(PDF) Small Price Changes, Sales Volume, and Menu Cost

Small Price Changes, Sales Volume, and Menu Cost*

Doron Sayag

Department of Economics, Bar-Ilan University

Ramat-Gan 5290002, Israel

Doronsayag2@gmail.com

Avichai Snir

Department of Economics, Bar-Ilan University

Ramat-Gan 5290002, Israel

Snirav@biu.ac.il

Daniel Levy**

Department of Economics, Bar-Ilan University

Ramat-Gan 5290002, Israel,

Department of Economics, Emory University

Atlanta, GA 30322, USA,

ICEA, ISET at TSU, and RCEA

Daniel.Levy@biu.ac.il

Revised: February 29, 2024

Keywords: Menu cost, (S, s) band, price rigidity, sticky prices, small price changes, small

price adjustments, sales volume

JEL Codes: E31, E32, L16, L81, M31

* This is a substantially revised version of the manuscript that was presented at the 2021 ECB-Federal Reserve Bank of

Cleveland Conference on Inflation: Drivers and Dynamics, at the 2021 ICEA’s 3rd Warsaw Money-Macro-Finance

Conference, at the 2022 annual conference of the Royal Economic Society, at the 2022 annual conference of the

Armenian Economic Association, at the 2023 annual conference of the Israeli Economic Association, at the 2023

International Conference on Empirical Economics at Pennsylvania State University, and at the Bank of Israel Research

Seminar. We thank the participants of these conferences for their helpful and constructive comments and suggestions.

All errors are ours.

Declarations of interest: None

** Corresponding author: Daniel Levy, Daniel.Levy@biu.ac.il

Small Price Changes, Sales Volume, and Menu Cost

Abstract

The finding of small price changes in many retail price datasets is often viewed as a puzzle.

We show that a possible explanation for the presence of small price changes is related to

sales volume, an observation that has been overlooked in the existing literature. Analyzing

a large retail scanner price dataset that contains information on both prices and sales

volume, we find that small price changes are more frequent when products’ sales volume

is high. This finding holds across product categories, within product categories, and for

individual products. It is also robust to various sensitivity analyses such as measurement

errors, the definition of “small” price changes, the inclusion of measures of price

synchronization, the size of producers, the time horizon used to compute the average sales

volume, the revenues, the competition, shoppers’ characteristics, etc.

1

1. Introduction

Extensive empirical analyses of price-setting behavior using various micro-level price

datasets show that individual prices tend to change at a significantly lower frequency than

the corresponding market conditions.

1

A leading model offered to explain the sluggish

response of prices to underlying shocks is the menu cost model, which posits that each

time a firm changes a price, it incurs a lump sum cost that is independent of the size or

the direction of the price change.

2

A key prediction of the simple menu cost model is that firms make infrequent but

relatively large price changes because making frequent small price changes is less

economical (Caplin and Spulber 1987). However, empirical studies find that 20%–44%

of the observed price changes are small, which many authors see as evidence against the

simple menu cost model.

3

To reconcile the existence of small price changes with menu costs, Dotsey et al.

(1999) model stochastic menu costs, which lead to small price changes when the realized

menu cost is small. Lach and Tsiddon (2007), Klenow and Malin (2011), Midrigan

(2011), Alvarez and Lippi (2014) and Alvarez et al. (2016) suggest economies of scope in

price adjustments, allowing both small and large price changes, as long as the average

price change is larger than the menu cost.

4

Chakraborty et al. (2015), Rotemberg (1982),

and Chen et al. (2008) suggest that consumer inattention can explain small price changes.

In this paper, which is primarily empirical, we use a large scanner retail price dataset

with over 98 million weekly observations to show that sales volumes can be another

explanation for small price changes. The empirical evidence we present suggests that

small price changes are significantly more likely for products with high sales volumes

than for products with low sales volumes. This result is robust. It holds across product

categories, within product categories, or at the level of individual products across stores.

1

Examples include Carlton (1986), Cecchetti (1986), Lach and Tsiddon (1992, 1996, 2007), Kashyap (1995), Blinder

et al. (1998), Slade (1998), Eden (2001, 2018), Dutta et al. (1999, 2002), Fisher and Konieczny (2000, 2006), Owen

and Trzepacz (2002), Chevalier et al. (2003), Baharad and Eden (2004), Bils and Klenow (2004), Levy and Young

(2004), Zbaracki et al. (2004), Álvarez et al. (2006), Dhyne et al. (2006), Knotek (2008, and forthcoming), Nakamura

and Steinsson (2008), Campbell and Eden (2014), Kehoe and Midrigan (2015), Konieczny and Skrzypacz (2005,

2015), Gorodnichenko and Talavera (2017), Anderson et al. (2015, 2017), and studies cited therein. For older surveys,

see Romer (1993), Weiss (1993), Taylor (1999), Willis (2003), and Wolman (2007). More recent surveys include

Klenow and Malin (2011), Leahy (2011), and Nakamura and Steinsson (2013).

2

See, for example, Barro (1972), Sheshinski and Weiss (1977 and 1992), Akerlof and Yellen (1985), Mankiw (1985),

and Konieczny and Rumler (2006).

3

See, for example, Bils and Klenow (2004), Nakamura and Steinsson (2008), Chen et al. (2008), Klenow and Kryvtsov

(2008), Msidrigan (2011), Bhattarai and Schoenle (2014), Klenow and Malin (2011), and Gautier et al. (forthcoming).

4

Alvarez et al. (2014), Eichenbaum et al. (2014), Cavallo and Rigobon (2016), and Cavallo (2018) suggest that many

of the reported small price changes are due to measurement errors. Even these studies, however, find a non-negligible

share of small price changes that cannot be explained by measurement errors.

2

It is also robust to various sensitivity analyses such as the definition of “small” price

changes in relative vs. absolute terms, measurement errors, the time horizon used to

compute the average sales volume, and the inclusion of controls for competition,

markups, pricing zones, producers’ size, etc.

Sales volumes as an explanation for small price changes seem to have been

overlooked by the existing literature, although it has a straightforward intuition. Under a

menu cost (i.e., non-convex lump-sum price adjustment cost), the firm incurs the same

price adjustment cost regardless of the number of units sold because it pays the menu cost

once to change the price of all units sold. If it sells one unit, it will change the price only

if the benefit from the change exceeds the menu cost. If it sells many units, the benefit

from changing the price is accumulated across all units sold, while the menu cost is the

same, which will likely make a small price change more profitable. Thus, comparing

products that differ only in sales volume, we expect that products with higher sales

volumes would have more price changes and that their price changes would be smaller,

on average, than products with lower sales volumes. In the appendix, we show that the

data is consistent with both predictions.

Particularly relevant to our work are Bhattarai and Schoenle (2014) and Kang and

Usher (2023). Bhattarai and Schoenle (2014) use the BLS micro-level price data

underlying the PPI to show that the average size of price changes is negatively correlated

with the number of products offered by a producer. They also present evidence

suggesting that producers that offer many products tend to have high sales volume.

We check if our results may be driven by large firms having higher sales volume or

more price changes. We find that controlling for (a) the number of products offered by

each producer, (b) the percentage of prices that change, and (c) the average size of all

price changes (excluding the current price change), has little effect on the estimated

coefficients of the sales volume.

Kang and Usher (2023) construct a model based on the assumption that the size of

price changes is negatively correlated with the revenue and therefore, small price changes

are possible if the revenue is sufficiently large. Because there is a strong correlation

between sales volume and revenues (in our data, the average correlation is 0.85), our

model and findings are consistent with their model and findings. Indeed, when we test the

correlation between the likelihood of small changes and revenue, we find a positive and

significant correlation. However, our empirical results further suggest that the positive

correlation between revenue and small price changes is driven by the sales volume

3

component of the revenue, and not by the price component.

Our results are likely to hold in other datasets as well. For example, the strong

correlation between sales volume and revenue suggests that our results are likely to hold

in Kang and Usher’s (2023) data. In addition, although the Bhattarai and Schoenle (2014)

data does not allow direct analysis of the correlation between small price changes and

sales volume, the observation that our results hold along with their results, suggests that

such a correlation exists in their data.

Further, our results suggest that a lack of correlation between the price gap and the

likelihood of a price change, as reported by Karadi et al. (forthcoming), for example, is

not necessarily evidence against selection. If the likelihood of a small price change

depends on sales volumes, then retailers might select to adjust prices of products with

high sales volumes even if the deviation of their price from the optimal price is small.

Thus, even when selection is present, in the wake of a monetary shock we are likely to

observe both large and small price changes.

We proceed as follows. To motivate our empirical analyses, in section 2, we extend

Barro’s (1972) model to derive a relationship between the width of the (S, s) band and the

sales volume. In section 3, we discuss the data. In section 4, we present the empirical

findings. In section 5, we discuss robustness. We conclude in section 6.

2. Sales volume and the width of the optimal (S, s) band

To motivate the empirical analyses of the relationship between sales volumes and the

prevalence of small price changes, we extend Barro’s (1972) model. Although the model

is highly stylistic, it is useful because one criticism of the canonical menu cost model is

that it fails to predict small price changes. We show that conditional on sales volume,

even this highly stylistic model can predict small price changes.

Following Barro (1972), consider a profit-maximizing monopolist producing a

homogenous good. The linear demand and the quadratic cost functions are given by

Y P u



  

and

2

()C Y a bY cY  

, respectively, where u is a symmetric demand

disturbance/shifter,

( ) 0CY



, and

, , , , 0abc





. The producer’s maximization problem

is thus given by:

 

2

max

s.t.

PY a bY cY

Y P u





  



  





(1)

Setting

MR MC

, and solving for P and Y, we obtain

4

 

   

212

*2 1 2 1

cb c

Pu

cc

   

   

   

 



   



   

(2)

and

   

1

*2 1 2 1

b

Yu

cc





   





   



   

(3)

The second-order condition for a maximum is given by

10c





.

In the absence of a disturbance, i.e. if

0u

, the profit-maximizing output is given by

 

0

*21

u

b

Yc











(4)

where

0b





, which is required for the output to be positive in the disturbance-free

equilibrium. We can think of

0

*u

Y

as the expected output.

Following Barro (1972, p. 19), suppose that the value of the disturbance changes from

0 to u. Assuming that the firm continuously adjusts its price and output to the change in

u, the resulting change in the firm’s profit, as Barro shows, is given by

 

   

(0, ) 0

0

2

()

1

2 1 4 1

u

ddu

du

P C Y du

buu

cc





   













   





   



   









(5)

Next, assume that the firm’s price is sticky, stuck at

ˆ

P

, which denotes the optimal

price in the disturbance-free equilibrium, such that

ˆ0dP du 

. Then, (2) implies that

 

2

ˆ21

cb

Pc

  







(6)

We follow Barro (1972, p. 20) to assume that the disturbance is not “too small” or “too

large”, i.e.,

min max

u u u

. This is necessary to avoid the situations of no production,

which will be the case if

min

uu

, or a shortage, which will be the case if

max

uu

. Then,

 

(0, ) 0

0

2

ˆ

ˆˆ

()

21

u

ddu

du

P C Y du

bu cu

c











































(7)

The expression in (7) is the change in the profit when the disturbance value changes from

5

0 to u, but the firm does not adjust its price, i.e. when the price is stuck at

ˆ

P

.

The firm’s profit gain, if it adjusts its price to the demand shock, is therefore given by

2

(0, ) (0, )

ˆ

uu

u

  

   

(8)

where

 

2

12 0

41

c











(9)

The expression in (8) can be interpreted as the loss the firm incurs for not adjusting its

price in response to the demand shock. As Barro (1972, p. 20) notes, the symmetry of this

loss means that what matters is the size of the demand shock, not its sign. It follows that

the optimal price adjustment rule (S, s), is symmetric. Also, for a given disturbance u, the

loss from not adjusting the price decreases with the price sensitivity of demand



, and

increases with the slope of the marginal cost curve

( ) 2C Y c

 

.

Barro’s (1972) main conclusion is that if u follows a symmetric random walk, then

the optimal (S, s) band is symmetric, given by

 

ˆˆ

,hh

, where

0.25

6

ˆ

h











(10)

where



is a fixed, lump-sum menu cost,

2



is the variance of the Bernoulli process

driving the symmetric random walk, and



is given by (9).

5

According to (10), the higher the menu cost, the wider the band of inaction. On the

other hand, a high



implies a narrow band of inaction. That is because according to

(8)–(9), a high



means a greater profit loss from not adjusting the price.

In models with CES demand, the optimal value of the barrier

ˆ

h

is independent of the

output produced, because of the constant price elasticity assumption. Here, however, the

demand is assumed linear and thus its price elasticity is not constant. We can therefore

take advantage of this property by extending the model to derive the relationship between

the optimal barrier, i.e., the optimal (S, s) band, and the output. Rewrite (9) as

 

   

 

2

12

41

12

2 1 2

c

b

cb









   





















(11)

5

The expression for the barrier

ˆ

h

as given above, is identical to the expression for the barrier that Dixit (1991, p. 144)

derives and reports in his equation (11).

6

By (4), the term in the first brackets is the optimal level of output in the disturbance-free

equilibrium

0

*u

Y

. Therefore, (11) can be written as a function of

0

*u

Y

,

   

 

2

00

12

**

2

uu

c

YY b



  















(12)

which shows that

 

0

*u

Y





, i.e.,



is a function of

0

*u

Y

.

To show the effect of changes in output

0

*u

Y

on the frequency of small price

changes, consider a change in



which by (4) affects the output

0

*u

Y

because of its

effect on the demand, while in parallel it also affects



by (11). Note that from the first

part of (11), it follows that

 

2

12

41

12

41

0

c





   













  







 



(13)

while from (10) it follows that

 

1

4

1

4

5

4

ˆ6

6

4

0

h





  







 







 







(14)

Now consider a situation where there is an increase in demand because of a decrease

in



, which leads to higher

0

*u

Y

because, using (4), we have

 

2

0

2(1 )

()

2( 1)

0

*ub

c

cb

c

Y



  













  





 



(15)

Then, the decrease in



which by (15) increases

0

*u

Y

, increases



by (13), which by

(14) decreases

ˆ

h

, making the (s, S) band narrower.

Another way to see this, is to find directly the sign of the partial derivative of

ˆ

h

with

7

respect to



, by first substituting (9) in (10). Then we obtain the partial derivative

1

4

ˆ6h





  



 







 



 

1

4

2

6

12

41

c

















































 

42 3 2

3

4

2

4 1 1

3

21 2 1 2 1 2

1

212

c c c

c

c c c

c

   

 

  

 











  

















(16)

   

 

4

3

4

3

2

3

2

1

2 1 2 12

c

cc



 

















0

The expressions in (13)(15), or alternatively (15)(16), constitute our main

analytical result. Consider, for example, a situation where there is an increase in demand

because of a decrease in



. Then, according to (15), output will increase. But according

to (16), the decrease in



will reduce

ˆ

h

, leading to a narrower optimal (S, s) band. In

other words, there is an inverse relationship between the level of output (as determined

by the demand) and the width of the (S, s) band. If the output of the monopolist is high

(low), then the (S, s) band will be narrower (wider), which means that we will see more

(less) frequent smaller price changes. Trivially, this will be true for small menu costs.

However, our result is independent of the size of the menu cost. That is, the model

predicts that we will likely see small price changes even if the menu cost is large.

Another implication of the reduction in the width of the (S, s) band is that as the sales

volume increases, the frequency of price changes, irrespective of their size, should also

increase. We test this second prediction in Appendix O, in the Online Supplementary

8

Appendix, and find that it is supported by the data.

3. Data

We use data from Dominick’s, a large US retail food chain with 93 stores in the

greater Chicago area with a market share of 25%. The data contain more than 98 million

weekly observations over 8 years, from September 14, 1989, to May 8, 1997, for 13,504

products in 29 categories, including food, cleaning products, hygienic products, and

pharmaceutical products.

6

Each weekly observation includes the retail price, the number

of units sold, the revenue, the retailer's markup, and some product attributes. These

features make Dominick's dataset especially well-suited for our analysis.

An important attribute of Dominick’s data is that its prices were set on a weekly

basis. Thus, each week there was one price. If manufacturer coupons were used, we

cannot account for these. During the sample period, however, the use of such coupons

was limited (Barsky et al. 2003, Chen et al. 2008, Levy et al. 2010 and 2011).

4. Empirical findings

4a. Results of pooled analysis

To study the correlation between sales volumes and small price changes, we follow Chen

et al. (2008) to define a small price change as a price change of 10¢ or less. We choose to

focus on the absolute rather than the relative size of price changes because our hypothesis

implies that a price change of a given size is profitable if the change in cents multiplied

by the sales volume is greater than the menu cost. For example, a change of 1 cent in a

price adds 1 cent to the revenue if the firm sells 1 unit and $10 if the firm sells 1,000

units, irrespective of the price prior to the change. For our purpose, therefore, it makes

sense to define small price changes in cents. In addition, a “unit” in our data may be

composed of multiple units, e.g., a six-pack of beer. In such cases, we count each pack as

a single unit, because the consumer pays once for the entire pack.

In the appendix, we show that our results hold (and are even stronger), if we exclude

multi-units packs. In the appendix, we also show that our findings are robust to

alternative definitions of small price changes, including 5¢, 15¢, 2%, and 5%, as well as

relative to the average product-level price change (Midrigan 2011, and Bhattarai and

Schoenle 2014). Thus, although we focus here on absolute price changes, the results also

6

Dominick’s data contains observations on 18,035 UPCs. However, some of the UPCs are re-launches of the same

product. See Mehrhoff (2018), and Dominick’s Data Manual (p. 9), available at https://www.chicagobooth.edu/-

/media/enterprise/centers/kilts/datasets/dominicks-dataset/dominicks-manual-and-codebook_kiltscenter.aspx.

9

apply to relative price changes, as in Alvarez et al. (2016).

Another possible source of noise in our data is measurement errors (Alvarez et al.,

2016). As Eichenbaum et al. (2014) note, prices reported in scanner datasets are weekly

average prices. This can result in spurious small price changes when shoppers pay

different prices, for example when some shoppers use coupons.

7

To control for this, we

use observations on price changes only if the post-change price lasted for at least two

consecutive weeks. As noted by Strulov-Shlain (2023), the likelihood that a spurious

price change would persist for more than one week is very low. In the appendix, we

report the results of two other robustness tests. In the first, we exclude observations

where price changes are



2¢ (Alvarez et al., 2016). In the second, we exclude

observations where Dominick’s dataset indicates that coupons were used.

As a first test of the correlation between small price changes and sales volumes, we

merge the observations in all 29 categories. Across all categories, 26.6% of all price

changes are small (i.e., smaller, or equal to 10¢), and the average sales volume is 10.0

units per week. We then divide product-stores into deciles according to their sales

volume. Figure 1 depicts the results. An increase in the sales volume is associated with a

significant increase in the percentage of small price changes. The percentage of small

price changes in the 10th decile, 33.36%, is 2.4 times higher than the percentage of small

price changes in the 1st decile, 13.89%.

