Reset Price Inflation and the Impact of Monetary Policy Shocks

Reset Price Inflation
and the Impact of Monetary Policy Shocks




Mark Bils
University of Rochester and NBER

Peter J. Klenow
Stanford University and NBER

Benjamin A. Malin
Federal Reserve Board


February 2009



Abstract

A standard state-dependent pricing model generates little monetary non-neutrality. Two
ways of generating more meaningful real effects are time-dependent pricing and strategic
complementarities. These mechanisms have telltale implications for the persistence and
volatility of “reset price inflation.” Reset price inflation is the rate of change of all desired
prices (including for goods that have not changed price in the current period). Using the
micro data underpinning the CPI, we construct an empirical measure of reset price inflation.
We find that time-dependent models imply unrealistically high persistence and stability of
reset price inflation. This discrepancy is exacerbated by adding strategic complementarities,
even under state-dependent pricing. A state-dependent model with no strategic
complementarities aligns most closely with the data.

____________
This research was conducted with restricted access to U.S. Bureau of Labor Statistics (BLS)
data. Rob McClelland provided us invaluable assistance and guidance in using BLS data.
We thank Jose Mustre Del Rio for excellent research assistance. The views expressed here
are those of the authors and do not necessarily reflect the views of the BLS or the Federal
Reserve System. We are grateful to Carlos Carvalho, Jon Steinsson, and numerous seminar
participants for helpful comments.
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1. Introduction
Consumer prices change every seven or eight months in the U.S.1 Yet the real effects
of monetary shocks have been estimated to last around thirty months.2 These figures suggest
real effects lasting roughly four times longer than nominal price stickiness – i.e., a “contract
multiplier” of around four in Taylor’s (1980) terminology. In contrast, research on calibrated
DSGE models obtains much lower contract multipliers, at least in the absence of strategic
complementarities and sticky information. Chari, Kehoe and McGrattan (2000) report
contract multipliers around one in a variety of time-dependent pricing models. Caballero and
Engel (2007) and Golosov and Lucas (2007) arrive at contract multipliers well below one in
their state-dependent pricing models. Dotsey, King and Wolman (1999) and Midrigan
(2008) obtain intermediate contract multipliers in their state-dependent models.
As has been well-known since Ball and Romer (1990) and Kimball (1995), strategic
complementarities in the pricing decisions of individual sellers can produce large contract
multipliers.3 A starting point for these models is that the nominal stickiness be staggered, to
create the possibility of coordination failure among price setters.4 In response to an
aggregate shock, strategic complementarities mute the size of price changes for those
changing prices, as price setters wait for the average price to respond.

1 Klenow and Krystov (2008) and Nakamura and Steinsson (2008a). This figure ignores price changes involving
sale prices, otherwise the number would be about four months.

2 Christiano, Eichenbaum, and Evans (1999), Romer and Romer (2004), and Bernanke, Boivin, and Eliasz
(2005), each based on U.S. data, are a few of the many examples.

3 Recent papers in this vein include Altig et al. (2005), Carvalho (2006), Blanchard and Gali (2007), Gertler and
Leahy (2008) and Nakamura and Steinsson (2008b).

4 Staggered price setting appears to describe the U.S. data well. Klenow and Kryvstov (2008) find that the
fraction of consumer prices changing does fluctuate but is not highly correlated with movements in inflation.
They also find big individual price changes. Golosov and Lucas (2007) show these facts can be explained by
large idiosyncratic shocks that govern both the timing and size of price changes at the micro level.

