Here Comes the Sun:Fashion Goods Retailing under Weather Shocks

Abdel Belkaid • Victor Martınez-de-Albeniz1

IESE Business School, University of Navarra, Av. Pearson 21, 08034 Barcelona, Spain

abelkaid@iese.edu • valbeniz@iese.edu

Abstract

The weather has been identified as an important driver of demand and constitutes a majorrisk for retailers, especially in goods for which usage is affected by weather conditions, such assoft drinks or fashion apparel. We empirically study the impact of weather variables on theoperations of a large fashion apparel retailer. We develop two models: one for store footfalland another for conversion of visits into product category sales. We find that rain has a verylarge effect on footfall, increasing it in shopping mall stores and decreasing it in street stores.Temperature has a milder effect on footfall but is the main driver of conversion, increasing salesof the “appropriate” categories: summer items are sold more under positive temperature shocksand winter items less. Furthermore, the weather has a moderating effect on price sensitivity, andspecifically rain makes customers less price-sensitive. This finding allows us to exploit weathervariations to improve profits: we demonstrate that weather-contingent pricing can increaserevenues by up to 2% during rainy days.

Submitted: February 16, 2017

Keywords: fashion retailing, footfall, conversion, choice probability, pricing.

1. Introduction

Retailers strive to better understand demand drivers so as to better plan their offer to delight

customers. Unfortunately, demand can be difficult to predict, especially if products are innovative

(Fisher 1997). Poor forecast accuracy is heavy of consequences: products either sell out and lost

sales diminish potentially high margins; or they cannot be all sold, which results in obsolescence,

discounted prices and lower margins again. In industries such as fashion apparel, Zara and other fast

fashion players have developed new operational strategies to better adjust supply to demand (Caro

and Martınez-de Albeniz 2015). The fast fashion business model is quite successful at reducing

product risk by adjusting production quantities to realized demand.

Despite these improvements, some risks remain difficult to predict and mitigate. One of the

most prominent factors of uncertainty is the weather. For example, the Swedish fashion chain H&M

1V. Martınez-de-Albeniz’s research was supported in part by the European Research Council - ref. ERC-2011-StG283300-REACTOPS and by the Spanish Ministry of Economics and Competitiveness (Ministerio de Economıa yCompetitividad) - ref. ECO2014-59998-P.

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attributed a decrease of profits to an unusually warm Winter in 2015 (Armstrong 2016). A similar

statement was made later in September 2016: sales had been negatively affected by unusually

hot weather (Monaghan 2016). On the other hand, the statement in the second quarter of 2016

blamed cold weather (Reuters 2016). This type of comment is common in the apparel industry:

The Gap and Macy’s attributed the poor sales trends in July 2016 to unfavorable weather (Derrick

2016); Next stated that demand in the Spring of 2016 was reduced due to cold and damp weather

conditions (Farrell and Butler 2016); financial analysts stated that “Britain’s erratic weather has

really taken its toll on retailers this year, and a warm September was the last thing that the high

street needed” (BBC 2016).

While it seems clear that the weather strongly affects customer behavior, it is not obvious in

which direction this impacts retailers, and how relevant these weather shocks are. To the very least,

this empirical question is a complex one. The literature has indeed studied it before, but does not

find strong effects despite the anecdotes described above. This is the case because most of the

earlier studies use aggregate data (weekly or monthly, and over regions or countries), so that effects

are usually averaged over multiple weather realizations, possibly reducing the estimated impact.

Moreover, and perhaps more worrisome, some papers that do have access to disaggregate data only

include the weather as one more covariate within a demand model (e.g., Divakar et al. 2005, Kok

and Fisher 2007, Eliashberg et al. 2009), but they do not use it to directly inform decisions. This

seems to suggest that the weather may have a large influence on demand, but better information

about its effect cannot be translated into any value for retailers. This is surprising in the current

times, where demand analytics can unlock value by better understanding the impact of different

environmental factors, such as queues or sales assistance (Lu et al. 2013, Kesavan et al. 2014,

Musalem et al. 2015, Jain et al. 2016).

The objective of this paper is thus to answer the two following questions. First, how does

weather affect retail performance? To be more precise, we are interested in detailing the impact

of different types of variation (temperature and rain) on two key retail variables: footfall (number

of visits to a store) and conversion (probability that a customer buys a product). This distinction

will help us understand better the mechanisms by which weather changes shopping behaviors. In

particular, there is numerous literature in psychology that links weather to moods and behavior.

We apply the existing theory to the two processes of interest, i.e., the decisions whether to visit a

store and, once inside, whether to purchase. Regarding footfall, it predicts that better weather (no

rain, higher temperatures) may be favorable to outdoor locations (street stores), but should always

be detrimental to indoor locations (shopping mall stores). Regarding conversion, it predicts that

warmer conditions will favor ‘summer’ products, and hurt ‘winter’ products. We seek to test these

theories by using highly disaggregated data, daily and over a large number of stores in different

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cities experiencing different weather shocks.

Second, what can the retailer do with this information? We propose to use pricing as a way to

turn weather shocks into an opportunity. Specifically, we find that the weather influences discount

sensitivity and hence we can set a weather-contingent price to improve retail profits. While this

may seem not easily applicable, some retailers are already using this type of pricing policies. For

instance, the Canadian apparel retailer Mark’s sets discounts according to the outside temperature

in a direct form: a -18◦C temperature triggers a 18% discount (Zorgel 2015). Another example

is the case of Adidas in Japan in the summer of 2011. In front of extremely hot temperatures,

the retailer developed a special discount campaign where the discount was equal to the outside

temperature: 35◦C implied a discount of 35% (Spikes Asia 2011). We study these two questions in

apparel retailing. This setting is representative of fashion goods, where product life cycles are short

and demand quite unpredictable, so it is likely that the empirical insights and the recommended

pricing approach extend to other contexts with innovative products.

We thus construct two empirical models for footfall and sales. We consider a reduced-form

log-linear model for footfall. Sales on the other hand follow a conditional Binomial model where

the probability of converting a visit into a purchase has a probability given by a logit specification.

The two models include temperature and rain as covariates. To avoid seasonality in the weather

patterns (we have separate controls for seasonality), we include temperature deviations instead

of actual temperatures, defined as the difference between the daily mean temperature and the

historical value of temperature on that day. In order to detect location- and time-specific effects,

we also use separate weather coefficients for different store locations and seasons. Finally, in the

sales model, we provide one different estimation for every product family. We focus on dresses and

coats, which are examples of summer and winter families respectively. The models are estimated

using a large dataset provided by a large apparel chain, also used in Boada and Martınez-de-Albeniz

(2014), with daily observations during 2013 and 2014, in 13 cities in 4 European countries, with at

least 3 different stores per city.

Our empirical results support all the existing theoretical predictions but one: price sensitivity

seems to be independent of temperature conditions, while the theory suggests that it should be

increasing in temperature. While these findings are to be expected, our study goes one step further

by documenting the magnitude of these effects and in particular pinpointing in which step of the

shopping process weather variables are most important. Specifically, we find that footfall is most

sensitive to rain, and impact is enormous: a day where complete rainy day imply a footfall reduction

of 29% in street stores and an increase of 16% in shopping mall stores; temperature also drives

store visits, but with a lesser impact. Conversion on the other hand is affected both by rain and

temperature deviations: an increase of 5◦C pushes units sales of dresses up by 9%, and those of

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coats down 5.5%; rainy days impact conversion in the opposite effect to that of footfall, because

visit ‘quality’ decreases with footfall. Our findings thus contribute to better understanding how

weather shocks impact retail operations, and can be used as future building blocks for modelling

and optimization.

Furthermore, our most relevant insight for the retailer is that price sensitivity is affected neg-

atively by rain. Indeed, on a rainy day, consumers tend to be less impacted by discounts. For

example, for dresses, price sensitivity goes from 0.82 when there is no rain, to 0.65 when it rains

100% of the day. This difference is quite large and we can use it to guide discounting policies at the

retailer. We provide a price optimization study where we compare optimal fixed pricing policies

to weather-contingent discounting. Such discounting policies would suggest to apply a higher price

during rainy days – or in other words, to fix a high price for rainy days and systematically offer

discounts when it is not raining. We find that such policy could increase revenues by about 2% on

rainy days, which can be quite significant for a retailer. Hence, while a retailer may be negatively

affected by rain overall, we suggest to exploit the opportunity to slightly increase revenues. We

thus offer a novel perspective on the issue compared to the existing literature, e.g., Steinker et al.

