Comments onMenu costs and price change distributions:evidence from Japanese Scanner Data
by Yukiko Umeno Saito and Tsutomu Watanabe

Mototsugu Shintani1
1 Bank of Japan

andDepartment of Economics
Vanderbilt University

December 1-2, 2007 / The 9th Macroeconomics Conferenceat Keio University

Organization of my presentation
I Quick summary of the findings of the paper
I Comment 1: Definition of price changes
I Comment 2: Small menu cost approximation?
I Comment 3: Symmetric assumption of target pricedistribution
I Comment 4: Common target price volatility grouping?
I Comment 5: US-Japan comparison
I Comment 6: Effect of deflation and inflation
I Comment 7: Duration independence of distribution?
I Comment 8: Positive duration-large price change

correlation?

Summary of Findings
I Investigate the statistical properties of prices from dailyscanner data for all products sold at 181 supermarkets for
1988-2005. Total number of products 284,000. Total
number of observations 290 million for one year, 2.9 billion
for entire sample!
I Use this highly detailed data to examine the implications of

the menu cost hypothesis. Three main findings are:(i) Small price changes are rare which supports menucost models(ii) Increasing duration of no price change results in higher
chance of large price change(iii) In the long-run price change distribution becomesasymmetric possibly due to deflation

Summary of Findings
I Investigate the statistical properties of prices from dailyscanner data for all products sold at 181 supermarkets for
1988-2005. Total number of products 284,000. Total
number of observations 290 million for one year, 2.9 billion
for entire sample!
I Use this highly detailed data to examine the implications of

the menu cost hypothesis. Three main findings are:(i) Small price changes are rare which supports menu
cost models(ii) Increasing duration of no price change results in higher
chance of large price change(iii) In the long-run price change distribution becomesasymmetric possibly due to deflation
I An important set of empirical findings which helps ourfurther understanding of price setting mechanism ... but isit necessary to make a connection to menu cost models?

Pit ≡ max{
, P̂it−1 , . .changes. , P̂it−k+1 }Comment 1: DefinitionofP̂itprice(1)

That is, P is the largest value of P̂ in the last k days. P coincides with theregular price under the assumption that (1) the selling price returns to theInregular
page price5, on days when there is no temporary sales and (2) there are notemporary sales of a consecutive k days. We set k = 5 throughout the paper.
We then define the index showing the occurrence of price adjustment as(1ifPit 6= Pit−dd
Iit ≡(2)0if
Pit = Pit−d
If one or multiple price adjustments occur between day t − d and day t, thendIit
becomes 1. On the other hand, if no price adjustment occurs during thisperiod, Itd is 0.

3.1
Heterogeity
acrossand years
I Whichone to use?
Both products,
seem to beoutlets,interesting.
The upper panel of Figure 1 shows the distribution of the price change probd
ability, Pr(Iit= 1), calculated by product and by outlet when d = 5. The
horizontal axis represents the price change probability divided into 20 bins.
The interval farthest to the right shows the (2−1/2 , 1] bin, the adjacent one is−2/2−1/2−3/2−2/2

group harehomogeneousin terms
their inactive
wherethe sizeof an ofinactive
range forranges?
productToi, show
whichtheis ofmethodcourse
i represents
closelyrelated
the sizeof apaper,menu cost,
Pit∗ byis thetarget priceproduct
ology weshall toadopt
in thislet usandstart
expressing
statefordependent

Comment 2: Small menu cost approximation?

In words,
as a price change occurs if and only if the actual price deviates from
Ini.pricing
page8,( by more than hi . Moreover,P ∗it is assumed that when firms
its target counterpart
it0if(1 + hi )−1 ≤ Pit−d≤ 1 + hidchange prices,from the target price, (3)soIit they≡ completely eliminate a deviation
1 rate fromotherwisethat the gross inflationt−d to t for product i, denoted by Πdit , satisfies
where hi represents the size of andinactive
Pit∗ range for product i, which is of course
Πit =.
(4)closely related to the size of a menu cost,
Pit−dand Pit∗ is the target price for producti. In words, a price change occurs if and only if the actual price deviates from
This pricing rule, with an additional assumption that hi is sufficiently small
its target counterpart by more than h . Moreover, it is assumed that when firms
relative to the volatility of the target iprice,3 implies
change prices, theya deviation from the target price, so( completely eliminate −10 rate from
if t−d(1 +tohit)for ≤Π∗d1 denoted+ hi
it ≤i,
that the gross dinflation
productby Πdit , satisfies
Iit ≡(5)1otherwise ∗PitdΠit =.
(4)
Pit−dandThis pricing rule, with an additional
assumption that hi is sufficiently smallΠdit = Π∗d(6)it .
relative to the volatility of the target price,3 implies
3 Under this assumption,∗ /P∗ /P ∗(Pitto Pit
it−d is almost equal
it−d .
0if(1 + hi )−1 ≤ Π∗dit ≤ 1 + hidIit ≡(5)
1otherwise
I Observed price
8always
optimal?
If menu cost is very small
and won’t it be almost identical to flexible price case?

