Weird steady state

Perfect foresight simulations
1

Hi everyone,
I am trying to find the steady state of an e-dsge model with a banking sector and I cannot understand why deposits turn out to be higher than assets, resulting in negative net worth and negative leverage.

Also, the steady state values the code produces are close to zero for all real variables and do not resemble the “usual” values one might expect from a steady state. Any idea about the numerical problem?
Thank for the support

Attached is a reduced form of the code
sec1_bank_notax.mod (3.1 KB)
sec1_bank_notax_steadystate.m (1.7 KB)
findsssec1_bank_notax.m (866 Bytes)

2

Your model has very low values for capital and labor. That is rather unusual. I can only recommend starting with a standard model without a banking sector to see whether the steady state makes sense. Only then add the banking sector.

3

This is what I have done, and the ss makes sense… It seems that the introduction of the monopolistic banking sector reduces some variables by two orders of magnitude, but I can’t see where the problem is, as the banking sector is only three equations.

Could the problem come from the calibration? SS values does not seem to be sensible to it

4

Then you should play around with the parameters. There must be parameter values for which the banking sector is (almost) neutral in the sense of not affecting the steady state and the dynamics. If that works out, see what happens if you increase the friction

5

Thank,
is it possible that this model has multiple steady states and that the algorithm is stuck in the one with low levels of capital and investment?

6

Yes, that may be possible. In that case, you need to provide an analytical steady state.

7

Thank you Professor,
Just one more comment; I have worked out the model and found that the introduction of a perfectly competitive banking sector does not change the realistic ss values of a model without it. Instead, it is the exact introduction of markups over the deposit rate that causes ss capital to fall by 2 orders of magnitude, giving negative bank profits.
Any suggestion on how to deal with it? Should I look for another type of friction?

8

That sounds strange. Shouldn’t a markup lead to profits?

9

I cannot know what is happening in your model but for many financial friction models, starting value to find the ss matters a lot. Sometimes, these models have numerical multiple equilibria (that are not economic equilibria but equations are solved with nonsensical numeric values).

I’d advise you to solve the financial system separately to make sure which starting value converges to the actual equilibrium

2 Likes
10

It should be the case but actually it is not working here; as you can see from the attacched code, if one sets rkb=r, then we end up having usual capital at the steady state while if one uses rkb=\frac{\epsilon_b}{\epsilon_b-1}r, capital is decreased and bank profits are negative. I cannot get why
timing.mod (3.2 KB)
timing_steadystate.m (1.8 KB)
findsstiming.m (865 Bytes)

11
  1. What do I need to change to move to the monopolistically competitive model?
  2. Shouldn’t net worth be predetermined?
  3. Could it be that you somehow fix profits and increasing the markup requires net worth to become negative to take up the profits.
12
  1. you should activate equation rkb=\frac{\epsilon_{b}}{\epsilon_{b}-1}r instead of rkb=r in all 3 files.
  2. Yes but in that case the rank condition would not be verified.
  3. I cannot get what you mean by fixing profits; since they do not have closed form expression in ss calculation, how could I have fixed profits?

Thank for the support professor Pfeifer

13
  1. Your whole timing looks extremely suspect. There is a unique correct timing and your current one is not it.
  2. You should sit down with pencil and paper and compute the steady state analytically. That looks rather feasible for your model. It will help you understand what drives what in your model. For example, what determined dep? You have
nw=qb*kb-dep;
nw=(1-delta_nw)*nw+prf;

which implies

prf=delta_nw*nw=delta_nw*(qb*kb-dep)

The expression in brackets is negative.