Comparing IRFs to actual data

Dear all,

I am puzzled about the comparison between IRFs and the actual development of variables e.g. GDP growth.

I would like to use the conditional forecast command or simply calibrate manually a sequence of shocks in order to match the quarterly GDP growth rate of France for a given period of time.

Assuming that French GDP growth rate in 2022Q1, 2022Q2, 2022Q3 and 2022Q4 was let’s say -0.2%, 0.5%, 0.2% and 0.1%. Since IRFs are deviations from the steady-state, my understanding is that I cannot compare the model’s GDP percentage deviation to the aforementioned figures, am I right?

Is there a way to compare the model’s deviations (IRFs), to actual GDP growth rates? ( for instance, would building a variable Y^{growth}_{t}=Y_{t}/Y_{t-1} be a solution to my comparison issue? )

Thanks in advance.

I am not sure that I understand your problem 100%. But an IRF is the propagation of a stochastic and unanticipated shock through the model. How do you want to compare that to actual data? We do these analyses in order to understand what would/could happen in the real world given some shocks.

That said, I think your second point makes much more sense. If you have a variable for GDP growth in your model and do forecast from the end of your sample, you get what the model predicts this variable would be. This out of sample projection is now comparable to actual realization of data.

Another option is to give the model a sequence of shocks within the perfect foresight environment.

Thanks a lot for your answer.

I will try to clarify what I want to do. I want to replicate the development of the french economy in 2022 in terms of GDP growth rate, by the mean of a sequence of shocks. I would then use this scenario as a baseline scenario and then model a couple of fiscal shocks in order to see how would have been the development of the French economy if these fiscal shocks had occurred.

In other words, as you pointed out in your first paragraph, I want to look at the propagation of shocks when the economy is not at the steady-state but is already hit by a sequence of shocks. ( I use a perfect foresight solver and do not rely on linearization)

My original question does not relate to the implementation but more to the interpretation of such a scenario.

Usually, you would run a smoother on your model to back out the shocks that explain the data. At first order, you can use the Kalman smoother. Then, equipped with the actual shocks and the extracted value for the state variables, you can conduct counterfactual analyses.

Thanks a lot for your response.

Actually, I had something much more rudimental in mind, I did not plan to estimate my model. But given your answer, I will maybe consider it.

You don’t need to estimate the model. You can use the calib_smoother on a calibrated model.

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