Wishing for bad weather: demand shocks and the labor supply behavior of Bologna Pizza Vendors
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Wishing for bad weather: demand shocks and the
labor supply behavior of Bologna Pizza Vendors
Alessandro Saia∗
University of Bologna and OECD
Job Market Paper
This version: October 2015
Download the most recent version here
Abstract
A number of recent influential papers have analyzed the labor supply behavior
of New York taxi drivers (Camerer et al., 1997; Farber, 2008; and Crawford and
Meng, 2011), the findings of which are in sharp contrast with the prediction of the
standard model of labor supply, but are consistent with alternative theories of labor
supply decisions with Reference-Dependent Preferences (Kőszegi and Rabin, 2006).
In the spirit of previous works, I study the labor supply behavior of Home Delivery
Pizza Vendors in Bologna who, like taxi drivers, experience temporary variations
in their earning opportunities, and are free to work more or less by accepting (or
not accepting) orders. Unlike previous papers, however, I can use weather shocks
as instrument for earning opportunities. By utilizing the variation in demand due
to adverse weather conditions, I find that the behavior of pizza vendors is perfectly
in line with the predictions of the standard model of labor supply. When truly
exogenous demand shifters are used, the target component plays no role in vendors’
labor supply decisions. Moreover, I show that using the identification strategies of
previous papers (in particular, Crawford and Meng, 2011), pizza vendors behave like
taxi drivers in terms of their labor supply decisions. This shows that the findings
of previous studies are driven by the (incorrect) way in which demand shocks are
identified.
Keywords: Labor Supply, Reference-Dependent Preferences, Elasticity of Intertemporal
Substitution
JEL Classification: D01, D03, J22
∗
Department of Economics, University of Bologna & Economics Department, OECD. E-mail: alessandro.saia@unibo.it.
I am particularly grateful to Andrea Ichino. I would like to thank Maria Bigoni, Matteo Cervellati, Juan J. Dolado, Irene
Ferrari, Riccardo Ghidoni, Giovanni Mastrobuoni, David Reiley, Alfonso Rosolia, Vincenzo Scoppa, Giulio Zanella and
seminar participants at Bologna, EUI, Aix-Marseille School of Economics, the BOMOPAV 2014 Meeting, the XIII Brucchi
Luchino Workshop and the XIV TIBER Symposium on Psychology and Economics. The views expressed in this paper are
those of the author and do not necessarily reflect those of the OECD and its member countries.1 Introduction
There is a growing list of influential papers documenting a series of behavioral anomalies
that question the validity of standard economic models. Several studies have provided
robust evidence of the fact that individuals tend to overweigh the present compared to
the future (Laibson, 1997), that they make decisions based purely on a subset of the
available information (Dellavigna and Pollet, 2009), and that the utility of the people in
question is also a function of the utility of other people (Charness and Rabin, 2002). An
assessment of the extent to which the core assumptions and the predictions of standard
economic models are correct, is of crucial importance to academics and policymakers alike.
Incorporating behavioral insights into the design of public policies not only could improve
the effectiveness of existing policies, but could also offer new tools for the future (Chetty,
2015).
The implications of behavioral biases may be particularly important within the context
of labor economics. For example, the current design of income taxes or unemployment
insurance policies is entirely based on the prediction of standard models of labor sup-
ply: labor supply should increase in response to transitory, positive changes in earnings
opportunities (i.e. positive Frisch elasticity). Is this prediction true?
Until recently, empirical research into the relationship between workers’ efforts and their
earning opportunities was conducted using individual panel data available for standard
workers. However, using standard workers to test the predictions of labor supply models
is problematic for two main reasons. First, these workers are faced with variations in
wages that are of a permanent nature, and are thus correlated with significant income
effects. Second, they usually operate within settings in which (at the intensive margin)
it is not possible to establish their own efforts. Therefore, while the external validity of
these results is beyond any doubt, what is difficult to identify is the underlying labor
supply behavior.
Due to the serious limitations of available data, scholars had gradually reduced their
interest in studying workers’ labor supply decisions. However, in recent years the extensive
body of literature within economics that focuses on the behavior of the underlying labor
supply, has once again become central to academic debate.
Instead of investigating the labor supply decisions of standard workers, recent papers have
analyzed the labor supply behavior of piece-rate workers such as taxi drivers (Camerer
et al., 1997; Farber, 2008; and Crawford and Meng, 2011) and bike couriers (Fehr and
2Goette, 2007). These specific categories of worker have proven to be ideal when investigat-
ing labor supply decisions. On the one hand, they operate in settings where they are faced
with constant changes in their earning opportunities (in other words, the income effects
on the labor supply are likely to be negligible). On the other hand, they are free to decide
whether to work, and to what degree, and this is also easy to measure. However, despite
the fact that their efforts can be set, these papers have provided evidence that is in sharp
contrast with the prediction of the standard model, but is consistent with alternative theo-
ries of labor supply decisions with reference-dependent preferences. Reference-dependent
preferences (henceforth, RDP ) labor-supply models predict that workers’ labor supply
depends not only on earning opportunities, as standard neoclassical theory claims, but
also on a target (Reference Point). The idea is that a taxi driver, for example, decides to
stop driving after having reached his/her target, for example a given level of income, and
not on the basis of whether future potential earnings are high or low.
Crawford and Meng (2011) is the most recent work analysing the daily labor supply of New
York City taxi drivers, and it suggests that the behavioral component is an important part
of labor-supply decisions. In their paper, the aforesaid authors derive a model of daily
labor supply as a survival model whereby at the end of each journey, a driver decides
whether to continue or to stop driving. They estimate a reduced-form model of the
probability of stopping as a linear function of cumulative hours and cumulative income,
and in order to investigate the relevance of target behavior they include two dummy
variables indicating whether hours or income exceed the targets. Building on Kőszegi
and Rabin’s (2006) theory of RDP, targets reflect the driver’ rational expectations in
terms of hours and income, and represent the driver’s belief concerning possible outcomes.
