Working Less and Bargain Hunting More:
Macro Implications of Sales during Japan’s Lost Decades
Nao Sudo∗, Kozo Ueda†, Kota Watanabe‡, and Tsutomu Watanabe§
August 15, 2016

Abstract

Standard New Keynesian models have often neglected temporary sales. In thisstudy, we ask whether this treatment is appropriate. In the empirical part of thestudy, we use Japanese point of sale scanner data covering the last two decades andfind a negative correlation between the frequency of sales and hours worked. Wethen construct a dynamic stochastic general equilibrium model that takes households’ decisions regarding their allocation of time for work, leisure, and bargain
hunting into account. Using this model, we show that the decline in hours worked
during Japan’s lost decades explains the rise in the frequency of sales we observein the data. We also find that the real effect of monetary policy shocks weakens
by around 40% due to the presence of temporary sales, but monetary policy stillmatters.
Keywords: sales; monetary policy; lost decades; time use
JEL classification: E31, E32, E52∗

Bank of Japan (E-mail: nao.sudou@boj.or.jp)
Waseda University (E-mail: kozo.ueda@waseda.jp)‡
Canon Institute for Global Studies and University of Tokyo (E-mail: watanabe.kota@canon-igs.org)§
University of Tokyo (E-mail: watanabe@e.u-tokyo.ac.jp). The authors would like to thank Kenneth West(the editor), two anonymous referees, Kosuke Aoki, Erwin Diewert, Kevin Fox, Michel Juillard, Herve Le Bihan,Peter Sinclair, Nicolas Vincent, Tack Yun, and other seminar and conference participants at the Bank of England,
the Bank of France, the Bank of Japan, Keio University, Kobe University, Kyoto University, the Summer
Workshop on Economic Theory, Tohoku University, and the University of Tokyo for their useful comments. The
authors are also grateful to Kevin Sheedy for sharing his code and Statistics Bureau for providing the confidential
survey data. The views expressed in this paper are those of the authors and do not necessarily reflect the official
views of the Bank of Japan.
†

1

1

Introduction

Standard New Keynesian models, such as those in Woodford (2003) and Gali (2008), often
neglect temporary sales, although the frequency of sales is far higher than that of regular pricechanges,1 hence it is not necessarily guaranteed that the assumption of sticky prices holds.
Researchers can justifiably ignore this fact if retailers’ decision to hold sales is independentof macroeconomic conditions. If this is the case, temporary sales do not eliminate the realeffect of monetary policy. In fact, Guimaraes and Sheedy (2011, hereafter GS) develop a dynamic stochastic general equilibrium (DSGE) model incorporating sales and show that thereal effect of monetary policy remains largely unchanged. Empirical studies such as Eichenbaum, Jaimovich, and Rebelo (2011), Anderson et al. (2012), and Berardi, Gautier, and Le
Bihan (2014) argue that retailers’ decision to hold a sale is actually orthogonal to changes inmacroeconomic conditions.
However, in Japan, there is a negative secular link between the frequency of temporary
sales and working hours. Since the start of the 1990s, the Japanese economy experienced
what has come to be called “lost decades,” a period of sluggish GDP growth and very low
inflation or deflation. During the lost decades, the frequency of sales increased gradually but
monotonically, allowing households to purchase a greater number of goods at sale prices rather
than at regular prices. At the same time, hours worked per worker followed a secular declineThus, there appears to be a negative correlation between the frequency of sales and working
hours.
This study has two aims. First, we examine empirically whether there is a link between thefrequency of temporary sales and changes in macroeconomic conditions, particularly working
hours, making extensive use of Japanese supermarket scanner data. Second, we investigate
whether temporary sales mitigate the real effect of monetary policy, employing a model thatconsiders households’ decisions about allocations of time for work, leisure, and bargain hunting.
To this end, we extend the GS model so that bargain hunting is endogenously determined. The
more bargain hunting, the more the household can substitute away from relatively expensive
items. However, the search for lower prices reduces the time available for work and leisure,
imposing a cost on the household. These two opposing effects constitute a household’s optimalbargain hunting intensity.
Our analysis provides new empirical and theoretical findings. Our empirical analysis using
Japanese supermarket scanner data spanning two decades reveals a secular correlation between
labor market conditions and the frequency of temporary sales. The frequency increased when1

See, for example, Bils and Klenow (2004) and Nakamura and Steinsson (2008) for the United States andSudo, Ueda, and Watanabe (2014) for Japan.

2

employment fell. Further, during these lost decades, households spent more time shopping. Our
analysis also shows a significant correlation between labor market conditions and the frequency
of sales over in terms of business cycles.
Our model calibrated to Japan illustrates that the secular decline in hours worked explains
the secular increase in the frequency of temporary sales during the lost decades. It also implies
that bargain hunting intensity has grown in and that households have become increasingly pricesensitive. In addition, the effect of a monetary policy shock on real economic activity is weaker
when the model includes both temporary sales and endogenous bargain hunting, althoughmonetary policy shocks still have real effects. For example, an expansionary monetary policy
shock increases hours worked, which in turn decreases bargain hunting intensity. Observing
this, firms lower the frequency of sales. Because the quantity of goods sold is typically higher
at sales prices than at regular prices, these changes in households’ and firms’ behavior lead to
downward pressure on aggregate demand for goods. The real effect of monetary policy thus
diminishes.2 According to our simulation, the real effect of monetary policy weakens by about
40% due to endogenous bargain hunting.
Consistent with our empirical results, an increasing number of recent studies such as Klenow
and Willis (2007) and Kryvtsov and Vincent (2015) show that business cycles in the UnitedStates and the United Kingdom influence sales decisions. Coibion, Gorodnichenko, and Hong(2015) find evidence of consumer switching from high- to low-end stores during recessions.
Regarding the interaction between hours worked and bargain hunting, Nevo and Wong (2015)
document the increase in shopping intensity and the decline in households’ opportunity costof time during the Great Recession. Aguiar and Hurst (2007) find that older households shop
the most frequently and pay the lowest prices. Lach (2007) finds that immigrants from theformer Soviet Union to Israel have a higher price elasticity and lower search costs than thenative population.3
The second strand of research relates to the models of temporary sales. While there areseveral reasons why retailers hold temporary sales, including the desire to liquidate excess stock
and implicit contracts between retailers and manufacturers, we focus here on retailers’ use ofsales to maximize profits by exploiting consumer heterogeneity. Specifically, our approach is2

An additional mechanism contributing to this effect is intensified strategic substitutability of sales. Supposethat all firms except for firm A raise the frequency of sales. As in GS, firm A does not have an incentive to follow
others and raise the frequency of sales because this decreases the marginal revenue from sales. In our model, an
additional channel emerges. When all firms except for firm A hold more frequent sales, the aggregate price level
falls. This increases aggregate demand for goods, and in turn, aggregate demand for labor. Households supply
more labor and lose time for bargain hunting. The proportion of loyal customers increases and that of bargain
hunters decreases. Observing this, firm A holds less frequent sales. This intensified strategic substitutability ofsales mitigates the real effect of monetary policy.
3
See also Pashigian and Bowen (1991), Sorensen (2000), Brown and Goolsbee (2002), McKenzie and Schargrodsky (2004), and Pashigian, Peltzman, and Sun (2003).