(2016).

The rest of the paper is organized as follows. §2 describes the relevant literature. We present

the basic approach, the data used and formulate the hypotheses in §3. We present the models and

estimation results in §4 for footfall and in §5 for sales. In §6, we study the pricing problem and

measure the potential of optimal pricing on retail sales. We conclude in §7. Supporting tables are

contained in the Appendix.

2. Literature Review

Our work is related to different streams of literature that we review here. First, we report the

theoretical work, mostly from psychology, that links weather stimuli to consumer behavior. Second,

we review the empirical studies in operations, marketing and economics fields on the effect of

weather on customers. Finally, we review analytical models that study pricing under uncertain

demand.

There are different ways by which weather can affect our physiology and psychology. For ex-

ample, the presence of rain produces discomfort (Miranda-Moreno and Lahti 2013) and sunshine

produces a positive effect on our mood (Hirshleifer and Shumway 2003, Cunningham 1979, Par-

rott and Sabini 1990). The main process by which weather affects our body is the vital human

necessity of maintaining our body at 37◦C and balancing the heat lost to the environment and the

heat produced by the body (Fanger 1973). This equilibrium depends on several weather variables

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like temperature, humidity, air velocity or pressure and other internal variables like activity level

or thermal resistance of clothing. When this heat balance is lost, it produces physiological and

behavioral consequences in order to return to the equilibrium point. For example, at the physio-

logical level, the body can change the heat produced increasing or reducing the cutaneous blood

flow, the sweat secretion and shivering or tensing muscles. People also take actions to maintain

this balance such as choosing different environments, adjusting thermal aspects of the environment,

e.g., by opening a window, or simply changing clothes (Baker and Standeven 1994, Nikolopoulou

et al. 2001). People feel stress and discomfort when they are outside the equilibrium zone, and

this usually affects customer behavior. The further they are from the equilibrium point, the more

uncomfortable they will feel (Humphreys et al. 2007). In the psychology literature, the concept of

thermal comfort refers to the effect of weather on people’s comfort (Nicol and Humphreys 2002,

Humphreys et al. 2007). This process is relevant to our topic as long as the election of clothing

and the store as thermal environment are two ways from which people could achieve thermal com-

fort. People can also feel changes in their emotions. For example, weather variables affect mood

(Sanders and Brizzolara 1982) and mood has a strong impact on consumer behavior (Gardner 1985,

Gardner and Hill 1988). In general, all results point to a positive relationship between mood and

shopping intentions, e.g., mood is positively associated with time spent in the store and the number

of products bought (Robert and John 1982, Sherman et al. 1997).

The behavioral evidence usually comes mainly from experimental and field work. However,

there is also literature based on data analysis that provide evidence of particular impact of weather

on different fields like economics, marketing and operations, but the number of works is more

limited.

In economics, there is an important stream of work that explores how people change their leisure

activities and the time dedicated for leisure according to weather. Connolly (2008) finds that on

rainy days, men transfer 30 minutes from leisure time to work on average, which implies that people

substitute leisure and work time according to the weather. Zivin and Neidell (2014) provide more

evidence that better conditions outdoors reduce the hours at work, and show that substitution

is not only occurring between work and leisure, but also across different leisure activities. More

evidence is provided by Izquierdo Sanchez et al. (2016) who show significant effect of temperature

on substitution between visiting the cinema and viewing large sports events, in a positive direction

for sports events as temperature rises. Li (2014) describes shopping as a leisure activity that should

also be subject to weather-driven substitution. In particular, rain can make the shopping place

less attractive because it becomes harder to get there in favor of other indoor leisure activities. It

is shown that rain affects negatively all outdoor leisure activities, while temperature has different

effects depending on the location of the store. This complements earlier work by Parsons (2001)

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who finds a significant relationship between temperature and rain with the number of people in

a shopping center in New Zealand. In studies of customer behavior regarding consumption, the

earliest study that we can report was Steele (1951), but not much more was done until the 2000s.

Murray et al. (2010) focuses on the effect of sunlight on one independent store specialized in tea

and finds a significant positive relationship between amount of sunlight and consumption of tea.

Closer to our application in apparel retailing, Bahng and Kincade (2012) shows that fluctuations in

temperature impact sales of seasonal garments (branded women’s business wear). Bertrand et al.

(2015) also show that fluctuations in temperature have an important and significant influence on

apparel sales. Badorf and Hoberg (2016) provide a similar study to ours focusing on daily sales

over different stores in Germany. They show that weather effects may be non-monotonic, and that

reaction to weather depends on the store location, as we also find. These works focus on establishing

the sign and magnitude of weather effects, but do not use these additional information to make

better decisions. The exception is Steinker et al. (2016), who uses the weather to improve demand

forecasts of online sales in Germany and to adjust workforce planning, which saves idle times and

excess costs. Interestingly, they find that online sales strongly increase with rain, which suggests

that shopping online resembles shopping at the mall and is a substitute to shopping at a street

store.

Our paper has three main differences with the literature: it uses disaggregated data at a large

scale (daily, store-level), which has only been used before in Bahng and Kincade (2012), Steinker

et al. (2016) and Badorf and Hoberg (2016), while other papers with daily data only consider

effects in a single location (Parsons 2001, Murray et al. 2010); it separates effects on store footfall

and conversion, which allows us to support our findings with existing theory; and it provides a

recommendation on how to make weather effects useful to retailers, through weather-contingent

pricing.

Finally, we use better information on shopping patterns to orient pricing. This falls within the

dynamic pricing literature, see e.g., Bitran et al. (1998), Bitran and Caldentey (2003). The main

innovation is to use more accurate demand information to price better, which resembles the idea

of price postponement Petruzzi and Dada (1999). Pricing after learning about the demand has

been studied recently by Ferreira et al. (2015), Ferreira et al. (2015) and Martınez-de-Albeniz et al.

(2017) in the context of online retailing. In our case, we use weather-contingent prices. This type

of scenario-dependent actions have been explored in other settings, e.g., for inventory control (Song

and Zipkin 1993, Bensoussan et al. 2011) or supply chain contracting (Chen and Yano 2010, Gao

et al. 2012), but to the best of our knowledge it has not been applied to customer pricing before.

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3. Context, Data and Expected Behaviors

3.1 Shopping process

Shopping is a complex process that has been studied for years in the field of consumer behavior in

marketing. In particular, different types of products entail different shopping behaviors. Hirschman

and Holbrook (1982) differentiate hedonic products from the utilitarian ones, defining the first ones

as those related with emotional experiences of the consumer. In this paper, we focus on fashion

apparel retailing which is a typical example of a hedonic product in marketing research (see p. 95

in Hirschman and Holbrook 1982). The consumption of this kind of products is very related to an

emotional experience while shopping and hence customers normally decide whether to buy once

they are in the store, as opposed to bringing a shopping list to the store. As a result, the contextual

environment at the moment of purchase plays a major role (Salkin 2005).

In this context, to generate a retail sale, a customer (female in this paper) goes through two

main decisions, described in Figure 1. First, she decides to travel to a store, which involves a

trade-off between that choice and other alternatives, such as staying at home or other leisure

activities. This step should be influenced by factors that drive the cost, time or convenience of

the different alternatives, such as the weather which is our focus here. Of course, there might

be other drivers such as transportation or parking congestion. Second, once in the store, the

customer decides whether to purchase a product in a certain category, or leave empty-handed.

This second step is driven by store variables, such as assortment variety or promotions, but may

also be impacted by the weather. Although within a store, there may not be a direct experience

of outside weather, customers use outside weather as a reference point and adapt their in-store

behavior to that benchmark. We detail below the theory behind these adaptation processes.

Our focus in this study is to identify the impact of different weather variables on the customer

decisions with respect to visits and purchases. Specifically, we consider two quantitative variables

affected by the weather: we use the count of people Nst that enter store s on a given day t, which

we call store footfall, and the number of units Sjst within a certain category j sold in store s that

day t, which we call category sales.

3.2 Data description

We obtained a large data set from a large apparel retailer with revenues of several hundred millions

of euros. This data has been used in the past by Boada and Martınez-de-Albeniz (2014). We

focused on 98 stores located in four different European countries, grouped in 13 different cities that

have at least 3 different stores each. We also have information about location: whether it is on the

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Figure 1: Diagram of the shopping process: store visit and purchase.

street (41 of them) or within a shopping center (57). We describe next the different variables used

in our empirical study.