However, due to the fact that targets are not observed, they operationalize them as
functions of endogenous variables. Given the lack of suitable demand-shifting instruments,
they compute sample proxies for drivers’ rational expectations using driver-specific sample
average income and hours prior to the current shift, allowing them to vary across days
of the week in order to take account of variations in demand throughout the course of
the week. Their results show a strong deviation from the standard neoclassical model of
worker behavior, and suggest that behavioral biases are a key component of drivers’ labor
supply decisions.
However, Crawford and Meng are not able to identify an exogenous demand shifter and
therefore why taxi drivers’ efforts vary throughout the day is not clear.
In the spirit of previous works, I analyze the labor supply behavior of a specific group of
3piece-rate workers: Home Delivery Pizza Vendors in Bologna. At the intensive margin
(i.e. during a day) vendors, like taxi drivers, can decide how much they want to work
by accepting (or not accepting) orders. A key feature of this paper is that unlike previ-
ous works, I am able to identify an exogenous, transitory labor demand shifter. Using
exogenous, transitory changes in weather conditions as instrument for vendors’ earning
opportunities, I invariably find that vendor’s behavior is consistent with the prediction
of the standard model of labor supply. This result contrasts sharply with the results of
previous studies, and I show that this difference in findings is due to differences in the
analytical approach adopted rather than in the data used.
The remainder of this paper is organized as follows. The next section describes the labor
market for Home Delivery Pizza Vendors and the data utilized in this paper. Section 3
presents empirical evidence of the relevance of adverse weather condition for pizza demand
using Web search data. In Section 4, I present the empirical approach and my findings.
Section 4.1 sets out initial evidence of the relationship between demand shocks and the
labor supply behavior of food vendors. In Section 4.2, I replicate the analysis of Crawford
and Meng (2011) using Pizza Vendors’ data, and the results I obtain are consistent with
those found for taxi drivers. In Section 4.3, I present the empirical results obtained by
utilizing the exogenous variation in rainfall as instrument for earning opportunities, and
I show that the behavior of home delivery pizza vendors is perfectly consistent with the
predictions of the standard labor supply model. Section 6 offers some conclusions.
2 Data and Background
The data used in this paper consists of high-frequency data regarding orders carried out
through an on-line takeaway pizza delivery service (henceforth, the Website). The Website
acts as a web-based intermediary between privately-owned restaurants and their customers
(a modern variant of the Yellows Pages, if you like). The Website allows customers to
select a restaurant delivering pizzas and to place their orders with that restaurant. When
the customer places an order, a message is sent to the restaurant through a 2-way till
receipt/order machine. Pizza vendors receive the order through the machine box, and
can then accept or refuse the order. If they accept it, a confirmation message is sent to
the customer with an indication of the delivery time (set by the vendors). Payments are
collected by the vendors on delivery of the pizzas, and the Website charges a commission
for each order.
4The pizza delivery restaurants in question are located in Bologna, and are privately owned
family businesses. Unlike normal restaurants, their distinguishing feature is that they do
not provide table service, and the majority of customer orders are carried out by telephone
or on the Web. Therefore, I only observe one part of total demand (i.e. those orders
received through the Website); however, it is reasonable to assume that the two main
channels (telephone and Web) are positively related.
Unlike previous works, this paper investigates the labor supply behavior of a group of
workers. In the rest of this paper I consider each single restaurant as a group of workers,
and I refer to all of the workers from one restaurant as its vendors. Moreover, I assume that
the group (in terms of size and composition) remains constant throughout the observation
period. Given the labor market characteristics in question (i.e. the restaurants are all
family businesses), it is fair to assume this to be true.
2.1 Data on Pizza Sales
The Website provided me with all orders placed with 59 pizza delivery restaurants during
the period February 2010-July 2011. As previously explained, vendors receive orders
through a machine box, whereupon they can choose whether to accept or reject them.
Rejected orders are vital if a credible estimate of the intertemporal substitution elasticity
for labor supply (Frisch elasticity) is to be provided. Unfortunately, as in previous works,
in this paper I rely only on the equilibrium outcomes (i.e. accepted orders), since rejected
orders were not recorded.
From February 2010 to July 2011 a total of 147,090 orders were observed. Figure 1 plots
the location of each pizza delivery restaurant in Bologna (the red dots in the left panel)
and the spatial distribution of orders observed in the sample (the blue dots in the right
panel). I have detailed information about the date and time each order was placed, the
total amount of the delivery, the distance between the restaurant and the place of delivery,
and the expected delivery time, all of which is communicated to customers when orders
are accepted by the vendors.
[Figure 1]
Summary statistics are shown in Table 1. Restaurants’ daily average earnings across the
whole sample amount to 68.15 e, while the average number of orders accepted in a day is
around 8. Not surprisingly, daily earning opportunities vary across days of the week and
across months. Earning opportunities are higher during the winter and at weekends (for
5example, daily earnings and daily orders on Sundays in the month of January are almost
twice those of the overall sample).
[Table 1]
Figure 2 shows the distribution of orders throughout the day. The number of orders
received varies greatly: orders are concentrated around lunch breaks (generally between
12 noon and 3 p.m.) and dinner hours (generally 6-9 p.m.).
[Figure 2]
2.2 Weather Data
Data for weather conditions in the city of Bologna over the entire period are provided by
the Emilia Romagna Regional Agency for the Protection of the Environment (ARPA).
Hourly rainfall data are provided by a weather station located in Bologna’s city center
(Bologna Urbana)1 .
[Figure 3]
Figure 3 plots the number of days per month with measurable rainfall. From February
2010 to July 2011 there were 206 rainy days (i.e. days on which there was at least 0.1 mm
of rain). As expected, the average monthly number of wet days varies considerable from
one season to the next: figures are much higher in winter, and much lower in summer.
Figure 4 shows changes in rainfall intensity,measured in terms of the number of rainy
hours observed during the course of the day2 . The considerable variation in the rainfall
observed during the period in question would seem to suggest that the intensity of rainfall
during the day needs to be taken into account.