3

most closely related to approaches adopted by Salop and Stiglitz (1977), Varian (1980), andGuimaraes and Sheedy (2011). Guimaraes and Sheedy (2011) assume that each household
is a bargain hunter for a fixed proportion of goods and loyal to the other goods. Our study
is closely related to Guimaraes and Sheedy (2011), but differs from it in that in our model
bargain hunting intensity is endogenously determined. Kryvtsov and Vincent (2015) constructa similar DSGE model incorporating endogenous bargain hunting by introducing heterogeneous
households with respect to fixed cost of shop searching.4
The structure of this paper is as follows. Using micro price data for Japan, Section 2
provides evidence that bargain hunting and the frequency of temporary sales are related tomacroeconomic conditions and hence are endogenously determined. In Section 3, we develop
the DSGE model of temporary sales to examine the implications of endogenous bargain hunting.
Section 4 applies our model to Japan to explain the increase in the frequency of temporary
sales during the lost decades and Section 5 considers the implications for the macroeconomy
by presenting impulse responses to a monetary policy shock. Section 6 concludes.

2

Evidence for Endogenous Bargain Hunting

This section presents the evidence related to endogenous bargain hunting. Using household
surveys for Japan, we first show that working time moves in the opposite direction of shopping
time. Second, using point-of-sales (POS) scanner data, we show that temporary sales had anincreasingly important role in retailers’ business during Japan’s lost decades. The frequency ofsales is significantly correlated with macroeconomic indicators, especially labor market indicators. We find that when hours worked are long, the frequency of sales tends to be low.

2.1

Survey on Time Use

We begin by looking at the Survey on Time Use and Leisure Activities for Japan. The Statistics
Bureau of Japan conducts the survey every five years. The survey asks around 200,000 membersin 83,000 households about their daily patterns of time allocation, including questions abouttime used for working and shopping. These questions help us to examine the relationshipbetween the time spent working and the time spent shopping, which is important for ourmodel.
4

These studies are related to the literature on consumer search regarding how consumers search across shops
and products influences how retailers set prices. Although they do not explicitly model temporary sales, studies
incorporating consumer search and price setting include those by Benabou (1988), Watanabe (2008), and Coibion,
Gorodnichenko, and Hong (2015). Our study is also related to that by Kehoe and Midrigan (2015), which has
a similar research interest to ours (i.e., examining the stickiness of the aggregate price level and the real effectof monetary policy), although they do not construct their model based on consumer heterogeneity.

4

Table 1 shows the time household members spent on shopping and working (including
commuting time to work or school). The sample consists of those aged 15 and over. The
table reports the weekly average minutes per day. Two trends are worth highlighting. First,
those not working tend to spend more time shopping than those who work. Moreover, womentend to spend more time shopping than men and spend less time working. Second, time spent
shopping steadily increased from 1986 to 2011. At the same time, hours worked continued to
decline, although they increased slightly between 2001 and 2006. These findings support ourassumption that bargain hunting negatively depends on hours worked.
Because this result may be caused by other structural changes, in particular, demographic
aging, we collect micro data for 2006 survey respondents and examine the relationship between
shopping and working, controlling for sex, age, and area of residence. We choose household
members who are either a household chief or spouse. We classify ages into 16 bins in five-yearincrements; the variable female is a dummy for female and non-city takes a value of one unlesshouseholds live in three major cities of Japan. We regress the time spent shopping with thetime spent working. Table 2 summarizes the results. The coefficient on time spent working is−0.06 and significant, regardless of whether we use the entire sample, only the persons whoreport that they mainly spend their time working, or only men who report that they mainly
spend their time working. This suggests that a one minute increase in time spent working
is associated with 0.06 minute decrease in time spent shopping, although this does not show
causality.5

2.2

POS Data

Next, we look at temporary sales using POS scanner data.6 Nikkei Digital Media collects these
POS data from retail shops around Japan. The data consist of daily data covering March 1,
1988 to October 31, 2013. There are 6 billion records, where each record contains the numberof units sold and the sales amount in yen for product i at shop s on date t. The data contain 1.8
million products (cumulative) during the sample period. The data include processed food anddomestic articles, but unlike the official consumer price index (CPI) released from the Ministryof Internal Affairs and Communications, do not include fresh food, recreational durable goods(such as television sets or personal computers), or services (rent and utilities). Overall, thePOS data cover 170 out of the 588 items in the CPI, which, according to data from the Family
Income and Expenditure Survey, make up 17% of households’ expenditure. We identify eachproduct i with its Japanese Article Number (JAN) code.
56

See Online Appendix A.1 for detail about the data and the estimation results.
See Abe and Tonogi (2010) and Sudo, Ueda, and Watanabe (2014) for earlier studies using these data.

5

Figure 1 compares the yearly inflation rates based on the CPI and POS-CPI. The CPI
consists of processed food and domestic articles to match the POS’ coverage. We calculate the
POS-CPI inflation rate as the Törnqvist index. This graph confirms that the POS data are
not considerably different from the CPI.
Our POS data have three noteworthy advantages. First, the data include quantity information as well as price information. Second, the data are at a daily frequency. This contrasts
with the U.S. weekly scanner data used in existing studies. Third, the POS data span a longobservation period, starting from 1988 and continuing to the present, thus covering the lost
decades.
To calculate the aggregated variables of interest, such as the frequency and magnitude ofsales, we aggregate the POS data using in four steps. First, at the lowest (i.e., most detailed)
JAN code level, we collect data for the variable of interest, such as price for product i at shop s
on date t. Second, we aggregate these data across shops using revenue as the weight to derive
the weighted mean. Third, we aggregate these values at the 3-digit code product level,7 again
using revenue as the weight to derive the weighted mean. Finally, we aggregate the values
obtained in the previous step across 3-digit codes, again using revenue as the weight to derive
the weighted mean. We base the weights on the monthly revenue. That is, if date t is January
1, 2012, for instance, we use the revenue for January 2012 as the weight.
2.2.1

Temporary Sales

We measure the price of a particular product at a particular retailer on a particular date fromthe POS records by dividing the revenue for product i at shop s on date t by the number ofunits sold of that product at that shop on that date. Recorded revenue excludes consumption
tax, which was introduced in April 1989 and raised in April 1997.
The POS data do not include information about whether a price is the regular price or atemporary sales price. Therefore, to isolate temporary sales prices, we use two kinds of sales
filters. First, following Eichenbaum, Jaimovich, and Rebelo (2011), and more precisely, Kehoeand Midrigan (2015), we define the most common (mode) price during a certain window lengthof period t as the regular price of a product at period t. We identify temporary sales when theposted price differs from the regular price. The benchmark window is 42 days before and after
the date (85 days, in total). Our choice of the window is similar to Eichenbaum, Jaimovich,and Rebelo (2011) and Kehoe and Midrigan’s (2015) settings, which use 1.5 and 2.5 months,
respectively. For robustness, we also use a 7-day window since the glossary of the Japanese
official CPI states that prices are not counted as regular prices if they last less than 7 days.
7

Nikkei Digital Media classifies products using 3-digit codes, where each code represents a product category
such as yogurt, beer, tobacco, toothbrushes, etc.

