metadata: authors: 0: author: Dillon,Brian
1: author: De Weerdt,Joachim
2: author: O'Donoghue,Ted
count: Tanzania
docna: 0: docna: Paying More for Less : Why Don't
            Households in Tanzania Take Advantage of Bulk Discounts ?
docty: Policy Research Working Paper
subtopic: Macro-Fiscal Policy,Economic Adjustment and Lending,Taxation & Subsidies,Public Finance Decentralization and
            Poverty Reduction,Public Sector Economics,Educational Sciences,Gender and Development,International Trade and Trade Rules,Demographics
teratopic: Macroeconomics and Economic Growth,Public Sector Development,Health, Nutrition and Population,International Economics and Trade,Education,Gender
abstracts: cdata!: Do poor households shop in a way that
            leaves money on the table? A simple way to maximize
            consumption, conditional on available cash, is to avoid
            regularly purchasing small amounts of nonperishable goods
            when bulk discounts are available at modestly larger
            quantities. Using two-week transaction diaries covering
            48,501 purchases by 1,493 households in Tanzania, this paper
            finds that through bulk purchasing the average household
            could spend 8.7 percent less without reducing purchasing
            quantities. Several explanations for this pattern are
            investigated, and the most likely mechanisms are found to be
            worries about over-consumption of stocks and avoidance of
            social taxation. Contrary to prior work, there is little
            indication that liquidity constraints prevent poorer
            households in the sample from buying in bulk, possibly
            because the bulk quantities under examination are not very large.
geo_reg_key: 119229,517191
repnme: repnme: Paying More for Less : Why Don't
            Households in Tanzania Take Advantage of Bulk Discounts ?
display_title: Paying More for Less : Why
            Don't Households in Tanzania Take Advantage of Bulk Discounts
listing_relative_url: /research/2020/02/31822590/paying-more-less-dont-households-tanzania-take-advantage-bulk-discounts
topicv3: Trade m1326924 698,Demographic Change m1327040 1448,Education m1327048 470,Taxation m1327615 1121,Gender m1327621 615
publishtoextweb_dt: 2020-02-27T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Public Sector Development,Health, Nutrition and Population,International Economics and Trade,Education,Gender
origu: DEC-Knowledge and Strategy (DECKS)
no_of_pages: 72
author_keys: 0: author_key: 992678
1: author_key: 669258
model_extractions: Policy Research Working Paper 9167

# Paying More for Less

Why Don’t Households in Tanzania Take Advantage of Bulk Discounts?

_Brian Dillon Joachim De Weerdt Ted O’Donoghue_ Development Economics Knowledge and Strategy Team February 2020
Policy Research Working Paper 9167

# **Abstract**

Do poor households shop in a way that leaves money on the table? A simple way to maximize consumption, conditional on available cash, is to avoid regularly purchasing small amounts of nonperishable goods when bulk discounts are available at modestly larger quantities. Using two-week transaction diaries covering 48,501 purchases by 1,493 households in Tanzania, this paper finds that through bulk purchasing the average household could spend 8.7 percent less without reducing purchasing quantities. Several explanations for this pattern are investigated, and the most likely mechanisms are found to be worries about over-consumption of stocks and avoidance of social taxation. Contrary - to prior work, there is little indication that liquidity con straints prevent poorer households in the sample from buying in bulk, possibly because the bulk quantities under examination are not very large.

This paper is a product of the Knowledge and Strategy Team, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at bmd28@cornell.edu.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Paying More for Less: Why Don’t Households in Tanzania Take Advantage of Bulk Discounts?<sup>_∗_</sup> Brian Dillon, Joachim De Weerdt, and Ted O’Donoghue

> _∗_ Brian Dillon (corresponding author) is an assistant professor at Cornell University, Ithaca, NY, USA; his email address is bmd28@cornell.edu. Joachim De Weerdt is Senior Lecturer at the University of Antwerp and Senior Research Fellow at KU Leuven, Belgium; his email address is Joachim.DeWeerdt@uantwerpen.be. Ted O’Donoghue is a professor at Cornell University, Ithaca, NY, USA; his email address is edo1@cornell.edu. For helpful discussions and comments the authors thank Jenny Aker, Abhijit Banerjee, Chris Barrett, Jim Berry, Ann Bostrom, Peter Brummund, Arun Chandrasekhar, Paul Christian, Kelly Husted, Joe Kaboski, Kelsey Jack, Supreet Kaur, Steve Kosack, Michael Kremer, Mujobu Moyo, Sendhil Mullainathan, Rohini Pande, Robert Plotnick, Imran Rasul, Jonathan Robinson, Mark Rosenzweig, Thaddeus Rweyemamu, Hilary Wething, Dean Yang, and seminar audiences at the ASSA conference, the CSAE conference in Oxford, University of Washington, University of Alabama, Cornell University, Michigan State University, and KU Leuven.
# **1 Introduction**