[Figure 4]
3 The Demand for Pizza Delivery in Bologna
Demand for pizza delivery fluctuates daily due to demand shocks caused by day-of-the-
week effects, sport events, holidays, etc. Among others, weather conditions are one of the
1
Note that the city of Bologna, with a population of about 384,000 and a total area of about 140.7
km2 , is relatively small. New York City, for example, has a population of over 8.4 million, living in an
area of 1,214 km2 .
2
Wet hours are defined as those in which more than 0.00 cm of rain was observed.
6key shifters of demand for pizza delivery services. Workers in the food delivery industry
recognize that rainfall is strongly correlated with positive short-term fluctuations in the
demand for pizza delivery services. For example, in 2012, while announcing a rise in
his firms’ profits, the CEO of Domino’s Pizza3 , Lance Batchelor said ”When the weather
turns nasty we always see sales turn upwards”. Why does rainy weather positively affect
demand for pizza delivery? Tony McNaulty, the owner of Papa Murphy, another chain
of pizza restaurants, suggests that ”if it’s going to take you 40 minutes to get home on
an average day with no rain...it’s going to take you an hour to get home. When it rains,
everybody’s running a little bit later and maybe the family doesn’t have enough time to
prepare dinner now, so they use us” 4 .
In this section I use Web search data to provide evidence of the positive effect of adverse
weather conditions on the demand for pizzas. Several studies have recently demonstrated
that Web search behavior correlates in near real time with individual activity, and that
search counts are predictive of economic outcomes, including unemployment levels (Et-
tredge et al., 2005), home sales (Wu and Brynjolfsson, 2013) and consumers activities
such as cinema attendance and music sales (Goel et al., 2010).
Likewise, I use daily Web searches to derive information about the elasticity of pizza
demand to rainy conditions. Pizza-related search queries are provided by Google Trends.
Google Trends provides me with an index5 that indicates the daily volume of queries
submitted to Google that include the Italian words for ”pizza restaurant Bologna” in the
area of Bologna.
Figure 5 plots Google Trends’ daily index of searches for the words ”pizza restaurant
Bologna” from February 2010 to July 2011. The pattern of Web searches is consistent
with the behavior of pizza demand: searches follow a seasonal trend that is compatible
with pizza consumption and the line peaks during the cold months.
[Figure 5]
I examine to what extent adverse weather conditions affect daily Web search volume,
3
Domino’s Pizza is an American restaurant chain and international franchise pizza delivery corporation
with 145,000 employees and more than 1 billion USD of revenue.
4
The full article is available here.
5
Google Trends data does not report the raw level of queries for a given search term; rather, it reports
a query index that indicates the volume of searches for the specific search term divided by the total
number of queries in a given geographic location at a certain point in time.
7using the following model:
log(Searchest ) = β + β1 Rainy Dayt + Zt β + t (1)
where Searches t represents the Google Index on day t, Rainy Day is a dummy variable
that takes value 1 if it has rained on the corresponding day, and Z is a vector of variables
that includes day-of-the-week, monthly and yearly fixed effects. Column (1) of Table
2 reports the results of the OLS estimation using the model that also includes day of
the week, monthly and yearly fixed effects. As expected, the coefficient of interest is
positive and statistically significant: adverse weather conditions during the day lead to
approximately 6% of search queries being related to pizza consumption.
[Table 1]
Not surprisingly, results are robust when investigating the effect of rainfall at the intensive
margin. Results in Columns (2) and (3) of Table 2 present estimates that alternatively
take, as their variables, the number of rainy hours in a day and the total amount of rainfall
(in millimeters), respectively. The corresponding estimate is sizable. For example, five
hours of rain are associated with an increase of around 4% in the daily volume of pizza-
related queries submitted to Google6 .
Finally, it should be pointed out that bad weather might also directly affect the supply
of pizza delivery services. For example, driving in the rain is harder, more difficult and
less enjoyable. Therefore, it is possible that adverse weather conditions negatively affect
the supply of pizza delivery services. In order to explore this possibility, I use the infor-
mation about delivery times contained in pizza sales data. The idea is that the expected
delivery time should provide information regarding the difficulty of delivering pizzas in
6
Previous works have suggested that ”rain may have a number of effects on the market for taxi rides.
First, it likely increases” (Farber, 2015). However, rain might also decrease demand for taxis. For
example, I usually try to avoid taking taxis when it rains because rainy weather affects traffic congestion,
it reduces average car speed and increases the average cost of the ride (see also Footnote 13 in Farber
(2005)). Using Google searches, I investigate the relationship between demand for taxis and the quantity
of precipitation. I collect data for the quantity of daily Web searches for the word ”Taxi” in New York
City from January 2010 to June 2011 (in order to have similar sample size, I have used an equivalent
time period to the one employed in the main text). Results are shown in Appendix A6. OLS estimation
results reported in Table 18 suggest that weather conditions do not affect Google searches for the word
“Taxi” in NYC. It is interesting to note that Taxi-related searches are correlated with other demand
shifters. The results reported in Table 19 show that the volume of searches is higher at the weekend and
during public holidays. These estimates suggest that Google searches are a good proxy for taxi demand,
and the lack of correlation that I observe between web searches for the word ”Taxi” and adverse weather
is probably due to the fact that adverse weather does not positively affect demand for taxis (if anything,
the corresponding point estimates are always negative).
8wet weather. Using information on delivery times, I estimate:
log(Delivery T imeih ) = α + β1 log(Ordersih ) + β2 Rainy Hourh +
+β3 Rainy Hourh ∗ log(Ordersih ) + ih
where Delivery T imeih represents the average delivery time observed for vendors i dur-
ing hour h, Ordersih is the number of orders accepted by vendors i during hour h and
Rainy Hour takes a value of 1 if it has rained during the corresponding hour. The co-
efficient of interest is β3 , and indicates the combined effect of the number of orders and
adverse weather conditions. Column (1) of Table 3 contains the corresponding OLS es-
timates. The coefficient of interaction term is positive and significant: expected delivery
times are thus longer when it is raining. This finding is in keeping with the idea that
rain complicates the delivery of pizzas. Similar results are reported in Column (2), where
millimeters of rain are used as a measure of bad weather.