6The second type of sales filter is Nakamura and Steinsson’s (2008) V-shaped filter. When wefind a V-shaped pattern, we identify its price dip as a sales price. More specifically, we follow
the procedure explained in Nakamura and Steinsson (2010) using a window of L = K = 42 or
7 days.
Table 3 provides summary statistics for posted, regular, and temporary sales prices. The
first row shows that the frequency of posted price changes is 0.202 daily, suggesting that firms
revise their prices every five days. The second row shows that the frequency of regular pricechanges ranges from 0.002 to 0.029 daily, depending on sales filters. Multiplied by 365/12, it
amounts to a monthly frequency of 0.061 to 0.392.
The third to eighth rows in the table show basic statistics for temporary sales. We focus
in particular on four variables: (i) the frequency of sales, (ii) the magnitude of sales discounts,(iii) the ratio of quantities sold at the sale price to those at the regular price, and (iv) the
ratio of revenue at the sale price to total revenue in a month.8 The quantity ratio (iii) shows
the amount of products sold at sale prices relative to the amount sold at regular prices on acertain date. The table also provides the amounts at sales and regular prices, computed by e
to the power of the weighted average of the logarithm amount. The revenue ratio (iv) shows
the contribution of temporary sales to a retailer’s total revenue in a certain month, meaningthat this variable depends on the frequency of sales.
The average frequency of temporary sales lies between 0.13 and 0.24 depending on the sales
filter. The magnitude of the sales discounts is about 0.1, implying 10% discounts from regular
prices. The quantity ratio is about two. The table shows the decomposition of total quantities
sold into the quantity at sales and regular prices. On average, retailers sell 12 units at sales
prices and six units at regular prices. The revenue ratio is about 0.2, which suggests that sales
account for 20% of revenue in a typical month.
Compared with other advanced economies, Japan has an extremely high frequency of posted
price changes, while that of regular price changes and temporary sales are not so different.
For example, Nakamura and Steinsson (2008) report that for the United States the mean
monthly frequency of posted price changes is 0.265, the mean monthly frequency of regular
price changes is 0.211, and the frequency of temporary sales is 0.15 for processed food. There
are two reasons for this phenomenon. First, Japan has shorter sales durations. Even with very
similar frequencies of sales, Japanese retailers do more frequent switches between regular andsales prices than U.S. retailers, which generates a higher frequency of posted price changes.
The second reason is that Japan’s POS data are collected at a daily frequency. Weekly ormonthly data miss high frequencies, such as 0.202 daily.
8

We denote these variables by s, 1 − µ, χ, and sχµ/(1 − s + sχµ), respectively, in the model described below.

7Figure 2 shows time-series changes in sales-associated variables, suggesting that, regardlessof the choice of sales filter, sales have become increasingly important for retailers during the lost
decades. The frequency of sales rose steadily by about 10% points. Parallel to the increase infrequency, the magnitude of sales discounts steadily declined. Despite these two developments,
the ratio of quantities sold at sales prices to those at regular prices has been relatively stable
at around 2. Consequently, revenue from temporary sales reached 30% of total revenue during
the 2000s compared to 20% in the 1990s.9

2.3

The Link between the Frequency of Sales and Macroeconomic Conditions

2.3.1

Labor Market Indicators

To examine the link between the frequency of sales and macroeconomic conditions, we start bylooking at labor market indicators. Figure 3 plots the frequency of sales against the unemployment rate in the upper panel and hours worked in the lower panel. We measure the frequency
of sales based on the mode filter with a 42-day window. The figure shows that during the two
decades, the unemployment rate increased, while hours worked decreased. These developments
reflect the deterioration in the labor market following the burst of the asset price bubble. In
addition, the decline in hours worked also reflects the reduction in the statutory workweek
length resulting from a revision of the Labor Standards Law.10
These secular developments in the unemployment rate and hours worked seem to have
implications for the secular increase in the frequency of sales.
2.3.2

Correlation between Sales and Macroeconomic Conditions

The relationship described in the previous subsection covers a relatively long time horizon(two decades). Next, we examine the link between the frequency of sales and macroeconomic
conditions for a shorter time horizon, the business cycle. We isolate the cyclical component of
the time series of temporary sales and macroeconomic conditions between 1.5 to 8 years using
the Baxter-King band pass filter and compute the contemporaneous correlation. The indicatorsof macroeconomic conditions we look at are the unemployment rate, total hours worked, andthe monthly growth rate of CPI. To account for the possibility that the Baxter-King band passfilter may yield spurious correlations, we calculate the 90% and 95% confidence intervals using
Monte Carlo simulation. That is, we first generate two i.i.d. time-series variables drawn from
9

Online Appendix A.2 decomposes goods into processed food and domestic articles.
The revision stipulated a gradual shortening of the workweek length from 48 to 40 hours. See Kawaguchi,
Naito, and Yokoyama (2008) for an analysis of the impact of the revision on hours worked, as well as Kuroda(2010), who argues that hours worked remained essentially unchanged after controlling for demographic changes.
108the standard normal distribution. Then, we extract their business-cycle components using the
Baxter-King band pass filter and calculate their correlations. The 90% and 95% confidence
intervals become 0.3316 and 0.3879, respectively.
Table 4 shows that the frequency of sales is significantly correlated with labor market
indicators, especially, hours worked. Regardless of the choice of sales filter, the correlationis negative for the aggregated product category. That is, when hours worked are high, thefrequency of sales tends to be low. The correlation with the unemployment rate is positive
but insignificant using a 42-day window. However, it is positive and significant using a 7-day
window. That is, the frequency of sales tends to be high when the unemployment rate is high.11
These results suggest that retailers raise the frequency of sales when households are less busy
working, which is plausible if such households increase time spent bargain hunting.
This cyclicality may depend on the product category. In the United States, Kryvtsov andVincent (2015) point out that the acyclicality in Coibion, Gorodnichenko, and Hong (2015)
arises because food products dominate their sample and these show an upward trend in thefrequency of sales, unlike other types of products. To examine this, we divide the sample into
processed food and domestic articles. In contrast to the U.S. case, the table shows that countercyclicality arises mainly from processed food in Japan, which dominates our POS data.12
There is no clear correlation between the frequency of sales and the CPI inflation rate.
Moreover, the bottom panel of the table shows that, except for domestic articles, there is no
significant correlation between the magnitude of sales discounts and macroeconomic factors.
Therefore, we focus on the frequency of sales in particular in the next section rather than themagnitude of sales to construct a DSGE model.13
2.3.3

Panel regression

Next, as in Coibion, Gorodnichenko, and Hong (2015), we extend our data to the cross-section
dimension and conduct a panel regression. To this end, we collect the monthly time seriesof hours worked for respondents working at establishments with more than 30 employees byprefecture based on the Monthly Labor Survey released from the Ministry of Health, Labour andWelfare. Because there were several revisions to the survey in terms of industry categorizations
and the scope of the sampled establishments, easily accessible and consistent panel data are
available only until December 2004. We apply seasonal adjustments using the X12 ARIMA
11

As for the differing results between hours worked and the unemployment rate, Braun et al. (2006) showthat in Japan, labor input adjustment occurs mostly through changes in hours per worker rather than changes
in number of workers, while in the United States, the adjustment occurs through changes in number of workers.
12
As Online Appendix A.2 shows, both processed food and domestic articles show an upward trend in thefrequency of sales in Japan. This trend does not influence our results per se, because the Baxter-King band passfilter filters this out in our analysis.
13
Online Appendix A.2 provides the correlations between sales and a number of macroeconomic variables.