As a formal test, we estimate the following fixed effect regression model using the

pooled data:

       

      (17)

where small price change is a dummy that equals 1 if a price change of product i in

store s in week t is less or equal to 10¢, and 0 otherwise. The average sales volume is for

product i in store s over the sample period.

8

By taking the average over a long period, we

obtain an estimate of the expected sales volume that does not depend on transitory shocks

7

Consider the following example. In week t, the price of a good was $1.99 and all units were sold at the posted price.

In week t+1, the posted price remained $1.99. 9 consumers bought at the posted price, and one used a coupon and paid

1.79. The price that would be recorded in the scanner dataset is $1.97, i.e, a 2 cents change relative to week t.

8

In calculating the average sales volume, we need to account for missing observations, because a missing observation

in week t implies that the product was either out of stock or had 0 sales on that week. Thus, averaging over the

available observations can lead to an upward bias for products that are sold in small numbers. Therefore, for each

product in each store, we calculate the average by first determining the total number of units sold over all available

observations. We then identify the first and last week for which we have observations, and calculate the average for

each product-store as 

. The resulting figure is smaller than we would obtain if we averaged over all

available observations (which would not include obsservations on weeks with 0 sales).

10

or sales. X is a matrix of other control variables. Month and year are fixed effects for the

month (to control for seasonality) and the year of the price change. To control for the

differences across stores and products, we add ,



and



which are fixed effects for

categories, stores and products, respectively. u is an i.i.d error term.

Table 1 reports the estimates of the coefficients of the key variable, average sales

volume. Column 1 reports the results of a baseline regression that includes only the

average sales volume and fixed effects for months, years, stores, and products. The

coefficient of the sales volume is 0.026, and it is statistically significant. This result

suggests that a 1% increase in the sales volume is associated with a 2.6 percentage points

increase in the likelihood of a small price change. In column 2, the matrix X includes the

following control variables: the log of the average price, to control for the price level

effect on the size of price changes, the percentage change in the wholesale price, and

control for sale- and bounce-back prices. The latter is important as price changes

associated with sales tend to be large (Nakamura and Steinsson 2008).

9

The coefficient of the sales volume remains positive and statistically significant. Its

value is 0.017, suggesting that a 1% increase in the sales volume is associated with a 1.7

percentage points increase in the likelihood of a small price change.

In column 3, we add a dummy for 9-ending prices as an additional control because

when the pre-change price is 9-ending, price changes tend to be larger than when the pre-

change price ends in other digits (Levy et al. 2020). Thus, if products with high sales

volume tend to have non-9-ending prices, then it might lead to small changes in their

prices. This has only a marginal effect on the coefficient; its value remains 0.017 and

statistically significant.

In column 4, we keep the same control variables as in column 3, but we focus on

regular prices by excluding the sale- and bounce-back prices. We do this for two reasons.

First, sale- and bounce-back prices tend to be large, and therefore, we need to account for

them properly. Second, it is often argued that changes in sale prices have smaller effect

on inflation than changes in regular prices (Nakamura and Steinsson 2008, Midrigan

2011, Anderson et al. 2017, Ray et al. 2023).

We find that the estimate of the coefficient of the sales volume is 0.033, and is

statistically significant. The pooled results, therefore, suggest that there is a positive and

9

To identify sale prices, we do not use the sales’ flag included in the Dominick’s data because it was not set on a

consistent basis (Peltzman 2000). Instead, we use the sales filter algorithm of Fox and Syed (2016) to identify sales.

This algorithm has the advantage that it was calibrated using Dominick’s data and, consequently, it is particularly

useful for identifying sales in the Dominick’s data.

11

statistically significant correlation between small price changes and sales volumes.

4b. Results of category-level analyses

Estimation using pooled data can hide large differences across categories. Therefore,

we study the category-level correlation between small price changes and sales volumes.

As a first test, for each category, we group the products into high, medium, and low

sales volume products, according to the average sales volumes over the sample period.

Low sales volume products are products with average sales volume in the bottom third of

the distribution, high sales volume products have sales volume in the top third of the

distribution, and medium sales volume products have sales volume in between.

Figure 2 shows, for every category, the frequency of price changes for each size of

price change from 1¢ to 50¢. The red dashed line depicts the frequency of price changes

for high sales volume products, the black dotted line depicts the frequency of price

changes for medium sales volume products, and the blue solid line depicts the frequency

of price changes for low sales volume products. The shaded area marks the range of small

price changes,

10¢P

.

The figure shows that the most common price changes are multiples of 10¢ (as

reported also by Chen et al. 2008 and Levy et al. 2011). It can also be observed that in all

categories except cigarettes (which are highly regulated), price changes are far more

common among high sales volume products than among low sales volume products.

Focusing on the shaded area, we see that the frequency of small price changes is in

general far greater among the high sales volume products than among low sales volume

products. Indeed, for high sales volume products, in most categories, the frequency of

small price changes exceeds the frequency of large price changes. This is less common,

and less dramatic, among low sales volume products. For the medium sales volume

products, the frequency of price changes, and the frequency of small price changes in

particular, fall in between the frequencies of the low and high sales-volume products.

As a formal test, we estimate a series of category-level fixed-effect regressions,

similar to (17). The only difference is that we now exclude the category fixed effects.

Table 2 reports the coefficients of the key variable, average sales volume, for each

product category. Column 1 reports the results of baseline regressions that exclude the X

matrix. I.e, the regressions include only the average sales volume and fixed effects for

months, years, stores, and products.

We find that in all 29 product categories, the coefficients are positive, and 27 are

statistically significant. One more is marginally significant. In other words, in 28 of 29

12

product categories, there is a positive and statistically significant correlation between the

likelihood that a price change is small and the average sales volume. The effect is

economically significant. The average coefficient is 0.026, suggesting that an increase of

1% in the sales volume is associated with an increase of 2.6 percentage points in the

likelihood that a price change will be small.

In column 2, we add the X matrix which includes the following control variables: the

log of the average price to control for the price level effect, the percentage change in the

wholesale price, and control for sale- and bounce-back prices, all as defined above. The

results are similar to column 1. The coefficients of the average sales volume are positive

and statistically significant in 27 categories, and marginally significant in 2 more. The

average coefficient is 0.019. Thus, even after including the controls, we still find that

increasing the average sales volume by 1% is associated with an increase of 1.9

percentage points in the likelihood of a small price change.

In column 3, we add a dummy for 9-ending prices as an additional control. Adding

this dummy does not change the main result appreciably. All 29 coefficients remain

positive. 27 are statistically significant, and 2 more marginally significant. Controlling for

9-ending prices, increasing the average sales volume by 1% is associated with a 2.0

percentage points increase in the likelihood of a small price change, on average.

In column 4, we focus on regular prices by excluding the sale- and bounce-back

prices. We find that all the coefficients remain positive. 27 are statistically significant,

and 1 more is marginally significant. The average coefficient is 0.038, implying that for

regular prices, an increase of 1% in the average sales volume is associated with an

increase of 3.8 percentage points in the likelihood of a small price change.

4c. Results of product-level analyses

A possible explanation for the correlation between sales volume and small price

changes is that products with high sales volume have some unobserved attributes that

make them prone to small price changes. We explore this possibility by estimating for

each product a separate regression. If the correlation between sales volume and small

price changes is found at the level of individual products, then it cannot be explained by

unobserved attributes, since in each regression we have data on only one product.

Before presenting the full regression results, consider as an example the bathroom

tissue category. In Figure 3, we show a scatter plot for each one of the 13 bathroom-tissue

products that have data for all 93 stores at Dominick’s. In each of the 13 panels, there are

93 dots, one for each store. In each figure, the x-axis in the figures gives the average

13

weekly sales volume of the product in a store, and the y-axis gives the share of small

price changes of the product in a store. The straight lines are regression lines.

According to the plots, the correlation between sales volume and the share of small

price changes is positive for 11 of the 13 individual products. None of the negative

correlations is statistically significant, while 8 of the 11 positive correlations (marked

with solid black regression lines) are statistically significant. The regression lines that are

not statistically significant are marked with red dotted lines.

For a more formal analysis, we calculate for each product in each of the 29 product

categories the average weekly sales volume and the share of small price changes in each

of the stores it was offered. Many products in the sample were offered for only short

periods or only in a small number of stores. To avoid biases, we drop products for which

we do not have information for at least 30 stores.

Using these data, we estimate for each product in each category an OLS regression

with robust standard errors. The dependent variable is the share of small price changes

for the product in each store. The independent variable is the average sales volume of the

product in each store. The estimation results are summarized in Table 3.

10

Column 1 gives, for each product category, the average of the estimated coefficients.

Columns 2–5 give information on the sign of the estimated coefficients: the total number

of coefficients, the % of positive coefficients, the total number of coefficients that are

statistically significant at the 5% level, and the % of coefficients that are both positive

and statistically significant at the 5% level.

According to the figures in the table, the average coefficients are positive in 28 of the

29 product categories. The only exception is the highly regulated cigarettes category,

which is often excluded from the analyses (Chen et al. 2008, p. 729, footnote 2). In

addition, the number of positive coefficients far exceeds the number of negative

coefficients. On average, the former is 3.2 times larger than the latter. Ignoring the

cigarettes category, more than 74.5% of the coefficients are positive.

Focusing on statistically significant coefficients, we find a far greater number of

positive coefficients than negative coefficients that are significant. Except for the

cigarettes category, in all categories, 81.40%–100% of the statistically significant

coefficients are positive. In other words, for the overwhelming majority of the individual

products in our sample, we find a positive relationship between sales volume and the

10

For robustness, we have also conducted an analysis using LPM regressions, as in the previous section. See the

discussion in Online Supplementary Web Appendix F.

14

share of small price changes.

To summarize, we find that the correlation between sales volume and the share of

small price changes is positive whether we look across categories, within categories, and

for individual products across stores. It seems unlikely, therefore, that the correlation is

due to unobserved characteristics of the products or the product categories.

4d. Sales volume versus revenue

Kang and Usher (2023) find that the size of price changes is negatively correlated

with the revenue. In column 1 of Table 4, we report the Pearson correlation coefficient

between the average sales volume and the average revenue for product-stores for each

product category. The average correlation is 0.85, suggesting that at the category level,

the correlation is very strong.

In column 2, we replicate one of Kang and Usher’s (2023) key findings by reporting

for each product category, the coefficient estimates of regression (16) where we replace

the log of the average sales volume with the log of the average revenue. The controls

include fixed effects for months, years, stores, and products. The estimated coefficients

are positive for all 29 product categories, and 28 of these are statistically significant. We

thus confirm that Kang and Usher’s (2023) findings hold in our data: there is a strong

positive correlation between revenue and the likelihood of a small price change.

Revenue, however, is a product of the sales volume and the price. Our hypothesis

implies that the revenue is correlated with the likelihood of a small price change via the

sales volume, rather than via the price. To test this, in columns 3 and 4, we show the

results of regressions that include both the sales volume and the revenue as independent

variables. Once we add the sales volume to the regression, the coefficients of the revenue

turn negative in 22 of the 29 categories. The coefficients of the sales volume, on the other

hand, are positive in 23 of the 29 categories.

These results suggest that holding the sales volume constant, the higher the price

level, the less frequent small price changes are. In other words, the positive correlation

between revenues and the frequency of small price changes seems to materialize through

the sales volume and not through the price.

4e. Sales volume, producer size, and price synchronization

According to Lach and Tsiddon (2007), Midrigan (2011), Alvarez and Lippi (2014),

Letterie and Nilsen (2014), and Alvarez et al. (2016), small price changes can be

explained by economies of scale in price adjustment, which makes small price changes

15

profitable if the average price change exceeds the menu cost. Lach and Tsiddon (2007)

and Bhattarai and Schoenle (2014) show that: (a) producers offering a large number of

products are more likely to make small price changes than producers offering a small

number of products, (b) small price changes are more likely when price changes are more

synchronized, and (c) small price changes are more likely when the average size of all

other contemporaneous price changes is high. In addition, Bhattarai and Schoenle (2014)

provide evidence suggesting that producers offering more products are more likely to

have a large sales volume. It is therefore of interest to examine whether our results hold

when accounting for economies of scope by adding controls for price changes

synchronization and the number of products per producer.

In column 1 of Table 5, we report the coefficients of the log of sales volume in

regression (17), where we also include the average number of products per category

offered by the same producer, as a proxy to the producer’s size.

11

The regression also

includes fixed effects for months, years, stores, and products. We find that all coefficients

of the sales volume are positive and 27 are statistically significant. In addition, the

coefficients of the sales volume are almost unaffected in comparison to the figures we

report in column 1 of Table 3. Thus, it appears that the effects of sales volume on the

likelihood of small price changes are unrelated to the effects of the size of the producers.

In column 2, we add a control for the percentage of the products that changed the

price in the same week, excluding the current observation. Again, the coefficients remain

almost unchanged in comparison to the figures we report in column 1 of Table 3.

In column 3, we further add the average size of contemporaneous price changes,

excluding the current observation. Lach and Tsiddon (2007) show that when price

changes are synchronized, a small price change is correlated with a large average

contemporaneous price change. However, we find that adding the average size of price

changes has little effect on the size of the coefficients of the sales volume. Also in this

specification, 27 of the 29 coefficients are statistically significant.

Finally, in column 4, we add the percentage of the products that are produced by the

same producer and changed price in the same week, excluding the current observation.

This forces us to drop some observations because we can only use an observation if the

producer offers at least two products on the relevant week. The upshot is that most of the

remaining observations are of products produced by relatively large producers which are

11

To calculate the average number of products offered by a producer, we follow Bhattarai and Schoenle (2014), by

first determining the nubmer of products offered by a producer each week, and then averaging over all weeks.

16

most likely to make small price changes (Bhattarai and Schoenle 2014).

Therefore, if our results are driven by the size of the producers rather than by the

sales volume, then focusing on large producers should lead to a substantial drop in the

coefficients of the sales volume. We find, however, that the results do not change

significantly. All the coefficients are positive, 27 of the 29 of them are statistically

significant, and 2 more are marginally significant.

As another test, we follow Bonomo et al. (2022). They show that a large share of

price changes takes place on “peak days.” We therefore follow their methodology and

create a dummy for peak days and then add it as a control to the regressions. The

estimation results, which we present and discuss in Online Supplementary Web Appendix

P, show that the correlation between sales volumes and small price changes holds also

when we control for peak days.

5. Robustness

To assess the robustness of our findings, we conducted 19 sets of robustness tests:

1) Measurement errors: Eichenbaum et al. (2014) conclude that prices based on scanner

data might include spurious small price changes. We mitigate this concern by

focusing only on price changes in which the post change price remained unchanged

for at least 2 weeks. As further tests, we exclude all 1¢ and 2¢ price changes

(Eichenbaum et al. 2014), and remove observations on price changes if Dominick’s

sale flag indicates that there was a coupon use because if some consumers used

coupons, this could result in measurement errors (Eichenbaum et al. 2014). We also

estimate the regressions using observations on all price changes, conditional on

observing the prices in weeks t and t+1.

2) Definition of small price changes: We define a small price change as a price change

of 5¢ or less, and 15¢ or less. Because the size of price changes may be larger for

more expensive products, we re-run the analyses by defining a small price change in

percent as a price change of 2% or less, and 5% or less. Following Midrigan (2011)

and Bhattarai and Schoenle (2014), we also define small price changes relative to the

average price change at the store-product level. I.e., a price change is small if it is

smaller or equal to 



, where 



 is the average price change for product  in

store , and  attains the values (8) 0.50, (9) 0.33, (10) 0.25 and (11) 0.10.

3) Time horizon for computing the average sales volume: Above, we use the average

sales volume over the entire period, which can be thought of as a proxy for the

17

expected sales volume that is based on 8 years of data. However, this implicitly

assumes that in the first years, the retailer can predict the future sales volume. An

alternative is that the retailer makes decisions based on recent sales data. We,

therefore repeat the analyses by calculating the average sales volume based on a

rolling 52-week window of past observations.

4) Competition effect: As another control for the effect of competition, we add control

for Dominick’s pricing zones. We re-estimate the product-level regressions by

augmenting the data with demographic information of the consumers that live in the

proximity of each store, including their median income, the share of minorities, and

the share of unemployed.

5) Controlling for revenue: In section 4d, we estimate regressions with both the sales

volume and the revenue at the category level. For robustness, we explore the effect of

adding further controls. In addition, at the category level, the high correlation

between the sales volume and the revenue may render the results suspect. Therefore,

we pool data from all categories together and re-estimate the regressions. We also test

an alternative definition of the average revenue, defining it as the product of the

average sales volume and the average price for estimating category-level regressions.

6) Controlling for the producers’ size: In section 4e, we calculate the number of

products offered by each producer at the category level. To test that the results do not

change for firms of different sizes, we follow Bhattarai and Schoenle (2014) in

dividing producers into bins according to the number of products they offer in each

category and estimate the correlation between sales volume and small price changes

for each bin separately. In addition, it is possible that producers that offer products in

more than one category synchronize price changes across categories, We, therefore,

pool the data together and repeat the analysis.

7) Controlling for profit margins: Some products have high sales volumes, yet they

have few, if any, small price changes. One example is iPhones, which have high sales

volumes, yet most of their price changes are large. A possible explanation is that

small price changes are less likely for products with large markups because large

markups imply that small price changes have, in percentage terms, only a small effect

on total profits. We, therefore, add Dominick’s measure of markups to the category-

level regressions as a further control variable.

8) Graphic illustration of the category-level correlation between small price changes

and sales volume: We include a figure similar to Figure 1, which shows that small

18

price changes are correlated with high sales volume at the category level as well as at

the aggregate level.

9) Reproduce Figure 2 using % price changes: In Figure 2, the most common price

changes are multiples of 10 cents. This is consistent with a large literature on price

points (Levy et al., 2011, 2020). However, because price changes that are multiples of

10 cents might be large for some products, we reproduce Figure 2 using the size of

price changes in % terms rather than in cents.

10) National brands vs. private labels: A possible explanation for our results is that the

correlation between sales volume and small price changes is an artifact of differences

in demand. We, therefore, separate the data into two groups: national brands and

private labels, since the demand for private labels is likely to exhibit different patterns

than for national brands.

11) Holiday price rigidity: Levy et al. (2010) provide evidence suggesting that menu

costs are higher than normal during the Thanksgiving-Christmas holiday period. It is,

therefore, possible that there are fewer small price changes during the Thanksgiving-

Christmas period, leading to a decline in the correlation between sales volumes and

small price changes. We, therefore, re-estimate equation 1, using only the

observations from the Thanksgiving-Christmas period.