Taken as a whole, the findings presented in this section indicate that while adverse weather
conditions positively affect demand for pizza delivery services, rainy weather has a negative
impact on pizza vendors’ working conditions.
4 Estimations of Labor Supply Models
4.1 Demand shocks and labor supply
I begin the analysis of vendors’ labor supply behavior by firstly providing preliminary
evidence of the relationship between demand shocks and labor supply behavior.
Pizza vendors are piece-rate workers, and their labor supply decisions concern how much
effort they want to make by accepting orders. Then, as a natural proxy of vendors’ efforts,
I use the number of orders accepted during the course of the day7 .
The results presented in the previous section suggest that adverse weather conditions
significantly increase pizza delivery demand. By utilizing the exogenous increase in pizza
delivery demand, I can investigate the relationship between labor supply and labor de-
7
In principle I could use the number of pizzas produced or total earnings during the day as alternative
measures of effort. The adoption of alternative measures of labor supply does not change results very
much. Appendices A3 and A4 show the results obtained with the dependent variable consisting of total
revenue collected, or the number of pizzas produced during the day, respectively.
9mand shocks using the following model:
log(Ordersit ) = α + β1 Rainy Hoursit + Zit β + it (2)
where the dependent variable is the number of orders accepted by vendors i in day t,
the variable Rainy Hours indicates the number of hours of adverse weather experienced
during the course of the day by vendors i and Z is a vector of variables including vendors-
day-of-the-week fixed effects and the full set of monthly and annual fixed effects.
For each pizza vendor, the number of rainy hours observed in a day is computed taking
a given hour as the starting point and the time at which the last order was placed as
the ending point. This starting hour corresponds to the earliest hour at which an order
was observed over the entire sample. Thus, while the starting hours vary among vendors,
it is assumed to be constant over the period in question. An alternative approach is to
consider the time at which the first order was placed during the day as the starting point.
This approach, which is implicitly adopted by Crawford and Meng (2011), allows starting
hours to vary among vendors and across days, but relies on the strong assumption that the
waiting time for the first order is always equal to zero. This approach seems inconsistent
with the daily activity of pizza vendors, since as with taxi drivers, a series of preliminary
steps are required (in this case, for example, a certain stable oven temperature is required
for pizzas to be made)8 .
[Table 4]
Column (1) of Table 4 contains OLS estimates obtained using the number of wet hours
observed in the day as the variable of interest. The corresponding coefficient is positive
and statistically significant. The demand for delivered pizzas is positively influenced by
adverse weather conditions, and consequently vendors react by making more effort. Simi-
lar results are obtained when the variable in question is the total rainfall (in millimeters)
during the day (Column 2).
Overall, the estimates shown in Table 4 provide evidence of the positive relationship
between labor demand and labor supply of food delivery vendors: vendors work more
when earning opportunities are greater. The size of the coefficients suggests that 5 rainy
hours (corresponding to the average number of wet hours observed on rainy days) result
in a 5% increase in the number of orders accepted by food delivery vendors. Moreover, it
8
It should be pointed out that when the alternative measure is adopted, all the results are qualitatively
similar.
10is interesting to note that the coefficients in Table 4 are fairly similar to the coefficients
obtained in Section 3 using Google Trend data.
However, it should also be noted that these results, while providing initial evidence of the
positive sign of labor supply elasticity, do not provide very much information. Positive
elasticity of labor supply is not inconsistent with the presence of target behavior. Vendors
fail to respond to a positive change in labor demand if, and only if, labor supply decisions
are exclusively driven by reference-dependent preferences9 . Since labor supply decisions
cannot plausibly be driven solely by the target behavior, it seems reasonable to investigate
vendors’ behavior using a more flexible empirical strategy permitting the co-existence of
the neoclassical component of labor supply with the reference-dependent effect.
4.2 Estimations using Crawford and Meng’s Target
In the next section I replicate the analysis of Crawford and Meng (2011) by using pizza
sales figures. Obtaining a similar finding is of crucial importance since it implies that
despite the intrinsic differences between taxi drivers and pizza vendors (e.g. single vs
group of workers, different settings and cities), any differences in the results are due to the
different econometric approach rather than to the differences between the two settings10 .
Using pizza-delivery data, I estimate a probit model of the probability that vendors i
will stop delivering on day t after order x has been accepted, as a function of cumulative
orders accepted during the day and a dummy variable indicating whether orders accepted
in a day exceed the target:
P (stopitx = 1) = Φ(δI[Yitx > Tit ] + γYitx + Zitx β) (3)
where Φ(·) is the standard normal cumulative distribution function, I[·] is a function that
takes value 1 if the number of orders accepted at that point in the day is more than the
target level of orders Tit and Z is a vector of variables that includes controls for weather
conditions and vendors’ day of the week fixed effects and the full set of hour of the day,
monthly and yearly fixed effects.
9
In a model of labor supply decisions where total utility is defined as a weighted average of consumption
utility and gain-loss utility, workers will not respond to a demand shock only in the case where the gain-
loss utility’s weight is equal to one. See Appendix A1.
10
I depart from their analysis by modeling pizza vendors’ labor supply decision solely as a function of
their effort. However, it is important to note that the fundamental results of this section are qualitatively
the same if I adopt a labor supply model with two targets, namely specific sample average income and
hours worked prior to the current day, like the one adopted by Crawford and Meng (2011).
11Following Crawford and Meng (2011), I compute the target using vendors’ monthly and
day-of-the-week specific sample average orders accepted in one day, prior to day t (i.e.
the target for vendors i, for day-of-the-week d in month m is the average number of
orders accepted by vendors i in previous days-of-the-week d in month m up to but not
including the day in question)11 . Despite the presence of endogenous regressors, the
empirical strategy proposed by Crawford and Meng (2011) has the advantage of isolating
the neoclassical component of labor supply from the reference-dependent effect. While
the estimated coefficient of cumulative orders provides evidence of that part of labor-
supply behavior related to standard preferences, the coefficient of the dummy indicates
the variation in the probability of the vendor continuing work after the target has been
reached. If positive and statistically significant, the coefficient of the target will provide
evidence of a significant deviation from the standard labor supply model.
