Identification issue with Bianchi & Ilut (2017) policy-switching on Eurozone data (2002-2019)

[FilipBlah]

Dear Professor Maih,

I am trying to estimate the Bianchi & Ilut (2017) model (https://www.sciencedirect.com/science/article/pii/S1094202517300315) on Eurozone data from 2002-2019 using the RISE toolbox. Following the advice from some other disscusions, I first estimated a single-regime version (calibrating some paramaters in order to force AM/PF regime), which worked perfectly and produced reasonable posteriors. However, when I try to re-implement the policy-mix switching (between the AM/PF regime and the PM/AF regime), the estimation fails, producing imaginary numbers and extremely large standard deviations. My question is: do you think it is fundamentally possible to identify these two specific policy regimes (AM/PF vs. PM/AF) on a sample like the 2002-2019 Eurozone data, which seems to contain only the stable AM/PF regime, or am I hitting an identification wall because the data lacks an example of the PM/AF regime? Thank you for any guidance.

[jmaih]

Dear FilipBlah, Short answer: You’re most likely facing an *optimization/numerics* issue, not a fundamental *identification* problem. Those “imaginary” standard deviations arise when the (numerical) *covariance/Hessian at the mode isn’t positive definite*, which typically means the optimizer stopped *before* a true peak (or landed on a saddle/thin ridge). This is common with strong nonlinearities and winding likelihood/posterior surfaces. Unless you’re doing *pure maximum likelihood*, the “standard deviations at the mode” aren’t especially meaningful. In a *Bayesian* setup, the goal is to *simulate the posterior*—you don’t need a perfect mode first. You can even *start MCMC from the point where optimization stopped*, provided you use a *well-behaved proposal covariance*—it *doesn’t have to be the Hessian at the mode*. Practical steps: 1. If you want to estimate the mode first, you should stabilize the numerics: use alternative optimizers, use more informative priors, etc. 3. You can start MCMC safely (even without a clean mode): E.g., Use a *robust initial proposal*: diagonal covariance with sensible scales, or a *regularized*/shrunken Hessian, or a short *pilot chain* to estimate a sample covariance (then adapt). Best regards, Junior

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On Mon, Nov 10, 2025 at 2:25 PM FilipBlah ***@***.***> wrote: *FilipBlah* created an issue (jmaih/RISE_toolbox#224) <#224> Dear Professor Maih, I am trying to estimate the Bianchi & Ilut (2017) model ( https://www.sciencedirect.com/science/article/pii/S1094202517300315) on Eurozone data from 2002-2019 using the RISE toolbox. Following the advice from some other disscusions, I first estimated a single-regime version (calibrating some paramaters in order to force AM/PF regime), which worked perfectly and produced reasonable posteriors. However, when I try to re-implement the policy-mix switching (between the AM/PF regime and the PM/AF regime), the estimation fails, producing imaginary numbers and extremely large standard deviations. My question is: do you think it is fundamentally possible to identify these two specific policy regimes (AM/PF vs. PM/AF) on a sample like the 2002-2019 Eurozone data, which seems to contain only the stable AM/PF regime, or am I hitting an identification wall because the data lacks an example of the PM/AF regime? Thank you for any guidance. — Reply to this email directly, view it on GitHub <#224>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AATKBT4TC5KWHFLU5273RMD34CG3LAVCNFSM6AAAAACLVDNJJ2VHI2DSMVQWIX3LMV43ASLTON2WKOZTGYYDQMBUG42TGNA> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>