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We show that models with high contract multipliers at the macro level display slow-
moving “reset” prices at the micro level. A reset price for an individual seller is that price it
would choose if it implemented a price change in the current period. Actual prices often
differ from reset prices, of course, because of nominal price stickiness. We define
“theoretical reset price inflation” as the weighted average change of all reset prices,
including those of current price changers and non-changers alike. We denote “reset price
inflation” as the weighted average change of reset prices for price changers only. In the
Calvo (1983) time-dependent pricing model, the probability of changing price is independent
of the desired reset price change, so reset price inflation is a pure reflection of theoretical
reset price inflation. In state-dependent models, sellers weigh the benefits of moving to the
reset price against the (menu) costs of doing so. For these models reset price inflation can
depart importantly from theoretical reset price inflation.
Strategic complementarities should dampen the volatility of reset price inflation and
boost its persistence. An individual seller will move by smaller amounts, requiring multiple
price changes to fully respond to a shock. We confirm this intuition by simulating DSGE
models featuring time-dependent pricing (TDP) or state-dependent pricing (SDP), with or
without strategic complementarities. The models feature a single aggregate shock (to money
or productivity) plus idiosyncratic shocks to each seller’s productivity. The
complementarities take the form of intermediate goods, as in Basu (1995). Intermediates can
slow down “monetary pass-through” because price changers have not seen their intermediate
costs fully adjust due to the sticky prices of their suppliers. Sellers are grouped into one of
two sectors: the flexible price sector (low menu cost, bigger idiosyncratic shocks) or the
sticky price sector (high menu cost, smaller shocks).

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Using the micro data on prices collected by the U.S. Bureau of Labor Statistics for the
Consumer Price Index, we construct an empirical index of reset price inflation for the months
January 1989 through May 2008. We impute to all items, both those changing and not, the
reset price changes exhibited by price changers. To arrive at the reset price change for an
item changing price, we compare the item’s new price to its estimated reset price the
previous month – not the item’s last new price, set perhaps months earlier. A useful analogy
is to home price indices constructed from repeat sales (e.g., Shiller 1991 and Zillow.com).
These indices estimate the value of residential homes even when they are not sold. Once a
home is sold, the difference between the transacted price and the previous period’s estimated
value is used to update the estimated value of other homes that were not sold. Our reset price
index is the analogue for all consumer items to these home price indices.
We compare the behavior of our empirical measure of reset price inflation to that of an
identically-constructed measure from simulated TDP and SDP models. As mentioned
previously, reset price inflation is the exact counterpart to theoretical reset price inflation in
the Calvo model. Even though our constructed reset price inflation is not the same as
theoretical reset price inflation for SDP models, we find that simulated SDP models yield
clear predictions for our constructed reset price inflation.
To delve further into the role played by price rigidity, we partition the CPI goods into
“flexible” and “sticky” groups. The former reflects 30 percent of consumer spending and
displays an average monthly frequency of price changes of 1/3. The latter constitutes 70
percent of spending and displays an average monthly frequency of around 1/10. Our
simulated models feature flexible and sticky-price sectors, with each sector’s frequency and
absolute size of price changes matching those statistics in the CPI data.

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We find the models with big contract multipliers fundamentally at odds with the data.
TDP models, with or without strategic complementarities, and the SDP models with strategic
complementarities, generate unrealistically high persistence and low volatility of reset price
inflation. These models predict that the impact of a nominal shock on reset prices will build
over time. But in the data we see the opposite. An increase in reset price inflation predicts
lower, not higher, reset price inflation in subsequent months, so that an index of reset prices
responds more on impact than over time. Another model prediction is that goods with
infrequent price changes (the sticky-price goods) will display relatively more persistent
inflation (overall, not reset). But we do not see this in the data.
The SDP model with no complementarities comes closest to matching the empirical
patterns. It features broadly realistic volatility and persistence of reset and actual price
inflation for all goods, flexible goods, and sticky goods. Related, a way to rescue strategic
complementarities might be to incorporate endogenous monetary policy. If monetary policy
quickly offsets the aggregate shock (to money itself or to aggregate productivity), then models
with complementarities no longer imply outsized persistence of reset and actual inflation.
This solution creates two problems, however. First, endogenous monetary policy essentially
gets rid of the contract multiplier. Second, this solution reduces reset inflation volatility to
around one-fifth of the observed level, and the variance of actual inflation to less than one-
tenth the observed level. If monetary policy offsets shocks, price setters respond little to these
shocks and inflation becomes much too smooth.
The literature on monetary policy has coalesced on strategic complementarities in
order to rationalize a large contract multiplier. But our results strongly reject the predictions

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of those sticky-price models we examine that feature sufficient complementarities to produce
an important contract multiplier.
The rest of the paper proceeds as follows. Section 2 describes the dataset and the
empirical properties of reset price inflation. Section 3 lays out the models and compares
statistics from the simulated models to their empirical counterparts. Section 4 concludes.

