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Joey Performs Econometrics

ResponsiblyIrresponsible
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12/28/2015 8:43:30 PM
Posted: 11 months ago
So i've commented a bit recently on why I believe the Fed's recent move was a mistake. In large part this is because it's rationale--the Phillips-curve framework, positing a negative correlation between unemployment and inflation, embedded in its models--has been wrong for so long. I decided to test this view by estimating, via EViews, a reduced-form New Keynesian Phillips curve controlling for employment duration.

Some context: there have been several ongoing debates in the academic literature whether the link between resource utilization and inflation is even remotely stable, or whether current inflation is a function of lagged inflation or of forward-looking expectations centered around the central bank's target. If that were the case, if we estimated a model like this (assume t's are subscripts):

pi t = pi t - 1 + pi t -2 + pi t - 3 + pi t-4 + UGAP + ......... + e

Then the coefficients on the lagged values of inflation should be fairly pronounced and statistically significant. Some recent work, most notably by Blanchard, Cerutti, and Summers find that the unemployment gap is not longer statistically significant in determining the current rate of inflation--suggesting that lagged inflation is likewise indistinguishable from zero--but that forward-looking inflation expectations are far more important.

Now, the Fed nevertheless embeds that framework that as unemployment falls, inflation ought to rise--and that's a fairly significant pass-through from wage inflation to price inflation. Another camp, associated most notably with Alan Krueger, suggests that employment *duration* is what's important, and the longer someone is unemployed, the less of an impact they have on the current rate of inflation.

So, ideally, I would estimate a model with (a) short-term, medium-term and long-term unemployment gaps; (b) forward-looking and lagged parameters (perhaps t+8 and t-8, respectively, with quarterly data, adjusting for policy lags) for inflation expectations; and (c) an interaction term comparing employment durations.

Here's the problem: data limitations. There's no estimate of the "natural rate" by duration--only of the headline measure, which you can think of as a weighted average of these component parts--and even that is skewed by marginally attached, or soon-to-be-marginally attached (in Alan Krueger's judgment, the long-term unemployment). Therefore, to use the CBO's NAIRU is to presuppose Krueger's conclusion, in which case the data gets whacky, and we get a problem of multicollinearity (unemployment gap is correlated with long-term unemployment rate, because as the latter rises, the gap shrinks because the NAIRU rises proportionally).

As for interaction terms...... (a) too lazy, and (b) I'm accustomed to STATA, but unlike my friends I don't possess--or desire to possess--an illegal copy, nor do I have $600 or w/e I would need to slap down to purchase a license. So that isn't going to happen.

Therefore, we'll have to make do with this relatively lackluster model I scraped together. Don't worry: there are a few data transformations, so it's still "cool."

Without further ado, the model!

Inflation = Beta * short-term unemployment + Beta * medium-term unemployment + Beta * long-term unemployment + Beta * lagged inflation * Beta * forward-looking inflation expectations.

where:

inflation = the current, year-over-year core (excluding food and energy) PCE inflation rate
short-term unemployment = number of unemployed 5 weeks or less / labor force
medium-term unemployment = number of unemployed 6 weeks to 27 weeks / labor force
long-term unemployment = number of unemployed 27 weeks or more / labor force
lagged inflation = weighted average of past 8 quarters of headline PCE inflation (the logic is that oil shocks feed into inflation expectations and pass through to core numbers, so I'd only want to "smooth" the numbers for the dependent variable, because all I actually care about is the degree of pass through).
forward-looking inflation: 10-year inflation expectations from the Survey of Professional Forecasters.

I use quarterly data from 1995 to the present, as this is largely seen as the "cut off point" beyond which inflation expectations became reasonable well-anchored and this relationship called into question.

I need to screw around with the data a bit more, but the results will come in my next post.
~ResponsiblyIrresponsible

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ResponsiblyIrresponsible
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12/28/2015 8:50:43 PM
Posted: 11 months ago
Correction:

The durations are a bit whacky, too, but I think it's best not to--as I initially planned, but changed when I wrote this post--mix data series, because I'd like to see when/if there's a cut-off point. Therefore, instead of "short," medium" and "long"-term, I'll be using the fulling durations:

<5
[5,14]
[14, 27]
[27, infinity)
~ResponsiblyIrresponsible

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ResponsiblyIrresponsible
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12/28/2015 8:52:36 PM
Posted: 11 months ago
The model also includes four estimates of trend, because.... why not? Serially correlated errors is without question an issue in any type of model of inflation because of downward nominal rigidities, so this might as well smooth over *some* of these problems.
~ResponsiblyIrresponsible

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12/28/2015 9:25:53 PM
Posted: 11 months ago
And.... success! Estimated the model. Results coming in a bit.

