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:

- 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?
- 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)