When smoothed shocks seem not iid

As u know, we assume iid structural shocks in the DSGE modeling. However, two of the smoothed shocks (risk-premium shock e_b, monetary policy shock e_r) derived from estimation present certain degrees of persistence (though not much).
Please see the attached figure.

As I understand it, from the perspective of econometrics, something that should be endogenously explained has been ascribed to exogenous shocks. But from the perspective of economic modeling, I’ve made variables of interest endogenous. I’m confused if I should modify the DSGE model to make the smoothed shocks strictly iid.

Any suggestions or comments are welcome. Many thanks.
smootheds shocks.zip (36.1 KB)

Some deviations from the iid assumption are expected as the cross-equation restrictions embedded in DSGE models are often misspecified (see the discussion in the DSGE-VAR literature). Often people accept this. What should not happen is a clear visible drift in shocks as is visible in two of your pictures. This suggests low-frequency movements in your data that the model is not able to capture. One way out is often filtering the data. For potential data treatments, see e.g. the Guide to Observation Equations at sites.google.com/site/pfeiferecon/dynare

Thanks heaps for your reply. Very nice notes on specifying measurement equations. Actually, other than inflation and federal funds rate, I’ve first differenced everything since I assume TFP is a random walk implying output, wage, consumption are trended. Also, vacancy (help-wanted index reported by conference board) and labor force participation rate are first differenced coz they are trended as well. So I think it should be fine.

But your comments on the low frequency behaviors of monetary policy (e_r) and risk-premium (e_b) shocks do remind me of something about the federal funds rate. If we look back at the series of FFR, it does present a downward trend which may be the source of the drift of e_r and e_b, though I’m not sure why the trend in e_b is more significant than that in e_r. Because I’m worried that a longer time series of FFR will cover various monetary policy regimes, only the series of FFR after the Great Moderation is studied in my work, however, which seems sloped downward “spuriously”. Please see the variable “r_obs” in the attached file.

So should I difference r_obs again? I would prefer differences to including longer time series based on my worries on policy regimes. Feel free to correct me. Thank you very much.
smoothed variables.zip (32.1 KB)

It depends, because it is impossible to fit all dimensions of the data with typically very stylized models. If you do not feel uncomfortable with the implied trend in the shocks, you could either use first differences for the FFR or linearly detrend the FFR (basically assuming that the inflation target of the central bank had a downward trend). Alternatively, you could allow for a drift in the FFR and estimate this drift.

I see. Thanks a lot.


I actually was wondering the same thing.

I used the BDS test for nonlinear dependence and unable to reject the null that the exogenous shocks are iid. Does this imply that perhaps the model is misspecified?

If you are unable to reject they are iid, everything is fine. From your post I infer it was rejected. In that case, if your estimator converged, from a strict statistical viewpoint your model is misspecified (typically assuming that asymptotics hold in your finite sample).

My apologies, indeed I meant I rejected the null of IID. Thank you for your reply, it is very much appreciated.