m using Matlab’s `fsolve()` to get a solution of the vector equation `F=0` by choosing parameters to calibrate, where the elements of `F` are the difference between model and data moments.

This sounds as if your weighting matrix is problematic as it gives not enough weight to some important moments.

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In the case I would lean better to a SSM I have a couple doubts:

1. Are ~50 real data observations good enough for a SMM?

2. As you mention the weighting matrix, is it correct if I choose its values arbitrarily? e.g. if I want to target for some special moment I would assign an arbitrary coefficient to it in the norm to minimize.

3. May you refer me to some guide or something beginner-wise to implement a SMM in a DSGE model. I have checked Ruge-Murcia and Duffie and Singleton references, but I fail to grasp if I’m correctly implementing (and even interpreting) the results I’d get, I mean I can perform the minimization and tweak (arbitrarily) the weighting matrix, but I fail to know what else should I do.

4. How can I assess the effects the initial guess values for parameters that I choose for the SMM minimization have in my final solution.

Thanks!

1. Yes, although the moments will be imprecise in this case.
2. Yes, any positive definite weighting matrix is fine. Only for inference, you need the theoretical one. For example, in Policy risk and the business cycle - ScienceDirect we use a diagonal matrix to put weight on the interpretable moments.
3. I am not aware of any practitioner’s guides.
4. Usually, you do that by varying the initial conditions.
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