EMPIRICAL ASSESSMENT OF THE PHILLIPS CURVE
Emi Nakamura Jón Steinsson
Columbia University
January 2018
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 1 / 55
BRIEF HISTORY OF THE PHILLIPS CURVE
Phillips 58 points out empirical relationship between wage inflation
and unemployment in UK 1861-1957
Samuelson-Solow 60 popularize idea in US
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 2 / 55
INFLATION AND UNEMPLOYMENT IN THE UK
1958] UNEMPLOYMENT AND MONEY WAGE RATES 285
year, an increase of 7 * 6 per cent. in 1900 and in 1910, and an increase of 7 0 per cent. in 1872. In no other year between 1861 and 1913 was there an increase in import prices of as much as 5 per cent. If the hypothesis stated above is correct the rise in import prices in 1862 may just have been sufficient to start up a mild wage-price spiral, but in the remainder of the period changes in import prices will have had little or no effect on the rate of change of wage rates.
U 0
cf.
E? 2 - 0 0~~~~ cl) ? -2 0
. ~~~~~~~~~~*
.-40 1 2 3 4 6 $ 7 8 9 10 11 Unemptoyment, %.
Fig,t. 1861 - 1913
A scatter diagram of the rate of change of wage rates and the per- centage unemployment for the years 1861-1913 is shown in Figure 1. During this time there were 61 fairly regular trade cycles with an average period of about 8 years. Scatter diagrams for the years of each trade cycle are shown in Figures 2 to 8. Each dot in the diagrams represents a year, the average rate of change of money wage rates during the year being given by the scale on the vertical axis and the average unemployment during the year by the scale on the horizontal axis. The rate of change of money wage rates was calculated from the index of hourly wage rates constructed by Phelps Brown and Sheila Hopkins,' by expressing the first central difference of the index for each year as a percentage of the index for the same year. Thus the rate of change for 1861 is taken to be half the difference between the index for 1862 and the index for 1860 expressed as a percentage of the index
IE. HI. Phelps Brown and Sheila Hopkins, "'The Course of Wage Rates in Five Countries, 1860-1939," Oxford Economic Papers, June, 1950.
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Source: Phillips (1958)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 3 / 55
INFLATION AND UNEMPLOYMENT IN THE UK 286 ECONOMICA [NOVEMBER
10
@i 10 X.
*-,Curve fitted to 1861-1913 data
6-
IV
4 64 63
c 2 E: 2- t-t 2 > ~~~~~62
-2 z ~~~~~~~~~67
I I I * a I I I I I B 0 0 1 2 3 4 5 6 7 8. 9 10 11
Unemployment, %.
Fig.2. 1861 - 1868
2 Curve fitted to 1861-1913 data 72
6-6 73
c) 0
3: 4l Z'% 70
C
0 Unmpoyen,74.
Fig.3. 1868 -1879 ~ ~ ~ 7
This content downloaded from 128.59.165.222 on Fri, 26 Jan 2018 16:23:32 UTCAll use subject to http://about.jstor.org/terms
Source: Phillips (1958)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 4 / 55
INFLATION AND UNEMPLOYMENT IN THE UK
286 ECONOMICA [NOVEMBER
10
@i 10 X.
*-,Curve fitted to 1861-1913 data
6-
IV
4 64 63
c 2 E: 2- t-t 2 > ~~~~~62
-2 z ~~~~~~~~~67
I I I * a I I I I I B 0 0 1 2 3 4 5 6 7 8. 9 10 11
Unemployment, %.
Fig.2. 1861 - 1868
2 Curve fitted to 1861-1913 data 72
6-6 73
c) 0
3: 4l Z'% 70
C
0 Unmpoyen,74.
Fig.3. 1868 -1879 ~ ~ ~ 7
This content downloaded from 128.59.165.222 on Fri, 26 Jan 2018 16:23:32 UTCAll use subject to http://about.jstor.org/terms
Source: Phillips (1958)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 5 / 55
INFLATION AND UNEMPLOYMENT IN THE UK 288 ECONOMICA [NOVEMBER
C
t1:
10-
-f1C Curve fitted to 1861 -1913 data
+' 6 \
06 0) 3 4 \9
o 90 E 87 86 -0 0 92 93 0) C -2
0 1 2 3 4 5 6 7 8 9 10 I
cr. Unemptoyment, %.
Fig.5. 1886- 1893
># 10
* \ Curve fitted to 1861-1913 data
6-
(U4
0 0 no4- \
E 0 @ ~~~~~01 02 os 04 94 93
X-2-
"o -4J 0 1 2 3 4 5 6 7 8 9 10 11
Unemployment, 1.
Fig.6. 1893 -1904
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Source: Phillips (1958)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 6 / 55
INFLATION AND UNEMPLOYMENT IN THE UK
288 ECONOMICA [NOVEMBER
C
t1:
10-
-f1C Curve fitted to 1861 -1913 data
+' 6 \
06 0) 3 4 \9
o 90 E 87 86 -0 0 92 93 0) C -2
0 1 2 3 4 5 6 7 8 9 10 I
cr. Unemptoyment, %.
Fig.5. 1886- 1893
># 10
* \ Curve fitted to 1861-1913 data
6-
(U4
0 0 no4- \
E 0 @ ~~~~~01 02 os 04 94 93
X-2-
"o -4J 0 1 2 3 4 5 6 7 8 9 10 11
Unemployment, 1.
