Price level in RBC Models

General DSGE Modeling
1

Hi everybody.

My question is that in some articles about RBC models I can see the price level in household’s budget constraint but in some of the other articles in the literature researcher did not use price level in the model or for household’s budget constraint.

2

It depends if the budget constraint is expressed in real terms or nominal terms.

3

If it’s an RBC model, there should be no price level showing up, just relative prices. If there are multiple goods, sectors, or changes in the relative price of investment, then there are price terms showing up.

4

Dear Professor Pfeifer,

is this true also for DSGE models? I’m studying your dynare code that replicates Galí 2015 Chapter 3 (nonlinear model), and if I’m not wrong it contains the variable p (price level).

Thanks in advance,
Francesco

5

That model is a New Keynesian model, not a real business cycle model (RBC). In the former, you have meaningful movements of the price level.

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6

So, writing a New Keynesian model Dynare code in terms of prices instead of relative prices is correct, isn’t it? I mean, I’m not obliged to rewrite the standard intermediate firms optimal price condition, the price dispersion term, etc. in terms of inflation.

Thanks again,
Francesco

7

Inflation is not a relative price, but a change in a nominal price. That’s different. Most NK models only determine inflation uniquely, not the price level. That’s why you have a unit root in prices.

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8

Hi all.

I am working with two country RBC model. Does anyone do have any suggestions on how to model relative prices in this case.

Relative price, e.g. pH, is defined as price of product H(home) in terms of the aggregate price in country H. which is essentially a CES combination of relative price of good H and good F.

1=(1-\gamma)p_H ^{(1-\eta)}+\gamma p_F^{(1-\eta)}

Thank you in advanced.
Look forward to hearing from any of you.

9

What do you mean? Relative prices are uniquely determined in these models. You should be able to work with the posted equation.

10

Thank you for the prompt response. More specifically, do you think it’s correct to have factor demand equations in this form.

Say, demand for labor input:
w = p_H MP_L

Since MP_L is expressed in terms of units of home production.

11

Without context it is impossible to tell.

12

I have goods produced in country H (y_H) in units of good H. Hence, the GDP for country H in terms of H’s aggregate price (cpi) becomes gdp_H = y_H p_H…

13

But what is w and what is MP_L? Generally, it is not usual for a relative price to appear if the real objects are measured in terms of different goods.

14

Sorry I don’t quite understand this. If the real objects are measured in terms of different goods, aren’t we suppose to at least normalized/ assign a numeraire to an object to make them comparable?

w is real wage in terms of country H’s CPI and MP_L is the marginal product of labor expressed in terms of good H. Agents in country H solve their problems given factor returns expressed in real terms (CPI of H) because they consume (and invest) in goods which are CES combination in good H and good F (imported).

15

That means you have units of the final consumption good on the right of your equation while the marginal product is in terms of the domestic goods. You need to make the comparison equal by transforming the right-hand side into the final good as well. That is what the relative price p_H does.

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