Matheson-Stavrev EL 2013

[TomDoan]

Thank you, Mr.Doan. I have not found this new version until this afternoon.
I am still working on it. Let me ask you sever questions about the model (the attached file).

1. I rewrite the equations in the type of reduced form in the attached file. In the reduced form, theta, anchoring coefficient, shows eventually the relationship between 'real inflation (headline CPI inflation)' and 'long-run inflation expectations' . So, can I say that the anchoring coefficient of this paper means how significantly 'long-run inflation expectations' affects 'real inflation', not 'weighted average inflation expectations'? This could sounds very natural or silly but the authors did not define 'anchoring', so I ask you.

The author would need to explain what an author means by a phrase in a paper. However, theta is the weight on the inflation expectation (compared with the recent observed inflation).

2. Can I think that your code is for one reduced form equation with time varying coefficients?

Since there are two observables, I'm not sure I would describe it that way.

3. State equations includes 4 varibles - kappa, theta, gamma, and u-u*. Unlike others which are estimated in the equations, u-u* is given exogenously - u* is hp filtered u. Is this OK, I mean, don't we have to estimate u* 'in the model'?

u is observable, so u* and u-u* are connected by an identity. You can either include them separately as states and have an identity measurement equation for u, or you can substitute one out in the equation for u. The two are equivalent.

Upon reviewing their program, they, in fact, use the full set of 5 states, but because the program they used for Kalman filter/smooth couldn't handle a zero variance on a measurement equation, they put in a small positive number.

[bok1234]

Thank you, Mr.Doan.
In question no.2, you said that there are 2 observables in the reduced form equation. But don't we have 4 observables - real inflation (phi, independent variable), u (unemployment rate), import price index (phi m), and long-run inflation expectations (phi bar)?

[TomDoan]

The others are treated as pre-determined. There are only the two that the model is designed to explain.

[bok1234]

Only the two observables are 'U' - you already mentioned this - and 'Pi'? I just guessed because this equation is Phillips curve..

[TomDoan]

The paper may be a little light on details, but yes, the model is designed to explain U and pi given lagged pi, the inflation expectations and the import price inflation.

[bok1234]

Dear Mr.Doan,

These are just questions for confirmation.
In ekfexample.rpf and ekfunconstrain.rpf, ‘pi’ is actual inflation rate and ‘pibar’, this is ‘ptrcpi’ is long-run inflation expectations. I rewrite those variables as below.

set u = unrate
set pi = 400.0*log(cpi/cpi{1})
set pim = 400.0*log(mdef/mdef{1})-pi
set pibar = ptrcpi
set pistar = .25*(pi+pi{1}+pi{2}+pi{3})


[ Question 1 ]
If ‘pi’ is ‘% change of CPI from previous calendar year,’ then the equation of pi should be changed as below, right?
pi = 400.0*log(cpi/cpi{4}) ; quarterly data case
pi = 200.0*log(cpi/cpi{2}) ; semi-annual data case

[ Question 2 ]
Is ‘ptrcpi’ the inflation expectations based on ‘% change of CPI from previous calendar year’ or
'% change of CPI from previous quarter’?

[ Question 3 ]
Please let me know the reason why we should minus 'pi' in equation 'pim'?

[TomDoan]

Dear Mr.Doan,

These are just questions for confirmation.
In ekfexample.rpf and ekfunconstrain.rpf, ‘pi’ is actual inflation rate and ‘pibar’, this is ‘ptrcpi’ is long-run inflation expectations. I rewrite those variables as below.

set u = unrate
set pi = 400.0*log(cpi/cpi{1})
set pim = 400.0*log(mdef/mdef{1})-pi
set pibar = ptrcpi
set pistar = .25*(pi+pi{1}+pi{2}+pi{3})


[ Question 1 ]
If ‘pi’ is ‘% change of CPI from previous calendar year,’ then the equation of pi should be changed as below, right?
pi = 400.0*log(cpi/cpi{4}) ; quarterly data case
pi = 200.0*log(cpi/cpi{2}) ; semi-annual data case

100.0 for the first.

