Replication: “Leveraged borrowing and boom-bust cycles”in the Review of Economic Dynamics

General DSGE Modeling Replication Attempts
1

Dear users and Johannes Pfeifer,

I have another questions on replication of another paper: Leveraged borrowing and boom-bust cycles”, by Patrick A. Pintus and Yi Wen in the Review of Economic Dynamics . This paper is also related with Kiyotaki and Moore (1997). I am trying to replicate the competitive equilibrium
with borrowing constraints (Section 2.3). For this section, this paper provides its the linearized version of the equations in Appendix A.

I think the equations in Appendix A of this paper are very good application of "Listing 3: Log-linearized baseline model:A Guide to Specifying Observation Equations for the Estimation of DSGE Modelsby Johannes Pfeifer. Then, I coded up Appendix A equations using Listing 3: Log-linearized baseline model.

However, I face some problems.

  1. in Listing 3: Log-linearized baseline model, I think steady state values defined after #, such as #k_ss or #y_ss are necessary. How we could find/compute steady state values in #k_ss or #y_ss ?

  2. With my best of understanding, I coded up the attached mod files for Appendix A . But these files show the following error messages:
    "Warning: Some of the parameters have no value (CL_ss, CB_ss, B_ss, K_ss, LL_ss, LB_ss, Q_ss, Y_ss, L_ss) when using steady. If these parameters are not initialized in a steadystate file or a steady_state_model-block, Dynare may not be able to solve the model… "

I would like to get advice to solve my situations.
Best regards,
Pintus_and_Wen.mod (4.3 KB)
1-s2.0-S1094202512000567-main Leveraged borrowing and boom–bust cycles.pdf (403.6 KB)

2

You have to compute them manually. They are the steady state values from the nonlinear model. That is why linearizing models is not easier than working with the nonlinear version. In your mod-file the problem is that the parameter definitions cannot be sequentially executed, because you still have a simultaneous equation system. K_ss enters Y_ss, but Y_ss is then used to compute K_ss.

1 Like
3

Thank you Johannes Pfeifer for your advice.

  1. After I posted my questions here, I tried another directions, usually similar to your advice.

I noticed that the linearized version of the equations in Appendix A are using steady-state value ratios, not directly values. Thus using provided parameters, I tried to compute manually these steady-state value ratios, which are denoted by such as, KtoY_ss (capita-to-output ratio in the steady state). Then I plug-in these manually computed steady-state ratios in the 10 equations in the Appendix A.

However, theta_hat seems to be questionable because I do not understand why this has time index. I assume theta_hat may be typo, so I set theta_hat=0 in eq(39). I again run modified Dynare considering my idea above, which works and shows IRFs. But still two variables return NaN and I got the same message as follows:
Warning: Some of the parameters have no value (CL_ss, CB_ss, B_ss, K_ss, Y_ss, L_ss) when using steady. If these parameters are not initialized in a steadystate file or a steady_state_model-block, Dynare may not be able to solve the model…

Still, I can compute ratios of steady-state values, not their each values. … Could you please give me some advice? I attach modified Dynare file for replicating left-column window in the bottom-row of Fig.1.
Pintus_and_WenV2.mod (6.2 KB)

  1. A Guide to Specifying Observation Equations for the Estimation of DSGE Models really helps me( I am beginner of Dynare !) understand more precisely how Dynare works. Another question. I guess “1/k_t” in the eq(31), page 32 should be “1/c_hat”. Please correct me if I am wrong.

Best,

4
  1. There are some parameters that are still NaN, but apparently they are not used in the model. For example, CL_ss does not appear anywhere in your computations. So that should be fine
  2. The variables with the NaN are constant. So all second moments like correlations are not well-defined and therefore NaN.
  3. Yes, indeed that is a typo. Thanks for reporting it.
1 Like
5

Thank you so much for your replies. Maybe I could improve my Dynare works.

Best regards,

6

Dear Sangwon, please be aware that equation (38) in Appendix A of Pintus and Wen (2012) is not correct. In particular, the term ((1+R)B/Y)(lambda(t-1)-lambda(t)) is missing. I’ve recently assigned the replication of Pintus and Wen (2012) as a takehome exam and I have found out the mistake. It turns out that if you follow eq.(38) as in the paper, you can replicate only the results for the case of risk neutral lenders

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7

Dear. It is already quite a long question I asked. But your comments are very appreciated. At that time, I just followed the equations in the paper without change.

Thank you so much.
Best regards,

1 Like
8

You’re welcome. For anyone interested, a replication of Pintus and Wen (RED, 2013) in Dynare is available on my github profile at https://github.com/aledinola/Replication