Fig.6. 1893 -1904
This content downloaded from 128.59.165.222 on Fri, 26 Jan 2018 16:23:32 UTCAll use subject to http://about.jstor.org/terms
Source: Phillips (1958)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 7 / 55
US MACRO POLICY IN THE 1960S
Phillips curve viewed as a menu of options
Policy makers can lower unemployment if they are
willing to tolerate more inflation
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 8 / 55
INFLATION AND UNEMPLOYMENT IN THE USU.S. in the 1960’s
46
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
2.00 4.00 6.00 8.00 10.00 12.00
Infla
tion Ra
te
Unemployment Rate
19601965
1969
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 9 / 55
FRIEDMAN AND PHELPS MAKE A PREDICTION
Friedman 68 and Phelps 67:
Policymakers cannot exploit a stable Phillips curve forever
Workers will demand wage increases in excess of expected inflation
As inflation rises, expectations of inflation will rise
Changes in expected inflation will shift the Phillips curve
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 10 / 55
INFLATION AND UNEMPLOYMENT IN THE USU.S. in the 1960’s
46
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
2.00 4.00 6.00 8.00 10.00 12.00
Infla
tion Ra
te
Unemployment Rate
19601965
1969
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 11 / 55
FRIEDMAN AND PHELPS WERE RIGHT!Friedman and Phelps Were Right!!
9
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
2.00 4.00 6.00 8.00 10.00 12.00
Infla
tion Ra
te
Unemployment Rate
19601965
1969
1980
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 12 / 55
MODERN PHILLIPS CURVE
πt = βEtπt+1 + κ(yt − ynt ) + ηt
Three drivers of inflation:
Expected inflation: Etπt
Output relative to potential: yt − yntCost-push shocks: ηt
Specific form above based on Calvo 83 sticky-price assumptions
But details may vary (e.g., sticky information yields Ēt−1πt )
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 13 / 55
ESTIMATING SLOPE OF THE PHILLIPS CURVE
πt = βEtπt+1 + κ(yt − ynt ) + ηt
Object of interest: Slope coefficient κ
How much does an increase in “demand” / “tightness” / “output gap”
affect inflation
Tricky identification issues:
Expected inflation unobserved
“Natural rate of output” (i.e., supply shocks) unobserved
Cost push shocks (e.g., variation in desired markups) unobserved
All three may cause omitted variables bias
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 14 / 55
ESTIMATING SLOPE OF THE PHILLIPS CURVE
πt = βEtπt+1 + κ(yt − ynt ) + ηt
Object of interest: Slope coefficient κ
How much does an increase in “demand” / “tightness” / “output gap”
affect inflation
Tricky identification issues:
Expected inflation unobserved
“Natural rate of output” (i.e., supply shocks) unobserved
Cost push shocks (e.g., variation in desired markups) unobserved
All three may cause omitted variables bias
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 14 / 55
EXPECTED INFLATION
Pre Friedman/Phelps Phillips curve: Change in output gap needed
to change inflation
Same is true for accelerationist Phillips curve
(i.e., Phillips curve with adaptive expectations)
πt = πt−1 + κ(yt − ynt )
Sargent 82: Hyperinflations end abruptly with little or no output cost
Clear violation of aforementioned Phillips curves
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 15 / 55
EXPECTED INFLATION
Pre Friedman/Phelps Phillips curve: Change in output gap needed
to change inflation
Same is true for accelerationist Phillips curve
(i.e., Phillips curve with adaptive expectations)
πt = πt−1 + κ(yt − ynt )
Sargent 82: Hyperinflations end abruptly with little or no output cost
Clear violation of aforementioned Phillips curves
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 15 / 55
GERMAN HYPERINFLATION
9
Sargent (1982): The Ends of Four Big Inflations
Source: Sargent (1982)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 16 / 55
EXPECTED INFLATION
In Calvo model, perfectly credible, unexpected disinflation can occurwithout any affect on output gap
Expected inflation does all the work
Theoretical victory: Potential explanation for Sargent facts
Empirical headache:
Movements in inflation potentially completely unrelated to output gap
Even if output gap moves during disinflation, not clear what fraction
of disinflation was due to shift in expected inflation
Measurement of expected inflation crucial but hard
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 17 / 55
EXPECTED INFLATION
In Calvo model, perfectly credible, unexpected disinflation can occurwithout any affect on output gap
Expected inflation does all the work
Theoretical victory: Potential explanation for Sargent facts
Empirical headache:
Movements in inflation potentially completely unrelated to output gap
Even if output gap moves during disinflation, not clear what fraction
of disinflation was due to shift in expected inflation
Measurement of expected inflation crucial but hard
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 17 / 55
SUPPLY SHOCKS
Slope of Phillips curve: Causal effect of output gap on inflation
But output gap is not directly observable
Ideal experiment:
Shifts in output holding potential output and expected inflation constant
Shifts in potential output (or natural rate of unemployment):
Shift the Phillips curve
Potentially lead to negative correlation between output and inflation
Bias estimated slope of Phillips curve downward
Cost push shocks cause similar problems
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 18 / 55
SUPPLY SHOCKS
Slope of Phillips curve: Causal effect of output gap on inflation
But output gap is not directly observable
Ideal experiment:
Shifts in output holding potential output and expected inflation constant
Shifts in potential output (or natural rate of unemployment):
Shift the Phillips curve
Potentially lead to negative correlation between output and inflation
Bias estimated slope of Phillips curve downward
Cost push shocks cause similar problems
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 18 / 55
IS THE PHILLIPS CURVE DEAD?