12) Another prediction of Barro’s (1972) model: In the paper, we study the correlation

between small price changes and sales volumes. However, Barro’s (1972) model, as

shown in section 2, also predicts that sales volume should also be correlated with the

number of price changes. In other words, prices of products with high sales volumes

should change more frequently than the prices of products with low sales volumes.

We test this hypothesis in the appendix.

13) Controlling for peak days: Bonomo et al. (2022) show that in their data, the majority

of price changes occur during “peak days.” Following their definition, for each

category in each store, we identify peak days as the subset of the most active days

that jointly account for one-half of all price changes in a store over the entire sample

period. We then control for peak days in the regressions.

14) Cross-category comparisons: We show that there are large variations in both the

average sales volume and the likelihood of small price changes across categories. We

then show that as we hypothesize, some of the variation in the likelihood of small

price changes can be explained by the average sales volumes.

15) Excluding observations on the multi-unit package: Some of the products in our

19

dataset are composed of several units. For example, we have products such as 6-packs

of beer, or a 4-pack of canned tuna. Above, we treat such packages as a single good,

because the consumer pays once for the entire package. However, these may add

noise to the regression, because it is unclear how consumers perceive such packages.

We, therefore, exclude such multi-unit packaged goods and focus on products that are

sold in single units.

16) Product level regressions: We show that the results we obtained for the product level

correlation between small price changes and sales volumes hold when we add further

controls and when we estimate the correlations using linear probability models.

17) Storable vs. non-storable products: Retailers might employ different strategies for

storable vs. non-storable products. We therefore test for the robustness of our results

by assessing them separately for storable and non-storable products.

18) Asymmetry in the correlations: Our model predicts a symmetric correlation between

sales volumes and the likelihood of small price changes. However, it is possible that

the correlation is asymmetric, for example, if shoppers are not attentive to small price

changes (Chen et al., 2008, Chakraborty et al., 2015). We therefore estimate separate

regressions for price increases and price decreases.

19) Cross-category analysis: We conduct further analysis comparing the likelihood of

small price changes and the sales volumes across categories.

The Online Supplementary Appendix contains the details of these analyses. Overall,

our main results are broadly unchanged, and are robust across the different specifications.

6. Conclusion and policy implications

The finding of frequent small price changes in many retail price datasets has been

interpreted by authors as prima facie evidence against simple menu cost models. We find,

however, that sales volume can explain some of the small price changes found in many

datasets. When a retailer expects to sell many units, then small price changes can be

profitable even in the presence of lump sum menu costs.

We use Dominick’s scanner price dataset to show a strong positive correlation

between the frequency of small price changes and products’ sales volume. This finding is

robust. It holds across product categories, within product categories, and for individual

products. It is also robust to a variety of sensitivity analyses such as the definition of

“small” price changes, measurement errors, the inclusion of control variables, firms’ size,

price synchronization, and the time horizon used to compute the average sales volume.

20

Our findings hold irrespective of how we measure price changesin absolute or relative

terms. The latter is useful if one wants to assess the “Calvo-ness” of the relevant model.

Our findings are consistent with the findings reported by Bhattarai and Schoenle

(2014) and Kang and Usher (2023), who employ more recent datasets. However, the

advantage of Dominick’s dataset, in comparison to more recent datasets is its richness. In

addition to prices and sales volume—two critical variables for our analyses, it also

contains data on wholesale prices, promotions and sales, pricing zones, shoppers’ socio-

demographics, markups, etc. We employ these additional variables to check robustness.

Above, we use Barro’s (1972) model to illustrate the theoretical correlation between

sales volumes and the size of price changes. However, Barro’s (1972) model is too

stylistic for deriving predictions about the distribution of the size of price changes. In

addition, it cannot predict the number of small price changes observed in many datasets

unless we assume unrealistically high sales volumes. Therefore, we believe that there is a

need for models that will account for sales volumes, perhaps along the lines of Golosov

and Lucas (2007). It would then be possible to evaluate the implications of heterogeneity

in sales volumes for the macro-level price rigidity.

Such a model might yield important insights. First, it might yield a non-trivial

distribution of the size of price changes even if all producers sell one product and the

menu costs are fixed. Second, if the size of price changes depends on the sales volume,

then the existence of small price changes does not rule out selection. Thus, unlike many

of the existing models, in such a model, the kurtosis of the distribution of the size of price

changes might not necessarily indicate selection (Alvarez et al., 2016). Therefore, for a

given frequency of price changes, we might obtain a result where a monetary shock has

only a small real effect even in the presence of many small price changes (Kang and

Usher, 2023). Related to this, Karadi et al. (forthcoming) find that the likelihood of a

price change does not depend on the gap between the price and the optimal price. They

interpret their finding as evidence against selection. However, in a model where price

changes depend on sales volumes, we may have selection together with both small and

large price changes in response to a monetary shock.

21

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25

Table 1. Pooled regressions of small price changes and sales volume

(1)

(2)

(3)

(4)

Average sales

volume

0.026***

(0.001)

0.017***

(0.001)

0.017***

(0.001)

0.033***

(0.001)

Observations

9,553,542

2,328,405

Notes: The dependent variable is “small price change,” which equals 1 if a price change of product i in

store s at time t is less or equal to 10¢, and 0 otherwise. The main independent variable is the log of the

average sales volume of product i in store s over the sample period. Column 1 reports the results of a

baseline regression that includes only the average sales volume and the fixed effects for months, years,

stores, and products. In column 2, we add the following controls: the log of the average price, the log of the

absolute change in the wholesale price, and a control for the sale- and bounce-back prices, which we

identify using a sales filter algorithm. In column 3, we add a dummy for 9-ending prices as an additional

control. In column 4, we focus on regular prices by excluding the sale- and bounce-back prices. All

regressions also include fixed effects for categories, stores, products, years, and months. We estimate

separate regressions for each product category, clustering the errors by product. * p < 10%, ** p < 5%,

*** p < 1%

26

Table 2. Category-level regressions of small price changes and sales volume

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient (Std.)

0.0262*** (0.0034)

0.019*** (0.0032)

0.0188*** (0.0031)

0.029*** (0.0068)

Observations

144,461

44,950

Bath Soap

Coefficient (Std.)

0.0293*** (0.008)

0.0277*** (0.0082)

0.0285*** (0.0081)

0.0972*** (0.0192)

Observations

15,295

3,208

Bathroom

Tissues

Coefficient (Std.)

0.0408*** (0.007)

0.0179** (0.0058)

0.0184*** (0.0057)

0.0386*** (0.0084)

Observations

149,441

47,041

Beer

Coefficient (Std.)

0.013*** (0.0012)

0.0147*** (0.0012)

0.0699*** (0.0063)

Observations

290,620

27,348

Bottled Juice

Coefficient (Std.)

0.0329*** (0.0053)

0.0239*** (0.0044)

0.0238*** (0.0045)

0.0304*** (0.0063)

Observations

496,557

133,714

Canned Soup

Coefficient (Std.)

0.0158*** (0.0056)

0.0108* (0.005)

0.0134** (0.0049)

0.0144** (0.0049)

Observations

495,543

176,235

Canned Tuna

Coefficient (Std.)

0.0237*** (0.0054)

0.0134** (0.0046)

0.0131** (0.0045)

0.0225*** (0.0058)

Observations

213,043

64,161

Cereals

Coefficient (Std.)

0.0204*** (0.0037)

0.0149*** (0.0034)

0.0148*** (0.0034)

0.0188*** (0.0046)

Observations

357,120

155,367

Cheese

Coefficient (Std.)

0.0201*** (0.0028)

0.0113*** (0.0025)

0.0112*** (0.0025)

0.0113*** (0.0033)

Observations

796,150

224,889

Cigarettes

Coefficient (Std.)

0.0084** (0.0046)

0.0073

(0.0045)

0.0074

(0.0044)

0.0069

(0.0054)

Observations

36,157

30,262

Cookies

Coefficient (Std.)

0.0267*** (0.0018)

0.022*** (0.0017)

0.0223*** (0.0017)

0.046*** (0.0035)

Observations

688,761

132,488

Crackers

Coefficient (Std.)

0.0379*** (0.0031)

0.0302*** (0.0026)

0.0306*** (0.0026)

0.0467*** (0.0072)

Observations

245,185

50,029

Dish

Detergent

Coefficient (Std.)

0.0393*** (0.0044)

0.028*** (0.0036)

0.0279*** (0.0035)

0.0361*** (0.0041)

Observations

189,633

53,289

Fabric

Softener

Coefficient (Std.)

0.0238*** (0.0048)

0.0123*** (0.0043)

0.0126*** (0.0043)

0.0325*** (0.0057)

Observations

181,056

56,234

Front-End-

Candies

Coefficient (Std.)

0.0047

(0.0041)

0.0057

(0.0033)

0.0059

(0.0032)

0.0053

(0.0031)

Observations

278,853

111,635

Frozen

Dinners

Coefficient (Std.)

0.0475*** (0.0034)

0.036*** (0.0028)

0.0389*** (0.0027)

0.0795*** (0.0066)

Observations

203,191

37,527

27

Table 2. (Cont.)

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient (Std.)

0.028*** (0.0021)

0.0259*** (0.0019)

0.0266*** (0.0019)

0.0443*** (0.0034)

Observations

864,832

213,545

Frozen Juices

Coefficient (Std.)

0.0273*** (0.0048)

0.0198*** (0.0042)

0.0206*** (0.0041)

0.0293*** (0.0062)

Observations

308,817

87,919

Grooming

Products

Coefficient (Std.)

0.0187*** (0.0023)

0.0209*** (0.0024)

0.021*** (0.0024)

0.0417*** (0.0069)

Observations

269,873

51,819

Laundry

Detergents

Coefficient (Std.)

0.0196*** (0.0032)

0.0093*** (0.0028)

0.0097*** (0.0028)

0.02*** (0.0045)

Observations

272,765

85,184

Oatmeal

Coefficient (Std.)

0.028*** (0.008)

0.0152* (0.0067)

0.0154* (0.0067)

0.0338*** (0.0098)

Observations

79,983

36,043

Paper Towels

Coefficient (Std.)

0.0454*** (0.0105)

0.0316*** (0.0118)

0.0321*** (0.0119)

0.0378*** (0.0115)

Observations

116,204

29,280

Refrigerated

Juices

Coefficient (Std.)

0.0357*** (0.0047)

0.0209*** (0.0039)

0.033*** (0.0056)

Observations

306,865

72,031

Shampoos

Coefficient (Std.)

0.0162*** (0.0015)

0.02*** (0.0016)

0.0201*** (0.0015)

0.046*** (0.0052)

Observations

261,778

40,996

Snack

Crackers

Coefficient (Std.)

0.0319*** (0.0032)

0.0282*** (0.003)

0.0284*** (0.003)

0.0518*** (0.0052)

Observations

398,665

78,581

Soaps

Coefficient (Std.)

0.0374*** (0.0055)

0.0226*** (0.005)

0.0237*** (0.005)

0.049*** (0.0076)

Observations

152,379

46,829

Soft Drinks

Coefficient (Std.)

0.0211*** (0.0017)

0.024*** (0.0013)

0.023*** (0.0012)

0.0517*** (0.0037)

Observations

1,350,618

156,004

Toothbrushes

Coefficient (Std.)

0.0204*** (0.0028)

0.02*** (0.0028)

0.0195*** (0.0028)

0.0498*** (0.0076)

Observations

125,380

24,955

Toothpastes

Coefficient (Std.)

0.0123*** (0.0026)

0.0111*** (0.0022)

0.0393*** (0.0063)

Observations

264,317

56,842

Average coefficients

0.0260

0.0195

0.0198

0.0384

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or equal to 10¢, and 0 otherwise. The main independent variable is the log of the average sales volume of product i in

store s over the sample period. Column 1 reports the results of baseline regression that includes only the average sales

volume and the fixed effects for months, years, stores, and products. In column 2, we add the following controls: the

log of the average price, the log of the absolute change in the wholesale price, and control for sale- and bounce-back

prices, which we identify using a sales filter algorithm. In column 3, we add a dummy for 9-ending prices as an

additional control. In column 4, we focus on regular prices by excluding the sale- and bounce-back prices. We estimate

separate regressions for each product category, clustering the errors by product. * p < 10%, ** p < 5%, *** p < 1%

28

Table 3. Product-level regressions of the % of small price changes and sales volume

by categories

Product

Category

Average

coefficient

estimate

(1)

Number

of

coefficients

(2)

Percentage of

positive

coefficients

(3)

Number of

significant

coefficients

(4)

% of positive and

significant

coefficients

(5)

Analgesics

0.031

213

83.20%

87

98.25%

Bath Soaps

0.034

33

69.77%

14

100.00%

Bathroom tissues

0.057

100

79.31%

34

90.24%

Beers

0.019

202

91.57%

142

97.80%

Bottled juices

0.051

370

83.67%

192

84.56%

Canned soups

0.041

348

77.41%

145

90.37%

Canned tuna

0.037

181

76.16%

60

80.00%

Cereals

0.047

345

80.13%

99

89.32%

Cheese

0.036

474

81.76%

224

90.26%

Cigarettes

-0.020

107

71.43%

4

40.00%

Cookies

0.034

667

82.42%

304

94.71%

Crackers

0.044

212

88.41%

118

98.84%

Dish detergents

0.041

199

85.71%

84

91.89%

Fabric softeners

0.043

226

85.35%

69

91.67%

Front end candies

0.053

275

75.28%

92

91.03%

Frozen dinners

0.053

215

92.06%

131

97.59%

Frozen entrees

0.052

671

89.32%

363

97.46%

Frozen juices

0.032

142

75.00%

62

97.67%

Grooming products

0.011

531

80.94%

229

90.65%

Laundry detergents

0.018

406

75.00%

101

81.40%

Oatmeal

0.047

69

76.81%

20

84.62%

Paper towels

0.052

90

73.61%

33

90.91%

Refrigerated juices

0.036

176

73.08%

77

85.92%

Shampoos

0.022

614

82.78%

282

96.72%

Snack crackers

0.041

282

87.36%

172

92.55%

Soaps

0.039

217

80.55%

421

84.31%

Soft drinks

0.032

902

82.49%

72

94.87%

Toothbrushes

0.026

204

82.84%

89

95.83%

Toothpastes

0.015

337

79.67%

99

92.75%

Average

0.035

303

73.29%

96

90.08%

Notes: For each product category, column 1 presents the average estimated coefficients. Column 2 presents the total

number of coefficients. Column 3 presents the % of positive coefficients out of all coefficients. Column 4 presents the

total number of coefficients that are statistically significant at the 5% level. Column 5 presents the % of coefficients

that are positive and statistically significant, at the 5% level. Products are identified by their UPCs.

29

Table 4. Category-level regressions of small price changes, sales volume, and revenue

Category

Correlation

Revenue

Sales volume and revenue

(1)

(2)

(3)

(4)

Analgesics

Coefficient (Std.)

0.8088

0.0244*** (0.0035)

0.2246*** (0.0463)

-0.201*** (0.0467)

Observations

144,461

Bath Soap

Coefficient (Std.)

0.7757

0.0319*** (0.0082)

-0.3214** (0.1271)

0.3527* (0.1279)

Observations

15,295

Bathroom

Tissues

Coefficient (Std.)

0.7838

0.036*** (0.0062)

0.8456*** (0.1168)

-0.8195*** (0.1169)

Observations

149,441

Beer

Coefficient (Std.)

0.8642

0.0131*** (0.0012)

-0.0562* (0.0288)

0.0692** (0.0287)

Observations

290,620

Bottled Juice

Coefficient (Std.)

0.9138

0.0305*** (0.0052)

0.8371*** (0.1025)

-0.8065*** (0.1027)

Observations

496,557

Canned Soup

Coefficient (Std.)

0.9458

0.0148*** (0.0056)

0.5075*** (0.0785)

-0.4943*** (0.0791)

Observations

495,543

Canned Tuna

Coefficient (Std.)

0.863

0.0201*** (0.0054)

0.5276*** (0.1175)

-0.5093*** (0.1183)

Observations

213,043

Cereals

Coefficient (Std.)

0.9311

0.0203*** (0.0038)

0.0634

(0.0429)

-0.0433 (0.0437)

Observations

357,120

Cheese

Coefficient (Std.)

0.86

0.018*** (0.0029)

0.4048*** (0.1085)

-0.3846*** (0.1091)

Observations

796,150

Cigarettes

Coefficient (Std.)

0.9938

0.0102** (0.0046)

-0.3209*** (0.0622)

0.3303*** (0.062)

Observations

36,157

Cookies

Coefficient (Std.)

0.9485

0.0273*** (0.0018)

-0.0045 (0.022)

0.0318

(0.0221)

Observations

688,761

Crackers

Coefficient (Std.)

0.9536

0.038*** (0.0031)

0.1257** (0.0554)

-0.0881 (0.056)

Observations

245,185

Dish

Detergent

Coefficient (Std.)

0.8123

0.038*** (0.0043)

0.4862*** (0.1382)

-0.4511*** (0.1376)

Observations

189,633

Fabric

Softener

Coefficient (Std.)

0.7951

0.0181*** (0.0048)

0.9508*** (0.2067)

-0.9307*** (0.208)

Observations

181,056

Front−End−C

andies

Coefficient (Std.)

0.8611

0.0045

(0.0042)

0.8471*** (0.075)

-0.8406*** (0.0755)

Observations

278,853

Frozen

Dinners

Coefficient (Std.)

0.726

0.0471*** (0.0033)

0.2111*** (0.0446)

-0.162*** (0.044)

Observations

203,191

502,792 502,792

30

Table 4 (Cont.)

Category

Correlation

Revenue

Sales volume and Revenue Correlation

(1)

(2)

(3) (4)

Frozen Entrees

Coefficient (Std.)

0.8584

0.0271*** (0.002)

0.1611*** (0.0155)

-0.1321*** (0.0153)

Observations

864,832

Frozen Juices

Coefficient (Std.)

0.9651

0.0255*** (0.005)

0.2732*** (0.068)

-0.2456*** (0.0687)

Observations

308,817

Grooming

Products

Coefficient (Std.)

0.811

0.0188*** (0.0024)

0.0026

(0.0378)

0.0162

(0.0382)

Observations

269,873

Laundry

Detergents

Coefficient (Std.)

0.9153

0.0174*** (0.0031)

0.3272***

(0.061)

-0.311***

(0.0604)

Observations

272,765

Oatmeal

Coefficient (Std.)

0.8775

0.0293*** (0.0082)

-0.0121

(0.0248)

0.0416

(0.0255)

Observations

79,983

Paper Towels

Coefficient (Std.)

0.7593

0.0395*** (0.0107)

0.8975***

(0.204)

-0.8574***

(0.2028)

Observations

116,204

Refrigerated

Juices

Coefficient (Std.)

0.9201

0.0351*** (0.0048)

0.1247** (0.0586)

-0.09

(0.0592)

Observations

306,865

Shampoos

Coefficient (Std.)