2. An empirical measure of reset price inflation
The CPI Research Database
We use the micro data underlying the non-shelter portion of the CPI to construct our
measure of reset price inflation. The BLS surveys about 85,000 items a month in its
Commodities and Services Survey. Individual prices are collected at around 20,000 retail
outlets across 45 large urban areas.5 The survey covers all goods and services other than
shelter, or about 70 percent of the CPI based on BLS consumer expenditure weights. The
CPI Research Database (hereafter CPI-RDB) maintained by the BLS Division of Price and
Index Number Research contains all prices in the Commodities and Services Survey since
January 1988. We use the CPI-RDB through May 2008, for a sample of “1988-2008”.
The BLS collects consumer prices monthly for food and fuel items in all areas. The
BLS also collects prices monthly for all items in the three largest metropolitan areas (New
York, Los Angeles, and Chicago). The BLS collects prices for items in other categories and
other urban areas only bimonthly. For our competing models, the impulse responses for reset
price inflation differ markedly in the initial periods after a shock, making it valuable to have

5 The BLS selects outlets and items based on household point-of-purchase surveys, which furnish data on where
consumers purchase commodities and services. The price collectors have detailed checklists describing each

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an empirical counterpart that captures the data at high frequency. For this reason, we restrict
our analysis to the top three areas that have monthly data on all goods.
The BLS defines 300 or so categories of consumption as Entry Level Items (ELIs).
Within these categories are prices for particular items (we call a longitudinal series of
individual price quotes at the micro level a “quote-line”). The BLS provided us with
unpublished ELI weights for each year from 1988-1995 and 1999-2004 based on Consumer
Expenditure Surveys in each of those years. We normalize the nonshelter portion of the
weights to sum to 1 in each year. We set the 1996 and 1997 ELI weights to the 1995 weights,
and the 1998 weights to their 1999 level. We set the 2005 and onward weights to their 2004
level. The CPI-RDB also contains weights for each price within an ELI. We allocate each
ELI’s weight to individual prices in each month in proportion to these item weights to arrive
at weights ? that sum to 1 across items (i’s) in each month.
it
The BLS labels each price as either a “sale” price or a “regular” price. Sale prices are
temporarily low prices (including clearance prices). Golosov and Lucas (2007), Nakamura
and Steinsson (2008a), and others filter out such sale prices on the grounds that they are
idiosyncratic deviations from stickier regular prices. Related, in classifying goods as
“flexible” or “sticky” and in calibrating the model economies, we do so based on the
frequency of regular price changes. We adopt this treatment because it yields more
conservative results with respect to our conclusions. If, alternatively, we encompass the
higher rate of price changes involving prices labeled by the BLS as sales prices, we would
obtain an average frequency of price change of a little over 25 percent monthly rather than 22
percent. In turn, this would require even larger contract multipliers for our model economies

item to be priced ? its outlet and unique identifying characteristics. They price each item for up to five years,
after which the item is rotated out of the sample.