The marginal value of consumption is very high for poor households. For this reason, one expects households in low-income countries to be especially mindful of ways to arrange purchases so as to maximize consumption per dollar. This paper studies the surprising, contrary finding that many households in Tanzania purchase non-perishable goods in small increments, multiple times, over a two-week period. If price schedules were linear and transaction costs minimal, frequent purchasing of small quantities would have no impact on the budget set. If bulk discounts were available, but only for large quantities representing several weeks or months of consumption, there could be many reasons not to buy in bulk. However, we find that many items exhibit bulk discounts over modest quantity ranges. Households appear to be systematically over-paying for consumption goods in order to maintain a pattern of frequent, small-quantity purchases.

The goal of this paper is to better understand this phenomenon. We aim to answer two questions. First, how much consumption is foregone because of small-quantity purchasing? Second, why do households make purchases in this way?

To answer the first question we analyze transaction diaries maintained by 1,493 Tanzanian households over a two-week period. Diary respondents recorded the date, quantity, price, and detailed description of every purchase. From these data we calculate the total quantity purchased at the household-item level over two weeks, the total amount paid, and the counterfactual cost if the household had purchased the total quantity in one transaction. This last step makes use of expenditure schedules that we estimate from the data (and validate with market price surveys). We limit our analysis to 19 standardized items that are non-perishable over the relevant quantity and time ranges. The item list includes numerous staples: maize, rice, cooking oil, kerosene, onions, dried sardines.

We find that across items purchased multiple times over two weeks, the value of forgone consumption is equal to 8.7% of the value of expenditure. By simply bundling purchases made over a short period of time, the average household could spend almost 9% less on a range of important goods without reducing consumption.<sup>1</sup> There is substantial heterogene-

> 1This should not be thought of as a 9% return on a two-week investment, which could be re-invested for annualized return of over 900%. The implicit return to the household is limited by the bundle it purchases,

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ity: 9% of households have zero forgone consumption, while nearly a quarter could reduce expenditure by 10% or more without reducing quantity purchased. If we take the alternative approach of holding expenditure constant and calculating the counterfactual quantities that could be purchased by buying in bulk, we find even larger average values. Households could purchase 33% more kerosene, 50% more cooking bananas, 24% more cooking oil, 46% more onions, 18% more dried sardines – surprisingly large amounts for goods that are part of daily life in Tanzanian villages.

It appears that there could be substantial welfare gains from rearranging purchases to avoid buying small quantities at high mark-ups. Whether that is actually true depends on the reasons that shoppers arrange purchases this way. The second half of the paper is dedicated to understanding why households forego bulk discounts. We consider a range of hypotheses that come from the literature, from discussions with Tanzanians, or from discussions with other researchers. These include: binding liquidity constraints prevent households from buying in bulk; people enjoy going to the market and shopping; it is too costly to transport bulk quantities; it is too costly to store bulk quantities; consumers are not aware of bulk discounts; coordination failures among household members lead to financially inefficient purchasing; frequent purchases are a way to avoid over-consuming stocks; frequent purchases are a way to avoid stocks that attract friends and neighbors requesting hand-outs.

The paper presents evidence against all of these hypotheses except the last two, for which there is support. The finding that households make frequent purchases as a way to ration consumption, perhaps due to worries that they will consume large stocks more quickly than they would like, is based on the analysis of shopping patterns for “temptation goods,” which we identified through a separate survey effort in Tanzania. The suggestive evidence that households purchase in small quantities in order to avoid social taxation—non-household members consuming a portion of their purchases—aligns with recent work on redistributive pressures in similar settings (Anderson and Baland, 2002; Platteau, 2006; Goldberg, 2016; Baland, Guirkinger and Mali, 2011; Alby, Auriol and Nguimkeu, 2013; Jakiela and Ozier, 2016; Squires, 2016).