0.7226

0.0162*** (0.0015)

0.0171

(0.0162)

-0.0008 (0.0162)

Observations

261,778

Snack

Crackers

Coefficient (Std.)

0.9124

0.0324*** (0.0033)

0.0736 (0.083)

-0.0414 (0.0839)

Observations

398,665

Soaps

Coefficient (Std.)

0.6725

0.0359*** (0.0055)

0.4935*** (0.0435)

-0.4684*** (0.0429)

Observations

152,379

Soft Drinks

Coefficient (Std.)

0.756

0.0207*** (0.0017)

0.5154*** (0.1761)

-0.4784*** (0.1763)

Observations

1,350,618

Toothbrushes

Coefficient (Std.)

0.82

0.0202*** (0.0029)

0.045

(0.0418)

-0.0247 (0.0419)

Observations

125,380

Toothpastes

Coefficient (Std.)

0.8902

0.0137*** (0.0026)

-0.1035*** (0.0373)

0.1181*** (0.0373)

Observations

264,317

Average coefficients

0.8523

0.03397

0.1902

0.1705-

Notes: Column 1 reports the Pearson correlation coefficient between the sales volume and revenues for each category.

Columns 2–4 report the results of category-level fixed effect regressions of the probability of a small price change. The

dependent variable in all columns is “small price change,” which equals 1 if a price change of product i in store s at time

t is less or equal to 10¢, and 0 otherwise. In column 2, the main independent variable is the log of average revenue for

product i in store s over the sample period. In columns 3 and 4, we report the results of a regression that includes both

the log of the sales volume and the log of the revenue as independent variables. Column 3 reports the coefficients of the

sales volume. Column 4 reports the coefficients of the revenue. All regressions also include fixed effects for months,

years, stores, and products. We estimate separate regressions for each product category, clustering the errors by product.

* p < 10%, ** p < 5%, *** p < 1%

31

Table 5. Category-level regressions of small price changes and synchronization

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient (Std.)

0.026*** (0.0034)

0.0258*** (0.0034)

0.024*** (0.0034)

0.0245*** (0.0033)

Observations

144,461

143,780

139,228

Bath Soap

Coefficient (Std.)

0.0313*** (0.0077)

0.0307*** (0.0077)

0.0266*** (0.0086)

0.0243*** (0.0088)

Observations

15,295

15,288

13,228

10,538

Bathroom

Tissues

Coefficient (Std.)

0.0406*** (0.007)

0.0402*** (0.007)

0.0398*** (0.007)

0.0436*** (0.0073)

Observations

149,441

148,926

139,207

Beer

Coefficient (Std.)

0.0123*** (0.0013)

0.0114*** (0.0012)

0.0119*** (0.0013)

Observations

290,620

290,617

290,524

267,233

Bottled Juice

Coefficient (Std.)

0.0357*** (0.0052)

0.0356*** (0.0052)

0.0348*** (0.0052)

0.0357*** (0.0054)

Observations

496,557

496,555

496,461

485,670

Canned Soup

Coefficient (Std.)

0.0174*** (0.0056)

0.0172*** (0.0055)

0.0169*** (0.0056)

Observations

495,543

495,276

490,981

Canned Tuna

Coefficient (Std.)

0.0229*** (0.0053)

0.0226*** (0.0053)

0.023*** (0.0053)

0.0234*** (0.0056)

Observations

213,043

212,567

202,922

Cereals

Coefficient (Std.)

0.0205*** (0.0037)

0.0195*** (0.0035)

0.0205*** (0.0034)

Observations

357,120

357,077

352,500

Cheese

Coefficient (Std.)

0.02*** (0.0028)

0.0198*** (0.0028)

0.0198*** (0.003)

Observations

796,150

796,148

796,142

758,753

Cigarettes

Coefficient (Std.)

0.007

(0.0051)

0.0076 (0.005)

0.0081

(0.0051)

0.0091* (0.0047)

Observations

36,157

36,152

35,824

35,408

Cookies

Coefficient (Std.)

0.0272*** (0.0019)

0.0278*** (0.0019)

0.0275*** (0.0019)

0.0277*** (0.0019)

Observations

688,761

688,759

688,726

681,886

Crackers

Coefficient (Std.)

0.0378*** (0.0031)

0.0379*** (0.0031)

0.0369*** (0.003)

0.0359*** (0.003)

Observations

245,185

245,183

244,898

236,163

Dish

Detergent

Coefficient (Std.)

0.0396*** (0.0045)

0.0387*** (0.0045)

0.0372*** (0.0043)

0.0394*** (0.0041)

Observations

189,633

189,182

185,996

Fabric

Softener

Coefficient (Std.)

0.0255*** (0.0048)

0.0252*** (0.0048)

0.0227*** (0.0047)

0.0239*** (0.0048)

Observations

181,056

180,721

168,434

Front-End-

Candies

Coefficient (Std.)

0.0042

(0.0041)

0.0032

(0.0041)

0.0054

(0.0034)

0.0064* (0.0035)

Observations

278,853

278,019

267,951

Frozen

Dinners

Coefficient (Std.)

0.0439*** (0.0037)

0.0426*** (0.0036)

Observations

203,191

203,064

202,953

32

Table 5. (Cont.) Category-level regressions of small price changes, synchronization

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient (Std.)

0.0317*** (0.0023)

0.0318*** (0.0023)

0.0309*** (0.0022)

0.0305*** (0.0022)

Observations

864,832

864,819

862,193

Frozen Juices

Coefficient (Std.)

0.0277*** (0.0048)

0.0279*** (0.0048)

0.0273*** (0.0046)

0.0273*** (0.0045)

Observations

308,817

308,802

298,899

Grooming

Products

Coefficient (Std.)

0.0188*** (0.0024)

0.019*** (0.0024)

0.0186*** (0.0024)

0.0186*** (0.0025)

Observations

269,873

269,872

269,780

268,124

Laundry

Detergents

Coefficient (Std.)

0.02*** (0.0033)

0.0198*** (0.0033)

0.0178*** (0.0032)

0.0176*** (0.0033)

Observations

272,765

272,695

269,543

Oatmeal

Coefficient (Std.)

0.0281*** (0.0079)

0.0281*** (0.008)

0.0282*** (0.0079)

0.0255*** (0.0081)

Observations

79,983

78,341

71,261

Paper Towels

Coefficient (Std.)

0.0447*** (0.0104)

0.0436*** (0.0103)

0.048*** (0.0109)

Observations

116,204

115,754

108,011

Refrigerated

Juices

Coefficient (Std.)

0.035*** (0.0046)

0.0352*** (0.0046)

0.0335*** (0.0044)

0.0344*** (0.0043)

Observations

306,865

306,841

293,807

Shampoos

Coefficient (Std.)

0.0146*** (0.0016)

0.0138*** (0.0016)

0.0128*** (0.0016)

0.0127*** (0.0016)

Observations

261,778

261,740

257,886

Snack

Crackers

Coefficient (Std.)

0.0338*** (0.0032)

0.0335*** (0.0032)

0.0328*** (0.0031)

0.0328*** (0.003)

Observations

398,665

398,573

389,240

Soaps

Coefficient (Std.)

0.0375*** (0.0056)

0.0372*** (0.0055)

0.0348*** (0.0055)

0.0345*** (0.0056)

Observations

152,379

152,104

149,407

Soft Drinks

Coefficient (Std.)

0.02*** (0.0019)

0.0197*** (0.0019)

0.0199*** (0.0019)

0.02*** (0.0019)

Observations

1,350,618

1,350,617

1,350,613

1,337,747

Toothbrushes

Coefficient (Std.)

0.023*** (0.0028)

0.0219*** (0.0028)

0.0204*** (0.003)

0.0205*** (0.0029)

Observations

125,380

124,743

122,787

Toothpastes

Coefficient (Std.)

0.0112*** (0.0026)

0.0093*** (0.0026)

0.0062** (0.0026)

0.0067*** (0.0026)

Observations

264,317

264,156

260,282

Average coefficients

0.0261

0.0259

0.0249

0.0253

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or equal to 10¢, and 0 otherwise. The main independent variable is the log of the average sales volume of product i in

store s over the sample period. Column 1 reports the results of a regression that includes the log of average sales

volume and the average number of products offered in the category by the same producer. In column 2, we add the

percentage of the products whose prices changed in the same week, excluding the current observation. In column 3,

we add the average size of contemporaneous price changes, excluding the current observation. In column 4, we add

the percentage of the products that are produced by the same producer and that changed price in the same week,

excluding the current observation. All regressions include fixed effects for months, years, stores, and products. We

estimate separate regressions for each product category, clustering the errors by product. * p < 10%, ** p < 5%, *** p

< 1%

33

Figure 1. Frequency of small price changes by sales volume deciles

Notes: The chart was obtained by merging all 29 product categories and dividing the resulting data into deciles

according to the products’ sales volume. The % of small price changes

( ¢0 )1P

was calculated for each decile

as a ratio of the number of small price changes to the number of total price changes in each decile.

34

Figure 2. Frequency of price changes by size for high, medium, and low sales volume

products

35

Figure 2. (Cont.)

Notes: For each category, the figure shows the frequency of price changes for each size of price change from 1¢ to

50¢, comparing high sales volume products to medium sales volume products, and low sales volume products. To

obtain the figures, we compute the average sales volume over the entire sample period for each product, in each

store. We then group the products into high, medium, and low sales volume products. High (low) sales volume

products are products in the high (low) third of the distribution. Medium sales volume products are in the middle

third of the distribution. The y-axis shows the frequency of price changes. The red dashed line depicts the frequency

of price changes for the high sales-volume products, the purple dotted line depicts the frequency of price changes

for the medium sales-volume products, and the blue solid line depicts the frequency of price changes for the low

sales volume products. The green shaded area marks the range of small price changes,

10¢P

.

36

Figure 3. Product-level correlations between sales volume and small price changes in

the Bathroom Tissues Category

Note: The figure depicts the correlation between average sales volume (x-axis) and the percentage of small price

changes for various products in the bathroom tissues category. Each dot in the figures represents the data for the

product in a specific store. There are 93 dots in each figure, one for each store. The straight lines in the figures are

the regression lines. Black solid regression lines indicate that the regression coefficient is significant at the 5%

significance level, which is the case for 8 of the 13 products. The regression lines that are not statistically significant

are marked with red dotted lines.

1

Online Supplementary Web Appendix

Not for Publication

Small Price Changes, Sales Volume, and Menu Cost

Doron Sayag

Department of Economics, Bar-Ilan University

Ramat-Gan 5290002, Israel

DoronSayag2@gmail.com

Avichai Snir

Department of Economics, Bar-Ilan University

Ramat-Gan 5290002, Israel

snirav@biu.ac.il

Daniel Levy

Department of Economics, Bar-Ilan University

Ramat-Gan 5290002, Israel,

Department of Economics, Emory University

Atlanta, GA 30322, USA,

ICEA, ISET at TSU (Georgia), and RCEA

Daniel.Levy@biu.ac.il

Revised: February 29, 2024

2

Table of Contents

Appendix A. Controlling for measurement errors 3

Appendix B. Alternative definitions of small price changes 10

Appendix C. Using all price changes 34

Appendix D. Using a rolling 52-week window to calculate the average 41

sales volume

Appendix E. Adding Dominick’s pricing zones 45

Appendix F. Robustness of the Product-level regressions of the % of small 49

price changes and sales volume

Appendix G. Robustness: sales volume, revenue, and small price changes 55

Appendix H. Producers’ size and the robustness of the correlation 64

between small price changes and sales volumes

Appendix I. Results of cross-category analysis 71

Appendix J. Sales volume, markup, and small price changes 80

Appendix K. Category level correlation between sales volumes and the 83

size of price changes

Appendix L. Frequency of price changes by size for high, medium, and 86

low sales volume products – in percentage terms

Appendix M. National brand vs. private label products 90

Appendix N. Sales volumes, small price changes, and holidays 103

Appendix O. The likelihood of a price change, irrespective of its size 108

Appendix P. Controlling for peak days 114

Appendix Q. Estimation using only data on products what are sold in 120

single units

Appendix R. Storable vs. non-storable products 124

Appendix S. The correlation between the sales volume and the 127

likelihood of price increases vs. decreases

References 134

3

Appendix A. Controlling for measurement errors

We use a scanner dataset. As Eichenbaum et al. (2014) note, the distribution of the

size of price changes in scanner datasets is prone to measurement errors. The errors may

arise because, in scanner datasets, the price of a product in a given week is calculated as

the ratio of the sales revenue to the quantity sold. Thus, if the price has changed during

the week, or if some consumers used coupons, the price in the dataset might differ from

the actual transaction price in that week.

This type of error is less of a concern in Dominick’s dataset, because prices at

Dominick’s are set on a weekly basis, and the use of coupons in the period we study was

limited. See Barsky et al. (2003), Chen et al. (2008), and Levy et al. (2010, 2011).

Nevertheless, to mitigate possible concerns, we use in the paper only those price change

observations after which the price has remained unchanged for at least 2 weeks. If a price

remains unchanged for more than one week, then it is unlikely to be a mistake, since it is

unlikely that the same error occurred two weeks in a row.

In this appendix, we conduct two more robustness checks. First, Table A1

presents the results of regressions equivalent to the regressions we present in Table 3 in

the paper. This time, however, we include all price changes but exclude price changes

smaller or equal to 2¢. Eichenbaum et al. (2014) suggest that such small price changes

could be the result of measurement errors. Alvarez et al. (2016) also use Dominick’s data,

and they remove observations on price changes of 1¢. We, therefore, are more

conservative by using a stricter rule than Alvarez et al. (2016). The regressions take the

following form:

, , , , ,

,,

ln( )

i s t i s i s t

t t s i i s t

small price change average sales volume

month year u

  



  

    

X

(A1)

where small price change is a dummy that equals 1 if a price change of product i in store

s at time t is less or equal to 10¢ and larger than 2¢, and 0 otherwise. The average sales

volume is the average sales volume of product i in store s over the sample period. X is a

matrix of other control variables. Month and year are fixed effects for the month and the

year of the price change.



and



are fixed effects for stores and products. u is an i.i.d

error term. We estimate separate regressions for each product category, clustering the

4

errors by product.

The values in Table A1 are the coefficients of the log of the average sales volume. In

column 1, the only control variables are the log of the average sales volume, and the

dummies for months, years, stores, and products. Consistent with the results we report in

the paper, we find that all the coefficients of the log of the average sales volume are

positive. 28 of the 29 coefficients are statistically significant. The average coefficient is

0.030, suggesting that a 1% increase in the sales volume is associated with a 3% increase

in the likelihood of a small price change.

In column 2, we add controls for the log of the average price, the log of the absolute

change in the wholesale price, and for sale- and bounce-back prices, which we identify

using the sales filter algorithm of Fox and Syed (2016). All the coefficients are positive

and statistically significant: 26 at the 1% level, two at the 5% level, and one at the 10%

level. The average coefficient is 0.025, suggesting that a 1% increase in the sales volume

is associated with a 2.5% increase in the likelihood of a small price change.

In column 3, we also add control for 9-ending prices. All coefficients remain

positive and statistically significant: 26 at the 1% level, one at the 5%, and two at the

10% level. The average coefficient is 0.023, suggesting that a 1% increase in the sales

volume is associated with a 2.3% increase in the likelihood of a small price change.

As a further control for the possible effects of sales on the results, in column 4 we

focus on regular prices by excluding all sale- and bounce-back prices. When we focus on

regular prices, the results are even stronger. All the coefficients are positive and

statistically significant at the 1% level. The average coefficient is 0.045, suggesting that a

1% increase in the sales volume is associated with a 4.5% increase in the likelihood of a

small price change.

As a second robustness test, we re-run the above regressions, after dropping

observations if Dominick’s sales flag indicated that there was a coupon use in either the

week the price changed or in the preceding week because according to Eichenbaum et al.

(2014), that might lead to spurious small price changes.

Table A2 reports the estimation results. The coefficient estimates are similar in

sign, magnitude, and statistical significance, to the corresponding figures in Table A1. In

all columns, the coefficient estimates are positive and significant, ranging between 0.025

5

and 0.046, on average.

To summarize, the exclusion of (a) very small price changes, or (b) the exclusion of

observations with coupon use, do not change our main result. The likelihood of small

price changes remains strongly correlated with the average sales volume. We, therefore,

conclude that our results are not likely to be driven by measurement errors.

6

Table A1. Category-level regressions of small price changes

(0¢)1P

and sales volume

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient

(Std.)

0.0343***

(0.0031)

0.0271***

(0.0026)

0.0224***

(0.0025)

0.044***

(0.0057)

Observations

275,225

73,576

Bath Soap

Coefficient

(Std.)

0.0396***

(0.0085)

0.044***

(0.0088)

0.0417***

(0.0086)

0.0897***

(0.0162)

Observations

35,377

6,362

Bathroom

Tissues

Coefficient

(Std.)

0.0311***

(0.0051)

0.019***

(0.0055)

0.0165***

(0.0052)

0.04***

(0.0071)

Observations

288,963

58,189

Beer

Coefficient

(Std.)

0.0212***

(0.0013)

0.023***

(0.0011)

0.0198***

(0.001)

0.0673***

(0.005)

Observations

456,740

54,870

Bottled Juice

Coefficient

(Std.)

0.0457***

(0.0042)

0.0343***

(0.0031)

0.0304***

(0.0032)

0.0395***

(0.0049)

Observations

881,264

188,079

Canned Soup

Coefficient

(Std.)

0.0202***

(0.0041)

0.0109***

(0.0037)

0.0121***

(0.0036)

0.0268***

(0.0051)

Observations

814,575

191,616

Canned Tuna

Coefficient

(Std.)

0.0322***

(0.0051)

0.0246***

(0.0045)

0.0216***

(0.0043)

0.0361***

(0.0057)

Observations

330,897

89,246

Cereals

Coefficient

(Std.)

0.0177***

(0.0025)

0.0144***

(0.0023)

0.0135***

(0.0024)

0.0251***

(0.0038)

Observations

685,899

227,390

Cheese

Coefficient

(Std.)

0.0301***

(0.0029)

0.0189***

(0.0024)

0.0159***

(0.0024)

0.0123***

(0.0044)

Observations

1,615,593

371,129

Cigarettes

Coefficient

(Std.)

0.0131

(0.0081)

0.0144*

(0.0071)

0.014*

(0.007)

0.0148***

(0.005)

Observations

15,395

9,130

Cookies

Coefficient

(Std.)

0.0348***

(0.0016)

0.0317***

(0.0016)

0.0273***

(0.0015)

0.05***

(0.0031)

Observations

1,305,448

205,310

Crackers

Coefficient

(Std.)

0.044***

(0.0029)

0.0365***

(0.0027)

0.0334***

(0.0026)

0.0516***

(0.0052)

Observations

453,298

78,127

Dish

Detergent

Coefficient

(Std.)