Phillips curve often pronounced dead
Many economists think Phillips curve is an empirical disaster
Prominent episodes:
Missing inflation in late 1990s
Missing disinflation in the Great Recession
Let’s take a closer look
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 19 / 55
STAGFLATION OF THE 1970S
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
2.0 4.0 6.0 8.0 10.0
Inflation
Unemployment
1969
1980
1961
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 20 / 55
STAGFLATION OF THE 1970S
Friedman and Phelps were right:
Phillips curve shifted up in 1970s
But why did inflation rise at higher and higher unemployment rates
as 1970s progressed?
Possible explanation: Rise in natural rate of unemployment
Baby boon generation was entering labor force in 1970s
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 21 / 55
VOLCKER DISINFLATION
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
2.0 4.0 6.0 8.0 10.0
Inflation
Unemployment
1969
1980
1983
1989
1961
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 22 / 55
MISSING INFLATION IN LATE 1990S
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
Inflation
Unemployment
1986
1990
19922000
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 23 / 55
MISSING INFLATION IN LATE 1990S
1986-1996: “Looks good”
1997-2000: Why doesn’t inflation rise?
Maybe it was just starting to in 2000 but Fed nipped it in the bud
Maybe the Phillips curve is highly non-linear
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 24 / 55
MISSING DISINFLATION IN THE GREAT RECESSION
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
Inflation
Unemployment
1986
1990
19922000
2003
2007
2010
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 25 / 55
MISSING DISINFLATION IN THE GREAT RECESSION
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
Inflation
Unemployment
1990
19922000 2007
2010
20142017
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 26 / 55
IS THE PHILLIPS CURVE DEAD?
Why did inflation not fall more in Great Recession?
Actually rose in 2010 and 2011
Why is inflation not rising now?
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 27 / 55
COIBION-GORODNICHENKO 15
“Is the Phillips Curve Alive and Well after All?”
Focus on “missing disinflation” during Great Recession
Population explanations insufficient
Anchored inflationary expectations
Movements in natural rate
Flattening of the Phillips curve
New explanation:
Household inflation expectations rose in 2009-2013
If firm’s expectation the same, this can explain missing disinflation
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 28 / 55
COIBION-GORODNICHENKO 15
“Is the Phillips Curve Alive and Well after All?”
Focus on “missing disinflation” during Great Recession
Population explanations insufficient
Anchored inflationary expectations
Movements in natural rate
Flattening of the Phillips curve
New explanation:
Household inflation expectations rose in 2009-2013
If firm’s expectation the same, this can explain missing disinflation
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 28 / 55
COIBION-GORODNICHENKO 15
πt = βEtπt+1 + κ(yt − ynt ) + ηt
Baseline assumptions:
Output gap measure: Unemployment rate
yt − ynt = ut
Expectations of inflation: backward looking
Etπt+1 =14
(πt−1 + πt−2 + πt−3 + πt−4)
Ignore discounting: β = 1
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 29 / 55
COIBION-GORODNICHENKO 15
πt − EπBackt+1 = κut + ηt
Estimate by OLS for sample 1960Q1-2007Q4
Implicitly assuming that ηt ⊥ utSimilar to VAR timing restriction. (Why?)
Consider whether Great Recession conforms with earlier relationship
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 30 / 55
MISSING DISINFLATION202 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2015
−10
−8
−6
−4
−2
0
2
4
6
8
Infla
tion
2010 2011 2013
07Q4
08Q1
08Q2
08Q3
09Q1
09Q2
09Q309Q4
10Q1
10Q2
10Q3
10Q4
11Q1
11Q2
11Q3
11Q4
12Q1
12Q2
12Q312Q4
13Q1
−8
−6
−4
−2
0
2
4
3 4 5 6 7 8 9 10 11
Unemployment rate
Panel A. CPI in�ation and US unemployment
2007 2008 2009 2012
Panel B. CPI inflation and predicted inflation from the Phillips Curve
Actual
Backward PC
π t−
Eπ t
Bac
k
Figure 1. The Missing Disinflation
Notes: Panel A shows the scatter plot of inflation surprises ( π t − E t π t BACK ) versus unemployment rate. E t π t BACK is calculated as in equation (2). Empty circles show observations for 1960Q1–2007Q3. Filled circles show observa-tions for 2007Q4–2013Q1. The solid line shows predicted inflation surprises as a function of the unemployment rate in the linear regression. The inflation surprise for 2008Q4 is outside the range of the figure and is not reported. Panel B plots time series of the actual CPI inflation rate (annualized; solid thick line) and the CPI inflation rate pre-dicted by the Phillips curve (equation (1); dashed line) which is estimated on the 1960Q1–2006Q3 sample.
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 31 / 55
MISSING DISINFLATION
202 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2015
−10
−8
−6
−4
−2
0
2
4
6
8
Infla
tion
2010 2011 2013
07Q4
08Q1
08Q2
08Q3
09Q1
09Q2
09Q309Q4
10Q1
10Q2
10Q3
10Q4
11Q1
11Q2
11Q3
11Q4
12Q1
12Q2
12Q312Q4
13Q1
−8
−6
−4
−2
0
2
4
3 4 5 6 7 8 9 10 11
Unemployment rate
Panel A. CPI in�ation and US unemployment
2007 2008 2009 2012
Panel B. CPI inflation and predicted inflation from the Phillips Curve
Actual
Backward PC
π t−
Eπ t
Bac
k
Figure 1. The Missing Disinflation
Notes: Panel A shows the scatter plot of inflation surprises ( π t − E t π t BACK ) versus unemployment rate. E t π t BACK is calculated as in equation (2). Empty circles show observations for 1960Q1–2007Q3. Filled circles show observa-tions for 2007Q4–2013Q1. The solid line shows predicted inflation surprises as a function of the unemployment rate in the linear regression. The inflation surprise for 2008Q4 is outside the range of the figure and is not reported. Panel B plots time series of the actual CPI inflation rate (annualized; solid thick line) and the CPI inflation rate pre-dicted by the Phillips curve (equation (1); dashed line) which is estimated on the 1960Q1–2006Q3 sample.