9

to the series of hours worked in each prefecture and classify 47 prefectures in Japan intonine regions: (i) Hokkaido, (ii) Tohoku, (iii) Minami-Kanto, (iv) Kita-Kanto and Koshin, (v)Hokuriku, (vi) Tokai, (vii) Kinki, (viii) Chugoku and Shikoku, and (ix) Kyusyu and Okinawa,
following the classification of the Ministry of Internal Affairs and Communication, and construct
the time series of hours worked for each region. We then regress the frequency of sales on timeand region dummies as well as hours worked in the region.
Table 5 shows that the coefficient on hours worked is significantly negative at the 5% level
using the mode filter to identify the frequency of sales. Even at a cross-section level, thefrequency of sales has a negative relationship with hours worked.

2.4

Differences from the United States

This section so far has provided various pieces of evidence about the frequency of sales andits relationship to the macroeconomic environment. The key finding is that the frequency of
temporary sales moves in the opposite direction of hours worked, not only in the long run but
also in the time horizon of business cycles. This is likely because when hours worked are lower,households have more time for bargain hunting and are therefore more price sensitive. Thus,
retailers hold more frequent temporary sales.
However, many studies show contradictory results for the United States. Eichenbaum,Jaimovich, and Rebelo (2011), Anderson et al. (2012), and Coibion, Gorodnichenko, andHong (2015) argue that retailers’ decision to hold sales is orthogonal to macroeconomic circumstances, although Klenow and Willis (2007) and Kryvtsov and Vincent (2015) argue thatbusiness cycles influence sales decisions. The relationship between the frequency of sales andthe macroeconomic environment in the United States is not so strong as that in Japan.
There are at least two possible explanations for this difference. First, pricing strategies
in Japan and the United States differ. Unlike in Japan, many retailers in the United States
use an every-day-low-price strategy. According to Coibion, Gorodnichenko, and Hong (2015),
it is mainly lower-priced stores such as Wal-Mart that adopt an every-day-low-price strategy,
while higher-priced stores hold temporary sales. Given this situation, if we assume a rise in
unemployment, customers are likely to switch from higher- to lower-priced stores to reduce theirexpenditure. Higher-priced stores give up on such price-sensitive customers and concentrateon loyal customers. They thus reduce the frequency of temporary sales. In Japan, by contrast,
even lower-priced stores conduct very frequent temporary sales. As Sudo, Ueda, and Watanabe(2014) point out, prices in Japan are revised ten times more frequently than those in the UnitedStates, due to frequent temporary sales.14 Although these differences yield different results in
14

Japanese households are said to go shopping more frequently from Monday to Sunday; they walk to super-

10

Coibion, Gorodnichenko, and Hong’s (2015) study of the link between unemployment and thefrequency of sales, the effect of unemployment on the average prices consumers pay (effective
prices) is in the same direction in both cases. That is, average prices decrease when theunemployment rate rises.
The second possible explanation is that our POS data cover a very long period, from1988 to 2013. This is considerably longer than the typical duration of business cycles, whichhelps illustrate both secular and cyclical developments in sale pricing. By contrast, Coibion,
Gorodnichenko, and Hong (2015) use U.S. price data for a relatively short period, from 2001
to 2011. The popular Dominicks supermarket dataset covers from 1989 to 1997. Unless theobservation period is sufficiently long relative to the duration of business cycles, it is difficult
to accurately estimate the link between the frequency of sales and macroeconomic conditions.
If the second reason explains most of the difference, our findings for Japan may hold moregenerally; that is, the frequency of sales decreases when hours worked rise.

3

Model

In this section, we present the DSGE model of temporary sales by extending the GS model
to incorporate endogenous bargain hunting. To this end, we introduce two innovations, eachof which corresponds to the cost and benefit of bargain hunting. On the one hand, bargain
hunting decreases the time for leisure and hence utility. On the other hand, bargain hunting
enables a household to optimize brand choices in each product type.15

3.1

Setup

The Household A representative household consists of a household chief and an infinite
number of shoppers responsible for purchasing the goods of brand b ∈ B of product type
τ ∈ T . GS gives the example of beer and dessert as product types, and Corona beer and
Ben & Jerry’s ice cream as brands falling into those product categories, respectively. These
shoppers are populated over the interval [0, 1]. The fraction, 1 − Lt (Lt ∈ (0, 1]), of shoppers
have sufficient time for bargain hunting and can purchase goods optimally. The fraction, Lt ,of shoppers do not have enough time for shopping and observe only the price of one brand forall product types. Whether a shopper belongs to the former or latter type and which brandthe latter type purchases are randomly chosen in each period and exogenous to the chief ofmarkets nearby, purchase a small amount of products, and bring them back on foot. In contrast, U.S. households
shop mainly on weekends and by car. According to the Survey of Consumer Behavior by the Japanese Meat
Information Service Center, the average shopping frequency in the 2000s was three to four times a week. These
country-specific characteristics may explain these differences in retailers’ pricing strategies.
15
See Online Appendix B for the model’s details.

11the household. We refer to the former and latter types of shoppers as bargain hunters andloyal customers, respectively, and call Lt and 1 − Lt loyalty and bargain hunting intensity,
respectively. This Lt is a choice variable for the chief of the household.16
Specifically, the household has the following lifetime utility function:(1 − Lt+j )θLh,β Et v(Ct+j ) − Zt+j υ Ht+j + φL H
Ut =(1 − λ)θL
j=0
∞
P

j

(3.1)

where Ct is an aggregate composite of differentiated consumption goods defined below and
Ht is hours worked. Parameter β ∈ (0, 1) is the subjective discount factor, φL represents theutility weight for bargain hunting, and θL > 0 represents the elasticity of loyalty with respect
to changes in hours worked. Zth represents a stochastic shock to the utility weight of labor
supply with unit mean, and we denote the logarithm deviation of the stochastic shock by εht .
A positive shock decreases labor supply and increase loyalty. The function v(Ct ) is strictlyincreasing and strictly concave in Ct , and v(Xt ) is strictly increasing and convex in Xt . H andλ represent the initial steady-state levels of Ht and Lt , respectively.
The household’s budget constraint is
Pt Ct∗ + Et [Θt+1|t At+1 ] ≤ Wt Ht + Dt + At ,(3.2)

where Pt and Ct∗ represent the average aggregate price level and aggregate consumption spending, respectively. That is, they satisfy
Pt Ct∗ ≡ZZ
pt (τ, b)ct (τ, b)dbdτ,

τ ∈T

(3.3)

b∈B

where pt (τ, b) and ct (τ, b) represent the price and consumption of brand b of product type τ ,respectively, and Ct∗ is different from Ct , as we discuss below. Wt is the wage, Dt is dividends
received from firms minus the lump-sum tax, Θt is the asset pricing kernel, and At is thehousehold’s portfolio of Arrow-Debreu securities.
The first innovation in our model is the inclusion of the last term, Lt+j , in equation (3.1).
This suggests that the utility of the representative household increases as bargain hunting
intensity falls. Bargain hunting, like supplying labor, decreases the time for leisure and hence
utility. Because of the convexity of v(·), more hours worked raise the marginal disutility of
bargain hunting.
16

Even if Lt is constant, this assumption gives a slightly different interpretation to the model from that of GS.
In the GS model, each household is a bargain hunter for a fixed proportion of goods and loyal for other goods.
In our model, a household consists of bargain hunters and loyal customers for each good.