0.0377***

(0.0037)

0.03***

(0.003)

0.0273***

(0.0029)

0.04***

(0.0047)

Observations

374,089

76,206

Fabric

Softener

Coefficient

(Std.)

0.0246***

(0.0036)

0.0176***

(0.0033)

0.0153***

(0.0034)

0.0378***

(0.0053)

Observations

357,746

86,846

Front-End-

Candies

Coefficient

(Std.)

0.0238***

(0.0036)

0.0146***

(0.0028)

0.0139***

(0.0028)

0.0121***

(0.0033)

Observations

415,331

121,111

Frozen

Dinners

Coefficient

(Std.)

0.0457***

(0.0026)

0.0381***

(0.0025)

0.0373***

(0.0025)

0.101***

(0.0067)

Observations

477,997

57,704

7

Table A1. (Cont.)

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient

(Std.)

0.0321***

(0.0016)

0.0284***

(0.0015)

0.0279***

(0.0015)

0.0572***

(0.0034)

Observations

1,768,979

295,796

Frozen Juices

Coefficient

(Std.)

0.0262***

(0.0036)

0.0216***

(0.0033)

0.0196***

(0.0032)

0.0308***

(0.0059)

Observations

602,210

112,532

Grooming

Products

Coefficient

(Std.)

0.0394***

(0.0022)

0.0426***

(0.002)

0.0379***

(0.002)

0.0637***

(0.0061)

Observations

658,707

95,757

Laundry

Detergents

Coefficient

(Std.)

0.0156***

(0.0029)

0.0133***

(0.0025)

0.0112***

(0.0023)

0.025***

(0.0047)

Observations

580,679

135,575

Oatmeal

Coefficient

(Std.)

0.0241***

(0.007)

0.0153**

(0.0059)

0.0139***

(0.0059)

0.0416***

(0.0073)

Observations

154,817

51,510

Paper Towels

Coefficient

(Std.)

0.0306***

(0.0119)

0.0255**

(0.0125)

0.0245*

(0.0127)

0.0359***

(0.0119)

Observations

215,951

36,645

Refrigerated

Juices

Coefficient

(Std.)

0.0239***

(0.0032)

0.0179***

(0.0028)

0.0158***

(0.0027)

0.029***

(0.0047)

Observations

749,239

127,091

Shampoos

Coefficient

(Std.)

0.0293***

(0.0013)

0.0337***

(0.0013)

0.0295***

(0.0012)

0.0644***

(0.0042)

Observations

708,002

83,652

Snack

Crackers

Coefficient

(Std.)

0.0365***

(0.0029)

0.0338***

(0.0028)

0.0305***

(0.0026)

0.0621***

(0.0041)

Observations

770,442

127,881

Soaps

Coefficient

(Std.)

0.0231***

(0.0011)

0.0205***

(0.0009)

0.0171***

(0.0008)

0.0442***

(0.0023)

Observations

4,243,492

305,545

Soft Drinks

Coefficient

(Std.)

0.0415***

(0.0058)

0.0342***

(0.0042)

0.0286***

(0.004)

0.0562***

(0.0069)

Observations

300,763

71,459

Toothbrushes

Coefficient

(Std.)

0.0248***

(0.0029)

0.0276***

(0.003)

0.0237***

(0.0029)

0.0562***

(0.0059)

Observations

291,093

42,658

Toothpastes

Coefficient

(Std.)

0.0242***

(0.0029)

0.0247***

(0.0025)

0.0218***

(0.0024)

0.0507***

(0.0059)

Observations

584,401

84,802

Average coefficients

0.0299

0.0255

0.0229

0.0450

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or equal to 10¢ and larger than 2¢, and 0 otherwise. The main independent variable is the log of the average sales

volume of product i in store s over the sample period. Column 1 reports the results of the baseline regression that

includes only the log of the average sales volume and the fixed effects for months, years, stores, and products. In

column 2, we add the following controls: the natural log of the average price, the natural log of the absolute change in

the wholesale price, and control for sale- and bounce-back prices, which we identify using a sales filter algorithm. In

column 3, we add a dummy for 9-ending prices as an additional control. In column 4, we focus on regular prices by

excluding the sale- and bounce-back prices. We estimate separate regressions for each product category, clustering the

errors by product. * p < 10%, ** p < 5%, *** p < 1%

8

Table A2. Category-level regressions of small price changes and sales volume, excluding

coupon sales

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient

(Std.)

0.0388***

(0.0033)

0.0305***

(0.0027)

0.0248***

(0.0025)

0.0475***

(0.0057)

Observations

278,043

75,945

Bath Soap

Coefficient

(Std.)

0.0409***

(0.0093)

0.0452***

(0.0095)

0.0422***

(0.0091)

0.0871***

(0.016)

Observations

35,795

6,555

Bathroom

Tissues

Coefficient

(Std.)

0.0372***

(0.0056)

0.0203***

(0.0053)

0.0177***

(0.0049)

0.0351***

(0.0069)

Observations

326,382

81,914

Beer

Coefficient

(Std.)

0.023***

(0.0015)

0.0249***

(0.0012)

0.0208***

(0.0012)

0.0691***

(0.005)

Observations

459,669

56,427

Bottled Juice

Coefficient

(Std.)

0.0554***

(0.0043)

0.0393***

(0.003)

0.0343***

(0.0031)

0.0368***

(0.0045)

Observations

959,958

244,198

Canned Soup

Coefficient

(Std.)

0.0272***

(0.004)

0.0151***

(0.0034)

0.0158***

(0.0033)

0.0217***

(0.0038)

Observations

947,633

278,451

Canned Tuna

Coefficient

(Std.)

0.037***

(0.0052)

0.0266***

(0.0044)

0.0225***

(0.0041)

0.0334***

(0.0047)

Observations

375,343

116,170

Cereals

Coefficient

(Std.)

0.0216***

(0.0026)

0.0168***

(0.0023)

0.0156***

(0.0024)

0.0263***

(0.0035)

Observations

724,232

260,035

Cheese

Coefficient

(Std.)

0.0374***

(0.0029)

0.0208***

(0.0022)

0.0168***

(0.0022)

0.0116***

(0.0031)

Observations

1,811,792

519,225

Cigarettes

Coefficient

(Std.)

0.019***

(0.0082)

0.0203***

(0.0068)

0.0197***

(0.0067)

0.0215***

(0.0045)

Observations

15,862

9,593

Cookies

Coefficient

(Std.)

0.0429***

(0.0017)

0.0372***

(0.0017)

0.0315***

(0.0015)

0.0542***

(0.0031)

Observations

1,356,845

229,139

Crackers

Coefficient

(Std.)

0.0544***

(0.0033)

0.0431***

(0.0031)

0.0389***

(0.0029)

0.0563***

(0.0061)

Observations

475,368

89,210

Dish

Detergent

Coefficient

(Std.)

0.0481***

(0.0038)

0.0357***

(0.003)

0.0315***

(0.0029)

0.0417***

(0.0043)

Observations

401,001

95,477

Fabric

Softener

Coefficient

(Std.)

0.0342***

(0.0038)

0.0245***

(0.0034)

0.0209***

(0.0035)

0.0428***

(0.0049)

Observations

378,773

101,926

Front-End-

Candies

Coefficient

(Std.)

0.0165***

(0.0039)

0.0091***

(0.0028)

0.0082***

(0.0028)

0.0113***

(0.0031)

Observations

490,220

155,203

Frozen

Dinners

Coefficient

(Std.)

0.0536***

(0.0027)

0.0408***

(0.0025)

0.0394***

(0.0025)

0.0907***

(0.006)

Observations

502,792

72,693

9

Table A2. (Cont.)

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient

(Std.)

0.0354***

(0.0019)

0.0301***

(0.0017)

0.0292***

(0.0017)

0.0602***

(0.0032)

Observations

1,848,166

353,120

Frozen Juices

Coefficient

(Std.)

0.0342***

(0.0037)

0.0253***

(0.0031)

0.0227***

(0.003)

0.03***

(0.0048)

Observations

659,295

150,129

Grooming

Products

Coefficient

(Std.)

0.0426***

(0.0024)

0.0455***

(0.0022)

0.039***

(0.0021)

0.0673***

(0.0061)

Observations

668,809

99,252

Laundry

Detergents

Coefficient

(Std.)

0.0185***

(0.0031)

0.0155***

(0.0027)

0.0126***

(0.0025)

0.0264***

(0.0047)

Observations

594,247

145,167

Oatmeal

Coefficient

(Std.)

0.0288***

(0.0071)

0.0172***

(0.0052)

0.0151***

(0.0052)

0.0319***

(0.0094)

Observations

168,988

63,575

Paper Towels

Coefficient

(Std.)

0.0376***

(0.0114)

0.0296***

(0.0116)

0.0284***

(0.0117)

0.0376***

(0.0096)

Observations

244,037

52,321

Refrigerated

Juices

Coefficient

(Std.)

0.031***

(0.0032)

0.0209***

(0.0027)

0.0182***

(0.0026)

0.0305***

(0.0041)

Observations

800,176

161,074

Shampoos

Coefficient

(Std.)

0.0323***

(0.0014)

0.0368***

(0.0014)

0.032***

(0.0013)

0.0674***

(0.0043)

Observations

713,652

86,458

Snack

Crackers

Coefficient

(Std.)

0.0435***

(0.0032)

0.0382***

(0.003)

0.0338***

(0.0027)

0.066***

(0.004)

Observations

801,599

143,154

Soaps

Coefficient

(Std.)

0.0306***

(0.0014)

0.0265***

(0.001)

0.0223***

(0.0009)

0.0586***

(0.0027)

Observations

4,372,346

346,106

Soft Drinks

Coefficient

(Std.)

0.0545***

(0.006)

0.0413***

(0.0044)

0.0336***

(0.0042)

0.0555***

(0.0057)

Observations

333,170

94,295

Toothbrushes

Coefficient

(Std.)

0.0291***

(0.0032)

0.0317***

(0.0034)

0.0265***

(0.0032)

0.0618***

(0.006)

Observations

295,275

44,690

Toothpastes

Coefficient

(Std.)

0.0289***

(0.0032)

0.028***

(0.0027)

0.0241***

(0.0026)

0.0561***

(0.0063)

Observations

596,900

91,759

Average coefficients

0.0356

0.0288

0.0254

0.0461

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or equal to 10¢, and 0 otherwise. We exclude observations on price changes if Dominick’s sales flag indicates a coupon

sale in either week t or t − 1. The main independent variable is the log of the average sales volume of product i in store

s over the sample period. Column 1 reports the results of the baseline regression that includes only the log of the

average sales volume and fixed effects for months, years, stores, and products. In column 2, we add the following

controls: the natural log of the average price, the natural log of the absolute change in the wholesale price, and control

for sale- and bounce-back prices, which we identify using a sales filter algorithm. In column 3, we add a dummy for

9-ending prices as an additional control. In column 4, we focus on regular prices by excluding the sale- and bounce-

back prices. We estimate separate regressions for each product category, clustering the errors by product. * p < 10%,

** p < 5%, *** p < 1%

10

Appendix B. Alternative definitions of small price changes

In the paper, we define a small price change as a price change smaller than or equal

to 10¢. In this appendix, we repeat our main analyses using 8 alternative definitions of

small price changes. First, we define small price changes as (1) price changes up to, and

including, 5¢, (2) price changes up to, and including, 15¢, (3) price changes up to, and

including 2%, and (4) price changes up to, and including, 5%.

Second, we follow Midrigan (2011) and Bhattarai and Schoenle (2014) to define

small price changes relative to the average price change in the corresponding category.

I.e., a price change is small if it is smaller than or equal to 



, where 



 is the

average price change of product  in store , and  attains the values 0.5, 0.33, 0.25 and

0.10.

As we do in the paper, we use observations on price changes only if we observe the

price in both weeks t and t + 1 and the post-change price remained unchanged for at least

2 weeks.

Table B1 presents the results of regressions equivalent to the regressions in Table 3

in the paper. The regressions take the following form:

, , , , ,

,,

ln( )

i s t i s i s t

t t s i i s t

small price change average sales volume

month year u

  



  

    

X

(B1)

where small price change is a dummy that equals 1 if a price change of product i in store

s at time t is less or equal to 5¢, and 0 otherwise. The average sales volume is the average

sales volume of product i in store s over the sample period. X is a matrix of other control

variables. Month and year are fixed effects for the month and the year of the price

change.



and



are fixed effects for stores and products, respectively, and u is an i.i.d

error term. We estimate separate regressions for each product category, clustering the

errors by product.

The values in the table are the coefficients of the log of the average sales volume. In

column 1, the only control variables are the log of the average sales volume, and the

dummies for months, years, stores, and products. We find that 28 of the coefficients of

the log of the average sales volume are positive, 16 of them are statistically significant.

The average coefficient is 0.010, suggesting that a 1% increase in the sales volume is

11

associated with a 1.0% increase in the likelihood of a small price change.

In column 2, we add controls for the log of the average price, the log of the absolute

change in the wholesale price, and a control for sale- and bounce-back prices, which we

identify using the sales filter algorithm of Fox and Syed (2016). 27 of the coefficients are

positive, 13 of the 27 are statistically significant, and 2 more are marginally statistically

significant. The average coefficient is 0.007, suggesting that a 1% increase in the sales

volume is associated with a 0.7% increase in the likelihood of a small price change.

In column 3, we also add control for 9-ending prices. 27 of the coefficients are

positive, 14 of them statistically significant, and 3 more are marginally statistically

significant. The average coefficient is 0.008, suggesting that a 1% increase in the sales

volume is associated with a 0.8% increase in the likelihood of a small price change.

As a further control for the effects of sales on the results, in column 4 we focus on

regular prices by excluding all sale- and bounce-back prices. We find that 28 coefficients

are positive. 20 of the positive coefficients are statistically significant, and 2 more are

statistically significant at the 10% level. The average coefficient is 0.019, suggesting that

a 1% increase in the sales volume is associated with a 1.9% increase in the likelihood of a

small price change.

Table B2 presents the results of similar regressions, where we define small price

changes as price changes of up to, and including, 15¢. In column 1, the only control

variables are the log of the average sales volume, and the dummies for months, years,

stores, and products. We find that 26 of the coefficients of the log of the average sales

volume are positive. 17 of the 26 are statistically significant, and 2 more are marginally

statistically significant. The average coefficient is 0.016, suggesting that a 1% increase in

the sales volume is associated with a 1.6% increase in the likelihood of a small price

change.

In column 2, we add controls for the log of the average price, the log of the absolute

change in the wholesale price, and a control for sale- and bounce-back prices, which we

identify using the sales filter algorithm of Fox and Syed (2016). 25 of the coefficients are

positive. 13 of the positive coefficients are statistically significant, and 2 more are

marginally statistically significant. The average coefficient is 0.012, suggesting that a 1%

increase in the sales volume is associated with a 1.2% increase in the likelihood of a

12

small price change.

In column 3, we also add control for 9-ending prices. 25 of the coefficients are

positive. 13 of the positive coefficients are statistically significant, and 5 more are

marginally statistically significant. The average coefficient is 0.012, suggesting that a 1%

increase in the sales volume is associated with a 1.2% increase in the likelihood of a

small price change.

As a further control for the effects of sales on the results, in column 4 we focus on

regular prices by excluding all sale- and bounce-back prices. 26 of the coefficients are

positive. 17 of the 26 are statistically significant, and 2 more are statistically significant at

the 10% level. The average coefficient is 0.019, suggesting that a 1% increase in the sales

volume is associated with a 1.9% increase in the likelihood of a small price change.

Table B3 presents the results where we define small price changes as price changes

of up to 2%. In column 1, the only control variables are the log of the average sales

volume, and the dummies for months, years, stores, and products. We find that 27 of the

29 coefficients of the log of the average sales volume are positive. Out of the 27, 20 are

statistically significant, and 3 more are statistically significant at the 10% level. The

average coefficient is 0.009, suggesting that a 1% increase in the sales volume is

associated with a 0.9% increase in the likelihood of a small price change.

In column 2, we add controls for the log of the average price, the log of the absolute

change in the wholesale price, and a control for sale- and bounce-back prices, which we

identify using the sales filter algorithm of Fox and Syed (2016). We find that 27 of the 29

coefficients are positive. 17 of the 27 are statistically significant, and 6 more are

statistically significant at the 10% level. The average coefficient is 0.007, suggesting that

a 1% increase in the sales volume is associated with a 0.7% increase in the likelihood of a

small price change.

In column 3, we also add a control for 9-ending prices. 27 of the 29 coefficients are

still positive. 17 of the 27 are statistically significant, and 5 more are statistically

significant at the 10% level. The average coefficient is 0.007, suggesting that a 1%

increase in the sales volume is associated with a 0.7% increase in the likelihood of a

small price change.

As a further control for the effects of sales on the results, in column 4 we focus on

13

regular prices by excluding all sale- and bounce-back prices. When we focus on regular

prices, 28 of the 29 coefficients are positive. 17 of the positive coefficients are

statistically significant, and 3 more are marginally statistically significant. The average

coefficient is 0.015, suggesting that a 1% increase in the sales volume is associated with a

1.5% increase in the likelihood of a small price change.

Table B4 presents the results where we define small price changes as price changes

up to 5%. In column 1, the only control variables are the log of the average sales volume,

and the dummies for months, years, stores, and products. We find that 23 coefficients of

the log of the average sales volume are positive. 17 of them are statistically significant,

and 2 more are marginally statistically significant. The average coefficient is 0.015,

suggesting that a 1% increase in the sales volume is associated with a 1.5% increase in

the likelihood of a small price change.

In column 2, we add controls for the log of the average price, the log of the absolute

change in the wholesale price, and a control for sale- and bounce-back prices, which we

identify using the sales filter algorithm of Fox and Syed (2016). 23 of the coefficients are

positive. 15 of the positive coefficients are statistically significant, and 2 more are

marginally statistically significant. The average coefficient is 0.010, suggesting that a 1%

increase in the sales volume is associated with a 1.0% increase in the likelihood of a

small price change.

In column 3, we also add a control for 9-ending prices. 23 of the coefficients are

positive. 15 of the 23 are statistically significant, and 2 more are marginally statistically

significant. The average coefficient is 0.010, suggesting that a 1% increase in the sales

volume is associated with a 1.0% increase in the likelihood of a small price change.

As a further control for the effects of sales on the results, in column 4 we focus on

regular prices by excluding all sale- and bounce-back prices. When we focus on regular

prices, 28 of the coefficients are positive. 16 of the 28 are statistically significant, and 2

more are marginally statistically significant. The average coefficient is 0.021, suggesting

that a 1% increase in the sales volume is associated with a 2.1% increase in the likelihood

of a small price change.