Footfall. Store footfall data provides the total number of visitors for each store and day. As

illustration, Figure 2 shows the daily footfall for two months in four different stores, for two different

markets and location types. We observe that seasonality is qualitatively similar in all the curves,

e.g., there are peaks on Saturdays (on most Sundays, the stores are closed). However the magnitude

of seasonality patterns is different between stores on the street and in a shopping mall, and the

same is true across different markets. For these reasons, we will include location type - city specific

seasonality covariates, as discussed later.

Category sales. We obtained product-level transaction data (products are defined by different

model and color, but may contain multiple sizes). We considered unit sales per product and

aggregated them into families, as defined by the retailer. Family classifies the type of garment:

dress, t-shirt, coat, pullover, skirt, trousers and shirt. In our study, we define the category as

the product family. Table 1 shows some descriptive statistics of the categories. Note that in the

table and our subsequent analysis, we focus on two different periods: March 1 to June 15 and

August 1 to December 31.2 The objective of this selection is to remove periods of clearance sales,

when shopping patterns may be different from the more stable parts of the Spring-Summer and

Fall-Winter seasons.

2In the case of Italy, the window of clearance sales starts later, so we use as first period March 1 to June 30.

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Sep 01 Sep 15 Oct 01 Oct 15 Nov 01 Nov 15 Dec 01

100

200

500

1000

2000

5000

Date

Foo

tfall

Street Store Market 1Street Store Market 2

Shopping Mall Market 1Shopping Mall Market 2

Figure 2: Comparison of daily footfall over three months of 2014 for four different stores.

Since we are working with the number of units sold per category, we need to control for pos-

sible occasional discounts. For this purpose, as suggested by the retailer, we used two sources of

information about the discount available on a store and day. First, we obtained merchandizing

information about discounts planned for each store and family of products, during the full-price

selling season (March to June and September to December). We found that planned discounts

always applied per store and family (e.g., discount of 20% for coats). There were also instances

other kinds of discounts that applied generally to all products within a store (e.g., 20% for the

second unit purchased). Given that these instances applied to all categories equally, we assume in

our model that customer behavior is affected by the average discount within a category.3 Second,

we obtained the total income per product per store per day from transaction data. Using this

information, we estimated the discount applied per family per store per day.4

3Note that our model considers aggregate sales within a category, so it is sufficient to use a single aggregate

discount metric for the category.4First, we calculated for every day, product and store the income per unit of product sold. That is, if we denote

INCist the total income for product i, in the store s and day t and Sist the number of units sold we obtain the

average unit price, denoted as pist =INCistSist

. This value may not coincide with the product price on that day due to

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FamiliesTotal number Average number of Average units

of products products in a store sold in a store

Dress 410 66.3 13.7

T-shirt 571 84.7 22.1

Skirt 87 12.3 2.4

Shirt 51 9.3 2.2

Denim trousers 46 9.9 2.1

Pullover 126 19.6 4.6

Coat 163 26.8 4.2

Table 1: Descriptive statistics of product categories. The interpretation is the following: in the

sample we observed 410 different dresses; in a given store on a given day, there were 66.3 dresses

offered on average (with a much higher average inventory depth) and 13.7 units were sold.

Weather. We used meteorological data from historical records at different airports in the four

countries of interest.5 To this end, for each store, we use historical weather data from the nearest

airport. Since our stores are all located in major cities, this provides accurate weather conditions

about each store. Note that the mean of the distances between the airports and the city of the

store is 18 km, with a standard deviation of 11 km.

There are many weather variables that one could use, such as maximum, mean and minimum

for temperature, humidity, barometric pressure, the amount of precipitation and/or snow. In the

previous literature, different types of weather variables have been used: Parsons (2001) only found

significant associations of footfall in a shopping mall with temperature and rain, although humidity

and sunlight were also considered, Murray et al. (2010) focused on sunlight only and Bertrand et al.

general discounts. With this time series it is possible to estimate the normal price of a product as the maximum of

the time series, denoted pis := maxt pist. This value is the price for the product without discount at that store. With

this value, we can estimate the discount applied for the product dist = 1− pispist

. This value may be biased due to the

general discount rules described above (e.g., 20% for the second unit purchased). To reduce this bias, we use that

the discount applied is the same within a family, store and day. We define the discount per family as the average of

the discount estimated per product. That is, the discount per family j is djst = meani∈j

{dist}. This procedure may be

problematic in the cases where we do not have any unit sold on that day for a family. In this case, the total income

is zero for all the products of the family, as well as the units sold. This cases occur in approximately 10% of the total

cases. In this situation we used the fact that normally, discounts were applied for all products of the store, not only

for one single family. Indeed, correlation between discounts across families is around 0.60. Hence, we defined djst as

the average discount for the other families in that store.5Data has been extracted from the website http://www.wunderground.com, which consolidates historical weather

measurements from different airports and current weather data for millions of weather stations around the world.

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(2015) and Bahng and Kincade (2012) only considered temperature.

In this study, we first focused our attention on temperature, rain, snow and cloud cover (equiv-

alent to sunlight). Specifically, we defined temperature as the absolute deviation between mean

daily temperature in Celsius and the historical mean on that calendar day between 1996 and 2012.

Taking this variable instead of the absolute temperature entails some advantages over using ab-

solute temperature. First, the absolute temperature has a substantial seasonal variation, so that

the effect of absolute temperature cannot be easily distinguished from seasonality. Instead, tem-

perature deviation is uncorrelated with calendar seasonality. Second, temperature deviation is by

construction the deviation from the norm, which is unpredictable at the time of product design.

Hence, this variable will not capture endogenous effects due to retailer decisions. Third, there is a

psychological aspect that is worth noting: it might seem that centering the temperature variable

is simply a numerical manipulation, but given that people are aware of historical temperatures,

temperature deviation captures the deviation of actual temperature from expectations of shoppers,

hence the response to deviations from the “normal”. In addition, rain and snow are taken as a nu-

merical variable that measure the percentage of hours between 9 and 21h where there was presence

of rain and snow respectively. We consider the range 9 to 21h because it is closely linked to the

interval in which a store is open, while rain and snow out of this range should not affect the retailer

at all. Finally, cloud cover is measured in oktas, which is a scale between 0 (completely clear) to 8

(completely covered) used in all weather stations to measure cloud coverage in the sky.

After defining these variables, we noted some strong correlations between them, as shown in

Table 2. This would create collinearity in the empirical analysis, and can bias the estimates. For

this reason, we decided to remove snow because of the correlation with temperature deviation, and

cloud cover because of the correlation with rain. We hence proceed with the analysis using only

rain and temperature deviation. We report in Table 3 the descriptive statistics of these variables.

Variables Rain Temperature deviation Snow Cloud Cover

Rain 1 -0.05 -0.02 0.41

Temperature deviation 1 -0.15 -0.06

Snow 1 0.13

Cloud Cover 1

Table 2: Correlations between weather variables.

Finally, in our study we differentiated the impact of weather by type of season: the hot season

in the Northern hemisphere takes place between April and September (Spring and Summer) while

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Temperature Rain

Germany

Mean 0.24 0.13

Sd 3.82 0.21

Min -13.13 0.00

Max 12.27 1.00

France

Mean -0.02 0.10

Sd 3.45 0.17

Min -11.88 0.00

Max 9.00 0.98

Temperature Rain

Italy

Mean 0.30 0.08

Sd 2.92 0.19

Min -11.88 0.00

Max 11.24 1.00

Spain

Mean 0.47 0.06

Sd 2.94 0.15

Min -10.00 0.00

Max 10.65 1.00

Table 3: Descriptive statistics of the selected weather variables.

the cold season takes place between October and March (Fall and Winter).6

3.3 Hypotheses

In §2, we reviewed the theoretical work that relates weather variables to human physiological and

psychological processes. Here we study the particular impact that temperature and rain causes to

shopping behaviors.

As mentioned before, rain causes discomfort in a direct way and reduces the sense of comfort of

pedestrians (Miranda-Moreno and Lahti 2013). In addition, it has also an impact on mood for two

reasons. First, rain is associated with more cloud cover, which results in a reduction of sunlight, and

hence reduces positive mood. Second, rain increases humidity, which has been associated negatively

with mood (Howarth and Hoffman 1984, Sanders and Brizzolara 1982): this implies that rain again

reduces positive mood.

In contrast, the impact of temperature occurs via the channel of thermal comfort (Fanger 1973).

