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Inflation
A. The Phillips Curve
B. Forecasting inflation
C. Frequency of price changes
D. Microfoundations
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A. Phillips CurveA. Phillips CurveA. Phillips CurveA. Phillips Curve
Irving Fisher (1926) found negative correlation 1903-25 between U.S. unemployment and change in overall price level
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A.W. Phillips (1958) documented relation between unemployment and rate of change of wages in
U.K., 1861-1948
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• Early literature sometimes interpreted this as wages rise when there is excess demand and fall with excess supply
• But neoclassical theory does not require excess demand in order for prices to change
• Example: in long-run equilibrium inflation = rate of growth of money with full employment
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• There is also a negative correlation over 1948-69 between U.S. unemployment rate and inflation rate (measured by year-over-year % change in PCE deflator)
• Newey-West tstat = -1.9
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Correlation seemed to break down in subsequent data
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But allowing different intercepts over different subsamples seems to salvage the relationship
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Traditional interpretation:
�t � inflation rate
�t� � expected inflation rate
u t � unemployment rate
u tn � natural unemployment rate
�t � �t� � ��u t � u t
n�
Consistent with long-run equilibrium
�t � �t� � log�Mt�1/Mt� when u t � u t
n
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�t � �t� � ��u t � u t
n�
Interpretation:
�t� � in response to rising �t in late 1960s
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Percent change in consumer price index from valuepreceding year, 1948:M1-2016:M11 11
Inflation rate
1950 1960 1970 1980 1990 2000 2010-4
-2
0
2
4
6
8
10
12
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Rising inflation expectations could account for upward shift in PC
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Interpretation based on Calvo sticky prices
(example of New Keynesian PC)
A fraction 1 � � of firms is allowed to set
optimal price p t� in period t, remaining �
keep fixed from t � 1
log Pt � � log Pt�1 � �1 � �� log pt�
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If those setting price were allowed to
change price every period, would choose
log p� t� � log Pt � ��log Yt � log Yt
n�
Yt � aggregate real output
Ytn � natural level of output
(what Yt would be if all prices flexible)
� � function of elasticity of MC with respect
to production (measure of “real rigidities”)
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If instead period t price setters realize they
will be Calvo frozen in future periods with
prob � (and discount future at rate �� then
log p t� � log Pt � �1 � �����log Yt � log Yt
n�
���Et�� t�1 � log p t�1� � log Pt�1�
which turns out to imply
� t � ���log Yt � log Ytn� � �Et� t�1
� � �1����1����� measures “nominal rigidities”
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Okun’s Law
u t � u tn � ��log Yt � log Yt
n�
� � �0. 5
Phillips Curve refers to broad class of relations
between inflation or wage inflation and
unemployment or real output.
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Lower inflation after 1984 brought expected inflation and Phillips Curve back down
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Return to traditional formulation:
� t � � t� � ��u t � u t
n�
� t� � Et�1� t
How measure � t�?
Suppose � t� � � t�1
� t � � t�1 � ��u t � u tn�
Plot change in inflation, not level of inflation,
on vertical axis.
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Phillips Curve as relation between unemployment and change in inflation (tstat = -2.4)
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But R2 = 0.06 and inflation was very steady despite huge drop in unemployment over last ten years
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Another way to measure � t�: ask people directly.
Michigan Survey of Consumers:
“By about what percent do you expect prices
to go (up/down) on the average, during the
next 12 months?”
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Source: Carola Binder, JME, June 2017
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PC with � t� � � t�1 estimated over 1960-84
or 1985-2007 significantly underestimates
inflation 2007-2018
Source: Coibion, Gorodnichenko and Kamdar (JELit, forthcoming)
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PC with � t� the average forecast from
Survey of Professional Forecasters does
not do any better
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But PC with inflation expectations from Michigan Survey accounts for much of “missing inflation”
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Inflation
A. The Phillips Curve
B. Forecasting inflation
Question: if our goal is to forecast inflation, should we pay any attention to unemployment rate?
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Stock-Watson (1999)
�t � inflation rate in month t (at annual rate)� 1200�log Pt � logPt�1�
�t12 � average inflation rate over past year
� �1/12���t � �t�1 � � � � t�11�
�t measured from either CPI or PCE (better)
t � 1959:M1 to 1999:M7
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�t12 � �t � � ��
j�1p �ju t�j
��j�1p �j�� t�j � � t�j�1� � t
Question 1: are coefficients stable?