Table B5 presents the results where we define small price changes as price changes

of up to 50% of the average price change of the product-store. In other words, a price

14

change, , of product  in store  in week is small if   



, where





 is the average size of a price change of product  in store . In column 1, the only

control variables are the log of the average sales volume, and dummies for months, years,

stores, and products. We find that 26 of the coefficients are positive. 22 of the positive

coefficients are statistically significant, and 1 more is marginally statistically significant.

The average coefficient is 0.021, suggesting that a 1% increase in the sales volume is

associated with a 2.1% increase in the likelihood of a small price change.

In column 2, we add controls for the log of the average price, the log of the absolute

change in the wholesale price, and a control for sale- and bounce-back prices, which we

identify using the sales filter algorithm of Fox and Syed (2016). We find that 26 of the

coefficients are positive. 18 of the 26 are statistically significant, and 2 more are

marginally statistically significant. The average coefficient is 0.020, suggesting that a 1%

increase in the sales volume is associated with a 2.0% increase in the likelihood of a

small price change.

In column 3, we also add a control for 9-ending prices. We find that 27 of the

coefficients are positive. 18 of the 27 are statistically significant, and 2 more are

marginally statistically significant. The average coefficient is 0.020, suggesting that a 1%

increase in the sales volume is associated with a 2.0% increase in the likelihood of a

small price change.

As a further control for the effects of sales on the results, in column 4 we focus on

regular prices by excluding all sale- and bounce-back prices. When we focus on regular

prices, 28 of the 29 are statistically significant. 23 of the positive coefficients are

statistically significant, and 3 more are marginally significant. The average coefficient is

0.041, suggesting that a 1% increase in the sales volume is associated with a 4.1%

increase in the likelihood of a small price change.

Table B6 presents the results where we define small price changes as price changes

up to 33% of the average price in the category. In other words, a price change, , of

product  in store  in week is small if   



 where 



 is the average

size of a price change of product  in store . In column 1, the only control variables are

the log of the average sales volume, and dummies for months, years, stores, and products.

We find that 27 of the 29 coefficients of the log of the average sales volume are positive.

15

22 of them are statistically significant, and 2 more is marginally significant. The average

coefficient is 0.016, suggesting that a 1% increase in the sales volume is associated with a

1.6% increase in the likelihood of a small price change.

In column 2, we add controls for the log of the average price, the log of the absolute

change in the wholesale price, and a control for sale- and bounce-back prices, which we

identify using the sales filter algorithm of Fox and Syed (2016). We find that 27 of the 29

coefficients are positive. 18 of them are statistically significant, and 3 more are

marginally significant. The average coefficient is 0.015, suggesting that a 1% increase in

the sales volume is associated with a 1.5% increase in the likelihood of a small price

change.

In column 3, we also add a control for 9-ending prices. We find that 27 of the 29

coefficients are positive. 18 of them are statistically significant, and 3 more are

marginally significant. The average coefficient is 0.015, suggesting that a 1% increase in

the sales volume is associated with a 1.5% increase in the likelihood of a small price

change.

As a further control for the effects of sales on the results, in column 4 we focus on

regular prices by excluding all sale- and bounce-back prices. We find that all the

coefficients are positive and 23 of them are statistically significant. 3 more coefficients

are marginally significant. The average coefficient is 0.031, suggesting that a 1% increase

in the sales volume is associated with a 3.1% increase in the likelihood of a small price

change.

Table B7 presents the results where we define small price changes as price changes

up to 25% of the average price in the category. In other words, a price change, , of

product  in store  in week is small if   



, where 



 is the average

size of a price change of product  in store . In column 1, the only control variables are

the log of the average sales volume, and the dummies for months, years, stores, and

products. We find that 28 of the 29 coefficients of the log of the average sales volume are

positive. 22 of them are statistically significant, and 1 more is marginally significant. The

average coefficient is 0.013, suggesting that a 1% increase in the sales volume is

associated with a 1.3% increase in the likelihood of a small price change.

In column 2, we add controls for the log of the average price, the log of the absolute

16

change in the wholesale price, and a control for sale- and bounce-back prices, which we

identify using the sales filter algorithm of Fox and Syed (2016). We find that 27 of the 29

coefficients are positive. 22 of them are statistically significant. The average coefficient is

0.012, suggesting that a 1% increase in the sales volume is associated with a 1.2%

increase in the likelihood of a small price change.

In column 3, we also add a control for 9-ending prices. We find that 27 of the 29

coefficients are positive. 22 of them are statistically significant. The average coefficient is

0.012, suggesting that a 1% increase in the sales volume is associated with a 1.2%

increase in the likelihood of a small price change.

As a further control for the effects of sales on the results, in column 4 we focus on

regular prices by excluding all sale- and bounce-back prices. We find that all the

coefficients are positive and 25 of them are statistically significant at the 1% level. One

more coefficient is marginally significant. The average coefficient is 0.025, suggesting

that a 1% increase in the sales volume is associated with a 2.5% increase in the likelihood

of a small price change.

Table B8 presents the results where we define small price changes as price changes

up to 10% of the average price in the category. In other words, a price change, , of

product  in store  in week is small if   



, where 



 is the average

size of a price change of product  in store . In column 1, the only control variables are

the log of the average sales volume, and the dummies for months, years, stores, and

products. We find that 24 of the 29 coefficients of the log of the average sales volume are

positive. 19 of them are statistically significant, and 2 more are marginally significant.

The average coefficient is 0.004, suggesting that a 1% increase in the sales volume is

associated with a 0.4% increase in the likelihood of a small price change.

In column 2, we add controls for the log of the average price, the log of the absolute

change in the wholesale price, and a control for sale- and bounce-back prices, which we

identify using the sales filter algorithm of Fox and Syed (2016). We find that 25 of the 29

coefficients are positive. 20 of them are statistically significant, and 2 more are

marginally significant. The average coefficient is 0.005, suggesting that a 1% increase in

the sales volume is associated with a 0.5% increase in the likelihood of a small price

change.

17

In column 3, we also add a control for 9-ending prices. We find that 25 of the 29

coefficients are positive. 20 of them are statistically significant, and 2 more are

marginally significant. The average coefficient is 0.005, suggesting that a 1% increase in

the sales volume is associated with a 0.5% increase in the likelihood of a small price

change.

As a further control for the effects of sales on the results, in column 4 we focus on

regular prices by excluding all sale- and bounce-back prices. We find that 25 of the

coefficients are positive. 20 of them are statistically significant, and 3 more are

marginally significant. The average coefficient is 0.010, suggesting that a 1% increase in

the sales volume is associated with a 1.0% increase in the likelihood of a small price

change.

18

Table B1. Category-level regressions of small price changes

(5¢)P

and sales volume

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient

(Std.)

0.0033

(0.0023)

0.0022

(0.0022)

0.0019

(0.0022)

0.0068

(0.0056)

Observations

74,451

24,729

Bath Soap

Coefficient

(Std.)

0.0128**

(0.0053)

0.0114**

(0.0051)

0.0113**

(0.0044)

0.0198

(0.0129)

Observations

6,650

1,466

Bathroom

Tissues

Coefficient

(Std.)

0.0481***

(0.0079)

0.0235***

(0.0066)

0.0233***

(0.0063)

0.0466***

(0.0074)

Observations

56,458

19,285

Beer

Coefficient

(Std.)

0.0003

(0.0002)

0.0005**

(0.0002)

0.0005**

(0.0002)

0.0051**

(0.0021)

Observations

187,691

12,080

Bottled Juice

Coefficient

(Std.)

0.0067

(0.0068)

0.0017

(0.0059)

0.0017

(0.006)

0.0398***

(0.0079)

Observations

224,857

60,015

Canned Soup

Coefficient

(Std.)

0.0055

(0.0086)

0.0028

(0.0084)

0.0052

(0.0082)

0.0148*

(0.0078)

Observations

233,779

95,310

Canned Tuna

Coefficient

(Std.)

0.0097**

(0.0047)

0.004

(0.0045)

0.0039

(0.0045)

0.0201***

(0.0064)

Observations

112,629

31,922

Cereals

Coefficient

(Std.)

0.0042

(0.0036)

0.0045

(0.0034)

0.0045

(0.0033)

0.019***

(0.0059)

Observations

141,087

72,789

Cheese

Coefficient

(Std.)

0.0004

(0.0029)

-0.0001

(0.0023)

-0.0003

(0.0023)

0.018***

(0.0051)

Observations

357,679

92,758

Cigarettes

Coefficient

(Std.)

0.0114***

(0.0021)

0.0107***

(0.0021)

0.0108***

(0.0021)

0.0114***

(0.0025)

Observations

24,553

20,692

Cookies

Coefficient

(Std.)

0.0043***

(0.001)

0.0037***

(0.001)

0.0036***

(0.001)

0.0149***

(0.0026)

Observations

317,932

66,087

Crackers

Coefficient

(Std.)

0.0006

(0.0016)

0.0001

(0.0016)

0.0002

(0.0016)

0.0141***

(0.0044)

Observations

115,658

24,771

Dish

Detergent

Coefficient

(Std.)

0.0175***

(0.003)

0.0123***

(0.0026)

0.0126***

(0.0024)

0.0289***

(0.0052)

Observations

85,222

26,735

Fabric

Softener

Coefficient

(Std.)

0.01**

(0.0044)

0.0027

(0.0039)

0.0032

(0.0039)

0.0157**

(0.0079)

Observations

85,337

27,488

Front-End-

Candies

Coefficient

(Std.)

-0.0038

(0.0034)

-0.0046

(0.0031)

-0.0045

(0.0031)

0.0011

(0.0028)

Observations

148,200

77,323

Frozen

Dinners

Coefficient

(Std.)

0.0252***

(0.0061)

0.0186***

(0.0052)

0.0198***

(0.0051)

0.0524***

(0.012)

Observations

52,893

12,287

19

Table B1. (Cont.)

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient

(Std.)

0.0132***

(0.0022)

0.0123***

(0.0019)

0.0125***

(0.0019)

0.0294***

(0.0028)

Observations

345,223

117,044

Frozen Juices

Coefficient

(Std.)

0.0185***

(0.0051)

0.0162***

(0.0044)

0.0168***

(0.0044)

0.0249***

(0.0073)

Observations

118,582

40,517

Grooming

Products

Coefficient

(Std.)

0.0028**

(0.0011)

0.0029***

(0.0011)

0.0031***

(0.0011)

0.0058

(0.0039)

Observations

101,944

22,102

Laundry

Detergents

Coefficient

(Std.)

0.0053**

(0.0024)

0.0024

(0.0022)

0.0027

(0.0022)

0.0073*

(0.0042)

Observations

121,566

42,121

Oatmeal

Coefficient

(Std.)

0.0421***

(0.0139)

0.0327***

(0.011)

0.0308***

(0.0104)

0.0564***

(0.0153)

Observations

25,523

13,605

Paper Towels

Coefficient

(Std.)

0.0113

(0.0101)

0.0095

(0.0097)

0.0107

(0.0095)

-0.006

(0.0108)

Observations

48,199

9,243

Refrigerated

Juices

Coefficient

(Std.)

0.018***

(0.0054)

0.0104*

(0.0057)

0.0104*

(0.0056)

0.0267**

(0.0108)

Observations

108,965

23,705

Shampoos

Coefficient

(Std.)

0.0007

(0.0006)

0.0008

(0.0006)

0.0008

(0.0006)

0.0038

(0.0023)

Observations

88,193

16,099

Snack

Crackers

Coefficient

(Std.)

0.0018

(0.0013)

0.0024*

(0.0013)

0.0025**

(0.0013)

0.0131***

(0.0034)

Observations

176,527

38,123

Soaps

Coefficient

(Std.)

0.0216***

(0.0084)

0.0125

(0.0082)

0.0157**

(0.0079)

0.0473***

(0.0109)

Observations

56,725

16,882

Soft Drinks

Coefficient

(Std.)

0.0026

(0.0018)

0.006***

(0.0015)

0.0048***

(0.0015)

0.0005

(0.0027)

Observations

243,837

49,989

Toothbrushes

Coefficient

(Std.)

0.0066**

(0.0026)

0.0059**

(0.0026)

0.0057**

(0.0025)

0.0121**

(0.0059)

Observations

52,185

13,695

Toothpastes

Coefficient

(Std.)

0.0036

(0.0026)

0.0036

(0.0023)

0.0038*

(0.0022)

0.0145***

(0.0055)

Observations

100,845

28,039

Average coefficients

0.0105

0.0073

0.0075

0.0195

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or equal to 5¢, and 0 otherwise. The main independent variable is the log of the average sales volume of product i in

store s over the sample period. Column 1 reports the results of the baseline regression that includes only the log of the

average sales volume and the fixed effects for months, years, stores, and products. In column 2, we add the following

controls: the log of the average price, the log of the absolute change in the wholesale price, and a control for sale- and

bounce-back prices, which we identify using a sales filter algorithm. In column 3, we add a dummy for 9-ending prices

as an additional control. In column 4, we focus on regular prices by excluding the sale- and bounce-back prices. We

estimate separate regressions for each product category, clustering the errors by product. * p < 10%, ** p < 5%, *** p

< 1%

20

Table B2. Category-level regressions of small price changes

(5¢)1P

and sales volume

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient

(Std.)

0.0177***

(0.0052)

0.0127***

(0.0049)

0.0118***

(0.0049)

0.0078*

(0.0091)

Observations

74,451

24,729

Bath Soap

Coefficient

(Std.)

0.0349**

(0.0189)

0.0296**

(0.0179)

0.0295**

(0.0177)

0.018

(0.0348)

Observations

6,650

1,466

Bathroom

Tissues

Coefficient

(Std.)

0.0592***

(0.01)

0.0333***

(0.0092)

0.0332***

(0.0094)

0.0323***

(0.0084)

Observations

56,458

19,285

Beer

Coefficient

(Std.)

0.0018***

(0.0006)

0.0042***

(0.0007)

0.0042***

(0.0007)

0.0219***

(0.0052)

Observations

187,691

12,080

Bottled Juice

Coefficient

(Std.)

0.015***

(0.0069)

0.0108**

(0.006)

0.0109**

(0.0058)

0.0161**

(0.0088)

Observations

224,857

60,015

Canned Soup

Coefficient

(Std.)

-0.0049*

(0.0056)

-0.0057*

(0.0056)

-0.0044

(0.0054)

0.0009

(0.0035)

Observations

233,779

95,310

Canned Tuna

Coefficient

(Std.)

0.0084*

(0.0077)

-0.0021

(0.0066)

-0.0022

(0.0066)

0.0098*

(0.0077)

Observations

112,629

31,922

Cereals

Coefficient

(Std.)

0.0054*

(0.0058)

0.0052*

(0.0053)

0.0052*

(0.0053)

0.0071*

(0.0061)

Observations

141,087

72,789

Cheese

Coefficient

(Std.)

0.0055**

(0.0042)

0.0052**

(0.0037)

0.0052**

(0.0037)

0.0104***

(0.0039)

Observations

357,679

92,758

Cigarettes

Coefficient

(Std.)

0.0008

(0.0046)

0

(0.0047)

0.0001

(0.0047)

-0.0025

(0.005)

Observations

24,553

20,692

Cookies

Coefficient

(Std.)

0.0117***

(0.0025)

0.0103***

(0.0024)

0.01***

(0.0023)

0.016***

(0.0043)

Observations

317,932

66,087

Crackers

Coefficient

(Std.)

0.0081***

(0.0032)

0.0081***

(0.003)

0.0083***

(0.0029)

0.0131***

(0.0053)

Observations

115,658

24,771

Dish

Detergent

Coefficient

(Std.)

0.0257***

(0.0054)

0.0194***

(0.0045)

0.0194***

(0.0045)

0.0219***

(0.0057)

Observations

85,222

26,735

Fabric

Softener

Coefficient

(Std.)

0.0138**

(0.0086)

0.0032

(0.0077)

0.0035

(0.0077)

0.0176***

(0.0086)

Observations

85,337

27,488

Front-End-

Candies

Coefficient

(Std.)

-0.0027

(0.0047)

-0.0025

(0.0034)

-0.0024

(0.0034)

-0.0012

(0.003)

Observations

148,200

77,323

Frozen

Dinners

Coefficient

(Std.)

0.0434***

(0.0076)

0.0362***

(0.0069)

0.0354***

(0.0068)

0.0729***

(0.0108)

Observations

52,893

12,287

21

Table B2. (Cont.)

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient

(Std.)

0.0209***

(0.0032)

0.0202***

(0.0029)

0.0202***

(0.0029)

0.0141***

(0.0037)

Observations

345,223

117,044

Frozen Juices

Coefficient

(Std.)

0.0177**

(0.0093)

0.0163**

(0.009)

0.0166**

(0.009)

0.0004

(0.0091)

Observations

118,582

40,517

Grooming

Products

Coefficient

(Std.)

0.0127***

(0.0039)

0.015***

(0.0038)

0.015***

(0.0038)

0.0203**

(0.0118)

Observations

101,944

22,102

Laundry

Detergents

Coefficient

(Std.)

0.0302***

(0.0055)

0.0192***

(0.0048)

0.0195***

(0.0048)

0.013***

(0.0058)

Observations

121,566

42,121

Oatmeal

Coefficient

(Std.)

0.0419***

(0.0152)

0.0366***

(0.0146)

0.037***

(0.0147)

0.0433***

(0.0171)

Observations

25,523

13,605

Paper Towels

Coefficient

(Std.)

0.014

(0.0168)

0.0084

(0.0176)

0.0084

(0.0175)

0.0279***

(0.0131)

Observations

48,199

9,243

Refrigerated

Juices

Coefficient

(Std.)

0.0236***

(0.0069)

0.013**

(0.007)

0.0131**

(0.0071)

0.0283***

(0.009)

Observations

108,965

23,705

Shampoos

Coefficient

(Std.)

0.0279***

(0.004)

0.0278***

(0.0038)

0.0278***

(0.0038)

0.0424***

(0.0114)

Observations

88,193

16,099

Snack

Crackers

Coefficient

(Std.)

-0.0041**

(0.0034)

-0.0033**

(0.0034)

-0.0031*

(0.0034)

0.0044

(0.0057)

Observations

176,527

38,123

Soaps

Coefficient

(Std.)

0.0169***

(0.0077)

0.007**

(0.007)

0.0094**

(0.0071)

0.0335***

(0.0113)

Observations

56,725

16,882

Soft Drinks

Coefficient

(Std.)

0.0079***

(0.0026)

0.0099***

(0.0025)

0.0096***

(0.0025)

-0.0003

(0.004)

Observations

243,837

49,989

Toothbrushes

Coefficient

(Std.)

0.0182***

(0.0061)

0.0119**

(0.0062)

0.0113**

(0.0061)

0.0385***

(0.013)

Observations

52,185

13,695

Toothpastes

Coefficient

(Std.)