> which we hold constant in calculating the value of foregone consumption. Hence, the expected financial savings over the course of an entire year is still in the neighborhood of 9%. Of course, the household might have other ways to reinvest that 9% savings and further improve its financial position.

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The final section of the paper shows that the rationing and social tax channels operate independently, rather than as manifestations of a single underlying set of choices. Nonetheless, these mechanisms do have an important feature in common. Both involve limiting the near-term consumption of a future agent—one’s self, other household members, or nonhousehold members—by avoiding stocks. This raises the question of whether the observed purchasing patterns are sub-optimal. While it is likely that some households could increase utility by buying in bulk, the calculation that the average household could increase consumption by 8.7% does not take into account the possibility of leakage through higher social taxes or over-consumption. In light of this, we are cautious about policy recommendations, discussing instead some directions for future research.

This paper makes four main contributions. The first is to provide a plausible estimate of the value of consumption foregone from paying high mark-ups on small-quantity purchases. There is a large literature from both developing and developed countries on consumer choice when there are bulk discounts (Frank, Douglas and Polli, 1967; Kunreuther, 1973; Wansink, 1996; Chung and Myers, 1999; Bray, Loomis and Engelen, 2009; Griffith et al., 2009; Beatty, 2010; Orhun and Palazzolo, 2016; Rao, 2000; Attanasio and Frayne, 2006; Mussa, 2015; Attanasio and Pastorino, 2015; Gibson and Kim, 2018). Yet, to our knowledge, this is the first paper to estimate the value of forgone consumption from not buying in bulk.

The second contribution is to provide evidence that liquidity constraints are not the key driver of small-quantity purchasing. This finding contrasts much prior work on this issue in developing countries (Rao, 2000; Attanasio and Frayne, 2006; Mussa, 2015; Attanasio and Pastorino, 2015), the exception being a recent paper from urban Papua New Guinea showing that households have sufficient liquidity to buy rice in bulk (Gibson and Kim, 2018). One of the benefits of the data is that we do not need to speculate about whether households have sufficient cash to buy in bulk. The diary of purchases reveals a lower bound on each household’s available liquid resources. We use the observed time path of expenditures at the household-item level to ask the following: how many days would a household have to delay buying the item, and delay buying non-essentials such as sugar and tea, before it had accumulated sufficient savings to buy the item in bulk? This is similar to an exercise in Mullainathan and Shafir (2013). After doing this once, the household could buy in bulk 4
in perpetuity, if a liquidity constraint were the problem. The average required delay in our sample is only 1.2 days. Among the poorest members of the subset of households that are the least financially efficient purchasers, the average is only 2.9 days. For various reasons described in Section 5, these figures are upper bounds. These durations are too short for liquidity constraints to drive the majority of financial losses in our data.<sup>2</sup> In a broad sense, this finding matches the spirit of the evidence in the _Portfolios of the Poor_ (Collins et al., 2010). In the _Portfolios_ , fine-grained details about household finances show that even the poorest in poor countries have complex financial lives. In our setting, a detailed picture of households’ liquid resources reveals greater cash flow than we may have otherwise assumed, and motivates us to look beyond liquidity constraints for other factors that deter bulk purchasing.

The third contribution is to document a clear connection between the temptingness of a good and consumers’ propensity to purchase it in bulk. We asked a set of experts on Tanzanian village life to identify which goods might be subject to over-consumption relative to one’s _ex ante_ plan (Banerjee and Mullainathan, 2010). Because not all goods exhibit bulk discounts in every location, the effect of temptingness on purchase frequency is identified even while controlling for household fixed effects. We find robust evidence that households purchase tempting items more frequently than non-tempting items, causing them to forego some bulk discounts.

The final contribution of the paper is to provide novel insights into the way that social taxation distorts the allocation of resources. Because we observe flows of both incoming and outgoing resources, we are able to construct a proxy measure of each household’s social tax rate, and examine the relationship between social taxes and bulk purchasing. We find a strong link: households that buy in bulk tend to face higher social tax rates. Additional analysis supports the interpretation that causality runs from buying larger quantities to higher social tax rates, rather than the other way around. It seems highly likely that it would be optimal for some households to reduce transaction quantities as a way to deter requests from friends and family, although this final piece is not something we can test

> 2If we were to examine other questions about bulk purchasing, such as why households do not buy large wholesale quantities of consumption items and store them for months at a time, we might arrive at a different conclusion about liquidity.

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directly.

