Moments comparison


Is comparison between std deviations of the data and those of the model using smoothed variables is a good way to evaluate the empirical fit of the model ?



It depends on the model and the variables. If your model does not have measurement errors, then the smoothed observed variables will be equal to the actual observed variables. In this case it makes no sense to compare the sample moments which are equal by definition.


Thank you Stéphane

The model estimated do have measurement errors and the results I got show a slightly different values between the smoothed and the actual variables.

That way, you only get an indication of the relevance of the measurement error. There is no economic meaning behind that comparison (beyond the fact that you can interpret measurement error as a measure of model misspecification)

The comparison provides a kind of R^2 measure, informing about the share of structural innovations relative to the measurement error in the explanation of a variable (under orthogonality conditions).

What do you mean about the economics? I am not comfortable with the smoothed variables in general because of the information set… But this is true for all we can do with it (shock contributions to the levels for instance). Is this your concern? Or something else?


Thank you both for your help