# Adding Covid-shock to Galí (2007)

Dear all,

We recently got our simulation of Galí, López-Salido & Vallés (2007) to work (see Gali_2007_v2.mod (2.7 KB) )
Thanks to prof. Pfeifer for guidance in that!

We are now interested in adding a Covid-like shock to the model, but we are struggling with where in the linearized model our shocks should appear.

We qualitatively wanted a simultaneous negative supply- and demand-shock, such that both production, consumption and more crucially also inflation, wages and labor hours decrease.
This is seemingly more difficult than we expected.
We thought of a simultaneous shock to labor disutility (decreasing labor supply, aggregate demand and thus inflation), combined with a negative shock to labor productivity (decreasing supply and labor demand - and thus wage).
We do realize that we thus shock in dual directions in terms of price-levels in both the goods- and labor markets.

The concrete shocks we are trying to include are:
Decrease to z in the production function: Y = K^alpha * (zN)^(1-alpha)
Increase to z in the utility function: U = lnC - ((zN)^(1+varphi))/(1+varphi)

We expect the shocks to hit (and have marked in the code):

• Production function (decrease in production)
• Wage equation from consumers’ N-FOC (we expect unions to demand a higher wage per N / lower N given wage). Here, we include z with a (1+varphi) as we do not expect consumers to take the shock into account when maximizing utility.
• Euler equation (together with - and with same effect as N)

We are unsure as to whether it should also shock firms’ markups - as their costs from labor are now relatively higher than before, and we want to model the decrease in labor demand.

We know this might be a long shot - but assumed this forum would be the best to go to.

Do anyone have experience with negative demand-shocks to this type of linearized DSGE with imperfect labor markets and HTM-consumers? Other shocks yielding the same negative effect to inflation, output, wages and hours are very welcome as well.

Thanks!

1. It’s not a good idea to add features to an already linearized system. It’s too easy to produce inconsistencies, like when you wrote “we do not expect consumers to take the shock into account when maximizing utility.”
2. Markups are time-varying and depend on production. You are not supposed to shock them, but to take their dependence on other shocks into account.
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Thank you prof. Pfeifer, very useful!

We came a bit further, found the shocks we wanted to simulate, and are now a bit uncertain about whether to do this stochastically or deterministically.

From reading past forum posts, we reckon the results from a deterministic and stochastic shock should be quite similar due to the certainty equivalence and the linearization.
We are a bit unsure of whether it is possible at all to use simul() instead of stock_simul() in the model above - and if it is, we have a question:

When shocking deterministically in the first period only (yielding a single unexpected shock in a deterministic setting), we get slightly different results from a stochastic shock. In the stochastic setting, inflation rose normally, whilst in the deterministic setting inflation decreases in the first (shock-)period, thereafter increases above zero and then converges back.
We are struggling a bit to understand why this is. It would be a great result if inflation decreases (also just for one period), but we are skeptical of our results and methodology.

Gali_2007_LINEAR.mod (3.0 KB)

Your Taylor rule contains a wrong constant that screws up the steady state.

How do we have to write the Taylor equation? I was not able to correct it. Thank you very much

Best Regards

Sebástian

Simply

``````r = phi_pi*pi ;
``````