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 32 / 55
MISSING DISINFLATION
204 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2015
movements during this period pushed inflation up despite the weak economy. The price of West Texas Intermediate (WTI) crude, for example, went from under 40 dollars per barrel in early 2009 to over 100 dollars per barrel in early 2011, precisely the period during which inflation was significantly higher than expected from historical Phillips curve correlations. To assess whether changing oil prices can account for the unusual inflation dynamics during this period via shifts in
07Q408Q1
08Q2
08Q3
08Q4
09Q109Q2
09Q3
09Q4
10Q1
10Q210Q310Q4
11Q111Q211Q3
11Q412Q112Q2
12Q312Q4
13Q1
07Q4
08Q1
08Q2
08Q3
09Q1
09Q2
09Q309Q4
10Q1
10Q2
10Q3
10Q4
11Q111Q2
11Q3
11Q4
12Q1
12Q2
12Q312Q4
13Q1
07Q4
08Q1
08Q2
08Q3
09Q1
09Q2
09Q3
09Q4
10Q1
10Q2
10Q3
10Q4
11Q1
11Q2
11Q3
11Q4
12Q112Q2
12Q3
12Q4
13Q1
−2 0 2 4 6
Unemployment rate, partial out oil price changes
07Q408Q1
08Q208Q3
09Q1
09Q2
09Q3
09Q410Q110Q210Q3
10Q411Q111Q211Q3
11Q4
12Q112Q2
12Q3
12Q413Q1
07Q408Q1
08Q2
08Q3
09Q1
09Q209Q3
09Q4
10Q110Q210Q310Q4
11Q1
11Q211Q3
11Q4
12Q1
12Q212Q312Q413Q1
07Q4
08Q1
08Q2 08Q3
09Q1
09Q2
09Q3
09Q4
10Q1
10Q210Q3
10Q4
11Q111Q2
11Q3
11Q4
12Q1
12Q2
12Q312Q4
13Q1
−8
−6
−4
−2
0
2
4
−8
−6
−4
−2
0
2
4
−6
−4
−2
0
2
4
−6
−4
−2
0
2
4
−8
−6
−4
−2
0
2
4
−8−6
−4
−2
0
2
4
3 4 5 6 7 8 9 10 11
Unemployment rate3 4 5 6 7 8 9 10 11
Unemployment rate
3 4 5 6 7 8 9 10 11Unemployment rate
3 4 5 6 7 8 9 10 11Unemployment rate
3 4 5 6 7 8 9 10 11
Unemployment rate
Panel A. PCE in�ation
Panel C. Core CPI in�ation Panel D. Core PCE in�ation
Panel E. SPF in�ation (CPI) forecasts Panel F. Controlling for oil prices
Panel B. GDP de�ator in�ation
π t −
Eπ t
BA
CK
PC
E in
flatio
n
π t −
Eπ t
BA
CK
GD
P d
efla
tor
infla
tion
π t −
Eπ t
BA
CK
CP
I CO
RE
infla
tion
π t −
Eπ t
SP
F
π t −
Eπ t
BA
CK
part
ial o
ut o
il pr
ice
chan
ges
π t −
Eπ t
BA
CK
P
CE
CO
RE
infla
tion
Figure 2. Robustness of the Missing Disinflation
Note: See notes for Figure 1 and the text for more details.
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 33 / 55
MISSING DISINFLATION
204 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2015
movements during this period pushed inflation up despite the weak economy. The price of West Texas Intermediate (WTI) crude, for example, went from under 40 dollars per barrel in early 2009 to over 100 dollars per barrel in early 2011, precisely the period during which inflation was significantly higher than expected from historical Phillips curve correlations. To assess whether changing oil prices can account for the unusual inflation dynamics during this period via shifts in
07Q408Q1
08Q2
08Q3
08Q4
09Q109Q2
09Q3
09Q4
10Q1
10Q210Q310Q4
11Q111Q211Q3
11Q412Q112Q2
12Q312Q4
13Q1
07Q4
08Q1
08Q2
08Q3
09Q1
09Q2
09Q309Q4
10Q1
10Q2
10Q3
10Q4
11Q111Q2
11Q3
11Q4
12Q1
12Q2
12Q312Q4
13Q1
07Q4
08Q1
08Q2
08Q3
09Q1
09Q2
09Q3
09Q4
10Q1
10Q2
10Q3
10Q4
11Q1
11Q2
11Q3
11Q4
12Q112Q2
12Q3
12Q4
13Q1
−2 0 2 4 6
Unemployment rate, partial out oil price changes
07Q408Q1
08Q208Q3
09Q1
09Q2
09Q3
09Q410Q110Q210Q3
10Q411Q111Q211Q3
11Q4
12Q112Q2
12Q3
12Q413Q1
07Q408Q1
08Q2
08Q3
09Q1
09Q209Q3
09Q4
10Q110Q210Q310Q4
11Q1
11Q211Q3
11Q4
12Q1
12Q212Q312Q413Q1
07Q4
08Q1
08Q2 08Q3
09Q1
09Q2
09Q3
09Q4
10Q1
10Q210Q3
10Q4
11Q111Q2
11Q3
11Q4
12Q1
12Q2
12Q312Q4
13Q1
−8
−6
−4
−2
0
2
4
−8
−6
−4
−2
0
2
4
−6
−4
−2
0
2
4
−6
−4
−2
0
2
4
−8
−6
−4
−2
0
2
4
−8−6
−4
−2
0
2
4
3 4 5 6 7 8 9 10 11
Unemployment rate3 4 5 6 7 8 9 10 11
Unemployment rate
3 4 5 6 7 8 9 10 11Unemployment rate
3 4 5 6 7 8 9 10 11Unemployment rate
3 4 5 6 7 8 9 10 11
Unemployment rate
Panel A. PCE in�ation
Panel C. Core CPI in�ation Panel D. Core PCE in�ation
Panel E. SPF in�ation (CPI) forecasts Panel F. Controlling for oil prices
Panel B. GDP de�ator in�ation
π t −
Eπ t
BA
CK
PC
E in
flatio
n
π t −
Eπ t
BA
CK
GD
P d
efla
tor
infla
tion
π t −
Eπ t
BA
CK
CP
I CO
RE
infla
tion
π t −
Eπ t
SP
F
π t −
Eπ t
BA
CK
part
ial o
ut o
il pr
ice
chan
ges
π t −
Eπ t
BA
CK
P
CE
CO
RE
infla
tion
Figure 2. Robustness of the Missing Disinflation
Note: See notes for Figure 1 and the text for more details.