# **2 Conceptual framework**

In this section we develop a conceptual framework for the empirical analysis. We begin with a stylized example, and then develop the approach formally.

## **Motivating example**

In one of the study districts, maize is sold in the following three quantities: 1 kg for 650 TZS; 2 kg for 1200 TZS; and 3 kg for 1350 TZS.<sup>3</sup> This price schedule exhibits bulk discounts. The unit (per-kg) price is 650 TZS for the 1 kg purchase, 600 TZS for 2 kg, and 450 TZS for 3 kg or more.

A household that wishes to consume 4 kg of maize over two weeks has (at least) three options: purchase 4 kilograms all at once and consume it over the two weeks; purchase 2 kilograms, consume it over the first week, then purchase another 2 kilograms at the start of the second week; or purchase 1 kilogram four times over the course of the two weeks. From a purely financial perspective, purchasing the 4 kg in a single transaction—buying in bulk—is most efficient. Suppose that instead, a household purchases a 1 kg bag on four occasions over the two weeks. This raises two questions. First, how large are the losses incurred from not buying in bulk? Second, why would the household do this?

The answer to the second question is the subject of Section 5. There are two ways to answer the first question. We can calculate a financial loss by taking the household’s actual expenditure on the 4 kg of maize (2600 TZS) and subtracting the cost of purchasing the entire 4 kg in bulk (1800 TZS).<sup>4</sup> In this case the financial loss from small-quantity maize purchasing is 800 TZS. Alternatively, we could calculate the quantity that could have been purchased by spending the 2600 TZS all at once at the lowest per-unit price. This is 5 _._ 78 kg—2600 TZS at 450 TZS per kg—which represents a potential quantity increase of 1 _._ 78 kg.

> 3These values represent three “focal quantities”–commonly observed quantities–and the median expenditures for those focal quantities. See Sections 2 and 4.

> 4Consistent with our formal approach, this example assumes that a household can purchase any quantity larger than 3 kg at the per-unit price that applies for a 3 kg transaction (see discussion in the next subsection).

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# **Framework for empirical analysis**

To formalize the above approach, we begin with a set of focal quantities. A focal quantity should be interpreted as roughly a package size or a common unit of trade, analogous to the three quantities in the maize example. In some cases these focal quantities correspond to actual package sizes from mass produced items, such as 1-liter bottles of cooking oil. In other cases, local units have emerged over time as vendors have adopted widely available canisters as standard units of trade.

Suppose item _i_ is available in _R_ focal quantities _{qr}_<sup>_R_</sup> _r_ =1<sup>,orderedsothat</sup><sup>_q_1</sup><sup>_<q_2</sup><sup>_<_</sup> _... < qR_ . Let _er_ denote the expenditure required to purchase quantity _qr_ , and let _pr_ denote the associated unit price, so _pr_ = _er/qr_ . If the focal quantities (weakly) exhibit bulk discounts, we have _p_ 1 _≥ p_ 2 _≥ ... ≥ pR_ . Our approach will be to identify focal quantities empirically, using commonly observed transaction quantities. In the following section we provide details. For now, we take it as given that focal points _{qr}_<sup>_R_</sup> _r_ =1<sup>and</sup><sup>_{pr}R_</sup> _r_ =1<sup>areknownforeachitem.</sup> Over the study period, household _h_ buys item _i_ in _K_ separate transactions. Let _k_ = 1 _, . . . , K_ index the household’s purchases, with the associated quantities and expenditures denoted _qhik_ and _ehik_ . Observed total expenditure is _ehi_ =<sup>�</sup><sup>_K_</sup> _k_ =1<sup>_ehik_,andobservedtotal</sup> quantity is _qhi_ =<sup>�</sup><sup>_K_</sup> _k_ =1<sup>_qhik_.Our goal is to calculate (i) the financial savings if</sup><sup>_h_had instead</sup> purchased _qhi_ in a single transaction, and (ii) the extra quantity if _h_ had instead spent _ehi_ in a single transaction.