The final specifications was:

inflation = constant + Urate1 + Urate2 + Urate3 + Urate4 + Backward-looking + Forward-looking + trend + trend^2 + trend^3 + trend^4

where:

inflation = current, year-over-year core PCE inflation rate

constant = random constant, a

Urate1 = number of unemployed 5 weeks or less / labor force * 100

Urate2 = number of unemployed 5 to 14 weeks / labor force * 100

Urate3 = number of unemployed 15 to 26 weeks / labor force * 100

Urate 4 = number of unemployed 27 weeks or more / labor force * 100

Backward-looking = 8-quarter moving average of headline PCE inflation rate

Forward-looking: SPF forecasts of 10-year CPI inflation, less the average 30-bps CPI-PCE differential.

Trend, Trend^2, Trend^3, Trend^4: accounts for factors left out of the model that behave in a linear, quadratic, cubic, etc. manner.
~ResponsiblyIrresponsible

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12/28/2015 9:38:39 PM
Posted: 11 months ago
Estimated Model

Inflation at time t = 0.562743 + 0.012967URate1 - 0.377135Urate2 - 0.535381Urate3 + 0.232210Urate4 + 0.459824Backward-looking + 0.535123Forward-looking -0.068053Trend + 0.004068Trend^2 - 7.76 * 10^-5 Trend^3 + 4.63 * 10-7 Trend^4

T-statistics

Urate1: 0.040005
Urate 2: -1.191914
Urate3: -1.887967
Urate4: 3.728099
Backward-looking: 6.338000
Forward-looking: 1.975965
Trend: -2.582447
Trend^2: 3.753210
Trend^4: 4.042466

With 83 observations and 11 parameters, we have 72 degrees of freedom. At the 5 percent level, that means a t-critical of 1.99. So anything greater than 1.99 in absolute value terms is statistically significant for our purposes.

This means that Urate4, backward-looking, and our four estimates of trend are statistically significant, and that Urate1, Urate2, Urate3, and forward-looking inflation expectations are not.

Our adjusted R-squared is 81.57%, suggesting that this model captures fairly well the factors bearing on inflation.

Conclusion

This model is a bit rough, but it gets the job done--it suggests not only that the bulk of downward-pressure on inflation from resource utilization is a direct byproduct of the gobs of long-term unemployed, calling into question Alan Krueger's research, but that inflation has followed a fairly stable trend; the current inflation rate is largely a byproduct of lagged inflation--meaning that yesterday's inflation rate has considerable implications for what inflation will be today, tomorrow, and a month from now. Therefore, it is very possible that persistent undershooting will result in unanchoring inflation expectations.
~ResponsiblyIrresponsible

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tejretics
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12/30/2015 2:34:02 PM
Posted: 11 months ago
There's no way I'm reading this whole thing.

What's the tl;dr?
"Where justice is denied, where poverty is enforced, where ignorance prevails, and where any one class is made to feel that society is an organized conspiracy to oppress, rob and degrade them, neither persons nor property will be safe." - Frederick Douglass
The-Voice-of-Truth
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12/30/2015 4:56:01 PM
Posted: 11 months ago
At 12/28/2015 9:38:39 PM, ResponsiblyIrresponsible wrote:

Oh gr8 Economics Messiah of DDO, enlighten me on your great econ wisdom. What is the tl;dr?
Suh dude

"Because we all know who the most important snowflake in the wasteland is... It's YOU, champ! You're a special snowflake." -Vaarka, 01:30 in the hangouts

"Screw laying siege to Korea. That usually takes an hour or so." -Vaarka

"Crap, what is my religion again?" -Vaarka

I'm Rick Harrison and this is my pawn shop. I work here with my old man and my son, Big Hoss, and in 23 years I've learned one thing. You never know what is gonna come through that door.
ResponsiblyIrresponsible
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12/30/2015 5:24:18 PM
Posted: 11 months ago
At 12/30/2015 4:56:01 PM, The-Voice-of-Truth wrote:
At 12/28/2015 9:38:39 PM, ResponsiblyIrresponsible wrote:

Oh gr8 Economics Messiah of DDO, enlighten me on your great econ wisdom. What is the tl;dr?

Regression models are cool.... when you don't misread coefficients, lol.

This one is pretty sloppy, so there isn't much to see here.
~ResponsiblyIrresponsible

DDO's Economics Messiah
The-Voice-of-Truth
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12/30/2015 5:26:48 PM
Posted: 11 months ago
At 12/30/2015 5:24:18 PM, ResponsiblyIrresponsible wrote:
At 12/30/2015 4:56:01 PM, The-Voice-of-Truth wrote:
At 12/28/2015 9:38:39 PM, ResponsiblyIrresponsible wrote:

Oh gr8 Economics Messiah of DDO, enlighten me on your great econ wisdom. What is the tl;dr?

Regression models are cool.... when you don't misread coefficients, lol.


This one is pretty sloppy, so there isn't much to see here.

Ah! Thank you, Oh Great Wise One.
Suh dude

"Because we all know who the most important snowflake in the wasteland is... It's YOU, champ! You're a special snowflake." -Vaarka, 01:30 in the hangouts

"Screw laying siege to Korea. That usually takes an hour or so." -Vaarka

"Crap, what is my religion again?" -Vaarka

I'm Rick Harrison and this is my pawn shop. I work here with my old man and my son, Big Hoss, and in 23 years I've learned one thing. You never know what is gonna come through that door.