Table 5 contains the marginal probability effects obtained using the reduced form model
of stop-working probability. Following Crawford and Meng (2011), the model in the
first column contains weighted estimates, where the weights are equal to the number of
observations used to compute the target. Since sampling error tends be larger in the first
part of the sample period, weighted estimates reduce the bias due to sampling variation.
Results from unweighted regression, where sampling variation is ignored, are shown in
Column (2). Results obtained using unweighted and weighted regressions are essentially
the same. In both models, the target’s coefficients are positive and statistically significant:
vendors are more likely to stop working when they hit their target. At the same time,
the level of orders accepted has a significant and negative effect, providing evidence of the
presence of a neoclassical component in the labor supply decisions of pizza vendors.
[Table 5]
Despite the differences between the two settings, the results presented in this section are
substantially consistent with those of Crawford and Meng (2011). Pizza vendors appear
to act like taxi drivers: being above the set target increases the probability that will stop
working. Overall these results suggest that reference-dependent preferences play a key role
in the labor supply behavior of pizza vendors: when demand is higher than expected (i.e.
11
An alternative approach would have been to construct the target as the expected rainfall for the
current day. The idea is that vendors may form their expectations regarding labor demand on the basis
of weather forecast data. I have collected hourly weather forecasts for the corresponding period from a
major weather forecast provider. The corresponding results are presented in Appendix A3. Results are
not consistent with the predictions of the reference-dependence model. However, the poor performance
of weather forecasts raises certain doubts about the fact that vendors rely on such forecasts to form their
expectations of pizza demand for the day in question.
12vendors have already reached their target for the day but pizzas are still being ordered),
vendors are more likely to stop working. However, it is not clear why vendors reach their
target (i.e. what are the factors that make pizza demand higher on that specific day),
and it also doubtful whether (and difficult to understand how) target is correlated to the
factors underlying demand for pizza delivery services.
Not surprisingly, the coefficient of the dummy variable indicating whether it was raining
during the corresponding hour12 is negative and statistically significant: workers’ efforts
are positively related to any positive variation in demand for pizzas. In other words,
when earning opportunities are temporarily higher, vendors’ behavior is consistent with
the prediction of the standard model of labor supply.
It should be pointed out that the role played by reference-dependent preferences in labor
supply decisions would indicate that workers will respond differently to demand shocks
if they have already reached their target13 . Unlike Crawford and Meng (2011), I can
investigate this theoretical prediction by combining the dummy indicating whether orders
accepted at that point in the day exceed the target, and the variable indicating whether
it was raining during the corresponding hour. If reference-dependent preferences play an
important role in determining vendors’ labor supply decisions, then the coefficient of the
interaction term is expected to be positive and statistically significant (i.e. if vendors
have reached their target they are less likely to respond to an increase in demand for
pizza delivery).
[Table 6]
Table 6 reports the coefficient of the interaction model. The coefficients of the inter-
action terms are not statistically significant at conventional levels. Results from both
the weighted and the unweighted models show that the coefficient in question is actually
positive, as theory predicts, but is far from significant: when earning opportunities are
temporarily higher, the fact of surpassing the target plays no role in vendors’ labor supply
decisions14 .
The results presented in this section indicate that i) adverse weather conditions are pos-
itively related to workers’ efforts, and ii) the role of target is unclear when demand is
actually temporarily higher (i.e. during rainy hours). Overall, these results raise cer-
12
Similar results are obtained when rain is measured in millimeters, see Appendix A5.
13
In Appendix A1 I formulate two alternative models of labor supply for piece-rate workers operating
in a market characterized by menu costs, designed to produce theoretical predictions
14
The coefficient of the interaction term is negative when adverse weather conditions are defined in
terms of the amount of rain (in millimeters) that falls within an hour.
13tain doubts about Crawford and Meng’s estimates and about the relevance of reference-
dependent preferences to vendors’ labor supply decisions.
4.3 Estimations using Rainfall Variation
Unlike Crawford and Meng, I can use changes in weather conditions to isolate exogenous
variations in vendors’ earning opportunities. In this section I investigate the relevance
of the target component, using demand shocks, defined in terms of rainfall variation, as
instrument for pizza demand during the day.
Using adverse weather conditions on a given day, I create two instruments for estimation
purposes. I construct the variable Cumulative Rainy Hours as the number of rainy hours
observed up to that point in the day15 . I also formulate a target variable labeled Target
Rainy Hours, using vendors’ day of the week/ monthly sample average daily number of
rainy hours observed up to, but not including, the day in question. As in the previous
section, the first variable isolates the neoclassical component of labor supply, while the
second variable is a proxy for the vendors’ rational point expectations of demand for pizza
during the day.
[Table 7]
Due to the non-trivial solution of a standard two-stage regression in a probit model with
multiple endogenous variables, I first present the reduced-form estimates16 .
Table 7 reports the marginal probability effect obtained using the reduced-form model,
where the probability that vendors end their working day is a function of the number of
rainy hours observed during the day, and a dummy variable indicating whether rainfall
reaches the estimated target. The left-hand panel shows the estimates of the weighted
model. The coefficient of cumulative rain is negative and statistically significant, and in
keeping with the results presented in Section 4.1 it suggests the presence of a neoclassical
component in the labor supply decisions of pizza vendors. However, the estimated coef-
ficient of dummy variables indicating whether daily rainfall exceeds the target is close to
zero, and is far from being statistically significant. Similar findings are reported in the
15
As explained in Section 4.1, cumulative rainfall is calculated for each pizza vendor using a given hour
as a starting point. The starting hour corresponds to the earliest hour at which an order was observed
over the entire sample. Thus, while the starting hour varies from one vendor to the next, it is taken to
be constant over the period in question.
