Steady state in BGG 1999

Has anybody ever replicated the steady state in the financial accelerator paper from BGG (1999)?

According to BGG they want a steady state threshold value that implies an annual bankruptcy rate of 3%. Given that the threshold is log normally distributed with the moment conditions they describe this should give a threshold value of 0.4936 (adjusted so that we can work with quarterly rates, as in the paper). BGG also declare that the annual spread between the return on capital and the risk free rate should be of 200 basis points and that the leverage ratio should be 2. I cannot find a way of having all these conditions matched. I have tried solving the steady state with fsolve and also sequentially, by hand, and the results are always a bit off (either the spread is different or the leverage ratio is different).

Looking around on google I found Christiano’s notes on CSV and BGG. They provide a roadmap on how to calculate these parameters (although with different conditions). I can replicate his results, but not the steady state conditions that BGG talk about.

I was wondering if anybody has actually replicated the steady state in BGG 1999 and if anybody would be willing to share their code.

Christiano’s notes: page 25 explains a roadmap for computing the threshold, leverage and lending rate. … andout.pdf

Original BGG paper. Page 1368 talks about parameters and the steady state … hapter.pdf


P.S. (I suspect that in page 1368 BGG refer to the return on capital as the primary lending rate. Shouldn’t the primary lending rate be Z, the one they describe in equation 3.3 and that governs at which rate bankers lend? Even if I define the spread with regards to Z, I cannot replicate their steady state results)

I have talked to a couple of people working in this area, and the answers seems to be: no, they did not succeed.

Hi Sophapi,

I have actually never tried to explicitly replicate those ‘stylised facts’. More specifically, I have been able to generate the spread of 200 basis points and a leverage of 2 (K/N), but never tried to match the business failure rate. I think mine was slightly higher.

Even if the paper is great and the theoretical mechanism they propose is really good, the discussion on calibration is not so good. Several of the parameters are not explicitly reported. Once I realised that, I didn’t put more effort in matching all their facts. But if you keep the leverage and the spread according to them, you will anyways get an interesting and very similar dynamics to them (assuming the rest of the parameters are kept int heir range).

Regarding the Z and RK, when there is no aggregate risk, then Z is the term determining the non-default repayment rate. However, when aggregate risk is introduced, then Z is actually dependent on Rk (on pages 1352-53 they discuss extensively what happens when Z is smaller than RK and so on). Thus, with aggregate risk, the key term determining the entrepreneurs cost and ability to repay is Rk (with Z just being an argument), so they reduce it to RK.

I hope this helps.
Good luck!