12

The overall aggregator of consumption isZ
Ct ≡  
−1 η(−1)
(η−1)
η−1ct (τ, b) η db
dτ 
.

Z

τ ∈T

(3.4)

b∈B

Following GS, we assume that η > , so household shoppers are more willing to substitutedifferent brands of a specific product type than different product types.
The household chief solves the expenditure minimization problem subject to equation (3.4).
Suppose, for the moment, that there are no loyal customers among shoppers; cost minimization
then leads to the following demand function for goods:
ct (τ, b) =pt (τ, b)
pB,t (τ )−η pB,t (τ )
Pt

−

Ct∗ ,

(3.5)

where the price index associated with a product type τ , pB,t (τ ), isZ

1−η

pB,t (τ ) =pt (τ, b)

 1
1−η
.
db

(3.6)

b∈B

The second innovation is the informational friction confronting loyal customers, who do
not have enough time to collect price information for other brands, say pt (τ, b̃), and observe
only the price of brand b, pt (τ, b), exclusively. They thus cannot construct the price index for
product type pB,t (τ ), which appears in the demand function for bargain hunters (3.5). The
shopper’s best guess is to assume pB,t (τ ) = pt (τ, b) and decide how much to spend on the goods
under this premise. Hence, the demand function is collapsed to17ct (τ, b) =pt (τ, b)
Pt

−

Ct∗ .

(3.7)

For the representative household as a whole, the demand function is the combination ofequations (3.5) and (3.7). For each brand b for product τ , a 1 − Lt portion of shoppers
purchase the goods following equation (3.5) and an Lt portion of shoppers purchase the goods
following equation (3.7) within a period. The former type of shoppers can optimize shopping.
By shopping around, they can observe the price index of a product type pB,t (τ ) and spend less
17

The demand function of a bargain hunter (3.5) and that of a loyal customer (3.7) can be simultaneously
derived by the household’s chief optimization problem, which maximizes the utility expressed in equation (3.4)
under a budget constraint that incorporates a wedge. The wedge, which we denote with γ t (τ, b), captures theinformational
frictionassociated with having loyal customers among the shoppers. The budget constraint isRR
given by τ ∈T b∈B γ t (τ, b)pt (τ, b)ct (τ, b)dbdτ. The wedge takes unity if a shopper is a bargain hunter, leading
to the demand function in (3.5). The wedge equals γ t (τ, b) = (pB,t (τ )/pt (τ, b))(η−)/η if a shopper is a loyal
costumer, leading to the demand function in (3.7).

13

on brand b if the price of the good from brand p(τ, b) is high relative to the price index pB,t (τ ).
The latter type of shoppers cannot observe the price index pB,t (τ ) and determine the amountto purchase without referring to pB,t (τ ). For a firm that produces goods ct (τ, b), the demand
functions have exactly the same form as that in GS, which drastically simplifies our analysis
below.18
In choosing the optimal Lt , the household chief faces a trade-off. On the one hand, anincrease in Lt raises the household’s utility. As equation (3.1) shows, the household increases
leisure time by decreasing the time spent on bargain hunting. On the other hand, the increasein Lt decreases the benefit of bargain hunting. The household decreases its utility by selecting
the sub-optimal amount of demand because it is forced to purchase products according to thedemand function (3.7). We illustrate this second effect by the relationship between utilityrelated consumption Ct and spending-related consumption Ct∗ : Ct depends not only on Ct∗ but
also on the following consumption wedge zt :


PB,t
Pt

−

Ct∗ ,

(3.8)

zt ≤ 1 and dzt /dLt < 0.

(3.9)

Ct = zt ·where

PB,t = pB (τ ) is the common value of the bargain hunters’ price index in equilibrium.19 As
the household engages in more bargain hunting, Lt decreases and zt increases. The household
enjoys higher utility from the same amount of consumption spending Ct∗ . If the household
engages in bargain hunting for all product types, that is, Lt = 0 , then zt is its highest value,zt = 1.
Additionally, following GS, we introduce Calvo-type wage stickiness into the model. Thatis, the household supplies differentiated labor input to firms, and wages can be adjusted at aprobability of 1 − φw .

Firms

An advantage of our model is that it describes firms’ behavior in exactly the same way

as in GS. Firms’ demand function, given by equations (3.5) and (3.7), is the same as that in GS.
18
This formulation is economically analogous to that in Kryvtsov and Vincent (2015) and Coibion, Gorodnichenko and Hong (2015). They introduce a fixed cost of shop searching, which enables a household to substitutefrom a relatively expensive brand b0 to a less expensive brand b00 elastically. The advantage of our model is that
we need not assume discrete two-price equilibria, as in Kryvtsov and Vincent (2015), but we can derive thisas firms’ optimal choices due to the following demand function (3.5). Similarly, Nevo and Wong (2015) simply
assume a reduced-form price function that is decreasing with shopping intensity.
19
Similar to GS, we assume that a firm takes the downward-sloping demand curve as given. In addition, we
assume that each firm’s decision takes loyalty Lt as given. The rationale for the latter assumption is that Lt is
the function of macroeconomic variables and not the function of a specific price pt (τ, b) that a specific firm sets.

14

Although loyalty Lt changes depending on returns on bargain hunting, each firm is sufficiently
small that it cannot influence PB,t in equation (3.8), and in turn, Lt . It is thus optimal forfirms to randomize their prices across shopping moments from a distribution with two prices
given Lt . Firms set a normal high price, PN,t , with a frequency of 1 − st and a low sale price,
PS,t , with a frequency of st . Following GS, we refer to the higher price as the normal priceinstead the regular price. While important, the only difference from GS is that firms optimize
their pricing decisions by observing changes in loyalty Lt .
As GS argues, the strategic substitutability of sales plays a crucial role in firms’ pricing.
The more other firms hold sales, the less an individual firm will want to have a sale. Supposethat other firms always have a sale. If an individual firm stops holding a sale and sells its goodat the normal price, its profit increases, since price-insensitive loyal customers tend to buy thegood even at the normal price. As the opposite case, suppose that other firms do not hold sales.
Because sales attract price-sensitive bargain hunters, an individual firm can increase its profit
by having sales. Such strategic substitutability leads firms to randomize their prices between
the high normal price and the low sale price.
We characterize firms’ adjustments to normal prices by Calvo-type price stickiness. Thatis, in each period, firms can reset their normal prices with a probability of 1 − φp . Firms canadjust sale prices freely.
Wholesalers produce goods using labor input:
Qt = Zta Htα ,(3.10)

where α represents the elasticity of output with respect to labor input and Zta represents a
stochastic shock to productivity, which has a mean of one, and where εat denotes the logarithm
deviation.

