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I want to calibrate some parameters of my DSGE model so that in the steady state some variable ratios, that are present in data, are met. My question is, how do I get such ratios from time series correctly?

For example, say I want to target the general government expenditure ($g_t$) to GDP ($y_t$) ratio, I get both time series, and then, how do I correctly get a ratio that is valid for targeting from these data? I've thought in three alternatives (not sure if any of them are correct): 1) Just compute the average of the ratio as it is, no matter how the resulting time series ratio behaves (i.e. $mean(g_t/y_t)$). 2) If the ratio is stationary, compute best ARMA (e.g. $(g/y)_t=c+\phi_1 (g/y)_{t-1}$) model and from that estimation use the resulting mean. 3) Test for cointegration between both variables without constant (coint. eq. would be $g_t=\beta_1 y_t$), and if there's cointegration my steady state target would be $\hat \beta_1$.

Is any of that the right approach? Which particular things should I care of?

Thanks!

PD: I've actually tried which results the three approaches yield and all three are very similar, nevertheless I'd like to know which is a "correct" way.

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  • $\begingroup$ Is this about calibration in general, or really about government expenditure? I am asking because government expenditure is a very special case, as it is driven by government policy, rather than by behavior of economic agents in a a market. $\endgroup$
    – BrsG
    Commented Jul 5, 2021 at 9:27
  • $\begingroup$ It’s in general. Nevertheless, probably I’ll be using government expenditure to gdp rato also. $\endgroup$
    – manifold
    Commented Jul 5, 2021 at 14:28
  • $\begingroup$ Leaving the general approach aside (it's just to general a question for me), there is no single correct way for government expenditure. If it's exogenous, in many cases the simple average will do But you could also exclude crisis periods from the sample, etc. It ultimately will depend on what exactly you are trying to model. And yes, government consumption over GDP often looks weird! $\endgroup$
    – BrsG
    Commented Jul 8, 2021 at 19:21

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