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to generate the same persistence in the impact of monetary shocks. But we find that the data
do not support large contract multipliers. We use all prices, including sale prices, when
constructing our inflation and reset price inflation series. To the extent sales are truly
idiosyncratic their impact on the time series for price inflation, given the large samples of
price quotes in each sector, will average close to zero. To the extent sales do affect aggregate
price inflation, they are not idiosyncratic and so should not be excluded. That said, we will
show that our results are robust to excluding sales prices from the series for price inflation.
Forced item substitutions occur when an item in the sample has been discontinued
from its outlet and the price collector identifies a similar replacement item (e.g., new model)
in the outlet to price going forward. The monthly rate of forced item substitutions is
consistently about 3 percent in the sample. Essentially all item substitutions involve price
changes. We include these price changes at substitutions in our statistics.6 But our results are
extremely robust to treating all price changes as zero at forced substitutions.
About 12 percent of the prices the BLS attempts to collect are unavailable in a given
month. The BLS classifies roughly 5 percent of items as out-of-season. We put zero weight
on out-of-season items when calculating both inflation and the frequency of price changes.
The BLS classifies the other 7 percent as temporarily unavailable. As these items may be
only intermittently unavailable during the month, we treat items out of stock as available at
the previously collected price. We employ this treatment both for calculating frequency of
price changes and time series of inflation rates.
Although the BLS requires its price collectors to explain large price changes to limit
measurement errors, some price changes in the dataset appear implausibly large. We exclude

6 For about half of forced substitutions the rate of price change imparted to the CPI reflects a BLS adjustment
aimed at capturing quality change. We employ these BLS adjustments in all price change statistics.

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price changes that exceed a factor of five. Such price jumps constitute less than one-tenth of
one percent of all price changes.

Defining Reset Price Inflation
Section 3 below illustrates how models with high contract multipliers exhibit inertia
not only in price inflation, but also in reset price inflation — so the behavior of reset price
inflation is a barometer for lasting real effects of monetary shocks.
Whether pricing is time-dependent or state-dependent, the desired price level for item i
in month t, *
P , satisfies an Euler equation taking into account effects on current and future
i,t
prices. Following Dotsey et al. (1999), the Euler equation is
??
? u c
V
?
?
i t
'(
)

,
t 1
?
i,t 1
? ?E ??
(1? ?
)
? ?
*
t
i,t 1
?
*
P
?
u '(c )
P
?
i,t
?
t
i,t
?
where ? denotes current profits, E refers to expectations at time t, ? u '(c ) / u '(c ) is the
i,t
t
t 1
?
t
familiar stochastic discount factor, ?i,t 1
? is the probability of a price change for item i in
month t ?1 , and V
is next period’s value function. Note that the reset price can differ from
i ,t 1
?
the optimal flexible price (the price that maximizes current period profits) because of future
price stickiness ( ?
1
i,t 1
? ? ). Related, the actual price can differ from the reset price if the
seller does not change its price in the current period.
Reset price inflation for a given seller is the log first difference of its reset price:
*
*
*
? ? ln(P ) ? ln(P ) .
i,t
i,t
i,t 1
?
This definition does not require a price change at either t or t ?1 . Aggregate reset price
inflation is then the weighted average of micro reset price inflation:

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(2.1)
*
*
? ? ?? ? ,
t
i,t
i,t
i
where the weights ? add to 1. By comparison actual inflation is ? ? ?? ? where
i,t
t
i ,t
i ,t
i
? ? p ? p and p denotes the log of the actual BLS price of item i at time t.
i ,t
i ,t
i ,t 1
?
i,t
Whereas starred variables denote reset values, those without stars represent actual
values. Let I be a price-change indicator:
i,t
1 i
? f p ? p
?
i,t
i,t 1
?
I ? ?

i,
.
t
0 if p ? p
?
?
i,t
i,t 1
?
To construct an empirical measure of aggregate reset price inflation, each month we divide
items into those that change price ( I ? 1) and those that do not change price ( I ? 0 ). For
i,t
i,t
prices that change, the reset price is simply the current price. For prices that do not change,
we index our estimate of the reset price to the rate of reset price inflation among price
changers in the current period. Our estimate of the log reset price level for item i in month t is
? p if p ? p
?
i,t
i,t
i,t 1
?
?
*
p
? ?

i,t
? *
? *
? p
?
p ? p
? i t? ? t if
, 1
i,t
i,t 1
?
where ^’s denote our estimates. In turn, our estimate of aggregate reset price inflation is
? *
?? (p ? p )I
i,t
i,t
i,t 1
i,t
(2.2)
?*
i
?
?
?
.
t
?? I
i,t
i,t
i

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