Questions Regarding a Replication Attempt of a DSGE Model

Hi all,

I’m trying to replicate the results in the second chapter of the Ph.D. thesis titled, “Essays on the Macroeconomic Effects of Imperfect Banking Competition and Other Financial Frictions.” [1] I was successful in deriving and understanding the equations used to build the model. However, I find great difficulty in building it using the dynare program. In page 126, the author lists the equations used in the dynare program and mentions in page 26 that the non-linear model is solved using a first-order Taylor approximation around the steady state.

My questions are:

  1. We have a total of 33 equations, as I’m interested in the role of imperfect banking competition in amplifying shocks to the economy I’ve left the equation (2.43) related to perfect banking competition out of the system of equations leaving me with a total of 32 equations. While the number of endogenous variables is 40 if we take the equations as they are specified by the author without any modification from my part. Dynare documentation states that the number of equations in the model block should be equal to the number of endogenous variables which is not the case in this DSGE model. I don’t know whether other equations were employed by the author in his program, or did she write some variables in terms of others thereby reducing their number or am I missing something?

  2. In the case I don’t have a closed form solution for the steady state but I would like to assign one or more endogenous variables to specific values at the steady state (e.g.: labor = 1/3) then how should I go on about writing the code. At which dynare code block should I specify them and how should I approach the associated parameters? Should I calibrate the latter or not? I’m a little bit confused here since calibrating the parameters will result in them staying fixed throughout the optimization process.

  3. Finally, if I have \lambda_t = 1/c_t or the real loan rate R_{rb,t}, real deposit rate R_{R,t} and real loan margin RLM_t = R_{rb,t} - R_{R,t} (see the banking sector block at page 126) should I specify them all in the model block and assign each an initial value at the initval block or would that create a redundancy in the code.

Below you will find the document and my rather poor attempt to replicate it.

Essays on the Macroeconomic Effects of Imperfect Banking Competition and Other Financial Frictions.pdf (2.1 MB)

jiaqili.mod (2.9 KB)

  1. Yes, you need as many equations as you have endogenous variables. Have you tried asking the author for his codes? That’s often the easiest way to sort out what is going on.
  2. We already had that discussion at Calibrate disutility of work
  3. Equations like that are definitions for newly defined objects. These equations may explain why you are missing some in point 1.
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Thank you Prof. Pfeifer for your answer. I’ve contacted the author five days now but haven’t heard back yet. Also, the thesis doesn’t specify whether the steady state was found analytically or numerically. I’ve tried using a paper and a pencil but was unsuccessful :frowning:

Dear Prof. Pfeifer,

I hope this message finds you well. I’ve been succesful in replicating the model. I’ve some questions if you don’t mind regarding equations which contain steady state variables such as the Taylor equation, the collateral shock process and others. Should the variables whose steady state values have been exogenously determined such as inflation be treated as parameters, e.g.: pi_bar = 1 rather than putting the concerned variable within the steady_state() function while the variables whose steady state are endogenously determined be located within the steady_state() function such as output for example? Finally, I would like to modify the balance sheet of the banks instead of assuming, loans = deposits, I would like to introduce reserve requirements to obtain, loans = (1 - reserve requirements ratio) × deposits. My question is should the ratio be transformed into quarterly frequency too? I have quarterly reserve requirements data from 2007 to 2022 giving an average of about 5% (which yield interest to the commercial bank) however after modifying the loan rate equation in the paper taking into account reserve requirements it gives me a 30% annual interest rate ((1.075 - 1) × 4) × 100 = 30% while the calculated average is only 5.5%. I don’t know wether we should transform the ratio or not? I apologize for the inconvenience Prof. Pfeifer and please accept my most distinguished greetings.

  1. Yes, those should typically be defined as parameters.
  2. Regarding the reserve requirements ratio: I cannot follow your computation. But this ratio is usually the ratio of two stocks. Hence, there is no change with frequency.