A question on estimation under different policy regimes!

Hi,

I have a question on estimating DSGE models under different policy regimes and hope to get some comments here!

This is a standard medium-scale NK model expanded by nontrivial fiscal policy block, following Leeper Traum and Walker (2017). Since monetary and fiscal policies can be either active or passive, we define two regimes, M or F, which delivers a unique equilibrium. Under M, we have an active MP and a passive FP. While under F, we have a passive FP and an active FP. The data is US pre-Volcker period, from 1955Q1 to 1979Q4, which is attached. Four mod files are also attached.

I consider two exercises: (a) start the data for estimation from 1955Q1 and set presample option in estimation command as 4. So the effective sample for likelihood computation is from 1956Q1. (b) start the data for estimation from 1956Q1 and set presample option as default 0. So, again, the effective sample for likelihood computation is from 1956Q1. The priors for these cases are the same. As I understand, the only difference is that Kalman filter in (a) initializes from the information in the 4 observations in 1955 while Kalman filter in (b) initializes from unconditional moments.

It turns out that these two cases deliver quite similar results under M, which can be replicated by M_551to794.mod and M_561to794.mod. However, under F, these two cases deliver very different results, which can be found in F_551to794.mod and F_561to794.mod. When starting from unconditional moments under F (case b), it is OK to find a mode and the posterior surface seems to be well-behaved. When conditioning on the first 4 observations under F (case a), the posterior surface seems to be drastically changing and ill-behaved. It is very hard to find a mode. The mode finder (e.g., mode_compute = 4, 9, 6) easily gets stuck at boundary and variance matrix of parameters cannot be computed.

It is quite confusing because the effective sample, prior, model are all the same for cases (a) and (b) under F. Can the initialization of Kalman filter have such a big effect? What is more interesting is that under M, this problem does not exist.

By the way, I have also done some extensive mode searches by repeatedly finding mode for many times. Under M, I found that out of 50 searches, for example, I can get repeating modes for both cases and they are quite similar. But under F, I can get repeating modes only for case (b). For case (a), 50 mode searches would result in 50 different modes, implying that the posterior surface is very badly behaved.

I have two questions now:

  1. What does presample option in estimation command do? With presample=4, do we still start Kalman filter from unconditional moments from 1955Q1 and throw away the contributions to likelihood of the first 4 observations?
  2. Why the problem only appears under F? Under M, adding or deleting some observations (initializing Kalman filter with different initial conditions) seems not change the posterior surface much. While under F, it does!!!

I would really appreciate if somebody could provide me some intuition behind my questions! Thanks in advance!

Data.mat (6.4 KB)
F_551to794.mod (9.1 KB)
F_561to794.mod (9.1 KB)
M_551to794.mod (9.1 KB)
M_561to794.mod (9.1 KB)

  1. A general remark: not all of your parameters are identified. That will create problems in any case during estimation.
  2. Looking at the mode_check-plots, it seems the mode found for M_551to794.mod is at the boundary of the stability/determinacy region. That will always complicate mode-finding.
  3. Yes, the difference between the two approaches is that the presample starts the Kalman recursion at the first data point with the unconditional covariance and the steady state, but only starts the log-likelihood summation after presample-periods.

Hi Johannes,

Thank you very much for your reply!!!

You are right. Not all of the parameters are identified. But this happens only under F in my estimation. Under M, I always got parameters away from the boundary whether or not the option “presample=4” is used. Please see the attached mode_check-plots for the case when data start from 1955Q1 and “presample=4” is used. I estimate the mode by using mode_compute = 4, 9, 6 iteratively. I agree that when F is considered, mode finding stops at the boundary whether or not “presample=4” is used. For example, please see the four figures for F.

In general, the posterior or likelihood surface of F is not as well-behaved and stable as M. Do you have any suggestions on how to deal with it?

Thanks again for your time and attention!!!

US_551to794_M_iterative_CheckPlots1.eps (45.5 KB)
US_551to794_M_iterative_CheckPlots4.eps (34.4 KB)
US_551to794_M_iterative_CheckPlots2.eps (43.1 KB)
US_551to794_M_iterative_CheckPlots3.eps (42.9 KB)
US_551to794_F_iterative_CheckPlots1.eps (47.0 KB)
US_551to794_F_iterative_CheckPlots4.eps (32.6 KB)
US_551to794_F_iterative_CheckPlots3.eps (49.6 KB)
US_551to794_F_iterative_CheckPlots2.eps (58.6 KB)

  1. The collinearity issue that gives rise to non-identification is a problem for the Hessian at the mode, but should not affect the maximum as the parameters are jointly identifiied
  2. You need to understand why under F you get to the boundary of the stability/determinacy region. There must be an economic reason. Is what you get different from the paper you are trying to replicate? If yes, did you change anything?

Thanks a lot, Johannes!

Estimation of F is problematic in many circumstances, which is sensitive to sample, model specification and etc. It should be related to the way in which the model is written down for that particular regime, i.e., the combination of monetary and fiscal policies. It seems to be a fundamental problem of the literature. I will keep thinking about it.

Thanks for your time and discussion!!!