Monetary Authority The monetary authority sets the nominal interest rate it based on
the following monetary policy rule:it = ρit−1 + (1 − ρ)φπ πtN + εit ,(3.11)

where πtN represents the change in the normal price. The official CPI excludes sales, so we
assume that the monetary authority refers to the inflation rate based on the normal price.
Policy parameters ρ and φπ represent interest rate inertia and the size of the response to the
inflation rate, respectively. εit represents a shock to monetary policy with zero mean.

15

Resource Constraint

The resource constraint for goods is given by
Yt = Ct∗ + Ztd ,(3.12)

where Ztd represents a stochastic shock to external demand. Its mean is zero and we denotethe logarithm deviation from the steady-state Y by εdt .

3.2

Log-Linearized Equations

We explain some key log-linearized equations to help explain the important mechanism in ourmodel. We denote log deviations of variables from the initial steady state with small letters.
Sale Pricing

It is optimal for a firm j to adjust its sale price, pS,j,t , one-for-one in line withany change in its nominal marginal cost, xt + pt , that is,
pS,j,t = xt + pt ,(3.13)

where xt denotes the real marginal cost.
The frequency of sales is
1 − θB 1xt −sst = −
ϕB 1 − ψ

1 − θB A1+
ϕB 1 − ψ (η − )(1 − λ)ϕBlt .

(3.14)The second term on the right-hand side, which is not in the original GS model, indicates that asloyalty lt increases, firms decrease the frequency of sales st . In other words, when households
reduce bargain hunting, the benefits of holding sales decreases, and firms thus decrease thefrequency of sales. Like in the GS model, an increase in the real marginal cost xt decreases thefrequency of sales. Because the sale price responds one-for-one to changes in marginal costs,
the sale price increases more than the normal price. This decreases the relative demand forgoods when they are on sale, thereby decreasing the frequency of sales.
Loyalty

Loyalty lt is given by!
θ−1
1 θh−1δ θh−10=− 1 yt −wt − h εat + εht − (θc−1 − 1)εdt
1 + γδ α
1 + γδ αα!
λλ1 θh−1−
B + (θL − 1)
+ θh−1 φL
lt
1 + γδ α
1−λ
1−λ



Ξ
η−1
1
−1
+
ξt +
ft , +(θc − 1) ft −  xt +lt1−Ξη(η − )(1 − λ)θc−1 +

16(3.15)

where θc and θh are the elasticity of consumption and the inverse of the elasticity of labor
supply, respectively.
Two things are worth noting. First, loyalty lt increases with aggregate demand, yt , andconsequently, hours worked, ht . As hours worked increase, the disutility from bargain hunting
increases, and hence loyalty increases.
Second, loyalty lt increases with the consumption wedge, ft . A larger consumption wedgemeans greater utility from a given amount of consumption spending. As the wedge grows, thebenefit from bargain hunting diminishes, thus increasing loyalty. We can also show that theconsumption wedge increases with the ratio of the sale price to the normal price, µt = PS,t /PN,t ,and decreases with the sale frequency, st . In other words, as the sale price converges to thenormal price or sales become less frequent, prices for different brands become more homogeneousand the consumption wedge grows.
Phillips Curve with Sales
πt = βEt πt+1 +The New Keynesian Phillips curve with sales is given by1{κxt + ψ(∆xt − βEt ∆xt+1 ) + κAlt + A(∆lt − βEt ∆lt+1 )} .
1−ψ

(3.16)

Compared with the standard New Keynesian Phillips curve, this equation has two additionalterms. First, as in GS, changes in the real marginal cost, ∆xt , influence the inflation rate,
πt . This is because the overall price depends on the sales price, which is itself proportional to
the real marginal cost, as shown in equation (3.13). Second, unlike in GS, loyalty lt influences
the inflation rate. As loyalty increases, the household substitutes less from relatively expensive
brands to cheaper brands. Observing this, firms lower the frequency of sales, and hence theoverall price index increases.

4

Why Did the Frequency of Sales Rise During Japan’s Lost
Decades?

As we saw in Figure 2, the frequency of sales, st , rose during Japan’s lost decades. In thissection, we examine why the frequency of sales rose using our model and argue that the decline
in hours worked explains this phenomenon. Moreover, we calibrate the elasticity of loyalty withrespect to changes in hours worked, θL , which plays an important role in determining the realeffect of monetary policy.

17

4.1

Calibration

We base most of the calibration of our model parameters on GS (see Table 6). The exceptions
are the parameters associated with sales, which we choose in order to maintain consistency
with the POS data for Japan shown in Table 3. Based on the mode filter with a 42-day
window, the average frequency of sales, s, is 0.211; the average ratio of quantities sold at thesale and normal prices, χ, is 2.055; and the average magnitude of sales discounts is 15.5%,
which means µ = 0.845. Then, we obtain the elasticity between product types  = 2.677, theelasticity between brands η = 13.640, and the mean of loyalty λ = 0.878. See Table 7. We
choose the value of θL =1.7 to match the historical change in the frequency of sales, as weshow below. We calculate the theoretical elasticity of loyalty with respect to the real wage asθh−1 (θL − 1)−1 = 2.0. Although not strictly comparable, this value is similar to the estimate by
Nevo and Wong’s (2015) point estimate of 1.7 for the elasticity of substitution between timeand market goods in home production.

4.2

Simulation Method

In conducting the simulation, we assume that the steady state in each year changes due toexogenous changes in the size of external demand Ztd . External demand changes annually andthe economy converges to a steady state consistent with the change in external demand. With
this assumption, we draw the time-series path of Ztd to account for the actual movements inhours worked in Japan. We choose Ztd exclusively because the GDP series the model generates
with Ztd replicates the actual GDP movements better than that with other factors, as we discuss
below. Moreover, prior empirical studies support this assumption.20
Using the value for Ztd we obtain from the method above, we simulate the time-series pathsof variables associated with temporary sales. We use two models for comparison: the GS modeland our model with endogenous changes in loyalty. We use hours worked multiplied by one
minus the unemployment rate to account for total labor input. The sample period is from 1981
to 2013.
20
For Japan, Sugo and Ueda (2008) estimate a sticky-price DSGE model similar to Smets and Wouters (2003),
and find that one of the main driving forces of business cycles was investment adjustment cost shocks. Bayoumi(2001) and Caballero, Hoshi, and Kashyap (2008) argue that financial shocks caused Japan’s lost decade(s).
Although investment adjustment cost and financial shocks do not necessarily represent demand shocks, thesestudies suggest that Japan’s business cycles do not only result from technology shocks. For the United States,
Nevo and Wong (2015) argue that the changes in household shopping behavior during the Great Recession were
driven not by non-market shocks such as shocks to labor supply in our model, but rather unanticipated income
and wealth shocks.