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 34 / 55
MISSING DISINFLATION
204 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2015
movements during this period pushed inflation up despite the weak economy. The price of West Texas Intermediate (WTI) crude, for example, went from under 40 dollars per barrel in early 2009 to over 100 dollars per barrel in early 2011, precisely the period during which inflation was significantly higher than expected from historical Phillips curve correlations. To assess whether changing oil prices can account for the unusual inflation dynamics during this period via shifts in
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Unemployment rate
3 4 5 6 7 8 9 10 11Unemployment rate
3 4 5 6 7 8 9 10 11Unemployment rate
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Unemployment rate
Panel A. PCE in�ation
Panel C. Core CPI in�ation Panel D. Core PCE in�ation
Panel E. SPF in�ation (CPI) forecasts Panel F. Controlling for oil prices
Panel B. GDP de�ator in�ation
π t −
Eπ t
BA
CK
PC
E in
flatio
n
π t −
Eπ t
BA
CK
GD
P d
efla
tor
infla
tion
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CK
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I CO
RE
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tion
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SP
F
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CK
part
ial o
ut o
il pr
ice
chan
ges
π t −
Eπ t
BA
CK
P
CE
CO
RE
infla
tion
Figure 2. Robustness of the Missing Disinflation
Note: See notes for Figure 1 and the text for more details.Source: Coibion and Gorodnichenko (2015) – SPF forecast over next four quarters.
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 35 / 55
POSSIBLE EXPLANATIONS
Does unemployment mismeasure forcing variable?
Has the slope of the Phillips curve declined?
Are inflation expectations by firms mismeasured?
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 36 / 55
ACCOUNTING FOR NATURAL RATE
More natural to think of ut − unt as forcing variable
Perhaps the natural rate of unemployment changed
during Great Recession
Two approaches:
Use CBO estimates of natural rate of unemployment
Ask what natural rate consistent with observed inflation dynamics?
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 37 / 55
ACCOUNTING FOR NATURAL RATE
More natural to think of ut − unt as forcing variable
Perhaps the natural rate of unemployment changed
during Great Recession
Two approaches:
Use CBO estimates of natural rate of unemployment
Ask what natural rate consistent with observed inflation dynamics?
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 37 / 55
ACCOUNTING FOR NATURAL RATE
Reestimating Phillips curve with unemployment gap has
no effect on slope
CBO estimate of natural rate only rose by 1 percentage point
in Great Recession
Minimal effect on missing disinflation
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 38 / 55
ACCOUNTING FOR NATURAL RATEVOL.7 NO.1 207COIBION AND GORODNICHENKO: THE MISSING DISINFLATION
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Panel A. Missing disin�ation with CBO unemployment gaps
Panel B. Changes in natural rate of unemployment needed to explain missing disin�ation
π t −
Eπ t
BA
CK
Predicted natural rate
95% CI for predicted rate
Actual CBO natural rate
Actual unemployment rate
Figure 3. Does the Missing Disinflation Reflect Structural Unemployment?
Notes: Panel A plots quarterly levels of the unemployment gap (the difference between actual unemployment and the CBO estimate of the short-term natural rate of unemployment) against quarterly deviations of inflation from expected inflation (measuring the latter as the average inflation rate over the previous four quarters). The trend line uses data from 1960Q1 to 2007Q3. The predicted natural rate of unemployment in panel B is estimated as follows. First, U E t − U E t n = α + β ( π t − E t π t+1 ) + ε t is estimated on the 1960Q1–2007Q3 sample, where U E t is the rate of unemployment, U E t n is the natural rate of unemployment from the CBO, E t π t+1 is the backward-looking mea-sure of inflation expectations. Second, predicted value of the natural rate of unemployment is ̂ UE t
n = U E t − α ̂ −
β ̂ ( π t − E t π t+1 ) . The solid line shows the path of ̂ UE t n , while the shaded region shows the 95 percent confidence
interval for the predicted value. The solid line with circle markers is the natural rate of unemployment from the CBO. The dashed line shows the path of actual unemployment rate.