0.0024

(0.0062)

0.0005

(0.0059)

0.0009

(0.0058)

0.0172**

(0.0088)

Observations

100,845

28,039

Average coefficients

0.0163

0.0121

0.0122

0.0188

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or equal to 15¢, and 0 otherwise. The main independent variable is the log of the average sales volume of product i in

store s over the sample period. Column 1 reports the results of the baseline regression that includes only the log of the

average sales volume and the fixed effects for months, years, stores, and products. In column 2, we add the following

controls: the log of the average price, the log of the absolute change in the wholesale price, and a control for sale- and

bounce-back prices, which we identify using a sales filter algorithm. In column 3, we add a dummy for 9-ending prices

as an additional control. In column 4, we focus on regular prices by excluding the sale- and bounce-back prices. We

estimate separate regressions for each product category, clustering the errors by product. * p < 10%, ** p < 5%, *** p

< 1%

22

Table B3. Category-level regressions of small price changes 󰇛Δ  󰇜 and sales

volume

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient

(Std.)

0.0097***

(0.0034)

0.0058**

(0.003)

0.0054**

(0.003)

0.0132**

(0.0072)

Observations

74,451

24,729

Bath Soap

Coefficient

(Std.)

0.0093**

(0.0054)

0.0085**

(0.0049)

0.0084**

(0.0046)

0.0004

(0.0127)

Observations

6,650

1,466

Bathroom

Tissues

Coefficient

(Std.)

0.022***

(0.0054)

0.0095***

(0.0044)

0.0095***

(0.0043)

0.015**

(0.0082)

Observations

56,458

19,285

Beer

Coefficient

(Std.)

0.0017***

(0.0004)

0.0034***

(0.0006)

0.0034***

(0.0006)

0.0196***

(0.004)

Observations

187,691

12,080

Bottled Juice

Coefficient

(Std.)

0.0115***

(0.0039)

0.0068***

(0.0032)

0.0068***

(0.0031)

0.0237***

(0.0095)

Observations

224,857

60,015

Canned Soup

Coefficient

(Std.)

-0.0032*

(0.0031)

-0.0038**

(0.0028)

-0.0034**

(0.0028)

-0.0061*

(0.006)

Observations

233,779

95,310

Canned Tuna

Coefficient

(Std.)

0.0069***

(0.0026)

0.0038**

(0.0023)

0.0038**

(0.0023)

0.0072*

(0.0063)

Observations

112,629

31,922

Cereals

Coefficient

(Std.)

0.01***

(0.0039)

0.011***

(0.0033)

0.011***

(0.0033)

0.0237***

(0.0063)

Observations

141,087

72,789

Cheese

Coefficient

(Std.)

0.0051**

(0.0027)

0.0043***

(0.002)

0.0042***

(0.002)

0.0149***

(0.0048)

Observations

357,679

92,758

Cigarettes

Coefficient

(Std.)

0.0041**

(0.0026)

0.0049**

(0.0026)

0.0049**

(0.0026)

0.0073***

(0.0029)

Observations

24,553

20,692

Cookies

Coefficient

(Std.)

0.0032***

(0.0008)

0.0025***

(0.0007)

0.0025***

(0.0007)

0.0073***

(0.0022)

Observations

317,932

66,087

Crackers

Coefficient

(Std.)

0.0015**

(0.0008)

0.0011**

(0.0008)

0.0012**

(0.0008)

0.0028*

(0.0031)

Observations

115,658

24,771

Dish

Detergent

Coefficient

(Std.)

0.0139***

(0.0022)

0.009***

(0.0018)

0.0091***

(0.0018)

0.0233***

(0.0047)

Observations

85,222

26,735

Fabric

Softener

Coefficient

(Std.)

0.0104***

(0.004)

0.0035*

(0.0033)

0.0037*

(0.0033)

0.0082*

(0.0078)

Observations

85,337

27,488

Front-End-

Candies

Coefficient

(Std.)

-0.002**

(0.0012)

-0.002**

(0.0011)

-0.0021**

(0.0011)

0.0009

(0.0015)

Observations

148,200

77,323

Frozen

Dinners

Coefficient

(Std.)

0.0227***

(0.005)

0.0156***

(0.0038)

0.0162***

(0.0037)

0.0246***

(0.0091)

Observations

52,893

12,287

23

Table B3. (Cont.)

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient

(Std.)

0.0097***

(0.0018)

0.0092***

(0.0016)

0.0093***

(0.0015)

0.0266***

(0.0027)

Observations

345,223

117,044

Frozen Juices

Coefficient

(Std.)

0.0152***

(0.0035)

0.0131***

(0.003)

0.0131***

(0.003)

0.0206***

(0.0068)

Observations

118,582

40,517

Grooming

Products

Coefficient

(Std.)

0.0026*

(0.0023)

0.0031**

(0.0023)

0.0033**

(0.0023)

0.0048

(0.0086)

Observations

101,944

22,102

Laundry

Detergents

Coefficient

(Std.)

0.019***

(0.0044)

0.0101***

(0.003)

0.0105***

(0.003)

0.0116**

(0.0059)

Observations

121,566

42,121

Oatmeal

Coefficient

(Std.)

0.0428***

(0.0153)

0.0314***

(0.0105)

0.0303***

(0.0102)

0.0511***

(0.0141)

Observations

25,523

13,605

Paper Towels

Coefficient

(Std.)

0.0053**

(0.0037)

0.0066**

(0.0035)

0.0068**

(0.0035)

0.0255**

(0.0147)

Observations

48,199

9,243

Refrigerated

Juices

Coefficient

(Std.)

0.0156***

(0.0038)

0.0082***

(0.0029)

0.0082***

(0.0029)

0.0212***

(0.0081)

Observations

108,965

23,705

Shampoos

Coefficient

(Std.)

0.0022***

(0.0011)

0.0025***

(0.0011)

0.0025***

(0.0011)

0.0127***

(0.0052)

Observations

88,193

16,099

Snack

Crackers

Coefficient

(Std.)

0.0005

(0.0009)

0.0008*

(0.0009)

0.0008*

(0.0009)

0.0035*

(0.0028)

Observations

176,527

38,123

Soaps

Coefficient

(Std.)

0.019***

(0.0059)

0.0088**

(0.0048)

0.0101**

(0.0048)

0.0273***

(0.0111)

Observations

56,725

16,882

Soft Drinks

Coefficient

(Std.)

0.0017***

(0.0008)

0.0015**

(0.0008)

0.0012**

(0.0008)

0.0003

(0.0027)

Observations

243,837

49,989

Toothbrushes

Coefficient

(Std.)

0.0056***

(0.0022)

0.0044***

(0.0021)

0.0044***

(0.0021)

0.0166***

(0.0066)

Observations

52,185

13,695

Toothpastes

Coefficient

(Std.)

0.0066***

(0.0021)

0.0054***

(0.0019)

0.0056***

(0.0019)

0.0157***

(0.0055)

Observations

100,845

28,039

Average coefficients

0.0094

0.0065

0.0066

0.0146

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or equal to 2%, and 0 otherwise. The main independent variable is the log of the average sales volume of product i in

store s over the sample period. Column 1 reports the results of the baseline regression that includes only the log of the

average sales volume and the fixed effects for months, years, stores, and products. In column 2, we add the following

controls: the log of the average price, the log of the absolute change in the wholesale price, and a control for sale- and

bounce-back prices, which we identify using a sales filter algorithm. In column 3, we add a dummy for 9-ending prices

as an additional control. In column 4, we focus on regular prices by excluding the sale- and bounce-back prices. We

estimate separate regressions for each product category, clustering the errors by product. * p < 10%, ** p < 5%, *** p

< 1%

24

Table B4. Category-level regressions of small price changes

( 5%)P

and sales volume

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient

(Std.)

0.0266***

(0.0065)

0.0214***

(0.0061)

0.0204***

(0.0061)

0.0135**

(0.0103)

Observations

74,451

24,729

Bath Soap

Coefficient

(Std.)

0.0207**

(0.0148)

0.0144*

(0.0135)

0.0144*

(0.0134)

0.0176

(0.0329)

Observations

6,650

1,466

Bathroom

Tissues

Coefficient

(Std.)

0.0236***

(0.009)

0.0005

(0.0081)

0.0003

(0.0082)

0.0048

(0.0091)

Observations

56,458

19,285

Beer

Coefficient

(Std.)

0.0066***

(0.0015)

0.0115***

(0.0016)

0.0115***

(0.0016)

0.0444***

(0.0069)

Observations

187,691

12,080

Bottled Juice

Coefficient

(Std.)

-0.0025

(0.0071)

-0.0068*

(0.0064)

-0.0067*

(0.0066)

0.0195***

(0.0075)

Observations

224,857

60,015

Canned Soup

Coefficient

(Std.)

-0.0201**

(0.0114)

-0.0226**

(0.0111)

-0.0202**

(0.011)

0.0133**

(0.0086)

Observations

233,779

95,310

Canned Tuna

Coefficient

(Std.)

-0.0021

(0.0058)

-0.0064*

(0.0057)

-0.0065*

(0.0057)

0.0129**

(0.0088)

Observations

112,629

31,922

Cereals

Coefficient

(Std.)

-0.0003

(0.0076)

-0.0001

(0.0073)

0

(0.0073)

0.014**

(0.0073)

Observations

141,087

72,789

Cheese

Coefficient

(Std.)

0.0047*

(0.0037)

0.0043*

(0.0034)

0.004*

(0.0034)

0.0126***

(0.0044)

Observations

357,679

92,758

Cigarettes

Coefficient

(Std.)

-0.0007

(0.004)

-0.0037*

(0.0039)

-0.0038*

(0.004)

-0.0062**

(0.0046)

Observations

24,553

20,692

Cookies

Coefficient

(Std.)

0.0109***

(0.002)

0.0097***

(0.0021)

0.0096***

(0.002)

0.0102***

(0.0036)

Observations

317,932

66,087

Crackers

Coefficient

(Std.)

0.0024

(0.003)

0.0015

(0.003)

0.0019

(0.003)

0.0147***

(0.0061)

Observations

115,658

24,771

Dish

Detergent

Coefficient

(Std.)

0.0308***

(0.0049)

0.0249***

(0.0042)

0.025***

(0.0041)

0.0256***

(0.0055)

Observations

85,222

26,735

Fabric

Softener

Coefficient

(Std.)

0.0207***

(0.0079)

0.0104**

(0.0069)

0.011**

(0.0069)

0.0232***

(0.0082)

Observations

85,337

27,488

Front-End-

Candies

Coefficient

(Std.)

-0.0033**

(0.0026)

-0.0033**

(0.0025)

-0.0033**

(0.0025)

0.0015

(0.0023)

Observations

148,200

77,323

Frozen

Dinners

Coefficient

(Std.)

0.0385***

(0.0071)

0.0296***

(0.0065)

0.0295***

(0.0065)

0.0684***

(0.0099)

Observations

52,893

12,287

25

Table B4. (Cont.)

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient

(Std.)

0.0186***

(0.0029)

0.0196***

(0.0026)

0.0197***

(0.0026)

0.0249***

(0.0035)

Observations

345,223

117,044

Frozen Juices

Coefficient

(Std.)

0.0244***

(0.0057)

0.0224***

(0.005)

0.0233***

(0.0048)

0.0323***

(0.0071)

Observations

118,582

40,517

Grooming

Products

Coefficient

(Std.)

0.0091***

(0.0038)

0.0104***

(0.0039)

0.0106***

(0.004)

0.0154**

(0.0097)

Observations

101,944

22,102

Laundry

Detergents

Coefficient

(Std.)

0.0273***

(0.006)

0.0153***

(0.0052)

0.0159***

(0.0052)

0.0119**

(0.0063)

Observations

121,566

42,121

Oatmeal

Coefficient

(Std.)

0.0424***

(0.0138)

0.0367***

(0.0135)

0.0362***

(0.0133)

0.0536***

(0.0115)

Observations

25,523

13,605

Paper Towels

Coefficient

(Std.)

0.0232**

(0.0126)

0.0226**

(0.0117)

0.0232**

(0.0115)

0.01

(0.0167)

Observations

48,199

9,243

Refrigerated

Juices

Coefficient

(Std.)

0.0264***

(0.0065)

0.0187***

(0.0064)

0.0187***

(0.0064)

0.0223**

(0.0116)

Observations

108,965

23,705

Shampoos

Coefficient

(Std.)

0.0176***

(0.0029)

0.0185***

(0.0029)

0.0185***

(0.0029)

0.0318***

(0.0089)

Observations

88,193

16,099

Snack

Crackers

Coefficient

(Std.)

0.0028*

(0.0026)

0.0035**

(0.0026)

0.0035**

(0.0026)

0.0173***

(0.0047)

Observations

176,527

38,123

Soaps

Coefficient

(Std.)

0.0295***

(0.009)

0.0182***

(0.0085)

0.0212***

(0.0084)

0.0509***

(0.0102)

Observations

56,725

16,882

Soft Drinks

Coefficient

(Std.)

0.0029***

(0.0013)

0.0028***

(0.0012)

0.0023**

(0.0012)

0.0012**

(0.0033)

Observations

243,837

49,989

Toothbrushes

Coefficient

(Std.)

0.0141***

(0.0059)

0.0108**

(0.006)

0.0103**

(0.006)

0.0314***

(0.0119)

Observations

52,185

13,695

Toothpastes

Coefficient

(Std.)

0.0083**

(0.0043)

0.0082**

(0.004)

0.0084***

(0.004)

0.0225***

(0.0083)

Observations

100,845

28,039

Average coefficients

0.0139

0.0101

0.0103

0.0212

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or equal to 5%, and 0 otherwise. The main independent variable is the log of the average sales volume of product i in

store s over the sample period. Column 1 reports the results of the baseline regression that includes only the log of the

average sales volume and the fixed effects for months, years, stores, and products. In column 2, we add the following

controls: the log of the average price, the log of the absolute change in the wholesale price, and a control for sale- and

bounce-back prices, which we identify using a sales filter algorithm. In column 3, we add a dummy for 9-ending prices

as an additional control. In column 4, we focus on regular prices by excluding the sale- and bounce-back prices. We

estimate separate regressions for each product category, clustering the errors by product. * p < 10%, ** p < 5%, *** p

< 1%

26

Table B5. Category-level regressions of small price changes (

P

50% of the

average price change) and sales volume

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient

(Std.)

0.0374***

(0.0074)

0.032***

(0.007)

0.0314***

(0.007)

0.0563***

(0.0108)

Observations

74,451

24,729

Bath Soap

Coefficient

(Std.)

0.0503***

(0.0138)

0.0433***

(0.0137)

0.0432***

(0.0136)

0.1405***

(0.0357)

Observations

6,650

1,466

Bathroom

Tissues

Coefficient

(Std.)

0.0184***

(0.0058)

0.0175***

(0.0068)

0.0174***

(0.0068)

0.0405***

(0.0097)

Observations

56,458

19,285

Beer

Coefficient

(Std.)

0.0057***

(0.0015)

0.012***

(0.0014)

0.012***

(0.0014)

0.0648***

(0.0084)

Observations

187,691

12,080

Bottled Juice

Coefficient

(Std.)

0.0132***

(0.0053)

0.01**

(0.0054)

0.0101**

(0.0054)

0.0193***

(0.0087)

Observations

224,857

60,015

Canned Soup

Coefficient

(Std.)

-0.0043

(0.0066)

-0.0003

(0.0069)

0.0017

(0.0068)

0.0129**

(0.0073)

Observations

233,779

95,310

Canned Tuna

Coefficient

(Std.)

0.0125***

(0.0048)

0.0118***

(0.0048)

0.0116***

(0.0049)

0.0222***

(0.0074)

Observations

112,629

31,922

Cereals

Coefficient

(Std.)

-0.0018

(0.0046)

-0.0012

(0.0048)

-0.0011

(0.0048)

0.0082*

(0.0074)

Observations

141,087

72,789

Cheese

Coefficient

(Std.)

0.0078***

(0.0036)

0.0066**

(0.004)

0.0065**

(0.004)

0.0158***

(0.0059)

Observations

357,679

92,758

Cigarettes

Coefficient

(Std.)

0.107***

(0.0084)

0.1075***

(0.0081)

0.1075***

(0.0081)

0.1225***

(0.009)

Observations

24,553

20,692

Cookies

Coefficient

(Std.)

0.0153***

(0.0031)

0.0127***

(0.0031)

0.0126***

(0.0031)

0.0367***

(0.006)

Observations

317,932

66,087

Crackers

Coefficient

(Std.)

0.0152***

(0.0049)

0.0138***

(0.005)

0.0139***

(0.005)

0.0253***

(0.0078)

Observations

115,658

24,771

Dish

Detergent

Coefficient

(Std.)

0.0092***

(0.0042)

0.004*

(0.0041)

0.0042*

(0.0042)

0.0137**

(0.0072)

Observations

85,222

26,735

Fabric

Softener

Coefficient

(Std.)

0.0125**

(0.0065)

0.0088**

(0.0065)

0.0093**

(0.0066)

0.0317***

(0.0102)

Observations

85,337

27,488

Front-End-

Candies

Coefficient

(Std.)

0.0199***

(0.0052)

0.0239***

(0.0052)

0.0241***

(0.0052)

0.0128***

(0.0043)

Observations

148,200

77,323

Frozen

Dinners

Coefficient

(Std.)

0.0285***

(0.0079)

0.0312***

(0.0085)

0.0305***

(0.0084)

0.0678***

(0.0128)

Observations

52,893

12,287

27

Table B5. (Cont.)

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient

(Std.)

0.0286***

(0.0032)

0.0377***

(0.0034)

0.0375***

(0.0034)

0.0308***

(0.0036)

Observations

345,223

117,044

Frozen Juices

Coefficient

(Std.)

0.0143***

(0.0066)

0.0125**

(0.0076)

0.013**

(0.0077)

0.0229***

(0.0103)

Observations

118,582

40,517

Grooming

Products

Coefficient

(Std.)

0.0417***

(0.0037)

0.0435***

(0.0038)

0.0434***

(0.0038)

0.0797***

(0.009)

Observations

101,944

22,102

Laundry

Detergents

Coefficient

(Std.)

0.0159***

(0.0044)

0.0113***

(0.004)

0.0117***

(0.004)

0.0198***

(0.0066)

Observations

121,566

42,121

Oatmeal

Coefficient

(Std.)

-0.0063

(0.0101)

-0.0135*

(0.012)

-0.0133*

(0.012)

0.0112

(0.0167)

Observations

25,523

13,605

Paper Towels

Coefficient

(Std.)

0.0111**

(0.0071)

0.0161***

(0.0071)

0.0167***

(0.0071)

-0.004

(0.0188)

Observations

48,199

9,243

Refrigerated

Juices

Coefficient

(Std.)

0.0068**

(0.0049)

0.0034

(0.0052)

0.0034

(0.0052)

0.0211**

(0.0113)

Observations

108,965

23,705

Shampoos

Coefficient

(Std.)

