Analysis of increase in energy prices

Stochastic simulations
1

Hi, I have a simple new Keynesian model with energy.
household: household decide on consumption, leisure, and money holding. their consumption is a combination of energy and final goods.
Firms: There are two types of firms in this model. Firms that produce intermediate goods are produced using capital, labor, and energy. firms that produce final goods aggregate these intermediate goods and sell them to households. firms that produce intermediate goods have a price rigidity using the Calvo method.
**government:**In this model, the government owns the energy and sells it to households and firms. When the price of energy increases, the government gives the same amount of subsidy to the household.
Now when I simulate a model with a permanent increase in energy price, production has strange behavior.
It’s logical that production must be decreasing.but when I turn on price rigidity, production jumps in period 1. And I do not understand the meaning of this jump.Can anyone help me?
I attach the production with price rigidity and without.

production
production3004×2427 133 KB

production_a
production_a3004×2427 175 KB

very thanks.

2

Try to investigate the path of the interest rate and whether the specification of the Taylor rule causes this.

3

In this model, I don’t have Taylor’s rule, but I have a specific money supply rule. That is, the central bank increases the volume of money by 30% in each period.
I attach irf for real and nominal interest rate.

interest_rate
interest_rate3051×2427 111 KB

4

That explains the issue. You get a massive kink in the real interest rate that spills into consumption and investment.

5

Can you explain more please?
Whats the role of price rigidity?
Why in zero price rigidity this jump not happen?

6

With flexible prices,money is neutral, i.e. monetary policy does not affect the real interest rate.