# 2 Problems With Estimation

Hi there,

First of all, thank you again to jpfeifer and StephaneAdjemian for their help on previous questions I’ve had. As it stands, I’ve almost completed what I set out to do, but there are a few things that are still stopping me from getting the results I want.

The first problem is the presence of a trend that shouldn’t exist. The GDP gaps I’m trying to calculate are measured as the percentage deviation of actual output from flexible-price equlibirium output. As such, the series should generally be centered around 0, with no growth trend, and should be positive during booms and negative during recessions. Here is a graph of the original authors’ results:

My graph, however, has a clear upward trend:

Note that the model should be stationary in technology (technology is controlled by a simple AR(1) process), and endogenous variables are percent deviations from steady-state values.

The second problem is that the parameter values aren’t in line with what the original authors produced, despite being derived from (essentially) the same data. Here, it seems as though the Markov chain isn’t exploring the entire state space, since some of the prior means and posterior means (especially for the shocks) are essentially identical. This is a big difference from the original paper. For comparison, here is a list of prior and posterior means both from the original paper:

as well as my own attempt (priors are the same):

tau 1.3752
h 0.9728
omega 0.8949
r_star 3.2630
eta 0.6969
phi_pi 1.5401
phi_y 0.5035
rho_r 0.8554
rho_d 0.3230
rho_z 0.8304
rho_a 0.5368
gamma_star 0.4707
pi_star 1.5905
sigma_r 0.4928
sigma_d 0.5024
sigma_z 0.4966
sigma_a 0.4976

I’ve tried checking and re-entering the equations a bunch of times, increasing the number of iterations, as well as re-examining the data, but everything seems to check out. I’ve attached links to the original paper, my code, and my data. If anyone out there could spare a minute to check it out I would really appreciate it.
newhirosedata1.m (3.47 KB)
newhirose.mod (1.98 KB)
2007 Hirose.pdf (766 KB)

You should take a look at your filtered shocks. The trend in the estimated output gap mirrors the downward trend found in interest rates. As the model is stationary, this downward trend has to be created by some trend in the shocks. Note also that your pi_star is very low, well below the sample mean of 3. This also has be reflected in a series of inflationary shocks. It might give you an indication where problems might be.
I find it striking that your posterior closely resembles the prior (in particular the standard deviations). Are you sure that your mode computation found the mode of the distribution? It might be that you are stuck at a lower mode. Moreover, have you tried comparing your likelihood to the one given in the paper?

Thank you very much. I’m going to take a look at the shocks in a moment, but I’m very interested in what you had to say here:

If I could ask one more question, how might I go about checking this? If you could point me toward a paper or something online I’d really appreciate it. Also, when you say “comparing the likelihood”, do you mean the value of the log of the likelihood function? In that case, the one in the paper is -287.6, compared with -401.6 for mine (at least, i believe so - the laplace approximation of marginal density in oo_ is the value of the log likelihood, right? Sorry, but the manual is a little light on info on this point).

Hi, the following starting values will for example give you a likelihood of -370:
xparam1=[1.37852025124548
0.975194602744556
0.902750727152468
3.24584885242381
0.765876302147127
1.51741964610390
0.483919479546525
0.844308634125369
0.328431275164429
0.881611234168072
0.508300377456318
0.472915734373511
1.85068910441482
0.430256170386325
0.429344215477243
0.426646642233764
0.429004151703470]

Hence, you did not find the mode yet. It is instructive to have a look at ideas.repec.org/a/eee/econom/v155y2010i1p19-38.html. In theory, the MCMC should find the mode. However, this might not be in finite time/only after very many draws. What you can try is to increase the number of iterations in the mode_compute=6 step. But first, try using the posterior mean given in the paper and check the Likelihood/Laplace-approximation to see if this gives you approximately the same likelihood in your model as stated in the paper. This serves as a check that it is not the model or the data that is wrong.

Unbelievable - I forgot to add (linear) in the first line of the model. Thanks again for all of your help.