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 39 / 55
ACCOUNTING FOR NATURAL RATE
VOL.7 NO.1 207COIBION AND GORODNICHENKO: THE MISSING DISINFLATION
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Panel A. Missing disin�ation with CBO unemployment gaps
Panel B. Changes in natural rate of unemployment needed to explain missing disin�ation
π t −
Eπ t
BA
CK
Predicted natural rate
95% CI for predicted rate
Actual CBO natural rate
Actual unemployment rate
Figure 3. Does the Missing Disinflation Reflect Structural Unemployment?
Notes: Panel A plots quarterly levels of the unemployment gap (the difference between actual unemployment and the CBO estimate of the short-term natural rate of unemployment) against quarterly deviations of inflation from expected inflation (measuring the latter as the average inflation rate over the previous four quarters). The trend line uses data from 1960Q1 to 2007Q3. The predicted natural rate of unemployment in panel B is estimated as follows. First, U E t − U E t n = α + β ( π t − E t π t+1 ) + ε t is estimated on the 1960Q1–2007Q3 sample, where U E t is the rate of unemployment, U E t n is the natural rate of unemployment from the CBO, E t π t+1 is the backward-looking mea-sure of inflation expectations. Second, predicted value of the natural rate of unemployment is ̂ UE t
n = U E t − α ̂ −
β ̂ ( π t − E t π t+1 ) . The solid line shows the path of ̂ UE t n , while the shaded region shows the 95 percent confidence
interval for the predicted value. The solid line with circle markers is the natural rate of unemployment from the CBO. The dashed line shows the path of actual unemployment rate.
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 40 / 55
HAS THE PHILLIPS CURVE FLATTENED?212 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2015
curve. Hence, it appears plausible that a flattening of the Phillips curve could explain some of the missing disinflation.
We investigate the statistical evidence for a change in the slope of the Phillips curve more formally by allowing for a break in the slope of the Phillips curve in 1985Q1 as follows:
(5) π t − E t π t+1 = c + κ × U E t gap + γ × U E t gap × I ≥85,t + θ × I ≥85,t + erro r t ,
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I)
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2007 Q3−2013 Q1
Panel A. Sample split in mid-1980’s, backward-looking PC
Panel B. Sample split in mid-1980’s, forward-looking PC
Panel C. Counterfactual in�ation paths from time-varying slopes
Actual
BACK PC, 1960−2007
SPF PC, 1981−2007
BACK PC, 1991−2007
SPF PC, 1991−2007
π t−
Eπ t
SP
F ,
GD
P d
efla
tor
π t−
Eπ t
Bac
k
Figure 5. Time Variation in the Slope of the Phillips Curve
(Continued)
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 41 / 55
HAS THE PHILLIPS CURVE FLATTENED?
212 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2015
curve. Hence, it appears plausible that a flattening of the Phillips curve could explain some of the missing disinflation.
We investigate the statistical evidence for a change in the slope of the Phillips curve more formally by allowing for a break in the slope of the Phillips curve in 1985Q1 as follows:
(5) π t − E t π t+1 = c + κ × U E t gap + γ × U E t gap × I ≥85,t + θ × I ≥85,t + erro r t ,
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tion
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I)
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2007 2011
1960 Q1−1984 Q4
1985 Q1−2007 Q3
2007 Q3−2013 Q1
Panel A. Sample split in mid-1980’s, backward-looking PC
Panel B. Sample split in mid-1980’s, forward-looking PC
Panel C. Counterfactual in�ation paths from time-varying slopes
Actual
BACK PC, 1960−2007
SPF PC, 1981−2007
BACK PC, 1991−2007
SPF PC, 1991−2007
π t−
Eπ t
SP
F ,
GD
P d
efla
tor
π t−
Eπ t
Bac
k
Figure 5. Time Variation in the Slope of the Phillips Curve
(Continued)
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 42 / 55
HAS THE PHILLIPS CURVE FLATTENED?
Phillips curve appears to have flattened after 1985
Although statistical significance is weak
(little variation in inflation after 1985)
Can this account for missing disinflation?
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 43 / 55
CAN THIS ACCOUNT FOR MISSING DISINFLATION?VOL.7 NO.1 213COIBION AND GORODNICHENKO: THE MISSING DISINFLATION
where I ≥85,t is a dummy variable equal to one for periods from 1985Q1 to 2007Q3 and zero prior to 1985. The interaction of this dummy variable with the unemploy-ment gap ( γ ) allows us to assess whether the slope of the Phillips curve changed around this period.
We report results from estimating this specification in Table 1 for several cases: CPI inflation and backward-looking expectations, GDP deflator inflation and back-ward-looking expectations, and GDP deflator inflation with forward-looking (SPF) expectations.7 In each case, we estimate the Phillips curve both by OLS and by IV, using as instruments a constant, one lag of unemployment, the dummy variable for post-84 periods, and the interaction of the dummy with the lag of unemployment.
The point estimates on the interaction term are always positive, so that the Phillips curve consistently appears to have flattened since the mid-1980s. However, the sta-tistical significance of this effect varies by specification: we cannot reject the null of no change in slope using the CPI but can reject the null at least at the 5 percent level for all specifications with the GDP deflator, with almost no difference between OLS and IV estimates in any case. Thus, the evidence for a change in the slope is mixed. What is consistent across specifications, however, is that the change in the slope (if there was one) was relatively large: on the order of a 60–80 percent reduction in most specifications. Furthermore, we cannot reject the null that the slope of the Phillips curve since 1985 was zero, pointing to a weak link between real and nominal economic activity during this period, consistent with Atkeson and Ohanian (2001). The absence of conclusive empirical evidence on a changing slope
7 We use GDP deflator inflation forecasts from the SPF because projections for the GNP/GDP deflator have been collected by the SPF since 1968 while CPI inflation projections have been collected by the SPF only since 1981. The short time series of the CPI projections in the SPF makes the analysis of structural breaks problematic.