Answer: no
(1) Instability seems to be in �j not � or �j
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31Lhmu25 = unemployment rate for males 25-54
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(2) IRF seems not to change much over samples
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(3) Will assess usefulness for forecasting separately on different subsamples
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�t12 � �t � � ��
j�1p �ju t�j
��j�1p �j��t�j � �t�j�1� � t
Estimate (and choose p� using data
through date T , look at forecast of �T�1212 .
Compare root mean squared error of
this forecast to that of model without u t
or with some alternative measure x t.
� weight for x t for best forecast
combining u t and x t.
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• Other measures of real activity sometimes better than unemployment
• capacity utilization
• manufacturing and trade sales
• first PC of activity measures (now called Chicago Fed National Activity Index).
• Non-output measures systematically forecast worse• other inflation data
• yield curve
• monetary aggregates
• exchange rates
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Faust and Wright (2013)
• Sample 1960:Q1 to 2011:Q4
• More observations from recent low-inflation regime
• Any model that implies reversion over long horizons to the full-sample mean will badly miss recent observations
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� Estimate model through date T using
unrevised data as reported at the time.
� Calculate forecast error for �T�h.
� Repeat for each T � 1985:Q1 to 2011:Q4.
� Calculate ratio of RMSE to that of a
baseline model.
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Examples of models that do badly:
Direct: �t�h � �0 ��j�1p �j� t�j � t�h
RAR: �t � �0 ��j�1p �j�t�j � t
� �� t�h|t�1 by recursion
PC: �t�h � �0 ��j�1p �j�t�j � u t�1 � t�h
RW: �� t�h � �t�1
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Model that beats all those (RMSE � 1.00)
�t � estimate of trend inflation at t
Blue-Chip forecast of 5-10 year inflation
g t � �t � �t
g t � �g t�1 � t
� �� t�h|t�1 � �t�1 � �h�1��t�1 � �t�1�
� � 0.46
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This also beats:
� Estimated AR for gt
� PC for gt instead of �t
What beats it? Subjective forecasts
� Blue Chip forecast for horizon h
� Survey of Profession forecasters
� Fed’s Green Book forecasts
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Subjective forecasts do better because
they have better “nowcast” ��� t�1|t�1�.
Can improve fixed � forecast considerably
by including Blue Chip nowcast
�� t�h|t�1 � �t�1 � �h�1��� t�1|t�1BC � �t�1�
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Does this mean nothing matters for inflation?
� Subjective forecasts may do
optimal job at inferring implications of
real output for � t�1.
� Fed may do optimal job in exploiting
PC to steer � t�h to its target (�t�1� within a
few quarters (no deviation from target is
predictable).
� Parsimony is very helpful in real-time
forecasting.
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Inflation
A. The Phillips Curve
B. Forecasting inflation
C. Frequency of price changes
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Bils and Klenow (2004) found 21% of
individual prices that go into calculating
CPI change each month.
Suggests Calvo fraction of firms keeping
prices fixed is � � 0.79 per month or
�3 � 0. 49 per quarter.
A shock that raises nominal demand 1%
would raise real output 0.5% within the quarter
but only 0.125% after 3 quarters.
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54Source: Nakamura and Steinsson (2013)
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Weekly price of 18-ounce jar of Peter Pan Creamy Peanut Butter at a supermarket in NW Chicago
55Source: Chevalier and Kashyap (2015)
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• Many items are characterized by a temporary sale after which their price goes back to the old “reference price”
• Should we exclude these changes and think of α as fraction of products for which the price-setter is able to change the reference price?
• Nakamura and Steinsson (2008): avg frequency of change in posted prices = 27.7% per month
• Avg frequency of change in regular prices (excluding substitution) = 21.5% per month
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• Different industries have very different frequencies of price change
• What matters for monetary nonneutrality is fraction who haven’t changed after n months
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Expenditure-weighted distribution of frequency of regular price changes across different entry-level CPI items
58Source: Nakamura and Steinsson (2013)
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• However, Bils et al. (2003) find that relative prices in flexible-price sectors fall following an expansionary monetary shock
• Mackowiak et al. (2009) find little difference in speed of response of prices to monetary shock across sectors characterized as sticky price versus flexible price
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Inflation
A. The Phillips Curve
B. Forecasting inflation
C. Frequency of price changes
D. Microfoundations
Why don’t firms change price more often?