we collect products that satisfy the following two conditions simulta

Comment 3: Symmetric assumption of target£ d price¤
Pr Iit=1 =adistribution£¤£¤dd
Pr Πdit ≥ 1 + ξ | Iit= 1 = Pr Πdit ≤ (1 + ξ)−1 | Iit=1 =b

ere a and b are parameters ranging between zero and unity. Thuations,with equation
indicatethat istheproducts"thetogether
gross inflation
rate for the(9),targetprice, whichassumedto colla symmetrics way haveshouldsatisfy distribution." (page 9)
£¤
£ ∗d
¤
−1Pr Π∗d= ab.
it ≥ 1 + ξ = Pr Πit ≤ (1 + ξ)

I Possible?
other words,
the products collected in this way should be homogen

ms of the volatility of the target price. Combined with the fact tce change probability depends on hi and the volatility of the targes means that those products should be homogeneous even in terms oare homogeneous in terms of h . A key is to make use of information both oniComment
4: Common target
price volatility grouping?
price change probabilities and on the tails of price change distributions. First ofall, we collect products that satisfy the following two conditions simultaneously.
£ d¤
Pr Iit=1 =a£¤£¤ddPr Πdit ≥ 1 + ξ | Iit= 1 = Pr Πdit ≤ (1 + ξ)−1 | Iit=1 =b(10)(11)

where a and b are parameters ranging between zero and unity. These twoequations, together with equation (9), indicate that the products collected inthis way should satisfy
£
¤£ ∗d
¤
−1Pr Π∗d= ab.
it ≥ 1 + ξ = Pr Πit ≤ (1 + ξ)

(12)

In other words, the products collected in this way should be homogeneous in

I a = 0.1 and b = 0.2

terms of the volatility of the target price. Combined with the fact that theI a = 0.2 and b = 0.1

price change probability depends on hi and the volatility of the target price,

Ithis
Can
it increasea homogeneousgroup of samevolatility
meansthat thosesample
products size
shouldinbe
even interms ofofhi .

the target price and same hi ?
9Comment 5: US-Japan comparison"Using the U.S. scanner data, Midrigan(2006) find that a pricechange distribution has tails fatter than those of a normal
distribution, and that density at the vicinity of zero inflation isgreater than those of a normal distribution. Our finding is
consistent with the first one, although it is in sharp contrast withthe second one." (pages 12-13)
I What about a dent at center - one of the main finding?
I Multi-products with a common menu cost (Midrigan,2006)?
I Multi-sector menu cost model (Nakamura-Steinsson,2007)?

Comment 5: US-Japan comparison

Source: Midrigan (2006)

Comment 5: US-Japan comparison
Predicted distribution of price changes from a single productmenu cost model of Golosov-Lucas (2007)

Japan better explained by multi-sector or multi-menu costmodels rather than US case even if current paper relies ongrouping?

Comment 6: Effect of deflation and inflation
Asymmetric distribution on a long time scale is found.
"we may allowed to interpret this asymmetry as reflecting
deflation deflation during this period." (page 16)"... there was another asymmetry at the beginning of the1990s... The observed asymmetry might have arisen from suchan inflationary pressure in the Japanes economy." (page 16)
I Can we observe larger magnitude of price change? - more

direct implication of inflation on menu cost models
I Ahlin-Shintani(2007) show wider (sS) band during higher

inflation period

Comment 7: Duration independence of distribution?
Two clear implications of menu cost models (pages 16-17):
I First, the hazard function should be upward sloping.
I Second, the price change distribution should beindependent of price duration.
Really?
1. Conditional probability of price changePr[Πit > 0|no price change between t − 1 and t − n] ⇑2. Conditional distribution of price changePr[Πit ≤ x|no price change between t − 1 and t − n]same for any x?

Comment 7: Duration independence of distribution?
Sheshinski-Weiss (1977) type menu cost model with constantinflation
Relative price (relative to aggregate price)

SS-ss

Comment 7: Duration independence of distribution?
Sheshinski-Weiss (1977) type menu cost model with constantinflation(Conditional) probability mass function

0This implies increasing hazard function

S-sPrice changeComment 7: Duration independence of distribution?
Golosov-Lucas (2007) type menu cost model with technology
shocks and stochastic inflation(Conditional) probability density function

0

Price change

If it is duration independent, (conditional) pdf cannot changeComment 8: Positive duration-large price change
correlation?
Implication to tail probability depends on the specificationSecond implication violated already?
Decreasing hazard function detected from data0

Price change

What type of menu cost models predict this? Need to rely on
simulation?