The comfort sensed in a given environment depends on many variables but it has been observed

that temperature has a unimodal relationship with comfort: very hot or very cold temperatures

produce discomfort, while intermediate temperatures are more comfortable. For example, Keller

et al. (2005) shows that temperature has an inverted U-shaped relationship with mood. Zivin

and Neidell (2014) find that, in several cities in the United States, the number of pedestrians on

the street increase with temperatures below 25◦C and decrease above. Attaset et al. (2010) finds

that the peak occurs at 27◦C for pedestrians at a certain county in California. Specific behaviors

also seem to have U-shaped relationships with temperature (Rotton and Cohn 2000). Given this

6Note that this does not coincide with the fashion terminology, where a Spring-Summer collection lasts between

January/February, and June/July.

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background, and the fact that in our data, historical average temperatures range from -5 to 26◦C,

we assume that the sensitivity of shopping variables to temperature variation may change from the

cold to the hot season. However, in the majority of our sample temperature falls in the region where

higher temperatures increase thermal comfort. In other words, the effect of higher temperature is

opposite of that of rain.

Finally, the main difference between rain and temperature is that rain creates large changes in

comfort, while temperature only brings small changes, which furthermore have an intensity that

depends on the base temperature level from which these deviations occur.

Footfall. Whether to go into a store or not is a decision that should be affected by the current

weather. This is particularly true for shopping of fashion items, a hedonic consumption which should

be more sensitive to the context (as opposed to grocery shopping when your fridge is empty).

We could even consider store visits as a form of leisure. Previous research indicates that one

should separate indoor and outdoor leisure, pointing out that when there is more comfortable

weather people prefer outdoor activities (Zivin and Neidell 2014, Spinney and Millward 2011).

These results suggest that when it rains, a shift to indoor activities occurs (Miranda-Moreno and

Lahti 2013); when temperature increases, a shift to outdoor activities occurs (Zivin and Neidell

2014), as one should expect from thermal comfort theory (Nikolopoulou et al. 2001). This implies

that rain should increase visits to shopping mall stores, while positive temperature deviations

should decrease them. The effect on street stores is slightly more complex: increases of outdoor

leisure do not necessarily imply rises in footfall in street stores. Indeed, it has been reported that

physical outdoor activities and sports also increase with temperature (Tucker and Gilliland 2007,

Izquierdo Sanchez et al. 2016), as well as other recreational activities such as going into nature,

beach, golf or sailing (Loomis and Crespi 1999, Mendelsohn and Markowski 1999, Loomis and

Richardson 2006). Li (2014) compares different outdoor leisure activities (e.g., visits to natural

spaces) vs. shopping and finds that in winter footfall in street stores increases with temperature

and decreases in summer, because of an increase of natural activities. This hypothesis is consistent

with the fact that in winter, natural activities are not easily accessible, while in summer they are a

strong alternative to urban outdoor activities, in the sense of providing similar comfort. We thus

hypothesize that in winter, when other natural outdoor activities are not accessible, shopping mall

and street stores are substitutes, and thus rain and negative temperature deviations decrease street

store footfall; in summer, when other outdoor activities are possible, rain and positive temperature

deviations decrease street store footfall.7 Figure 3 shows visually the hypothesis that we propose

7We could make an alternative, weaker, hypothesis: the coefficient of temperature deviation is higher in the winter

compared to the summer.

13

for temperature.

Cold Season

Shopping mall

stores

Street stores

Other outside

activities

Hot Season

Shopping mall

stores

Street stores

Other outside

activities

Indoor Outdoor Indoor Outdoor

Figure 3: Diagram of the proposed hypothesis regarding the impact of temperature to footfall,

for shopping mall and street stores. Arrows indicate the movement of the indifference curves,

when temperature deviation increases; increased spaces indicate more people choosing that type of

leisure.

In summary, we construct two hypotheses, for rain and temperature:

H1: Rain will increase footfall on shopping center stores and decrease it in street stores.

H2: During the hot season, store footfall decreases with higher temperature deviations.

During the cold season, store footfall decreases with higher temperature deviations in

shopping mall locations while it increases in street locations.

Category sales. In addition to the effect on footfall, people will also take actions during the

shopping process to reduce thermal discomfort. The choice of clothing is an act that can increase

thermal comfort (Humphreys et al. 2007). In particular, some types of clothes provide more or

less insulation than others. As one should obviously expect, Humphreys et al. (2007) show that

people wear warmer clothes (with more insulation properties) during colder conditions. Bertrand

et al. (2015) also find that sales of winter collection products decrease with temperature while they

increase for summer collection products. We expect the same effect in sales: people will feel more

attracted to product families like dresses in warmer conditions and families like coats in colder

conditions. This variation is due to higher thermal comfort of these products which increase the

perceived attractiveness of the product.

14

H3: Sales of “summer” clothes (e.g., dresses) increase with higher temperature de-

viations, and sales of “winter” clothes (e.g., coats) decrease with higher temperature

deviations.

Finally, we should determine the impact of rain on sales. Given that there is no particular

effect related to comfort once in the store, we consider an indirect effect, via footfall. Indeed, we

hypothesized that rain impacts negatively street store footfall. In this case, people that go to a

street store despite the rain should have a stronger motivation to make a purchase; people that go

a to a shopping mall store under rain should in contrast have a weaker motivation to purchase. In

other words, rain can affect the quality of footfall.8 9

H4: In the presence of rain, sales increase in street stores and decrease in shopping mall

stores.

Sensitivity to discounts. Finally, in addition to the impact on footfall and sales, the weather

can also moderate the effect of discounts. This moderating effect is particularly relevant because

pricing seems to be the most actionable lever that a retailer can use to react to changes in weather.

It has been suggested that mood affects evaluations of people and objects in the same direction

of their current mood (Forgas and Bower 1987, Gardner 1985, Gorn et al. 1993). This effect is

a consequence of the fact that people in positive mood can remember more easily and pay more

attention to positive information (Bower 1981, Blaney 1986, Tamir and Robinson 2007). Hence we

expect that people on positive mood are more capable of integrating discounts into their decision-

making and, since mood bias evaluations in a positive direction, consumers will perceive a better

monetary transaction, so that even a small extra discount may increase their utility significantly.

Indeed, Hsu and Shaw-Ching Liu (1998) found in a lab experiment that people in positive mood

are more sensitive to discounts than those in negative mood. Given the relationship between

temperature and rain with mood (positive and negative respectively), we expect that:

H5: Rain will decrease discount sensitivity.

H6: Positive temperature deviations will increase discount sensitivity.

8Note that the same argument of “better” or “worse” footfall can be made for the effect of temperature. However,

the direct effect from insulation properties should dominate, so we omitted this discussion in the development of H3.9In addition, when it rains, customers may prolong the duration of a store visit. This may increase sales in street

stores even more, and counterbalance the decrease in conversion expected in shopping mall stores. Since our data

does not contain visit duration, we omit this explanation in the development of H4 and pose it as a future question

to investigate.

15

4. Modelling Footfall

4.1 Model description

We use a reduced-form log-linear model to adjust the daily store footfall: as dependent variable,

we use the logarithm of the footfall, which can handle better size effects (e.g., seasonal variations

in a larger store will be larger in absolute terms). Thus, the regression estimated coefficients can

be interpreted as a change in the percentage of footfall.

As mentioned in §3.3, stores have been classified according to their location: in a shopping mall

or on the street. We expect a different impact of weather on footfall depending on the location.

Moreover, previous descriptive analysis shows different seasonality depending on the type of store

(cf. Figure 2). Given these facts, we use the following independent variables in our model. First,

we include a store fixed effect αs where s is the store, to take into account fixed store properties

(e.g., location, market population, accessibility, etc.). Second, Xm,t is a seasonality factor, where

m is the market and t is the date. We include market-level day of the week and week of the

year dummy variables, as well as national holidays dummies. These capture the different trends

by market, in particular the historical temperature in that market. We consider different day of

the week dummies across the hot and cold seasons. We also consider a linear trend that captures

evolution in footfall over time. Furthermore, we capture possible cannibalization effects due to

different stores being open on certain dates (which is due to some stores being closed on Sunday

usually): we include as covariate the number of stores open in the same market on each day. Finally,

Wm,t is the set of weather variables. Letting l ∈ {Street,Mall}, the resulting model can be written

using the following vectorial form for coefficients and covariates:

Model F1: log(Nst) = αs + βl(s),mXm,t + γl(s)Wm,t + es,t (1)

where l(s) is the type of store s, and es,t is the residual.