18

4.3

Simulation Results

Figure 6 shows the simulated paths of variables associated with temporary sales; namely, thefrequency of sales (st ), the magnitude of sales discounts (1 − µt ), the quantity ratio (χt ),and the revenue ratio along with the macroeconomic variables of hours worked and real GDP
growth rates. The top-middle panel illustrates that our model explains the secular increase in
the frequency of sales, st , both qualitatively and quantitatively. By contrast, the GS model
predicts no change in the frequency of sales. However, as for the magnitude of sales discounts
and the quantity ratio, the simulated paths show no fluctuations. In summary, these simulation
results suggest that our model improves on the GS model in explaining the extensive margin ofsales (the frequency of sales) but not the intensive margin (sales discounts). As for the revenue
ratio, our model performs well in accounting for its movement.
Our model also shows changes in loyalty and household price elasticity, which are unobservable. The middle-right panel indicates that loyalty remained almost constant in the 1980s,
but shows a downward trend during the lost decades of the 1990s and 2000s. Put differently,
bargain hunting intensity increased. Obviously, in the GS model, loyalty remains constant.
In the bottom-left panel, we report a path of household price elasticity, which we calculate
by a weighted average of the elasticity of bargain hunters and that of loyal customers. The
household price elasticity showed a secular increase. Finally, the bottom-middle panel showsthat the model-based real GDP changes move very closely to the actual changes. The former explains the latter with an R-squared measure of 0.35 for the full sample period. The
R-squared increases to 0.60 when we compute the number based on the subsample period of
the lost decades from 1992 to 2013.
When we assume technology (Zta ) or labor supply (Zth ) factors instead of external demand
as a driver of the actual hours worked, the model performs poorly.21 Most notably, changes in
Zth yield a decrease in the frequency of sales together with the decrease in hours worked, whichis contrary to what we observed in the data. An increase in Zth increases the disutility of thelabor supply, decreasing both hours worked and bargain hunting. Thus, a positive correlationis generated between hours worked and the frequency of sales. This result is in line with Nevoand Wong (2015), who investigate the Great Recession in the United States and find that theelasticity between expenditures on market goods and time spent on home production did notchange in the wake of the Great Recession. In that regard, they argue that the recession was
not driven by shocks to the non-market sector, that is, labor supply shocks. Moreover, in ourmodel, when we assume technology Zta , the frequency of sales increases, which is consistent
with the data. However, it fails to explain the actual changes in the GDP. Our simulation
21

See Online Appendix C.

19

implies, similar to Nevo and Wong (2015), that the secular decline in hours worked and thesecular increase in the frequency of sales in Japan were driven by stagnant demand rather than
supply factors.

5

Impulse Response Functions

To study the implications for the macroeconomy, we simulate impulse response functions (IRFs)
of economic variables to an accommodative monetary policy shock, εit .22 Different from GS,
we assume that the central bank follows an interest rate monetary policy rule, with ρ = 0.8
and φπ = 1.5, while in GS the central bank follows a money growth rate rule. We set twoalternative values for θL : 1.7 and 100. A lower θL implies a higher elasticity of loyalty withrespect to changes in hours worked.

5.1

The Effects of Endogenous Bargain Hunting

We examine the IRFs of our model and compare them with those of the GS model. Figure 6
shows the IRFs of eight economic variables, with the blue solid lines representing the IRFs of
the GS model. The thick solid lines and the lines with asterisks represent the IRFs of our modelwith endogenous changes in loyalty for the two different elasticity parameter values θL =1.7
and 100, respectively. The horizontal axis shows the time up to 12 quarters after a shock.
The figure indicates that temporary sales dampen the monetary policy effect on aggregate
demand by around 40%. The mechanism runs as follows. In response to the monetary policy
shock resulting from a lower nominal interest rate, aggregate demand increases. This increases
hours worked. Since the household spends more time working, its disutility from bargain
hunting increases. With endogenous bargain hunting, loyalty (bargain hunting) increases (decreases). Observing this, firms lower the frequency of sales. Since firms sell a higher quantityof goods when goods are on sale, the decrease in the frequency of sales dampens the increasein aggregate demand. The effect of monetary policy on demand decrease as θL decreases.
The increased strategic substitutability of sales also explains the attenuated real effect ofmonetary policy. Suppose that all firms except for firm A raise the frequency of sales. As
in GS, this reduces the incentive for firm A to increase the frequency of sales, since doing sowould decrease the marginal revenue from sales. In our model, an additional channel emerges.
When all firms except for firm A raise the frequency of sales, the aggregate price level falls.
This increases aggregate demand for goods and, in turn, aggregate demand for labor. The
22

The IRFs to an external demand shock, which we used in the previous section, are qualitatively similar to
those to a monetary policy shock. To conserve space, we report the IRFs to the other three types of shocks,
that is, wholesalers’ production technology, external demand, and labor supply, in Online Appendix D.

20household supplies more labor and reduces time for bargain hunting. Observing this, firm A
lowers the frequency of sales. This intensified strategic substitutability of sales mitigates thereal effect of monetary policy.
The inflation rate excluding sales (i.e., changes in normal prices) also fluctuates less in thismodel than in the GS model. As we explained in the previous section, an increase in loyalty
decreases the real wage and the real marginal cost. Although the accommodative monetary
policy shock increases hours worked and puts upward pressure on the real marginal cost, theeffect of the increase in loyalty dominates when θL is low. On the other hand, the modelyields greater increases in the inflation rate including sales than the GS model because theaggregate price level increases due to the rise in loyalty and the decline in the frequency ofsales in response to the shock.
Finally, although our model shows that temporary sales dampen the real effect of monetary
policy shocks, we should emphasize that monetary policy shocks still have real effects. Temporary sales do not fully eliminate the real effect of monetary policy shocks, despite the factthat aggregate price levels including sales look perfectly flexible.

6

Concluding Remarks

In this study, we first examined empirically whether there is a link between the frequency ofsales and changes in macroeconomic conditions. Based on Japanese supermarket scanner dataspanning two decades, we found a significant negative correlation between the frequency ofsales and hours worked. Second, we constructed a DSGE model with temporary sales andendogenous bargain hunting to examine the cause of the increase in the frequency of sales inJapan, and to examine the implications of endogenous sales frequency for monetary policy
transmission. The model showed that the decline in hours worked during Japan’s lost decades
accounts for the actual rises in the frequency of sales and implies that the fraction of pricesensitive bargain hunters has increased. Because firms in Japan frequently hold sales andendogenous bargain hunting increases the strategic substitutability of sales, the real effect ofmonetary policy shocks weakens by around 40%, although monetary policy still matters for thereal economy.
There are several potential avenues for future research. The first would be to pursue further
qualitative and quantitative evidence for endogenous bargain hunting. In particular, more
empirical research using micro data on how individuals optimize time spent between bargain
hunting and working is necessary. Second, studies could improve our model to account for
both the extensive margin (the frequency of sales) and the intensive margin (the size of sales
discounts).
21

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24

Table 1: Time Spent (minutes per day)

1986
1991
1996
2001
2006
2011

(who work)
Shopping
6
9
11
13
14
15

Men
(who work)
Working
493
481
469
456
470
466

(who do not work)
Shopping
9
12
15
18
20
22

(who work)
Shopping
27
30
30
31
31
32

Women
(who work)
Working
371
358
345
324
335
326

(who do not work)
Shopping
37
38
39
39
39
40

Note: Working time includes commuting time. Source: Statistics Bureau, Survey on Time Use and Leisure
Activities.