0.0522***

(0.0035)

0.0521***

(0.0035)

0.0521***

(0.0035)

0.1111***

(0.0112)

Observations

88,193

16,099

Snack

Crackers

Coefficient

(Std.)

0.0048*

(0.0048)

0.0007

(0.0052)

0.0008

(0.0052)

0.0215***

(0.0063)

Observations

176,527

38,123

Soaps

Coefficient

(Std.)

0.0137***

(0.0067)

0.0049

(0.0069)

0.0077*

(0.007)

0.0332***

(0.0118)

Observations

56,725

16,882

Soft Drinks

Coefficient

(Std.)

0.0137***

(0.0022)

0.0119***

(0.0024)

0.0122***

(0.0024)

0.0152***

(0.0043)

Observations

243,837

49,989

Toothbrushes

Coefficient

(Std.)

0.0445***

(0.0058)

0.0394***

(0.0055)

0.0387***

(0.0056)

0.0881***

(0.0125)

Observations

52,185

13,695

Toothpastes

Coefficient

(Std.)

0.0287***

(0.0046)

0.0287***

(0.0047)

0.0288***

(0.0047)

0.0613***

(0.0092)

Observations

100,845

28,039

Average coefficients

0.0213

0.0201

0.0203

0.0415

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or equal to





 where 



 is the average size of a price change of product  in store , and 0 otherwise. The

main independent variable is the log of the average sales volume of product i in store s over the sample period. Column

1 reports the results of the baseline regression that includes only the log of the average sales volume and the fixed

effects for months, years, stores, and products. In column 2, we add the following controls: the log of the average price,

the log of the absolute change in the wholesale price, and a control for sale- and bounce-back prices, which we identify

using a sales filter algorithm. In column 3, we add a dummy for 9-ending prices as an additional control. In column 4,

we focus on regular prices by excluding the sale- and bounce-back prices. We estimate separate regressions for each

product category, clustering the errors by product. * p < 10%, ** p < 5%, *** p < 1%

28

Table B6. Category-level regressions of small price changes (

P

33% of the average

price change) and sales volume

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient

(Std.)

0.0293***

(0.0045)

0.0248***

(0.0043)

0.0242***

(0.0042)

0.0414***

(0.0088)

Observations

74,451

24,729

Bath Soap

Coefficient

(Std.)

0.0304***

(0.0113)

0.026***

(0.0107)

0.026***

(0.0105)

0.0736***

(0.0225)

Observations

6,650

1,466

Bathroom

Tissues

Coefficient

(Std.)

0.0057*

(0.005)

0.0107**

(0.0064)

0.0106**

(0.0064)

0.0297***

(0.0123)

Observations

56,458

19,285

Beer

Coefficient

(Std.)

0.0023***

(0.0006)

0.0065***

(0.0008)

0.0064***

(0.0008)

0.0526***

(0.0069)

Observations

187,691

12,080

Bottled Juice

Coefficient

(Std.)

0.0184***

(0.0041)

0.0157***

(0.0044)

0.0157***

(0.0044)

0.0183***

(0.0081)

Observations

224,857

60,015

Canned Soup

Coefficient

(Std.)

-0.0072*

(0.0057)

-0.0028

(0.006)

-0.0014

(0.0058)

0.0121**

(0.0073)

Observations

233,779

95,310

Canned Tuna

Coefficient

(Std.)

0.0102***

(0.0036)

0.0082***

(0.0032)

0.0081***

(0.0032)

0.0161***

(0.0063)

Observations

112,629

31,922

Cereals

Coefficient

(Std.)

0.0081***

(0.0039)

0.0088***

(0.004)

0.0088***

(0.004)

0.0163***

(0.0069)

Observations

141,087

72,789

Cheese

Coefficient

(Std.)

0.0078***

(0.0033)

0.0068**

(0.0035)

0.0068**

(0.0035)

0.0142***

(0.0061)

Observations

357,679

92,758

Cigarettes

Coefficient

(Std.)

0.0476***

(0.0061)

0.0492***

(0.0059)

0.0493***

(0.0058)

0.0588***

(0.0065)

Observations

24,553

20,692

Cookies

Coefficient

(Std.)

0.0121***

(0.0023)

0.0103***

(0.0025)

0.0102***

(0.0024)

0.0148***

(0.0043)

Observations

317,932

66,087

Crackers

Coefficient

(Std.)

0.0104***

(0.0041)

0.0092***

(0.0041)

0.0093***

(0.0041)

0.0195***

(0.006)

Observations

115,658

24,771

Dish

Detergent

Coefficient

(Std.)

0.0073***

(0.0028)

0.0034**

(0.0029)

0.0036*

(0.0029)

0.0181***

(0.0048)

Observations

85,222

26,735

Fabric

Softener

Coefficient

(Std.)

0.0098**

(0.0061)

0.0066**

(0.0059)

0.0069*

(0.006)

0.033***

(0.0097)

Observations

85,337

27,488

Front-End-

Candies

Coefficient

(Std.)

0.0107***

(0.0046)

0.0132***

(0.0045)

0.0134***

(0.0045)

0.0115***

(0.0039)

Observations

148,200

77,323

Frozen

Dinners

Coefficient

(Std.)

0.0312***

(0.0078)

0.0339***

(0.0087)

0.0339***

(0.0086)

0.0534***

(0.0144)

Observations

52,893

12,287

29

Table B6. (Cont.)

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or to





 where 



 is the average size of a price change of product  in store , and 0 otherwise. The main

independent variable is the log of the average sales volume of product i in store s over the sample period. Column 1

reports the results of the baseline regression that includes only the log of the average sales volume and the fixed effects

for months, years, stores, and products. In column 2, we add the following controls: the log of the average price, the log

of the absolute change in the wholesale price, and a control for sale- and bounce-back prices, which we identify using

a sales filter algorithm. In column 3, we add a dummy for 9-ending prices as an additional control. In column 4, we

focus on regular prices by excluding the sale- and bounce-back prices. We estimate separate regressions for each product

category, clustering the errors by product. * p < 10%, ** p < 5%, *** p < 1%

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient

(Std.)

0.0332***

(0.003)

0.0405***

(0.0031)

0.0404***

(0.0031)

0.0311***

(0.0034)

Observations

345,223

117,044

Frozen Juices

Coefficient

(Std.)

0.0251***

(0.0067)

0.0228***

(0.0076)

0.0232***

(0.0077)

0.0289***

(0.009)

Observations

118,582

40,517

Grooming

Products

Coefficient

(Std.)

0.0279***

(0.0031)

0.029***

(0.003)

0.0291***

(0.003)

0.0645***

(0.008)

Observations

101,944

22,102

Laundry

Detergents

Coefficient

(Std.)

0.0092***

(0.0033)

0.005**

(0.0032)

0.0053**

(0.0032)

0.0104**

(0.0057)

Observations

121,566

42,121

Oatmeal

Coefficient

(Std.)

-0.0023

(0.0102)

-0.0087

(0.0121)

-0.0094

(0.012)

0.0159*

(0.0172)

Observations

25,523

13,605

Paper Towels

Coefficient

(Std.)

0.0122**

(0.009)

0.0174**

(0.0092)

0.0179**

(0.0092)

0.0161**

(0.0151)

Observations

48,199

9,243

Refrigerated

Juices

Coefficient

(Std.)

0.0095**

(0.005)

0.0061*

(0.0049)

0.0061*

(0.0048)

0.0122**

(0.0126)

Observations

108,965

23,705

Shampoos

Coefficient

(Std.)

0.0328***

(0.0027)

0.0325***

(0.0026)

0.0325***

(0.0026)

0.0829***

(0.0094)

Observations

88,193

16,099

Snack

Crackers

Coefficient

(Std.)

0.0037*

(0.0039)

0.0001

(0.0042)

0.0002

(0.0042)

0.0177***

(0.0047)

Observations

176,527

38,123

Soaps

Coefficient

(Std.)

0.0143***

(0.0055)

0.0083**

(0.0056)

0.01**

(0.0057)

0.0216**

(0.0121)

Observations

56,725

16,882

Soft Drinks

Coefficient

(Std.)

0.0143***

(0.0021)

0.0121***

(0.0024)

0.0119***

(0.0024)

0.0137***

(0.0031)

Observations

243,837

49,989

Toothbrushes

Coefficient

(Std.)

0.0277***

(0.0043)

0.0238***

(0.0041)

0.0234***

(0.0041)

0.0611***

(0.0108)

Observations

52,185

13,695

Toothpastes

Coefficient

(Std.)

0.0211***

(0.0034)

0.0204***

(0.0035)

0.0205***

(0.0035)

0.0425***

(0.0078)

Observations

100,845

28,039

Average coefficients

0.0160

0.0152

0.0153

0.0311

30

Table B7. Category-level regressions of small price changes (

P

25% of the average

price change) and sales volume

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient

(Std.)

0.0211***

(0.0035)

0.0177***

(0.0032)

0.0172***

(0.0032)

0.0337***

(0.0074)

Observations

74,451

24,729

Bath Soap

Coefficient

(Std.)

0.0209***

(0.0083)

0.0177***

(0.0077)

0.0176***

(0.0074)

0.0616***

(0.0241)

Observations

6,650

1,466

Bathroom

Tissues

Coefficient

(Std.)

0.0036

(0.005)

0.012***

(0.0057)

0.0119***

(0.0057)

0.028***

(0.0127)

Observations

56,458

19,285

Beer

Coefficient

(Std.)

0.0025***

(0.0006)

0.0054***

(0.0007)

0.0054***

(0.0007)

0.0377***

(0.0059)

Observations

187,691

12,080

Bottled Juice

Coefficient

(Std.)

0.016***

(0.004)

0.0134***

(0.0041)

0.0135***

(0.0041)

0.0221***

(0.0071)

Observations

224,857

60,015

Canned Soup

Coefficient

(Std.)

-0.0121**

(0.0062)

-0.0077*

(0.0065)

-0.0064*

(0.0064)

0.0152***

(0.0065)

Observations

233,779

95,310

Canned Tuna

Coefficient

(Std.)

0.0089***

(0.0037)

0.0066***

(0.0031)

0.0065***

(0.0031)

0.014***

(0.0063)

Observations

112,629

31,922

Cereals

Coefficient

(Std.)

0.0105***

(0.0035)

0.0111***

(0.0035)

0.0112***

(0.0034)

0.0195***

(0.0059)

Observations

141,087

72,789

Cheese

Coefficient

(Std.)

0.0085***

(0.0029)

0.0077***

(0.0029)

0.0077***

(0.0029)

0.0152***

(0.0053)

Observations

357,679

92,758

Cigarettes

Coefficient

(Std.)

0.0193***

(0.004)

0.0209***

(0.0039)

0.0209***

(0.0039)

0.025***

(0.0045)

Observations

24,553

20,692

Cookies

Coefficient

(Std.)

0.0086***

(0.0018)

0.0073***

(0.0019)

0.0072***

(0.0019)

0.0143***

(0.0035)

Observations

317,932

66,087

Crackers

Coefficient

(Std.)

0.0045**

(0.0025)

0.0038**

(0.0026)

0.0038**

(0.0025)

0.0068**

(0.0041)

Observations

115,658

24,771

Dish

Detergent

Coefficient

(Std.)

0.0093***

(0.0021)

0.006***

(0.0021)

0.0061***

(0.0021)

0.0183***

(0.0046)

Observations

85,222

26,735

Fabric

Softener

Coefficient

(Std.)

0.0128***

(0.0044)

0.0098***

(0.0043)

0.0101***

(0.0043)

0.0278***

(0.0087)

Observations

85,337

27,488

Front-End-

Candies

Coefficient

(Std.)

0.0125***

(0.0042)

0.0147***

(0.0042)

0.0148***

(0.0042)

0.0132***

(0.0041)

Observations

148,200

77,323

Frozen

Dinners

Coefficient

(Std.)

0.0373***

(0.0064)

0.0398***

(0.0076)

0.0401***

(0.0075)

0.0586***

(0.0123)

Observations

52,893

12,287

31

Table B7. (Cont.)

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or to





 where 



 is the average size of a price change of product  in store , and 0 otherwise. The main

independent variable is the log of the average sales volume of product i in store s over the sample period. Column 1

reports the results of the baseline regression that includes only the log of the average sales volume and the fixed effects

for months, years, stores, and products. In column 2, we add the following controls: the log of the average price, the

log of the absolute change in the wholesale price, and a control for sale- and bounce-back prices, which we identify

using a sales filter algorithm. In column 3, we add a dummy for 9-ending prices as an additional control. In column 4,

we focus on regular prices by excluding the sale- and bounce-back prices. We estimate separate regressions for each

product category, clustering the errors by product. * p < 10%, ** p < 5%, *** p < 1%

Category

(1)

(2)

(3)

(4)

Frozen Entrees

Coefficient

(Std.)

0.0324***

(0.0032)

0.0389***

(0.0035)

0.0389***

(0.0034)

0.0321***

(0.0039)

Observations

345,223

117,044

Frozen Juices

Coefficient

(Std.)

0.0279***

(0.0062)

0.0255***

(0.0068)

0.0259***

(0.0068)

0.0312***

(0.0089)

Observations

118,582

40,517

Grooming

Products

Coefficient

(Std.)

0.0149***

(0.0021)

0.0156***

(0.0022)

0.0157***

(0.0022)

0.0368***

(0.0062)

Observations

101,944

22,102

Laundry

Detergents

Coefficient

(Std.)

0.0013

(0.0025)

-0.0018

(0.0024)

-0.0017

(0.0024)

0.0011

(0.0054)

Observations

121,566

42,121

Oatmeal

Coefficient

(Std.)

0.0065

(0.0082)

0.0011

(0.0095)

-0.0002

(0.0094)

0.0022

(0.0145)

Observations

25,523

13,605

Paper Towels

Coefficient

(Std.)

0.0074

(0.0102)

0.0116*

(0.0106)

0.0123*

(0.0105)

0.0265**

(0.0132)

Observations

48,199

9,243

Refrigerated

Juices

Coefficient

(Std.)

0.0094***

(0.0041)

0.006**

(0.0041)

0.0061**

(0.0041)

0.0151**

(0.0108)

Observations

108,965

23,705

Shampoos

Coefficient

(Std.)

0.018***

(0.0021)

0.018***

(0.002)

0.018***

(0.002)

0.054***

(0.0077)

Observations

88,193

16,099

Snack

Crackers

Coefficient

(Std.)

0.0044**

(0.0027)

0.0015

(0.0027)

0.0015

(0.0027)

0.0126***

(0.0046)

Observations

176,527

38,123

Soaps

Coefficient

(Std.)

0.0184***

(0.005)

0.0138***

(0.005)

0.015***

(0.0051)

0.0251***

(0.0109)

Observations

56,725

16,882

Soft Drinks

Coefficient

(Std.)

0.016***

(0.0026)

0.0136***

(0.0027)

0.0131***

(0.0028)

0.0132***

(0.0032)

Observations

243,837

49,989

Toothbrushes

Coefficient

(Std.)

0.0156***

(0.0043)

0.013***

(0.004)

0.0127***

(0.004)

0.0427***

(0.0095)

Observations

52,185

13,695

Toothpastes

Coefficient

(Std.)

0.0178***

(0.0027)

0.0168***

(0.0026)

0.0169***

(0.0026)

0.0315***

(0.007)

Observations

100,845

28,039

Average coefficients

0.0129

0.0124

0.0125

0.0253

32

Table B8. Category-level regressions of small price changes (

P

10% of the average

price change) and sales volume

Category

(1)

(2)

(3)

(4)

Analgesics

Coefficient

(Std.)

0.0067***

(0.0018)

0.0057***

(0.0017)

0.0055***

(0.0017)

0.0122***

(0.0047)

Observations

74,451

24,729

Bath Soap

Coefficient

(Std.)

0.005***

(0.0021)

0.0045***

(0.0019)

0.0044***

(0.0019)

-0.0015

(0.0107)

Observations

6,650

1,466

Bathroom

Tissues

Coefficient

(Std.)

-0.0058**

(0.0029)

0.0069**

(0.0039)

0.0069**

(0.0039)

0.0207***

(0.0078)

Observations

56,458

19,285

Beer

Coefficient

(Std.)

0.0015***

(0.0004)

0.0031***

(0.0006)

0.0031***

(0.0006)

0.0191***

(0.004)

Observations

187,691

12,080

Bottled Juice

Coefficient

(Std.)

0.0029**

(0.0015)

0.0019*

(0.0015)

0.0019*

(0.0015)

0.0039*

(0.0045)

Observations

224,857

60,015

Canned Soup

Coefficient

(Std.)

0.0001

(0.002)

0.0031**

(0.0023)

0.0033**

(0.0023)

0.0128***

(0.004)

Observations

233,779

95,310

Canned Tuna

Coefficient

(Std.)

0.0032***

(0.0013)

0.0021***

(0.0011)

0.0021**

(0.0011)

0.0089***

(0.0029)

Observations

112,629

31,922

Cereals

Coefficient

(Std.)

0.0038***

(0.0015)

0.004***

(0.0015)

0.004***

(0.0015)

0.0094***

(0.003)

Observations

141,087

72,789

Cheese

Coefficient

(Std.)

0.0018***

(0.0008)

0.0015***

(0.0008)

0.0015**

(0.0008)

0.0075***

(0.0026)

Observations

357,679

92,758

Cigarettes

Coefficient

(Std.)

-0.001

(0.0013)

-0.0004

(0.0013)

-0.0004

(0.0013)

-0.0004

(0.0015)

Observations

24,553

20,692

Cookies

Coefficient

(Std.)

0.0013***

(0.0005)

0.0012***

(0.0005)

0.0012***

(0.0004)

0.0028***

(0.0011)

Observations

317,932

66,087

Crackers

Coefficient

(Std.)

-0.0002

(0.0005)

-0.0003

(0.0005)

-0.0002

(0.0005)

0.0014*

(0.0015)

Observations

115,658

24,771

Dish

Detergent

Coefficient

(Std.)

0.0047***

(0.0013)

0.0036***

(0.0012)

0.0037***

(0.0012)

0.0087***

(0.0033)

Observations

85,222

26,735

Fabric

Softener

Coefficient

(Std.)

0.0014

(0.0018)

0.0009

(0.0018)

0.001

(0.0018)

0.0034

(0.0055)

Observations

85,337

27,488

Front-End-

Candies

Coefficient

(Std.)

0.0077***

(0.0025)

0.0093***

(0.0028)

0.0093***

(0.0028)

0.0079***

(0.0032)

Observations

148,200

77,323

Frozen

Dinners

Coefficient

(Std.)

0.028***

(0.0056)

0.0279***

(0.0061)

0.0288***

(0.006)

0.0425***

(0.0124)

Observations

52,893

12,287

33

Table B8. (Cont.)

Notes: The table reports the results of category-level fixed effect regressions of the probability of a small price change.

The dependent variable is “small price change,” which equals 1 if a price change of product i in store s at time t is less

or to

