SOS variables timing

General DSGE Modeling Replication Attempts
1

Hi everyone.

I know that there are already many topics about timing conventions, but I am really struggling to adapt them to my specific case.

I am trying to run a very simplified model inspired from Jakab and Kumhof (2015) “Banks are not intermediaries of loanable funds - and why this matters”. The banking system is taken from the celebrated Gerali model.

My problem is about the timing of some variables (loans, deposits, bank capital). I used the end of the period convention, but it is probably wrong for loans and deposits. What is even more confusing to me is that, according to the authors of the original paper, in Model 1 loans and deposits should be forward looking variables, while in Model 2 they should be predetermined.

I attach the mod files for Model 1 and Model 2 and a short pdf with the equations.

Thank you very much for considering my question,

Aldo.

Model1.mod (3.1 KB)

Model2.mod (3.4 KB)

Question.pdf (123.5 KB)

2

Sorry, but you have to narrow down the problem. Please describe the setup and the timing that you are trying to achieve. The mod-file is an implementation, but there seems to be confusion about what exactly is to be implemented. When you say

that already implies that you consider those variables as predetermined.

3

Thanks Professor Pfeifer for your reply.

In summary, in Model 1 there is a single representative household that is at the same time borrower and depositor and that faces the following budget constraint:

P_tC_t+D_{t}=w_tN_t+(1+R_t^D)D_{t-1}+L_{t}-(1+R_t^L)L_{t-1}

plus a cash in advance condition:

P_t{C_t}\le{D_{t-1}}

In Model 2 there are two representative households (saver and borrower) and the original budget constraint is then split into:

P_tC^S_t+D_{t}=w_tN^S_t+(1+R_t^D)D_{t-1}

and

P_tC^B_t=w_tN^B_t+L_t-(1+R_t^L)L_{t-1}

In the paper by Kumhof, it is said that, by budget constraint of Model 1, loans and deposits are jumpers, while, by the budgets constraints of Model 2, they are predetermined.

I am wondering why is that (the conditional expectations-based definition of forward looking variables does not help me) and - if it makes sense economically - how to implement it using Dynare conventions.

Thanks

Aldo

4

I am afraid I won’t be able to answer your question. I had a look at the paper you are referring to (https://www.bankofengland.co.uk/-/media/boe/files/working-paper/2015/banks-are-not-intermediaries-of-loanable-funds-and-why-this-matters.pdf) and it makes no sense to me. The claim on page 24 is that equations (15) and (18) make loans and deposits predetermined variables. But that clearly is not the case if one uses the usual definition of predeterminedness. In both equations there are clearly variables on the right-hand side that change at time t with the shocks that arrive (like consumption).

5

This seems indeed quite puzzling, especially because the claim of the paper (that in Model 1 loans and deposits can adjust more rapidly than in Model 2) is said to arise from this. My guess would be that, working with the single budget constraint, one equation is missing and one has to add another condition (bank’s balance sheet) “representing fast-moving financing, created through matching gross positions on the balance sheets of banks”, but I don’t know if it makes sense.

Anyway, I would like to ask you if it is possible to work out a closed expression for the bonds evolution in the basic maximization problem under the budget constraint with one asset, like

P_tC_t+B_{t}=w_tN_t+(1+R^B_{t-1})B_{t-1}

Many thanks for your patience

6
  1. The only way to answer this is to ask the authors of the original paper.
  2. What do you mean with

?
You could iterate on that equation, but it will result in an infinite sum.

7

Ok, thank you anyway.

8

Sorry for re-opening the topic, but I still have a question.

I have quite understood what is to be implemented and I have simplified my model as to have as few equations as possible. I also decided to use level variables instead of percentage deviations and I took your New Keynesian non-linear code, introducing the minimum number of new equations.

I would like to have a saver household and a borrower one.
Everything works fine when these two households are alone in the model, but when I insert the two Euler equations and the aggregate consumption equation (C=\lambda C_S +(1-\lambda) 0.5C_B ) in the same mod file, indeterminacy arises (There are 7 eigenvalue(s) larger than 1 in modulus for 8 forward-looking variable(s)).

Surfing the forum, I found that this seems to be quite a common problem when heterogeneity comes into play. In particular, I saw that in a similar situation you suggested to consider Galì paper “Understanding the effects of government spending on consumption” in which a unique Euler equation is derived for aggregate consumption and then consumption of the two household is pinned down from it.

I really do not understand the reason of this indeterminate dynamics and how to fix it.

I upload the three mod files; as said in saver.mod and borrower.mod everything works, while in saverplusborrower.mod the error appears.

Once more, I thank you.

saver.mod (10.9 KB)
borrower.mod (11.4 KB)
saverplusborrower.mod (13.1 KB)

9

Are you sure your timing is correct? Why is there a variable dated (+1) appearing in your budget constraint? Budget constraints need to be satisfied in all states of the world, not just in expectations.