16
The information underlying the relationship between rainfall-based and orders-based variables is
provided in Table 10.
14right-hand panel containing estimates of the unweighted regression.
Table 8 shows the conventional two-stage least-square estimates17 . Columns (1) and (2)
contain the 2SLS results from the weighted and unweighted models respectively. In both
cases, the Angrist-Pischke first-stage F statistics (Angrist and Pischke (2008) are suitably
high, and confirm that initial stage relationships are strong enough. Reported estimates
are consistent with the reduced-form results, and provide no support for the relevance of
reference-dependent preferences to the labor-supply records of pizza vendors. The effect
of cumulative orders during the day is negative and highly significant, while the coefficient
indicating whether orders accepted exceed the target, is devoid of statistical significance
in both models.
[Table 8]
Overall, these results contrast with the estimates obtained in Section 4.2. When truly
exogenous demand shifters are used, the behavior of pizza vendors is perfectly consistent
with the predictions of the standard model of labor supply, and reference-dependent
preferences play no role in vendors’ labor supply decisions.
5 Conclusions
It is vitally important to understand the role played by behavioral components in workers’
labor supply decisions. If behavioral factors play an important role in labor supply deci-
sions then policies that neglect such anomalies are going to be sub-optimal. In this paper I
investigate the role of behavioral anomalies in the context of labor supply decisions. Using
high frequency data for pizza sales, I study the labor supply behavior of Home Delivery
Pizza Vendors in Bologna. Building on Crawford and Meng’s (2011) analysis, I show that
when targets are defined as average sample realizations of previous labor supply decisions,
I find evidence of reference-dependent behavior. As Crawford and Meng (2011) also dis-
covered, the probability of vendors stopping work is higher when they reach their targets.
However, unlike with previous works, I am able to identify an exogenous, transitory de-
mand shifter. Unlike Crawford and Meng (2011), I can investigate the relevance of the
target behavior using rainfall figures as an instrument for earning opportunities. When
truly exogenous demand shifters are used, the target component plays no role in vendors’
labor supply decisions, and the observed behavior is consistent with the prediction of the
standard labor supply model.
17
The comparable linear probability model’s estimates using Target Orders and Cumulative Orders are
given in Table 9.
15References
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foreshadow housing prices and sales. NBER Chapters.
17Tables and Figures
Figure 1: Pizza Delivery Restaurants and Orders Across the City of Bologna.
Figure 2: Distribution of Orders over the Day.
Orders by Clock hour
.2
.15
Frequency
.1
.05
0
9 11 13 15 17 19 21 23 01 03
Clock hour
18Table 1: Descriptive Statistics
Full Sample Sundays January
Obs. Mean St. Dev. Obs Mean St. Dev. Obs. Mean St. Dev.
Number of Orders 19,746 7.44 7.54 2,916 10.89 9.80 1,319 8.26 7.93
19
Daily Revenues (in e) 19,746 68.15 66.71 2,916 96.25 89.43 1,3198 80.03 76.41
Number of Pizza Produced 19,746 14.91 17.45 2,916 20.91 22.07 1,319 16.77 16.26
Daily Precipitation (in mm) 19,746 1.04 3.24 2,916 1.66 3.84 1,3198 0.66 2.23
Number of Rainy Hour in a Day 19,746 0.87 2.18 2,916 1.55 3.33 1,319 0.83 2.66
Notes: Notes. The table reports the summary statistics for all the variables used throughout the empirical analysis. The unit of observation is the pizza delivery restaurant in each day.Figure 3: Number of Rainy Days per Month.
Figure 4: Number of Rainy Hours per Day.
20Figure 5: Daily Search Volume for the Words ”Pizza Restaurant Bologna”
Table 2: Google searches for the words ”pizza restaurant Bologna” and weather conditions
(log) Searches (log) Searches (log) Searches
Rainy Day 0.0635**
(0.026)
Number of Rainy Hours in the Day 0.0072***
(0.002)
Daily Precipitation (in mm) 0.0069***
(0.002)
Controls Yes Yes Yes
R-squared 0.7030 0.7030 0.7046
Observations 546 546 546
Notes: *** Significant at the 1% level, ** at the 5% level, * at the 10%. Robust standard error are in parentheses. Estimates based on data
on daily search Google Index provided by Google Trends. I used the GI of the Italian word for ”pizza restaurant Bologna” for the period
February 2010 - July 2011. All columns include dummies for day of the week, month, year.
21Table 3: Adverse Weather and Delivery Time
(1) (2)
(log) Delivery (log) Delivery
Time Time
Orders * Rainy Hour 0.0063**
(0.003)
Orders * Hourly Precipitation (in mm) 0.0027**
(0.001)
Controls Yes Yes
R-squared 0.7401 0.7400
Observations 75,944 75,944
Notes: *** Significant at the 1% level, ** at the 5% level, * at the 10%. Standard error by vendors and day are assumed. Columns include
vendors-day of the week FEs, month FEs, year FEs and hour of the day FEs and the average distance of delivered orders in the
corresponding hour. The variable Rainy Hour takes value 1 if in the corresponding hour it has rained.
22Table 4: Adverse Weather Conditions and Vendors’ Labor Supply
(log) Orders (log) Orders
Number of Rainy Hours in the Day 0.018***
(0.002)
Daily Precipitation (in mm) 0.010***
(0.001)
Controls Yes Yes
R-squared 0.6782 0.6778
Observations 19,746 19,746
Notes: *** Significant at the 1% level, ** at the 5% level, * at the 10%. Standard error clustered by vendors are assumed. Columns include
vendors-day of the week FEs, month FEs, year FEs and hour of the day FEs.