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Infla
tion
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I)
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−1
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2007 2011
1960 Q1−1984 Q4
1985 Q1−2007 Q3
2007 Q3−2013 Q1
Panel A. Sample split in mid-1980’s, backward-looking PC
Panel B. Sample split in mid-1980’s, forward-looking PC
Panel C. Counterfactual in�ation paths from time-varying slopes
Actual
BACK PC, 1960−2007
SPF PC, 1981−2007
BACK PC, 1991−2007
SPF PC, 1991−2007
π t−
Eπ t
SP
F ,
GD
P d
efla
tor
π t−
Eπ t
Bac
k
Figure 5. (Continued)
Notes: Panels A and B show changes in the slope of the Phillips curve over time. Panel A uses CPI inflation rate. Panel B uses GDP deflator inflation rate. Panel C shows the path of actual inflation and inflation predicted by Phillips curve estimated with forward-looking expectations (SPF) and backward-looking expectations (BACK) and over different time samples.
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 44 / 55
INFLATION EXPECTATIONS
Perhaps inflation expectations of firms differ from backward-looking
expectations and SPF forecasts
Household expectations (Michigan survey) quite different
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 45 / 55
INFLATION EXPECTATIONS218 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2015
well-proxied by professional forecasts. While one might expect very large firms to have professional forecasters on staff or to rely on the services of professional forecasters to guide their economic decisions, this need not be the case for small and medium enterprises for whom the gains from having precise information about aggregate conditions may be small (especially relative to local or industry-specific conditions), as in Mackowiak and Wiederholt (2009). For such firms, household forecasts could very well be a better proxy of their beliefs than professional forecasts.
Does it matter for the Phillips curve and the missing disinflation whether one assumes that firms hold beliefs closer to those of professional forecasters or house-holds? We showed in panel E of Figure 1 that using professional forecasts of inflation did not meaningfully affect the estimated slope of the historical Phillips curve or the presence of missing disinflation during the Great Recession. In panel B of Figure 6, we present the Phillips curve relationship between the unemployment gap and the difference between CPI inflation and household expectations of inflation. Several
Infla
tion
Unemployment gap
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tion
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2008
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2010
ActualBackward PCSPF PCMSC PC
Panel A. In�ation expectations for different economic agent
Panel B. Phillips Curve with household in�ation expectations
Panel C. Counterfactual in�ation (CPI) paths for different expectations
Panel D. Relative contribution of slopes and in�ation expectations
1960Q1−1984Q41985Q1−2007Q32007Q3−2013Q1
MSC exp, SPF κMSC PC MSCκ, SPF expSPF PC
Actual
Asset pricesMichiganSPF (CPI)
π t −
Eπ t
MSC
12Q1
Figure 6. The Phillips Curve and the Missing Disinflation with Household Inflation Expectations
Notes: Panel B shows the scatter plot of inflation (CPI) surprises versus unemployment gap as well as fitted linear regressions for two subperiods. Panel C plots actual inflation rate (CPI) as well as inflation rate predicted by Phillips curves (equation (1)) estimated on the pre-Great Recession samples. Phillips curves are estimated with unemploy-ment gap as the forcing variable. Panel D presents decomposition of differences between predicted inflation rates from Phillips curves (equation (1)) estimated with inflation expectations from the Michigan Survey of Consumers (MSC) and Survey of Professional Forecasters (SPF). “XYZ exp” denotes which inflation expectations are used (SPF or MSC), while “XYZ κ ” denotes what data was used to estimate the slope of the Phillips curve. Phillips curves are estimated with unemployment gap as the forcing variable.
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 46 / 55
INFLATION EXPECTATIONS
Not clear whether firm expectations behave like SPF
or like household expectations
But if they do behave like household expectations, does it matter?
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 47 / 55
INFLATION EXPECTATIONS218 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2015
well-proxied by professional forecasts. While one might expect very large firms to have professional forecasters on staff or to rely on the services of professional forecasters to guide their economic decisions, this need not be the case for small and medium enterprises for whom the gains from having precise information about aggregate conditions may be small (especially relative to local or industry-specific conditions), as in Mackowiak and Wiederholt (2009). For such firms, household forecasts could very well be a better proxy of their beliefs than professional forecasts.