4.2 Results

We estimate this model via ordinary least squares, although we report robust errors to avoid issues

with heteroscedasticity. We compare model F1 in (1) to a more basic model F0 where γl ≡ 0. Table

4 shows the results of the estimation.

We can see that rain has a different impact depending on the location, as discussed in §3.3.The impact of rain on footfall is extremely strong: when it rains all day, it implies a change of

approximately e−0.34 − 1 = −29% of footfall in street stores and an increase of e0.15 − 1 = 16% in

shopping mall stores. Hence, hypothesis H1 cannot be rejected.

16

Models

Location Variables F0 F1 F2 F3 F4

Street

Rain -0.34***

Weekday -0.33***Autumn -0.36*** Germany -0.10*

Winter -0.43*** France -0.30***

Weekend -0.38***Spring -0.30*** Italy -0.44***

Summer -0.11** Spain -0.30***

Temp .- Cold 0.0035**

Weekday 0.0019 Autumn 0.00020Germany 0.0018

France 0.0046*

Weekend 0.0082** Winter 0.0078***Italy 0.0054*

Spain 0.0012

Temp .- Hot -0.0050***

Weekday -0.0043*** Spring -0.00039Germany -0.012***

France -0.0083***

Weekend -0.0076** Summer -0.0077***Italy -0.0022

Spain -0.003

Mall

Rain 0.15***

Weekday 0.10***Autumn 0.056** Germany 0.11***

Winter 0.12*** France 0.13***

Weekend 0.32***Spring 0.25*** Italy 0.22***

Summer 0.31*** Spain 0.16***

Temp .- Cold -0.0041***

Weekday -0.0035*** Autumn -0.0084***Germany -0.0053***

France 0.00028

Weekend -0.0063*** Winter 0.00066Italy 0.0039

Spain -0.0084***

Temp .- Hot -0.0085***

Weekday -0.0084*** Spring -0.0057***Germany -0.016***

France -0.0061*

Weekend -0.0084*** Summer -0.0083***Italy -0.0093**

Spain -0.0016

Degrees of freedom 44,697 44,691 44,685 44,681 44,673

Variables 1,702 1,708 1,714 1,718 1,726

R2 0.8760 0.8784 0.8787 0.8789 0.8788

Table 4: Estimates of models F0 (where γl ≡ 0) and F1 (where γl is estimated) from (1), together

with alternative models with interactions discussed in §4.3. P-values: *** (< 0.1%), ** (< 1%), *

(< 5%). Robust errors are reported.

Temperature deviation also has different effects according to the location and the season. In the

case of shopping mall stores, warmer temperatures decrease footfall, 0.85% and 0.41% per degree

in the hot and cold seasons respectively. Given that the average absolute temperature deviation is

about 3 to 4 degrees, this means that the average deviation in the hot season results in differences

of about plus or minus 3% in footfall, and plus or minus 1% in the cold season. This effect is

thus weaker than that of rain. In the case of street stores, temperature deviations affect footfall

differently across seasons: in the hot season, warmer temperatures reduce footfall, and in the cold

season, they increase footfall. These findings are in line with hypothesis H2, which cannot be

rejected.

Finally, let us comment on the coefficients βl,m, which are omitted in Table 4. We find that

seasonality factors are quite important: the average across markets varies from -0.24 on Tuesday

17

(lowest during the week) to 0.22 on Saturday (highest), and from -1.1 on week 48 (lowest during

the year) to 0.0 on week 27 (highest). Furthermore, when an additional store in a market is open

on a given day, footfall falls by about 3%.

4.3 Other Interactions and Robustness Checks

To establish the robustness of our model, we introduce here further interactions between weather

variables and other time and location variables, by further studying the variation of the coefficients

across day types, seasons and countries. These are denoted models F2, F3 and F4 in Table 4.

Because of the magnitude of the rain effect, we also investigate the variation of the impact of rain

by rain intensity, and whether there is a memory effect in that variable.

Differences between weekday and weekend. We argued that the effect of weather on footfall

is based on how leisure time is allocated between shopping and outdoors based on actual weather.

Thereby, we should expect that the impact is stronger in days where people have more leisure

time, i.e., on weekends. Model F2 includes the interaction of weather variables with day type: the

results show that the impact of weather is indeed stronger on week-ends compared to weekdays,

e.g., the effect of rain in shopping malls is more than three times stronger on weekends compared

to weekdays.

Differences by season. The same argument applies to differences across the year. We added in

model F3 the interaction of weather variables with four different periods: Winter (January-March),

Spring (April-June), Summer (July-September) and Fall (October-December). We see in Table 4

that the qualitative impact of rain does not vary, in spite of the fact that the strongest impact

occurs in the colder seasons for street stores and warmer seasons for shopping mall stores. The

impact of temperature deviation is also quite stable and consistent with model F1. Note that

warmer than average temperatures increase footfall in the Winter, more strongly in street stores

(as in model F1). The coefficient becomes non-significant in shopping mall stores (in contrast with

F1).

Differences between countries. Finally, model F4 introduces interactions of the weather vari-

ables with the location of the stores across the four countries for which we have data: Spain,

Germany, France and Italy. We see that the insights from model F1 all remain true with the fur-

ther observation that Germany is the least sensitive to rain (this is also the country with the most

frequent occurrence), while Italy is the most sensitive to rain.

18

Rain intensity. The most significant impact of weather on footfall comes from the rain variable.

Given our choice of variables, our regression results suggest that street store footfall is 29% lower

on a day where it rains from 9 to 21h, compared to a day where it does not rain in the same period;

the difference is 16% higher for shopping mall stores. The impact is assumed to be linear in model

F1, but there may be hidden non-linearities. We have explored using the rain variable as a factor

with 13 levels (i.e., whether it rained k hours within the interval 9-21h, where k = 0, . . . , 12). Figure

4 shows the results. We see that the impact of rain in street store footfall is indeed approximately

linear (left panel). The effect in shopping mall stores (right panel) is steeper for low levels of rain

and flatter for high levels of rain, which suggests that visitors choose to go to the shopping mall as

soon as a little rain appears.

0.0 0.2 0.4 0.6 0.8 1.0

−0.

30−

0.20

−0.

100.

00

Rain as factor

Coe

ffici

ent

Street Stores

0.0 0.2 0.4 0.6 0.8 1.0

0.00

0.05

0.10

0.15

Rain as factor

Shopping Mall Stores

Figure 4: Coefficient estimates for the rain variable taken as a factor with 13 levels.

Memory effects. One additional robustness check for the rain variable is to check whether it

is the effect comes from the current conditions or it is an adaptive process that includes past rain

experience. To shed light on the issue, we have incorporated lagged rain variables (up to a week)

into the model,10 and the resulting estimation is shown in Table 5. We see that the value of the

coefficient identified in model F1 does not change. In addition, the past does not matter much,

10The correlation of rain in two consecutive days is quite low, only 0.27, which means that it essentially vanishes

after two days.

19

expect for a minor effect from the previous day, which reinforces the findings from our model: if

there was rain the day before, a shopper would visit a shopping mall store even more and a street

store even less. The magnitude of this memory effect is much smaller than that from the current

day, which suggests that F1 does capture the main impact of weather on the behaviors of shoppers.

Store Location

Lagged Rain Street Mall

Rain -0.34*** 0.15***

Rain - Lag 1 -0.040** 0.054***

Rain - Lag 2 -0.0063 0.0023

Rain - Lag 3 -0.0068 0.019

Rain - Lag 4 -0.025 0.0098

Rain - Lag 5 -0.0095 -0.016

Rain - Lag 6 -0.035* -0.0044

Rain - Lag 7 -0.024 -0.028**

Table 5: Coefficient estimates for the rain variable with lags. P-values: *** (< 0.1%), ** (< 1%),

* (< 5%). Robust errors are reported.

Effects of average store discount. We have not introduced discounts as a covariate in the

footfall model, because price information is usually provided within the store and should not affect

the decision of customers to visit the store. We have nevertheless estimated a model with store

discount as a covariate. We find that discounts slightly increase footfall, although the magnitude of

this increase is small: at most 0.14 for the discount across all categories, i.e., footfall increases by

no more than 14% when a 100% discount is given in a certain category. Moreover, the interaction

of this coefficient with any of the weather variable is not significant. Finally, all the weather

coefficients identified in model F1 change in very small amounts, so all the insights discussed so far

remain the same.

