Standard deviation model vs data

Hello, I was thinking about the analysis of moments that is usually done to see how well the model explains the data, i.e. when comparing the S.D. of the data with the S.D. of the model, and I see that researchers often claim that the volatility of their model variables is similar to that of the data, but it seems a bit arbitrary to me, what measure or rule of thumb is used to really know or evaluate if two standard deviations are close enough? for example in this case:

Variable Mean S.D. data S.D. Model
Y 0.0005 0.0183 0.0286
C -0.0003 0.0179 0.0355
\Pi_t^c 1.0103 0.0044 0.0094
\Pi_t 1.0122 0.0081 0.0117
R_t 1.0168 0.0063 0.0094
{\rm dS}_t 1.0108 0.0479 0.0509

Can we say that the model explains well the volatility of the data? Is there a reference measurement?

Greetings to all

Unfortunately, the answer is typically: it’s reasonably close if your referee accepts it. In your case, I would probably say that the model is a bit too volatile, but the relative volatilities mostly fit. The biggest issue for me would be consumption, which is twice as volatile in the data and more volatile than output, while it is less volatile than output in the data.

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