These calculations require knowing the expenditure associated with any transaction quantity. To reflect the reality of shopping in these markets, we base such estimates on the expenditure required to make purchases with the focal quantities. Specifically, we define the expenditure schedule, _e_<sup>_∗_</sup> _i_<sup>(</sup><sup>_q_) as the weighted average of the expenditures for the nearest focal</sup> quantities on either side of _q_ : Similarly, the lowest unit price ( _pR_ ) is assigned to any quantity greater than the largest focal quantity (i.e., _e_<sup>_∗_</sup> _i_<sup>(</sup><sup>_q_)=</sup><sup>_qpR_forany</sup><sup>_q>qR_),andthehighestunitprice(</sup><sup>_p_1)isassignedto</sup> any quantity less than the smallest focal quantity (i.e., _e_<sup>_∗_</sup> _i_<sup>(</sup><sup>_q_)=</sup><sup>_qp_1forany</sup><sup>_q<q_1).The</sup> 7
expenditure schedule can be converted into a unit price schedule using _p_<sup>_∗_</sup> _i_<sup>(</sup><sup>_q_) =</sup><sup>_e∗_</sup> _i_<sup>(</sup><sup>_q_)</sup><sup>_/q_.</sup> There are two interpretations of these weighted averages. The first relates to behavior in the market. Consider a shopper in the above example trying to buy 2.5 kg of maize in a single transaction. She may argue that she should pay at most the 2 kg unit price, and perhaps the lower 3 kg unit price. If the probability of receiving a particular unit price is proportional to the distance to the nearest focal quantities, our measure assigns the expected value. A second interpretation relates to our choice of an aggregation period of two weeks, a necessary but somewhat arbitrary decision. In most cases, _qhi_ , the aggregate quantity purchased over two weeks, will not correspond to an exact focal quantity. We could just as easily aggregate purchases over a longer or shorter time period to ensure that _qhi_ is equal to a focal quantity. Our approach effectively calculates the expenditure associated with aggregating to the next lower or next higher focal quantity, and then takes a weighted average.

In the next section it will be apparent that bulk discounts are clearly identifiable within-village and even within-household. For power reasons, we will construct _e_<sup>_∗_</sup> _i_<sup>(</sup><sup>_q_)atthe</sup> district level. This is not as restrictive as it may sound. The identifying assumption required to still permit household-specific price schedules is that any within-district differences in expenditure schedules take the form of linear shifts over the relevant ranges. That is, if _e_<sup>_∗_</sup> _i_<sup>(</sup><sup>_q_)</sup> is the district-level price schedule for item _i_ , but household _h_ faces price schedule _e_<sup>_∗_</sup> _i_<sup>(</sup><sup>_q_)+</sup><sup>_γhiq_</sup> for some scalar _γhi_ , then our loss estimates are unbiased. What matters for the analysis are the relative unit price differences across quantities, not overall differences in price levels. With this approach, households in a district can still face different price schedules for any number of reasons (variation in bargaining power, village effects, or others).

The majority of observed transactions take place at focal quantities. For those that do not, and for focal quantity transactions that are not at focal prices, we project all observed transactions onto the expenditure schedule prior to aggregation. That is, if observed expenditure is represented as _ehik_ = _e_<sup>_∗_</sup> _i_<sup>(</sup><sup>_qhik_) +</sup><sup>_νhik_,wherethe</sup><sup>_νhik_isanidiosyncraticcomponent,</sup> then the adjusted expenditure is _e_ ˆ _hik ≡ e_<sup>_∗_</sup> _i_<sup>(</sup><sup>_qhik_).Thehousehold’sadjustedtotalexpendi-</sup> ˆ ture on item _i_ is _ehi_ =<sup>�</sup><sup>_K_</sup> _k_ =1<sup>_e_ˆ</sup><sup>_hik_.Usingadjustedtotalexpendituresinourcalculationsof</sup> losses ensures that our results are not distorted when a household’s actual expenditure in a 8
particular transaction happens to be above or below the expenditure schedule.

We define the financial loss (or “bulking loss”) on item _i_ as the forgone financial ˆ savings from purchasing _qhi_ in a single transaction. This is calculated as _Lhi ≡ ehi −e_<sup>_∗_</sup> _i_<sup>(</sup><sup>_qhi_) =</sup> _K k_ =1<sup>_e_</sup> _i_<sup>_∗_(</sup><sup>_qhik_)</sup> _− e_<sup>_∗_</sup> _i_<sup>(</sup><sup>_qhi_).The related measure, expressed as a percentage of expenditure, is</sup> �� � the percentage loss _L_<sup> ̃</sup> _hi ≡ Lhi/e_ ˆ _hi_ . Alternatively, to find the extra quantity that household _h_ could purchase if it held expenditure constant but aggregated its spending on _i_ into a single transaction, we invert the expenditure schedule and calculate the quantity loss as _Qhi ≡ e_<sup>_∗−_</sup> _i_<sup>1</sup> (ˆ _ehi_ ) _− qhi_ . Likewise, percentage quantity loss is _Q_<sup> ̃</sup> _hi ≡ Qhi/qhi_ . By construction, all four measures are zero if a household buys an item only once over two weeks.<sup>5</sup> For most of the analysis we focus on the financial-loss measures, _Lhi_ and _L_<sup> ̃</sup> _hi_ , because these can easily be aggregated across items (we will typically refer to these as “loss” and “percentage loss”). The quantity-loss measures provide an additional way to understand the magnitude of the purchasing inefficiencies in the data.