5. Modelling Sales

5.1 A Category Choice Model

To model the retail sales for a given category, we should first note that there is a very high

positive correlation between that and store footfall. As a result, we adopt a conditional structural

model, where upon a store visit, the shopper makes a purchase in a given category with a certain

20

probability, which is independent of the footfall. Specifically, we use a logistic (logit) model where

the probability of transforming a store visit into a category j purchase at time t and store s is

denoted as pj,t,s, where:

pj,t,s =euj,t,s

1 + euj,t,s. (2)

We let uj,t,s be the attractiveness of category j at time t and store s, which we specify as a linear

model:

Model S1: uj,t,s = ϕj,s + χj,l(s),mXm,t + λjdj,t,s + µj,l(s)Wm,t + θjdj,t,sWm,t (3)

The store and seasonality factors, ϕj,s and χj,l,m, which are category-specific, control for the

same covariates as those in (1). In addition to these controls, we include the impact of discounts dj,t,s

through the discount sensitivity λj (see §3.2 for the description of how discounts are calculated).

Finally, now the role of weather appears in two parts: the direct impact µj,l(s) which captures the

shift in conversion due to the weather;11 and the moderating effect of the weather on discount

sensitivity θj .

Note that in (2), we ignore substitution across categories. In fact, we also tested a multinomial

logit model, but given that the probabilities pj,t,s are quite small (of the order of 0.01), substitution

effects can be safely ignored. Using independent logit models across categories also makes estimation

much faster.

Furthermore, we could have included variety in the category as another covariate in the model,

measured as number of products or SKUS, or total inventory in store. We tested this and found that

there was little variation in number of products over time in the store, so this effect is already taken

into account in the store fixed effect. Furthermore, as shown in Boada and Martınez-de-Albeniz

(2014), in the sample the service level offered for each product is extremely high, so demand

censoring is negligible.

Finally, although our model can be applied to any definition of category, we consider the re-

tailer’s main product families (dress, t-shirt, shirt, skirt, denim trousers, pullover and coat). We

illustrate the results for the more distinctive summer product (dress) and winter product (coat).

We illustrate the results for the rest of products in Table 8 in the Appendix. For robustness, we

include additional interactions in the model and discuss them in §5.3.11Note that we did not separate the effect of temperature by hot and cold season, or by store location (street vs.

mall), although we check these interactions in our robustness analysis.

21

5.2 Results

In Table 9 of the Appendix we show the complete results of model (3) together with alternative

models with different control conditions. We find that the interaction between temperature devi-

ation and discounts is either not significant (for dresses) or not robust (for coats, see for example

model S4 of the Table 9: in Spain the coefficient is very positive and in Germany very negative).

Hence hypothesis H6 is not supported. For that reason, and to avoid introducing additional vari-

ables that reduce the significance and robustness of the other variables, we present our results

without the interaction of temperature and discounts. We hence focus only on the effect of rain on

discount sensitivity, which is much stronger and robust. In other words, we study model (3) with

the coefficient of the interaction between temperature and discounts to zero. Table 6 shows the

results of this new model S1 and other interactions with control variables that we discuss later in

§5.3.The coefficients of model S1 are consistent with our hypotheses. For instance, temperature

increases sales for dresses and decreases them for coats, as expected from hypothesis H3. Note that

this effect is quite strong: a variation of 5◦C between two days produces an increase of 9% of sales for

dresses and a reduction of 5.5% in the case of coats. As shown in Table 8 in the Appendix, the same

insight of the hypothesis H3 holds true for the rest of categories. There is one exception though,

pullovers: in winter season, pullover conversion increases with positive temperature deviations; the

opposite is true for the warm season. Therefore, pullovers, which one would associate with winter

clothing, have a summer-type behavior in the cold season. Indeed, we looked for samples of these

products and found that pullovers of this brand are not the typical thick, warm pullovers that one

may imagine: they are instead thin-fabric products that resemble woolen dresses, most of them

without a high neck. This suggests that one could infer the nature of the product category directly

from its sensitivity to weather, as opposed to using an intuitive, traditional categorization.

Furthermore, the impact of rain on sales is positive and negative respectively for street stores

and shopping malls stores, according with hypothesis H4, via the effect of footfall quantity on

customer predisposition to shop. Note that the effect varies across product families (dress vs.

coat). For example, in both street stores and shopping malls the effect of rain on the sales of coats

is always larger and the difference between these two categories remains quite constant: the impact

of rain on coats is approximately 0.1 larger than that of dresses, for both street stores and shopping

malls. So one may conjecture that, apart from the effect of rain on footfall quality, there may also

be a particular family effect, where winter categories benefit from rain more than summer ones.

Interestingly, the effect of rain on conversion is lower than the one of temperature, compared

to the effects on footfall. For instance, the coefficient of rain was about 100 times higher than that

22

Models

S0 S1 S2

Variables Dress Coat Dress Coat Dress Coat

Rain - Street 0.042* 0.15***Weekday 0.044 0.17***

Weekend 0.037 0.12*

Rain - Mall -0.094*** 0.00035Weekday -0.071** 0.025

Weekend -0.13*** -0.039

Temperature Deviation 0.018*** -0.011***Weekday 0.017*** -0.014***

Weekend 0.020*** -0.0055**

Discount x Rain -0.17* -0.11Weekday -0.42*** -0.16

Weekend 0.17 -0.034

Discount 0.80*** 0.63*** 0.82*** 0.64***Weekday 0.84*** 0.61***

Weekend 0.78*** 0.70***

Degrees of freedom 62,235 62,227 62,217

Variables 2,796 2,804 2,814

Log-likelihood -159,907 -159,484 -159,457

McFadden’s R-squared 0.4615 0.4630 0.4630

Models

S3 S4 S5

Variables Dress Coat Dress Coat Dress Coat

Rain - Street

Autumn 0.099** 0.16*** Germany -0.1 0.11

Street 0.034 0.12***Winter 0.14 0.12 France 0.064 0.32***

Spring 0.027 0.013 Italy 0.15*** 0.16**

Summer -0.035 0.24** Spain -0.011 0.0098

Rain - Mall

Autumn -0.055* -0.049 Germany -0.078* 0.12*

Mall -0.089*** 0.026Winter 0.0056 -0.085 France 0.064 0.037

Spring -0.12*** 0.068 Italy -0.17*** -0.14*

Summer -0.097 0.11 Spain 0.0031 0.041

Temperature Deviation

Autumn 0.015*** -0.0066*** Germany 0.023*** -0.0011Street 0.015*** -0.015***

Winter 0.011*** 0.0098 France 0.021*** -0.011***

Spring 0.022*** -0.018*** Italy 0.022*** -0.014***Mall 0.021*** -0.0070***

Summer 0.016*** -0.012*** Spain 0.0097*** -0.015***

Discount x Rain

Autumn -0.28 -0.18 Germany -0.69*** -0.67**Street -0.17 0.17

Winter 0.040 0.25 France -1.1*** -0.59*

Spring -0.30 0.98** Italy 0.27* -0.083Mall -0.17 -0.30

Summer -0.36* -0.37 Spain 0.094 0.61*

Discount

Autumn 0.66*** 0.69*** Germany 0.88*** 0.81***Street 0.82*** 0.64***

Winter 1.2*** 0.70*** France 1.1*** 0.59***

Spring 0.79*** -0.041 Italy 0.89*** 0.61***Mall 0.82*** 0.64***

Summer 0.91*** 0.95*** Spain 0.70*** 0.63***

Degrees of freedom 62,197 62,197 62,221

Variables 2,834 2,834 2,810

Log-likelihood -159,293 -159,342 -159,469

McFadden’s R-squared 0.4636 0.4634 0.4630

Table 6: Estimates of models S0 (where µj,l(s), θj,l(s) ≡ 0) and S1 (where both µj,l(s) and θj,l(s) are

estimated) from model (3), together with alternative models with interactions discussed in §5.3.P-values: *** (< 0.1%), ** (< 1%), * (< 5%).

23

of temperature in the footfall model; it is only about 3-4 times higher in the conversion model.12

Thus, it seems that the weather variable that most affects footfall is rain, while the variable that

really drives conversion is temperature.

Finally, the effect of rain on discount sensitivity is negative. Rain thus reduces the appreciation

for promotions, for both categories, and this makes customers less price sensitive. This supports

hypothesis H5, at least for the dress category. Note that the effect is quite high: in a rainy day

(i.e., 100% of the time raining), discount sensitivity will reduce from 0.82 to 0.65 for dresses, and

from 0.64 to 0.53 for coats.

