SOS variables timing


#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.