Figure 1 gives a visual example. Imagine a household that buys maize in the market described in the previous subsection. The household reports three maize purchases over the observation period: 1 kg for 650 TZS, 1 kg for 750 TZS, and 1.5 kg for 975 TZS. The _×_ in Figure 1 mark the actual transactions, with the unit price schedule in the left panel and the expenditure schedule in the right panel. Observed expenditure is 2375 TZS (point A). Adjusted expenditure is _e_<sup>_∗_</sup> (1) + _e_<sup>_∗_</sup> (1) + _e_<sup>_∗_</sup> (1 _._ 5) = 650 + 650 + 925 = 2225 (point B). Counterfactual expenditure from bulk purchasing is _e_<sup>_∗_</sup> (3 _._ 5) = 1575 (point C). These three expenditure values are associated with the total observed quantity of 3.5 kg. The counterfactual quantity that could be purchased using the total adjusted expenditure of 2225 all at once is _e_<sup>_∗−_</sup> _i_<sup>1</sup> (2225) = 2225 _/_ 450 = 4 _._ 9 kg (point D). For this example, the financial measures of loss are _Lhi_ = 2225 _−_ 1575 = 650 (the vertical distance between points B and C), and _L_<sup> ̃</sup> _hi_ = 650 _/_ 2225 = 29 _._ 2%. The quantity measures of loss are _Qhi_ = 4 _._ 9 _−_ 3 _._ 5 = 1 _._ 4 kg (the horizontal distance between points B and D), and _Q_<sup> ̃</sup> _hi_ = 1 _._ 4 _/_ 3 _._ 5 = 40%. This household could reduce expenditure on rice by 29.2% without reducing quantity consumed, or increase the quantity of rice consumed by 40% without increasing expenditure.

> 5In this respect the approach is conservative. The items we study are popular consumer goods in Tanzania, and in many cases they can be stored for months. Households that purchase item _i_ only once over the study period could in all likelihood reduce expenditure by bulk purchasing for a longer time period.

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This approach to constructing a counterfactual never requires that households have access to additional cash in order to buy in bulk (although they might need the cash a little sooner, once in the lifetime of the household—see the extensive analysis in the first subection of Section 5). Because we use observed total two-week quantities in constructing the counterfactual—not large, hypothetical purchases off of the observed support—buying in bulk as defined here can only increase, not decrease, the household’s cash reserves over the total two-week period.

Because we are estimating price schedules, not demand curves, the approach is not threatened by censoring concerns related to the two-week observation window. The most likely form of data censoring is that very large purchases, e.g., of wholesale bags of grain, are too infrequent to appear as focal quantities, even though they may be widely available at markets. The absence of these large-quantity purchasing opportunities means that our calculations are likely to be lower bounds on actual losses.

# **3 Data and descriptive patterns**

The data for this paper are from the Survey of Household Welfare and Labor in Tanzania (SHWALITA). The survey was part of an experiment to test the impact of questionnaire design on consumption measures (see Beegle et al. (2012) for details). In one arm of the study, 9 households per village were randomly assigned to complete a consumption diary. Three of these households completed a single, household-level diary, with no monitoring by project staff. Three completed a single household diary but received multiple follow-up visits from field staff. For the last three households each adult member kept their own diary, with children placed on the diary of the most knowledgeable adult. Households in the third group received multiple follow-up visits, similar to those in the second group. The differences between module arms are small but not zero, and they have no impact on the findings in this paper. We control for diary type whenever relevant.