5.3 Robustness

We check here the robustness of model S1 (without the interaction between discount sensitivity

and temperature), by separating the influence of weather by different control variables, as we did in

§4.3: between midweek and weekends, between seasons, countries and store locations. We denoted

these models S2, S3, S4 and S5 in Table 6 respectively.

Differences between weekday and weekend. First we check possible differences in the coef-

ficients between between weekdays and weekends in S2. We observe that there are no qualitative

differences, in spite that many of the coefficients have lost their significance; this is a sign of less

powerful estimation and even overfitting. Our explanation of the more positive impact of rain on

coats remains coherent. Note that impact of rain on discount sensitivity on weekends is positive

but not significant.

Differences by season. We added in model S3 the interaction between seasons. In this case,

all coefficients lose their significance, again an indication that we are disaggregating the coefficients

too much. If we focus only on the significant ones, they remain quite consistent, except for two

exceptions. First, we find a positive and significant coefficient of temperature on coats sales in the

Winter, which could be due to the summer-type nature of coats in Spring-Summer collection, as

discussed for pullovers in §5.2. Second, we obtain a positive coefficient of rain on discount sensitivity

for coats in the Spring, which changes its sign. In this case, we also see that the discount sensitivity

drops from 0.64 to approximately zero, which suggests that including this interaction is picking

up a subsample in which discount sensitivity is very different from the rest of the sample. The

conclusion is that we might find episodes during the season in which there may be seasonality in

the discount sensitivity. Unfortunately, to include this feature in the model, we would need more

12The variables of rain and temperature have different variations, with range of 1 for rain and range of about 10

for temperature.

24

structure or more data to be able to capture the effect of weather on sensitivity without losing

estimation power.

Differences between countries. The comparison between countries corresponds to model S4.

Again, we are disaggregating to much the weather coefficients, so that significance is lost. This is

especially true for the interaction between discounts and weather, so that the coefficients are not

very significant and contain more error estimation. As in model S3, we identify changes in the sign

of the interaction of discounts and rain for dresses in Italy and coats in Spain, which we can again

associate with local market pricing conditions not captured in our model.

Differences between store locations. Since we did not include store locations in the conversion

model (as opposed to the footfall model), we check in S5 the interaction of temperature and discount

sensitivity with store location. We report that there are no changes in any of the findings, because

there are no significant coefficients that change signs.

6. Better Decisions with Weather Information

Once we have determined the impact of weather on footfall and conversion, one naturally wonders

how a retailer can use this information to take better decisions. Given the nature of weather

variations, the retailer can only change decisions that can be made daily (or at least in less than

two or three days). As a result, assortment decisions, which require restocking a store, would be

impossible to change under such a short notice. Similarly, product inventory decisions can also not

be modified easily. Perhaps product display decisions, e.g., what is displayed in the store window,

could make a difference, but we do not have data on this unfortunately.

The only possible decision that can be easily changed daily is pricing. Specifically, the retailer

can apply discounts that could be adapted to the weather. The current discount policy is decided

at headquarters but some room for store freedom exists: the store manager is free to apply any

discount she desires, within certain limits. We found in our empirical results that rain changed

price sensitivity, so we can anticipate that weather-contingent price adjustments will create value

for the retailer.

We study next how the retailer should set prices taking into account weather variations.

25

6.1 Fixed Pricing with Uncertain Weather

The retailer is interested in maximizing sales revenues13 by setting the right price. The first pricing

model that one can consider is that of a fixed price, but set in a way that considers the effect of

weather variations.

Letting djs be the fixed variation (with respect to the current price) for category j in store

s during days t = 1, . . . , T , the exact conversion probability is equal toVjste

λjtdjs

1+Vjsteλjtdjs

where Vjst is

the realized category-j attractiveness in store s after the weather is realized in day t, and λjt is

the discount sensitivity for category j, which depends on t because it varies with the weather (see

model S1).

Letting Nst be the (weather-dependent) store footfall, the objective function of the retailer thus

becomes

πjs := (1− djs)E

[T∑t=1

NstVjste

λjtdjs

1 + Vjsteλjtdjs

]This function can now be optimized over djs ∈ (−∞, 1]. It turns out that, even though πjs is

not concave in djs, it is usually quasi-concave. The optimal djs is thus determined by first order

condition:

(1− djs)E

[T∑t=1

NstλjtVjste

λjtdjs(1 + Vjsteλjtdjs

)2]− E

[T∑t=1

NstVjste

λjtdjs

1 + Vjsteλjtdjs

]= 0. (4)

Finally, note that the optimal fixed price will be the same for two stores experiencing the same

external shocks every single day. Indeed, according to our model, these two stores will only differ

by their store fixed effect αs, which means that this is a proportionality factor in Equation (4). As

a result, even if we have allowed prices to differ across stores, the resulting prices will be the same

in all the stores within a market.

6.2 Pricing on Weather

An alternative approach to fixed pricing is to change price according to the current weather condi-

tions. Specifically, we can now allow the discount to be depending on the current weather, i.e., we

set djst for all t, with full knowledge of λjt. As a result, the optimization becomes

maxdjst

(1− djs)NstVjste

λjtdjst

1 + Vjsteλjtdjst.

13In the fashion apparel industry, contribution margins are very high, of the order of 60-80% of sales, so focusing

on revenue instead of gross margin is a good proxy for retail performance.

26

This is a quasi-concave objective that reaches the maximum d∗jst at the unique djst that satisfies

λjt(1− djst)(1 + Vjsteλjtdjst

) = 1. (5)

It is easy to verify that d∗jst is increasing in λjt: the more price sensitive customers are, the higher

the discount should be. Note that in our case, since Vjst is small, the solution to this equation is

approximately equal to

d∗jst ≈ 1− 1

λjt. (6)

In our model, we find that λjt ∈ [0.54, 0.82] (0.54 for coats when it rains 100% of the day, 0.82

for dresses when it does not rain). As a result, we find that optimal prices are such that d∗jst < 0,

i.e., the retailer is currently pricing too low. Our optimization suggests that prices should increase

between 22% and 85% compared to the current policy.

6.3 Numerical Results

To quantify numerically the potential gain associated with weather-contingent discounts, we com-

pare the revenues obtained by different strategies, taking footfall as given and adjusting conversion

according to model S1. Of course, our numerical simulations use the demand distribution derived

from the estimated model. Ideally, this approach should be complemented by field experimentation.

Specifically, we compare the expected revenue in our model according to the current discount

policy, against three other policies. As suggested above, with the current price sensitivity estimates

we find that the current price seems to be too low. For this reason, the first policy we consider

is called OneFixed, the best fixed price policy (i.e., stores always have the same price) taking

into account uncertain weather. The second one denoted TwoFixed uses two prices: a price for

days without rain, and another price for days with some rain. This is very simple to implement14

and captures the highest gain as suggested in §6.2. Note that we can introduce variations of this

policy by removing discounts when the rain is higher than a threshold, which lead to significant

improvements too although smaller in size. The third policy that we consider is Contingent, the

fully optimized discount policy that changes prices according to the weather experienced, according

to §6.2, without any constraint on price flexibility.

14Same-day weather forecasts tend to be extremely accurate.

27

0 2 4 6 8 10 12

0 %

0.5 %

1 %

1.5 %

2 %

Impr

ovem

ent

Dress − 2013

ContingentTwo Fixed

0 2 4 6 8 10 12

0 %

0.5 %

1 %

1.5 %

2 %

Dress − 2014

0 2 4 6 8 10 12

0.2 %

0.6 %

1 %

1.4 %

Hours of Rain

Coat − 2013

Impr

ovem

ent

0 2 4 6 8 10 12

0.2 %

0.6 %

1 %

1.4 %

Hours of Rain

Coat − 2014

Figure 5: Improvement of the total income of two different discounts policies compared with the

one fixed policy.

Figure 5 shows the variation of expected total revenues respect to OneFixed policy for the two

years considered on the analysis, for dresses and coats. We observe that using TwoFixed instead

of one improves revenues compared to using a fixed price by 0.5% when the day is completely rainy.

The difference between the two prices is on average 5%, which suggests that this policy may not be

so aggressive. The potential of fully optimized discounts with Contingent is higher, increasing

revenues by 2% in comparison with OneFixed for fully rainy days. In contrast, the increase is

very low when there is no or little rain (less than 3 hours), which happens about 80% of the time.

This implies that the aggregate effect of contingent pricing is limited, below 1%.