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(1) Menu cost
• Small cost of changing price
• Even though cost is of second-order importance for firm’s profits), cost to economy could be first-order if there are distortions such as monopoly power (Akerlof & Yellen, 1985; Mankiw, 1985)
• But does not explain why inflation matters-- just speed up rate at which prices change (Caplin and Spulber, 1987)
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(2) Sticky information (Mankiw and Reis, 2002)
• Firms update information infrequently (e.g., Calvo fairy arrives)
(3) Rational inattention (Sims, 2003)
• Processing information more accurately is more accurate
• Mackowiak et al. (2009) found firms change prices more quickly in response to sectoral shocks than to aggregate shocks
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Carlsson and Skans (2012)
• Carlsson and Skans (AER, 2012) proposed to distinguish these explanations using matched firm-level data on product prices and unit labor costs in Sweden
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Associated with firm f is a local labor market j,
specific goods g produced by firm, and
sector s
w jt � vector of wages paid to different types
of workers (age, gender, education,...)
in local area j and year t
L ft � vector of different types of labor
hired by firm f
w jt� L ft � wage bill
�w jt� L ft/Yft � marginal cost � �MC ft
Pgt � price of some good g sold by firm f
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lnPgt � �g � �st � ln�w jt� L ft/Yft� � gt
OLS: � � 0. 265 with std error 0.019
IV: � � 0. 334 with std error 0.055
instruments: dg, dst, MC f,t�1, MC f,t�2, MC f,t,MC f,t�1
MC f,t � w jt� L f,t�1/Yf,t�1
Caution: if there is endogeneity concern,
typically not solved by lags (if explanatory
variables serially correlated, error is likely also)
� �� 1 � some kind of stickiness
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All variation in MC here comes from local
conditions.
Also find no difference between firms facing
high variance of local shocks and those with low.
Inconsistent with rational inattention.
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Under sticky information, should find
coefficient near unity for component
predictable far in advance.
When instruments are lagged 4-9 years,
coefficent rises to 0.516 with std error 0.154.
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Calvo model implies price at t reflects
expected future marginal costs
lnPgt � �g � �st � 1 ln�w jt� L ft/Yft�
� 2 ln�w j,t�1� L f,t�1/Yf,t�1� � gt
Using date t instruments find
� 2 � 0. 364 with std error 0.154
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Zbaracki, et al. (2004)
• Zbaracki, et al. (REStat, 2004) studied billion-dollar firm that produces 8,000 products used to maintain machinery sold to other firms
• Goal: study details of what happens when price is changed
• Conclusion: firm spent $1.216 M in 1997 changing its prices
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• Interview firm managers to ask how they make decisions
• Sit in on meetings where pricing decisions were made
• Study database of price changes
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(1) Pricing season: company develops price plans for coming year beginning in August
• Low cost?
• High quality?
• Competitors?
• Spent $280,000 (23% of total) on this process
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Communicating plans to customers
• Flights, meetings, phone calls $369,000
• Negotiation costs $524,000
• 73% of total
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(3) Print and distribute price list in Nov
• Cost $43,000 (3.5% of total)
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Other evidence on microfoundations
• Kashyap (QJE, 1995) studied prices in catalogs of Bean and Orvis and REI
• Found sometimes prices stayed same for years despite printing new catalog each 6 months
• When prices did change, sometimes changed very little
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• Nakamura and Steinsson (2017) noted that Calvo-based models imply the cost of inflation is greater dispersion of relative prices
• Found no evidence there was more dispersion during the Great Inflation of 1970s
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Conclusions
• Abundant evidence of price rigidities and monetary nonneutrality from multiple sources
• Tradeoff between tractable representation (Calvo) and detailed reconciliation with how decisions are actually made and implemented
• Need to exercise caution in taking implications of New Keynesian models (e.g., welfare costs of inflation) too literally
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