The SHWALITA survey was conducted in 24 villages per district, in 7 districts. The resulting data set includes responses for 1,512 diary households. After dropping households that did not purchase any of the items that we study or that did not complete the end-line 10
survey, we are left with a sample size of 1,493. Data were collected from September 2007 to August 2008. All households in a village completed their diaries over the same 14 days. Survey work in each district was completed in less than two months.<sup>6</sup> Each study household maintained a transaction diary for 14 days. The diary took the form of a paper log book, with a separate row for each transaction. On each day during the observation window, diary keepers noted the quantity, unit, value, and description of every item that entered or exited the household. If multiple items were purchased during a single shopping trip, each item received its own entry (row) in the diary. Purchases, gifts, own production, and stock adjustments were recorded separately. Because this paper deals with purchasing behaviors, we use only those rows of the transaction diaries that indicate purchases, unless otherwise specified.

After collecting the diaries from respondents, project staff used the item descriptions to assign each purchased item to one of 73 categories, covering 58 food items and 15 non-food items. These categories are similar to those that would be available in a typical consumption survey. However, because we have access to the raw diary data, we use the detailed descriptions of each item to further narrow the definitions of the study items. We do this by dropping entries for which the description does not match that of the modal entry within the item category. For example, we drop “unrefined sugar” from “Sugar,” retain only “dried beans” (excluding soy beans) from the original category of “Peas, beans, lentils and other pulses,” keep only “immature coconuts” in the “Coconut” category, restrict the “Dried fish” group to only “dried sardines,” excluding larger fish, and so on. This removes much of the bias from grouping goods of different variety under a single heading. The end result is a data set in which items are far more uniform than those in a typical consumption survey.

We also drop items with too few observations, and drop perishable items that cannot be stored for two weeks by most households (such as beef, milk, and fresh fish). We do not drop or retain items based on whether the price schedule exhibits bulk discounts. After selecting the items, we remove outliers by dropping any observations for which the quantity or unit price is more than 4 standard deviations from the item-level mean, and dropping

> 6More details are available at the project page, accessible here: http://edi-global.com/publications/. Data are available by contacting the lead SHWALITA researchers listed on the project page.

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observations from item-district cells that have insufficient representation to construct a price schedule (fewer than 15 observations). This reduces the sample size by roughly 1%.

A further cleaning step was required to standardize units. Respondents reported many quantities in kilograms and liters, but others in bunches, heaps, tins, ladles, buckets or bundles. For some items these units were measured during the market price survey. For other commonly reported units, the team went back specifically to measure the kg or liter conversion. We use the median, district-level conversion rates to convert local units into kilograms or liters.<sup>7</sup> The final data set contains details for 48,501 purchase transactions. Descriptive details for the final set of 19 study items are reported in Table 1. Maize and cooking bananas— staple carbohydrates—are the items purchased in the largest kilogram quantities. Comparing transaction quantity to total 2-week consumption in Table 1, it is clear that households tend to buy items multiple times over two weeks. Table 2 provides more details on this and other patterns in the diary data. The total number of observed transactions ranges from 688 (maize) to 5319 (cooking oil). The average item was purchased by just under half of the sample (733 households), and was purchased multiple times by just over a third of the sample (505 households). Some items, such as cooking oil, kerosene, sugar, dried sardines, and onions, were purchased more than once by a majority of households. Among the households that purchase each item, the highest average expenditure is on maize at 7,354 TZS/household, and the lowest is on matches at 187 TZS/household. The average number of purchases per item is 3.6.<sup>8</sup> The SHWALITA team also conducted a market price survey in each village, in conjunction with the household survey. Markets are relatively dense in Tanzania: 97% of study households live within 10 kilometers of the nearest market, and the median distance is 1.15 km. For 42 food items (10 of which meet the criteria for inclusion in this study), enumerators visited the village market and recorded the most common units in which each item was sold. They precisely measured the unit in kilograms or liters, and noted the price. Unit prices were

> 7Helpfully, 98.7% of purchases recorded in units other than kilograms or liters were recorded as integer values. Most of the decimal entries in kilograms or liters stem from unit conversions, not from respondents being forced to convert non-standard units into kilograms or liters on the spot.

> 8Additional descriptive statistics for the survey households are provided in Appendix S1.

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collected for up to three different units at the item-vendor level, with the units determined by the vendor based on the most common units of trade. This was done for three vendors per market, with 1-3 visits per vendor. The team repeated the exercise at multiple markets if there was more than one in a village.