7. Conclusions and Further Research

In this paper, we empirically studied the effect of weather, through temperature and rain, on

physical retail, at a mass-market fashion retailer. We decomposed the analysis on two key metrics

of the retailer: footfall (the number of visitors on a store) and conversion (the probability of

28

purchasing an item in a given category for a random visitor). We proposed a log-linear model for

footfall and a logit model for sales conditional on footfall. These models included weather effects as

well as typical controls such as fixed store effects, day-of-the-week and weekly seasonality, holidays

or number of nearby open stores, and other important drivers such as discounts. We estimated the

models using a large data set with daily observations over 2 years and 98 stores in 13 European

markets.

We found that footfall is mostly governed by rain, which has different effect depending on the

location of the store, whether it is on the street or within a shopping mall: in a very rainy day (rain

during all opening hours), footfall is reduced by 29 % in street stores, while it increases by 16%

in shopping malls stores. In contrast, conversion is more driven by temperature, so that warmer

temperatures increase the sales probability of “summer” products such as dresses, and decrease

that of “winter” products such as coats. The overall effect on units sold, assuming no variation on

prices, follows the same direction and is shown in Table 7: the impact of rain is positive or negative

depending on store location, via footfall mainly; the impact of warmer temperatures is positive or

negative depending on product characteristics, via conversion mainly.

Rain Temperature

Location Dress Coat Dress Coat

Street -26% -17% 1.7% -1.2%

Mall 6% 16% 1.2% -1.7%

Table 7: Change in total units sold in a day with 100% rain vs. no rain (left), and in a warmer

day with an increased temperature of 1◦C (right, averaged across hot and cold season), following

models F1 and S1.

In addition to these direct effects, we also found that rain indirectly decreases price sensitivity,

by about 0.17 in dresses for instance (from 0.82 to 0.65). This implies that the retailer can use

weather information to increase its revenues by setting a weather-contingent pricing policy. Through

a numerical counterfactual, we found that using rain/no-rain pricing can increase revenues in a

complete rainy day by 0.5% compared to a fixed-price policy, while using flexible pricing can lift

revenues by 2% over the fixed-price benchmark, for a completely rainy day. This suggests that

using weather information in retail store operations can unlock some value for the retailer.

Our findings are in line with the theoretical work on physiology and psychology. Indeed, the

theory predicts that bad weather (rainy, too cold or too hot) produces negative mood and comfort

and thereby affects consumer choices. Specifically, it takes customers away from the street on rainy

days, while they seek shelter in shopping malls. This affects footfall along the lines of our empirical

29

results. Bad weather also drives customers to choose the products more appropriate for the current

weather, as we find. Finally, we also find that customers are more sensitive to discounts when the

day is not rainy and they are in better mood, as predicted by the theory. The only deviation from

the theoretical hypotheses is that price sensitivity does not increase with warmer temperatures: we

do not find support for this statement.

Finally, our work is one of the first attempts to link weather to retail success, using disaggregate

data. We hope to inspire future research to better understand the phenomenon. There are several

directions worth investigating further. First, there seems to be a transfer of shoppers between

street and shopping mall locations. In reality, the transfer should also include online shopping,

as suggested by Steinker et al. (2016). We hope to complement our work with online retail data

and show that the bad weather drives online traffic and sales up. This also suggests that to make

the retailer less sensitive to weather fluctuations, it should seek a balance across channels, so that

customer fluctuations balance each other across channels. For instance, in our case, if the retailer

would have 35% of footfall coming from street stores and 65% from shopping mall stores, then it

would be indifferent to rain in a given market, because 35%× (−29%) + 65%× (+16%) = 0. This

means that information on weather sensitivity could help retailers build natural operational hedges

by balancing store locations properly. In addition, we have found that our empirical sensitivity to

weather at the category level reveals the nature of the products within a category. This suggests

that these measurements could potentially allow a better classification of products. Also, we worked

with large product families where products may not necessarily have the same response to weather

variations. Further work could use product characteristics to understand what makes them sensitive

to the weather.

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Appendix: Additional Tables

Family

Variable Dress T-shirt Skirt Shirt Denim Trousers Pullover Coat

Rain - Street 0.050* 0.030 -0.053 0.073 0.16*** 0.10*** 0.14***

Rain - Mall -0.086*** -0.062*** -0.16*** -0.068 -0.050 0.024 -0.012

Temperature - Cold Season 0.014*** 0.026*** 0.007** 0.027*** 0.013*** 0.017*** -0.0050**

Temperature - Hot Season 0.021*** 0.0068*** 0.035*** 0.012*** 0.0061* -0.016*** -0.019***

Discount x Rain -0.18* -0.046 0.42* -0.11 -0.56* 0.071 -0.11

Discount 0.82*** 0.66*** 0.26*** 0.40*** 0.12** 0.51*** 0.65***

Table 8: Coefficients of model 3 for all the families considered. The coefficients of temperature

are separated by seasons and the coefficient of interaction between temperature and discount it is

supposed not significant. P-values: *** (< 0.1%), ** (< 1%), * (< 5%).

35

Models

S0 S1 S2

Variables Dress Coat Dress Coat Dress Coat

Rain - Street 0.044* 0.15***Weekday 0.048* 0.17***

Weekend 0.035 0.11*

Rain - Mall -0.092*** -0.0036Weekday -0.068** 0.022

Weekend -0.13*** -0.042

Temperature Deviation 0.019*** -0.013***Weekday 0.018*** -0.016***

Weekend 0.020*** -0.0085***

Discount x Rain -0.19* -0.092Weekday -0.46*** -0.14

Weekend 0.18 -0.021

Discount x Temperature -0.0076 0.022**Weekday -0.015** 0.017

Weekend 0.0048 0.028*

Discount 0.80*** 0.63*** 0.83*** 0.63***Weekday 0.85*** 0.60***

Weekend 0.78*** 0.68***

Degrees of freedom 62,235 62,225 62,213

Variables 2,796 2,806 2,818

Log-likelihood -159,907 -159,478 -159,449

McFadden’s R-squared 0.4615 0.4630 0.4631

Models

S3 S4 S5

Variables Dress Coat Dress Coat Dress Coat

Rain - Street

Autumn 0.10** 0.16*** Germany -0.10 0.13

Street 0.042 0.11**Winter 0.16* 0.12 France 0.065 0.32***

Spring 0.029 0.0059 Italy 0.15*** 0.16**

Summer -0.049 0.21** Spain -0.0032 -0.021

Rain - Mall

Autumn -0.055* -0.048 Germany -0.077* 0.12*

Mall -0.091*** 0.022Winter 0.014 -0.08 France 0.065 0.036

Spring -0.12*** 0.059 Italy -0.18*** -0.14*

Summer -0.11* 0.079 Spain 0.011 0.0015

Temperature Deviation

Autumn 0.014*** -0.0075*** Germany 0.024*** 0.0065Street 0.018*** -0.016***

Winter 0.015*** 0.012* France 0.021*** -0.011***

Spring 0.022*** -0.020*** Italy 0.021*** -0.014***Mall 0.020*** -0.0097***

Summer 0.012*** -0.020*** Spain 0.012*** -0.025***

Discount x Rain

Autumn -0.29* -0.19 Germany -0.69*** -0.62*Street -0.25 0.20

Winter -0.087 0.14 France -1.1*** -0.58

Spring -0.33 1.2** Italy 0.31* -0.081Mall -0.15 -0.29

Summer -0.27 -0.19 Spain 0.026 0.79**

Discount x Temperature

Autumn 0.0078 0.0077 Germany -0.0047 -0.057***Street -0.03*** 0.018

Winter -0.042* -0.034 France -0.0079 0.0050

Spring -0.0058 0.035 Italy 0.011 0.0015Mall 0.0071 0.023*

Summer 0.020* 0.042** Spain -0.023** 0.10***

Discount

Autumn 0.65*** 0.68*** Germany 0.88*** 0.83***Street 0.84*** 0.63***

Winter 1.2*** 0.73*** France 1.1*** 0.59***

Spring 0.79*** -0.059 Italy 0.88*** 0.61***Mall 0.81*** 0.63***

Summer 0.91*** 0.94*** Spain 0.72*** 0.54***

Degrees of freedom 62,189 62,189 62,217

Variables 2,842 2,842 2,814

Log-likelihood -159,281 -159,303 -159,455

McFadden’s R-squared 0.4636 0.4636 0.4630

Table 9: Estimates of models S0 (where µj,l(s), θj,l(s) ≡ 0) and S1 (where both µj,l(s) and θj,l(s) are

estimated) from model (3), together with alternative models. P-values: *** (< 0.1%), ** (< 1%),

* (< 5%).

36