Does it matter for the Phillips curve and the missing disinflation whether one assumes that firms hold beliefs closer to those of professional forecasters or house-holds? We showed in panel E of Figure 1 that using professional forecasts of inflation did not meaningfully affect the estimated slope of the historical Phillips curve or the presence of missing disinflation during the Great Recession. In panel B of Figure 6, we present the Phillips curve relationship between the unemployment gap and the difference between CPI inflation and household expectations of inflation. Several
Infla
tion
Unemployment gap
−10−8−6−4−2
02
46
8
Infla
tion
2007
2008
2009
2010
2011
2012
2013
−10−8−6−4−2
02468
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2013
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1980 1985 1990 1995 2000 2005 2010
2012
2007
2008
2009
2010
ActualBackward PCSPF PCMSC PC
Panel A. In�ation expectations for different economic agent
Panel B. Phillips Curve with household in�ation expectations
Panel C. Counterfactual in�ation (CPI) paths for different expectations
Panel D. Relative contribution of slopes and in�ation expectations
1960Q1−1984Q41985Q1−2007Q32007Q3−2013Q1
MSC exp, SPF κMSC PC MSCκ, SPF expSPF PC
Actual
Asset pricesMichiganSPF (CPI)
π t −
Eπ t
MSC
12Q1
Figure 6. The Phillips Curve and the Missing Disinflation with Household Inflation Expectations
Notes: Panel B shows the scatter plot of inflation (CPI) surprises versus unemployment gap as well as fitted linear regressions for two subperiods. Panel C plots actual inflation rate (CPI) as well as inflation rate predicted by Phillips curves (equation (1)) estimated on the pre-Great Recession samples. Phillips curves are estimated with unemploy-ment gap as the forcing variable. Panel D presents decomposition of differences between predicted inflation rates from Phillips curves (equation (1)) estimated with inflation expectations from the Michigan Survey of Consumers (MSC) and Survey of Professional Forecasters (SPF). “XYZ exp” denotes which inflation expectations are used (SPF or MSC), while “XYZ κ ” denotes what data was used to estimate the slope of the Phillips curve. Phillips curves are estimated with unemployment gap as the forcing variable.
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 48 / 55
INFLATION EXPECTATIONS
Three differences versus SPF:
No evidence of flattening
Flatter throughout
No evidence of missing disinflation!
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 49 / 55
INFLATION EXPECTATIONS
218 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2015
well-proxied by professional forecasts. While one might expect very large firms to have professional forecasters on staff or to rely on the services of professional forecasters to guide their economic decisions, this need not be the case for small and medium enterprises for whom the gains from having precise information about aggregate conditions may be small (especially relative to local or industry-specific conditions), as in Mackowiak and Wiederholt (2009). For such firms, household forecasts could very well be a better proxy of their beliefs than professional forecasts.
Does it matter for the Phillips curve and the missing disinflation whether one assumes that firms hold beliefs closer to those of professional forecasters or house-holds? We showed in panel E of Figure 1 that using professional forecasts of inflation did not meaningfully affect the estimated slope of the historical Phillips curve or the presence of missing disinflation during the Great Recession. In panel B of Figure 6, we present the Phillips curve relationship between the unemployment gap and the difference between CPI inflation and household expectations of inflation. Several
Infla
tion
Unemployment gap
−10−8−6−4−2
02
46
8
Infla
tion
2007
2008
2009
2010
2011
2012
2013
−10−8−6−4−2
02468
2011
2013
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08Q2
08Q3
09Q1
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10Q1
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0
2
4
6
8
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12
1980 1985 1990 1995 2000 2005 2010
2012
2007
2008
2009
2010
ActualBackward PCSPF PCMSC PC
Panel A. In�ation expectations for different economic agent
Panel B. Phillips Curve with household in�ation expectations
Panel C. Counterfactual in�ation (CPI) paths for different expectations
Panel D. Relative contribution of slopes and in�ation expectations
1960Q1−1984Q41985Q1−2007Q32007Q3−2013Q1
MSC exp, SPF κMSC PC MSCκ, SPF expSPF PC
Actual
Asset pricesMichiganSPF (CPI)
π t −
Eπ t
MSC
12Q1
Figure 6. The Phillips Curve and the Missing Disinflation with Household Inflation Expectations
Notes: Panel B shows the scatter plot of inflation (CPI) surprises versus unemployment gap as well as fitted linear regressions for two subperiods. Panel C plots actual inflation rate (CPI) as well as inflation rate predicted by Phillips curves (equation (1)) estimated on the pre-Great Recession samples. Phillips curves are estimated with unemploy-ment gap as the forcing variable. Panel D presents decomposition of differences between predicted inflation rates from Phillips curves (equation (1)) estimated with inflation expectations from the Michigan Survey of Consumers (MSC) and Survey of Professional Forecasters (SPF). “XYZ exp” denotes which inflation expectations are used (SPF or MSC), while “XYZ κ ” denotes what data was used to estimate the slope of the Phillips curve. Phillips curves are estimated with unemployment gap as the forcing variable.
Source: Coibion and Gorodnichenko (2015)
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 50 / 55
IMPORTANCE OF VOLCKER DISINFLATION
Much of evidence for slope on Phillips curve comes from
Volcker Disinflation
Details turn out to matter for results
Important methodological change in CPI in 1983
(housing switched to rental equivalence)
12-month inflation versus quarterly inflation matters
No missing disinflation with 12-month PCE
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 51 / 55
MISSING DISINFLATION? +
Pre‐2008 Post‐2008 Missing Disinflation?
4‐quarter PCE inflation, SPF exp.
‐0.09(0.05)
‐0.06(0.06)
No
4‐quarter core PCE,SPF exp.
0.27(0.03)
‐0.08(0.05)
No
Quarterly PCE, SPF exp.
‐0.29(0.07)
0.02(0.12)
Yes
Quarterly PCE, 4‐quarter lagged exp.
‐0.31(0.05)
0.10(0.16)
Yes
Slope Coefficients () from Different Specifications
Source: Nakamura (2018): Discussion at AEA Meetings
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 52 / 55
MISSING DISINFLATION?
Source: Nakamura (2018): Discussion at AEA Meetings
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 53 / 55
DID Etπt+1 DO ALL THE WORK?
Source: Nakamura (2018): Discussion at AEA Meetings
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 54 / 55
DID Etπt+1 DO ALL THE WORK?
Source: Nakamura (2018): Discussion at AEA Meetings – Quarterly PCE rather than 12-month
Nakamura-Steinsson (Columbia) Phillips Curve January 2018 55 / 55
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