Unexpected deterministic shocks

Good afternoon everyone,

I would like to shock my economy with an exogenous variable for which I know the entire path from 0 to T. If I understood correctly, only at period 1 the shock on that variable is unanticipated, while from period 2 to T shocks on that variable are anticipated.

Is there a way to implement an unexpected shock at every period given that the exogenous variable takes different values for each periods? Or should I, given the future path of the exogenous variable, transform my deterministic exogenous variable into a stochastic exogenous variable by somewhat matching the volatily?

The extended path won’t work in my case as the exogenous variable takes different values from 1 to T.

Thank you in advance.

Best regards,

If you are trying to solve the model fully nonlinearly, this will indeed by a challenge.

Thank you @jpfeifer. So there is no way I can shock my economy with a different value for the exogenous variable every year and the economy will not expect this after period 1 ?

Essentially, you would need to run a sequence of perfect foresight simulations where shocks happen by surprise each period and the initial conditions need to be made consistent. That is not easy to do.

There was some discussion here: MIT shocks in deterministic environment

Thank you @jpfeifer. That’s what I saw on Sebastien Villemot PPT on deterministic shocks. But it would be so time consuming. Gonna try that.

Good evening @jpfeifer,

I’ve followed your advice "Essentially, you would need to run a sequence of perfect foresight simulations where shocks happen by surprise each period and the initial conditions need to be made consistent. " and managed to do so.

I was wondering, is this method reflects some kind of bounded rationality, since agents have an imperfect knowledge of the states of the economy and are surprised at each date by the shocks?

Thanks!

Best regards,

You could interpret it this way. But usually people do this out off analytical convenience. It boils down to imposing certainty equivalence.

Good mornin @jpfeifer,

I would like to know if disaggregated the firm into 4 different firms (tertiary, industry, transport and agriculture) comes at a high cost ?

How is it done ? I have a very simple growth model with two heterogenous agents, a representative firm that produces one good, and the government. If I disaggregate into 4 different firms, what happens to the aggregate good consumed by households ? Should I aggregate the production of the 4 different firms into one common good?

Thank you!

Best regards

Either you have a final good firm that does the bundling or that aggregator is part of the utility function. Both are equivalent.

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Dear @jpfeifer, I have a question that may sound rather silly.

It is standard to assume that labor-augmenting productivity follows : A(t)=(1+g)^t . A(0). g is commonly mesure in data as the hourly labour productivity. I assume that my economy grows at g, and I know perfectly the path of g through time. I have detrended my model.

When I want to add the trend back after the simulation, I multiply my endogenous variables by A(t). But, shouldn’t I multiply these by (1+g) simply ? Because at each point of time, my economy grows at g. So I should multiply at each point of time my results by (1+g) and not A(t) (which “stacks up” g through time).

Let’s say that my economy grows at 2% per year. At t+3, I should add the trend back by multiplying my endogenous variables by the effective growth rate of the economy that is (1+2%). But, papers seems to add the trend back by multiplying the endogenous variables by A(t), which values to 1.061 here.

What is the right way to do?

Thank you.

Best regards,

Levels grow exponentially, log-levels linearly. See for a standard level, A_t is the right way to go.

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Good morning @jpfeifer,

Under “certainty equivalence”, you mean that agents make decisions such that future perturbations to the economy are zero in mean, conditionally on the information they have? Why is it that constraining? Because uncertainty is not taken into account ?

Thank you

PS: I do simulations in a perfect foresight set up where agents do not expect shocks at every point in time.

Yes, because they do not take uncertainty into account.

Does it really matter if I perform simulations for a perfect foresight model initially? All of my shocks are known from t=0 to T. I mean, by construction a perfect foresight model does not take into account uncertainty.

Thanks!

That depends on your point of view about proper information structures. Having everything known is often not viewed as a problem. People usually dislike people ignoring uncertainty, but then being surprised by shocks.