Table 5: Marginal Effects on the Probability of Stopping - Crawford and Meng’ Target
Weighted Unweighted
Cum. Orders > Target Orders 0.034*** 0.040***
(0.003) (0.003)
Cumulative Orders /10 -0.047*** -0.054***
(0.004) (0.004)
Rainy Hour -0.024*** -0.021***
(0.005) (0.005)
Controls Yes Yes
Log likelihood -114,775.29 -28,521.724
Pseudo R2 0.3847 0.3866
Observations 493,517 120,209
Notes: *** Significant at the 1% level, ** at the 5% level, * at the 10%. Standard error clustered by vendors and day are assumed. Columns
include vendors-day of the week FEs, month FEs, year FEs and hour of the day FEs. The model in the first column contains weighted
estimates, where the weights are equal to the number of observations used to compute the target. Results from unweighted regression, where
sampling variation is ignored, are shown in the second column. The variable Rainy Hour takes a value of 1 if it has rained during the
corresponding hour. Evaluation point: after 10 orders on a rainy hour at 9:00 pm.
23Table 6: Target Behavior and Heterogeneous Response to Demand Shocks
Weighted Unweighted
Cum. Orders > Target Orders 0.144*** 0.164***
(0.015) (0.014)
Cumulative Orders /10 -0.200** -0.225***
(0.017) (0.016)
Rainy Hour -0.125*** -0.099***
(0.035) (0.032)
(Cum. Orders > Target Orders) * Rainy Hour 0.042 0.024
(0.046) (0.043)
Controls Yes Yes
Log likelihood -114,773.62 -28,521.592
Pseudo R2 0.3847 0.3866
Observations 493,517 120,209
Notes: *** Significant at the 1% level, ** at the 5% level, * at the 10%. Standard error clustered by vendors and day are assumed. Columns
include vendors-day of the week FEs, month FEs, year FEs and hour of the day FEs. The model in the first column contains weighted
estimates, where the weights are equal to the number of observations used to compute the target. Results from unweighted regression, where
sampling variation is ignored, are shown in the second column. The variable Rainy Hour takes a value of 1 if it has rained during the
corresponding hour.
Table 7: Marginal Effects on the Probability of Stopping - Crawford and Meng’s Target
Reduced-Form Estimates using Rainfall Variations.
Weighted Unweighted
Cum. Rainy Hours> Target Rainy Hours 0.003 0.008
(0.005) (0.005)
Cumulative Rainy Hours /5 -0.015*** -0.018***
(0.004) (0.004)
Controls Yes Yes
Log likelihood -115,103.21 -28,630.311
Pseudo R2 0.3829 0.3842
Observations 493,517 120,209
Notes: *** Significant at the 1% level, ** at the 5% level, * at the 10%. Standard error clustered by vendors and day are assumed. Columns
include vendors-day of the week FEs, month FEs, year FEs and hour of the day FEs. The model in the first column contains weighted
estimates, where the weights are equal to the number of observations used to compute the target. Results from unweighted regression, where
sampling variation is ignored, are shown in the second column. Evaluation point: after 5 wet hours at 9:00 pm.
24Table 8: Probability of Stopping - 2SLS Results
Weighted Unweighted
Cum. Orders> Target Orders 0.067 0.118
(0.088) (0.078)
Cumulative Orders /10 -0.120** -0.144***
(0.050) (0.047)
AP 1st Stage F-stat: Cum. Orders > Target Orders 16.95 22.70
AP 1st Stage F-stat: Cumulative Orders /10 8.32 13.70
Controls Yes Yes
Observations 493,519 120,210
Notes: *** Significant at the 1% level, ** at the 5% level, * at the 10%. Standard error clustered by vendors and day are assumed. Columns
include vendors-day of the week FEs, month FEs, year FEs and hour of the day FEs. The model in the first column contains weighted
estimates, where the weights are equal to the number of observations used to compute the target. Results from unweighted regression, where
sampling variation is ignored, are shown in the second column.
Table 9: Probability of Stopping - OLS estimates - Crawford and Meng’s Target
Weighted Unweighted
Cum. Orders> Target Orders 0.070*** 0.070***
(0.002) (0.002)
Cumulative Orders /10 -0.097** -0.095***
(0.002) (0.002)
Controls Yes Yes
R-squared 0.2826 0.2888
Observations 493,519 120,210
Notes: *** Significant at the 1% level, ** at the 5% level, * at the 10%. Standard error clustered by vendors and day are assumed. Columns
include vendors-day of the week FEs, month FEs, year FEs and hour of the day FEs. The model in the first column contains weighted
estimates, where the weights are equal to the number of observations used to compute the target. Results from unweighted regression, where
sampling variation is ignored, are shown in the second column.
25Table 10: Relationship between precipitation-based and orders-based variables
Weighted Unweighted
Cum. Orders Cumulative Cum. Orders Cumulative
> Target Orders Orders /10 > Target Orders Orders /10
Cum. Rainy Hours > 0.113*** -0.026 0.124*** -0.022
Target Rainy Hours (0.043) (0.049) (0.041) (0.042)
Cumulative Rainy Hours /5 0.054 0.211*** 0.023 0.191***
(0.042) (0.058) (0.038) (0.049)
Controls Yes Yes Yes Yes
Log likelihood -209,824.46 n.a -52,032.884 n.a
R-squared 0.2888 0.7131 0.2579 0.7034
Observations 493,517 493,519 120,209 120,210
Notes: *** Significant at the 1% level, ** at the 5% level, * at the 10%. Standard error clustered by vendors and day are assumed. Columns
include vendors-day of the week FEs, month FEs, year FEs and hour of the day FEs. The model in Column (1) and (2) contains weighted
estimates, where the weights are equal to the number of observations used to compute the target. Results from unweighted regression, where
sampling variation is ignored, are shown in Column (3) and (4).
26Appendix A1: RDP and heterogenous responses to demand shocks
In the following sections I develop two models of labor supply for piece-rate workers that
operate in a market with menu costs. Reference-dependent preferences model predicts
that workers should respond differently to demand shock if they are above the target.
Evidence of the reference-dependent preferences in labor supply decision can be obtained
by interacting the dummy variable indicating whether effort exceeds the target with the
rainfall variable. The results reported in Tables 6 and 17 do not provide such support.
A standard model of labor supply
Pizza vendors operate in a monopolistically competitive framework. The market is char-
acterized by the following demand function:
q = (A − p) (4)
where p and q represent price and quantity of pizza and A>0.