[ Question 2 ]
Is ‘ptrcpi’ the inflation expectations based on ‘% change of CPI from previous calendar year’ or
'% change of CPI from previous quarter’?

Annualized. All the inflation measures are intended to be annualized.

[ Question 3 ]
Please let me know the reason why we should minus 'pi' in equation 'pim'?

It's supposed to be an import-price "push", thus the excess of import prices over regular inflation.

I don't know if you noticed it but this paper is included in the 2nd edition of the State Space e-course.

[bok1234]

Dear Mr.Doan,

Thank you. Every answer is clear except the second one.
I already know that every variable got annualized for the model.
But my question is about the stage before annualization.
I am going to change the second question a little for your understanding my question.
The below table is just for example made of virtual CPI.
I want to know whether ‘ptrcpi’ is the inflation expectations based on ‘% change of CPI from previous calendar year (the third column)’ or % change of CPI from previous quarter (the fourth column)’.

[TomDoan]

I'm not sure what you're asking. They're long-term expectations, not calculations.

[bok1234]

Yes, ptrcpi is long-term inflation expectations. I just wanna know whether the long-term inflation expectations rate are '% change of CPI from previous calendar year' or '% change of CPI from previous quarter'. Actual inflation rates can be calculated by those methods. Just like actual inflation rates, Inflation expectations can be surveyed differently. I guess that general method to survey inflation expectations is asking long-term - for example 5 or 10 years - average inflation expectation based on '% change of CPI from previous calendar year'.

[bok1234]

Dear Mr.Doan,

When both filtering and smoothing results of Kalman Filter are reported simultaneously, these results should be generated through same options in the code (e.g. presample, condition, method, data begining point, etc)? The reason why I ask you this is that under some options filtering result is meaningful - statistically significant and theoretically appropriate - but smoothing result is non-sense, and vice versa under another options. It is rational, I guess, that filtering and smoothing results 'under same options' should be reported but it's very hard to find the case which both results are meaningful simultaneously.

[TomDoan]

Yes, ptrcpi is long-term inflation expectations. I just wanna know whether the long-term inflation expectations rate are '% change of CPI from previous calendar year' or '% change of CPI from previous quarter'. Actual inflation rates can be calculated by those methods. Just like actual inflation rates, Inflation expectations can be surveyed differently. I guess that general method to survey inflation expectations is asking long-term - for example 5 or 10 years - average inflation expectation based on '% change of CPI from previous calendar year'.

You're confusing concept with calculation. Inflation is the rate of change of prices---theoretically a derivative of an unobservable continuous time variable. 400.0*log(cpi/cpi{1}) and 100.0*log(cpi/cpi{4}) are just two different ways to estimate the rate of inflation (the first as an average rate over the past quarter, and the second as the average rate over the past year). The expectations variable is the expected average rate over the next five or ten years.

[TomDoan]

Dear Mr.Doan,

When both filtering and smoothing results of Kalman Filter are reported simultaneously, these results should be generated through same options in the code (e.g. presample, condition, method, data begining point, etc)? The reason why I ask you this is that under some options filtering result is meaningful - statistically significant and theoretically appropriate - but smoothing result is non-sense, and vice versa under another options. It is rational, I guess, that filtering and smoothing results 'under same options' should be reported but it's very hard to find the case which both results are meaningful simultaneously.

The whole literature on "PC-Gap" models is full of what would best be described as disappointing results. It appears that no one has hit upon a method which gets out more than is put in in the form of restrictions. The likelihood function on the "gap" analysis is flat across very different looking estimates, and adding it into the PC and jointly estimating doesn't resolve that because the PC really doesn't react much to the estimated gap.

[hgz2373294jh]

Hello every one!
when i read the paper of matheson_stavrev_el2013,titled the great recession and the inflation puzzle,
i found the figure 3,namely the decompostion of inflation in the great recession, can't be get ,according to the code of the paper.
Can you help?give me some suggestion.
Thanks in advance

[TomDoan]

That paper has quite a few technical issues (see the thread to which I've now attached it), one of which is that it's not clear what Figure 3 is actually graphing.