Table 2: Regression Results for Time Spent Shopping (minutes per day)All
working time
non-city
femaleage control
Observations-0.059***(0.002)4.911***(0.619)12.034***(1.295)
Y
180,240

Persons who spend their time
mainly working-0.063***(0.003)
2.996***(0.388)11.646***(1.200)Y
91,188Men who spend their time
mainly working-0.058***(0.003)3.389***(0.460)Y62,878Notes: Figures in parentheses represent robust standard errors. ***, **, and * represent significance at the 1,
5, and 10 percent levels, respectively.

25

Table 3: Basic Statistics for the POS Data
FilterWindow
Frequency of posted price changes
Frequency of regular price changes
Frequency of sales
Magnitude of sales discounts
Quantity ratio
Quantity at sales
Quantity at regular
Revenue ratio

mode
42d
0.202
0.002
0.211
0.155
2.055
12.524
6.043
0.247

V-shaped
42d
0.202
0.005
0.244
0.167
2.155
12.2535.630
0.269(0.061)(0.001)(0.034)(0.020)(0.222)(3.199)(1.200)(0.034)(0.061)(0.002)(0.033)(0.018)(0.247)(1.200)(0.034)(0.036)

mode
7d
0.202
0.011
0.142
0.117
1.812
12.132
6.679
0.192(0.061)(0.002)(0.038)(0.016)(0.127)(3.031)(1.559)(0.039)V-shaped
7d
0.202
0.029
0.129
0.144
1.871
12.7566.767
0.192

Notes: Figures in parentheses represent standard deviations. The sample is from March 1, 1988 to October 31,
2013 (daily). The frequency of price changes is daily.

Table 4: Correlation between the Frequency/Magnitude of Sales and the Macroeconomy

FilterWindow
Goods
Macro variables
Unemp
Hours
CPI

FilterWindow
Goods
Macro variables
Unemp
Hours
CPI

mode
42d
all

V-shaped
42d
allFrequency of salesmode
V-shaped
7d
7d
all
all

mode
42d
food

mode
42d
domestic

V-shaped
42d
food

V-shaped
42d
domestic

0.215-0.428**-0.2430.147-0.393**-0.2050.479**-0.480**-0.2510.239-0.471**-0.3300.017-0.0200.150

0.162-0.385*-0.284-0.048-0.096
0.261

mode
42d
all

V-shaped
42d
all

Magnitude of sales discounts
mode
V-shaped
mode
7d
7d
42d
all
all
food

mode
42d
domestic

V-shaped
42d
food

V-shaped
42d
domestic-0.1220.249-0.066-0.1570.305-0.105-0.1470.419**-0.024-0.1610.290-0.038-0.1120.421**-0.203-0.0070.282-0.1660.505**-0.444**-0.261-0.1350.325-0.088

-0.13
0.253
-0.04

Note: ** and * represent significance at the 5 and 10 percent levels, respectively.

26(0.061)(0.004)(0.031)(0.017)(0.177)(3.483)(1.558)(0.034)

Table 5: Panel Regression Results for the Frequency of Sales
FilterWindowmode
42d

V-shaped
42d

mode
7d

V-shaped
7d-0.006**(0.003)Y
Y-0.005(0.005)YY-0.006***(0.002)YY-0.004(0.003)Y
Y

Observations
1684
Number of Regions
9
Sample: April 1988 to Dec 2004

1684
9

1,696
9

1,696
9

Explanatory variables
Hours worked
Time dummy
Region dummy

Note: Robust standard errors in parentheses. ***, **, and * represent significance at the 1, 5, and 10 percent
levels, respectively.

Table 6: Model Parameters
Parameters
β
θc
θh
ς
α
γ
φp
φw
ρ
φπ

Discount factor
Elasticity of consumption
Inverse elasticity of labor supply
Elasticity btw differentiated labor
Elasticity of output to hours
Elasticity of marginal cost
Calvo price stickinessCalvo wage stickiness
Monetary policy rule inertia
Monetary policy response to inflation

0.9975
0.333
0.7
20
0.667
0.5
0.889
0.889
0.8
1.5

Table 7: Parameters Related to Sales
Target variablessµχ
Calibrated parametersηλFrequency of sales
1-sales discounts
Quantity ratio

0.211
0.845
2.055

Elasticity btw product types
Elasticity btw brands
Loyalty

2.677
13.6400.878

Calibrated parametersφL

Utility weighton loyalty

27

2.5 10−4
0.0146

θL = 100
θL = 1.7

0.06
0.05
0.04

CPI

POS-CPI

0.03
0.02
0.01
0
-0.01
-0.02
-0.03
89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

Figure 1: Inflation Rates Based on CPI and POS-CPI

28

Magnitude ofsales discounts

Frequency of sales
0.4

0.2

0.3

0.15

0.2

0.1

0.1

0.05

0
1990

2000

0
1990

2010

Quantity ratio ofsales to regular
4

2000

2010

Revenue ratioof sales
0.4
0.3

3

0.2
2

0.1

1
1990

2000

0
1990

2010

mode 42d
V−shaped 42d2000 mode
2010
7d

1990

1995

1995

2000

2000

2005

2005

Unemployment rate

0.4
0.35
0.3
0.25
0.2
0.15
0.1
1985

1990

2010

6
5
4
3
2
1
0
2015

2010

120
115
110
105
100
95
90
2015

Hours worked

Frequency of sales

0.4
0.35
0.3
0.25
0.2
0.15
0.1
1985

Frequency of sales

Figure 2: Variables Associated with Temporary Sales

Figure 3: Frequency of Temporary Sales and Labor Market Indicators

29

HoursFreq of sales

Mag of sales

0.1

0.2

0.05

0.25

0

0.2

−0.05

0.15

−0.1
1980

2000

0.1
1980

Q ratio
3

0.15

0.1
1980

2000

Loyal

Rev ratio
0.92

0.45
0.4

2.5

2000

0.9

0.35
2
1.5
1980

0.88

0.3
2000

0.25
1980

Elasticity
4.2

2000

0.86
1980

0.05
ActualModel
GS Model

4.1
4

0

3.9
3.8
1980

2000

GDP chg

2000

−0.05
1980

2000

Figure 4: Model Simulation30

Infl πN

Infl πOutput
4

5

0.1

2

0

0

0

2 4 6 8 1012
Int Rate

0−5

2 4 6 8 1012
Hours

−0.1

2 4 6 8 1012
Loyal

4
4

−0.5
−1

2
2 4 6 8 1012
Sale Freq002
2 4 6 8 1012

0

2 4 6 8 1012

Real MC
5−50

GS modelModel θL=1.7

0Model θ =100
−100

2 4 6 8 1012

−5L

2 4 6 8 1012

Figure 5: Impulse Responses to an Accommodative Monetary Policy Shock31