The vendors’ utility is
U = p · q − c(q) (5)
where p and q represent price and quantity of pizza produced and c(q) = θq represents
linear effort cost.
Using (1) and (2) the vendors’ maximization problem can be written as
max U = (A − q) · q − θq (6)
q
The first order condition of (3) w.r.t. q is
∂U
=A−2·q−θ =0 (7)
∂q
utility maximization yields
? A−θ
q = (8)
2
and a price of
? A+θ
p = (9)
2
Consider a demand shock (AR >A) and suppose that the food vendors are able to change
the price but only at a menu cost of z (i.e. the cost of literally printing new menus).
27In the presence of menu cost the food vendors might find it optimal to not adjust pizza’s
price to the level
AR + θ
p?R = (10)
2
rather, they might choose to keep the price at p? and adjust its output to18
AR − θ
qR? = (11)
2
In a market with the presence of menu costs a change in aggregate demand affects quantity
but not prices.
A model with reference-dependent preferences
Following Kőszegi and Rabin (2006), I write the vendors’ total utility V (q|q T ), as a
weighted average of standard utility U (q) and gain-loss utility R(q|q T ), with weights
1 − η and η, as follows:
V (q|q T ) = (1 − η)U (q) + ηR(q|q T ) (12)
where the gain-loss utility
R(q|q T ) = µ(q − q T ) (13)
where q T is the effort target value19 ,and µ(·) is a ”universal gain-loss function” that
satisfies the following properties:
• µ(x) is strictly increasing
• µ00 (x) ≥ 0 for x0
The vendor’s maximization problem is
max V (q|q T ) = (1 − η) ((A − q)q − θq) + η µ(q − q T )
q
(14)
18
I observe such behaviour whenever z > ∆Ũ where ∆Ũ (∆Ũ =UR − U˜R = pR · qR − C(qR ) − (p · q̃R −
C(qR )).
19
Following Kőszegi and Rabin (2006), I model target as set equals to the agents’ rational expectation.
Building on Crawford
and Meng (2011), I treat them as point expectations rather than distributions
E(A)−θ
q T = E(q) = 2 .
28The first order condition of (11) w.r.t. q is
∂V
= (1 − η)(A − 2q − θ) + η µ0q (q − q T ) = 0
(15)
∂q
20
I can identify the relation between A and q through
∂λ
∂q 1−η
= − ∂A
∂λ
=− 00 (q − q T )
(16)
∂A ∂q
−(1 − η)2 + η µ qq
if η = 1 (i.e. the standard utility weight is equal to 0):
∂q
=0 (17)
∂A
if (q − q T ) < 0 (i.e. the vendor is below his target):
∂q − ∂λ
∂A 1−η
= − ∂λ = − 00 (·)
(18)
∂A ∂q
−(1 − η)2 − η µ qq
if (q − q T ) > 0 (i.e. the vendor is above his target):
∂λ
∂q + 1−η
= − ∂A
∂λ
=− 00 (·)
(19)
∂A ∂q
−(1 − η)2 + η µ qq
and
∂q + ∂q −
< (20)
∂A ∂A
20
λ indicates equation (12).
29Appendix A2: Target using Forecast Data
An alternative approach would have been to construct the target as the expected rainfall
for the current day. The idea is that vendors could form their expectations regarding po-
tential labor demand for the day using weather forecast data. Since adverse weather con-
ditions positively affect demand for pizza delivery, when vendors observe adverse weather
forecasted for following day, they expect demand to be higher. I have collected hourly
weather forecasts for the period between February 2010 and July 2011 provided by one of
Italy’s main weather forecast providers (http://www.3bmeteo.com/). Forecast data are
provided the day before the day in question, and refer to the Bologna urban area.
Despite the short-term nature of forecasts, they tend to perform rather poorly. During the
period from February 2010 to July 2011 there were 212 days for which weather conditions
were wrongly predicted (i.e. when the actual number of rainy hours in the day was
different from the corresponding forecast). Figure 6 shows the days for which the weather
was wrongly forecasted (dark lines).
Figure 6: Days With Wrongly-Forecasted Weather.
The frequency of dark lines suggests the poor accuracy of weather forecasts. Figure 7
plots the number of days per month for which the weather was wrongly forecasted, and
provides additional information about the low level of forecast accuracy. On average, the
weather was wrongly forecast 11 days per month, and in two cases (February 2010 and
December 2010), the number of days when the weather was wrongly forecasted exceeded
the number of days for which it was correctly forecasted.
30Figure 7: Number Of Days per Month on which the Weather was Wrongly Forecast.
Bearing in mind the unreliability of weather forecasts, I replicated the analysis of Section
4.1 using the following model:
log(Ordersit ) = β1 + β2 (N o. of Rainy Hours during the Dayit > F or. N o. of Rainy Hours during the Dayit )+
+β3 N o. of Rainy Hours during the Dayit + Zit β + it
where the dependent variable is the (log) number of orders accepted by vendors i on day t,
the variable (N o. of Rainy Hours during the Dayit > F or. N o. of Rainy Hours during the Day)
is a dummy indicating that the day’s rainfall hit the forecasted number of rainy hours for
that day. Z is a vector that includes vendors’ day of the week fixed effects and the full
set of monthly and yearly fixed effects.
The results are shown in Column (1) of Table 11. The coefficient of the variable indicating
the actual number of rainy hours is positive and statistically significant. This result
confirms the findings presented in Section 4.1: vendors respond positively to changes in
earning opportunities. Moreover, the coefficient of the variable indicating whether rainy
hours in a day exceed the forecasted number of wet hours, is positive and statistically
significant. Similar results are obtained when adverse weather conditions are defined in
terms of milliliters of rain (Column 2), the only difference being that the target coefficient
is no longer statistically significant.
While the results of this section do not provide any precise general predictions, and are
only meant to offer supplementary evidence, the sign and significance of the estimated
coefficients provide no evidence of the presence of target behavior.
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