While writing this paper we collected two types of additional data. The first came from informal interviews and focus groups in Tanzania, during the years 2012-2015. We conducted 10 interviews with consumers or shopkeepers, and held three informal focus groups, each with 5-6 people. These discussions helped us identify hypotheses for why households might forego bulk discounts, and provided relevant anecdotes about consumer behavior. Our second data collection effort was an on-line survey conducted in June-July 2016. This short survey was sent to a group of Tanzanians with extensive knowledge of household decisionmaking around economic issues. We describe this survey in the relevant subsection of Section 5.

# **4 Quantifying the value of forgone consumption**

In this section we estimate the value of consumption that households forego by not buying in bulk. The first subsection describes the bulk discounts and the estimated expenditure schedules. The next subsection uses the estimated expenditure schedules to provide estimates of the financial losses and quantity losses, and examines heterogeneity.

## **Bulk discounts in the data**

While our main analysis uses focal points in the diary data to estimate price schedules (as described in Section 2), it is easy to see that bulk discounts are present in simple linear models. We first estimate such regressions using the market price survey data, which was collected in tandem to the diaries. Columns 1–3 of Table 3 show slope coefficients from itemspecific, transaction-level regressions, with log unit price as the dependent variable and log quantity as the independent variable. These regressions include district (column 1), village (column 2), or vendor (column 3) fixed effects, with standard errors clustered at the village 13
level.<sup>9</sup> The majority of coefficients in columns 1–3 are negative and statistically significant. There is only one positive and significant slope coefficients, on cooking bananas (column 2), but it is statistically indistinguishable from zero when we look within vendor (column 3).

For comparison purposes we estimate similar regressions using the diary data. Columns 4 and 5 of Table 3 show the slope coefficients. These estimates are not directly comparable with those in columns 1–3, because for some items the quantity support is different across the two data sets. Our interest is primarily in the signs of the estimated coefficients.

In columns 4 of Table 3, all but two estimated slope coefficient are negative, and none are positive and statistically significant. Looking within household (column 5), all coefficients are negative and 16 of 19 are statistically significant.<sup>10</sup> Taken together, the clear pattern in the market survey and diary data sets is that unit price is decreasing in quantity for many items. This finding holds within village-day, within-vendor, and within-household.<sup>11</sup> Having established that bulk discounts exist, we turn to the non-parametric approach of Section 2 to estimate expenditure schedules. The focal-point approach is less susceptible to measurement error than one based on parametric approximations of price schedules, and it reflects the reality of shopping in these markets. We designate a quantity as focal if it accounts for at least 5% of all observations at the item-district level.<sup>12</sup> By this definition there are 1-8 focal quantities per item-district, with 3.4 on average. Overall, 69% of purchases are at focal quantities. We use the median unit price at the focal quantity to estimate the focal price.

To provide a visual example of the estimated schedules, Figure 2 depicts expenditures and unit prices by quantity for 702 purchases of kerosene in one of the study districts. The

> 9For these descriptive regressions there would be no benefit to pooling and using a full set of interactions. The units and scale vary across items, so we allow the levels of the fixed effects to vary as well. 10To verify that the negative relationship between quantity and unit price is not due to division bias (from constructing unit price as the quotient of two variables measured with error), we also estimate expenditure schedules by regressing transaction-level expenditure on quantity and its square, suppressing the constant and fixed effects to enforce regression through the origin. The coefficient on _q_<sup>2</sup> is negative and significant for 13 of 19 items, and never positive and significant. This indicates that expenditure schedules are generally concave, which is consistent with bulk discounts. Results in Appendix S2.

> 11In Appendix S3 we show that the extensive margin probability that households purchase an item is not related to the degree of bulk discounts, as measured by the slope coefficients from column 5 of Table 3.

> 12We drop the roughly 1 in 5 candidate focal quantities that either require greater total expenditure than a larger-quantity focal point, or that have a higher unit price than a smaller-quantity focal point, because these points can never be part of an optimal counterfactual purchase. This is a conservative step. Because this also impacts adjusted expenditure, dropping these points slightly attenuates losses.

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size of the circles corresponds to the number of transactions at the circle center. The triangles represent the estimated focal points, and the solid lines mark the unit price (left panel) and expenditure (right panel) schedules. At left, the downward orientation of the unit prices is clear. On the right, the changing slope of the expenditure line represents the drop in unit prices as quantity increases. The clustering of purchases at focal quantities is also clear.

In each district there are some items that do not exhibit bulk discounts. Estimated unit price schedules are flat for 51 of the 126 item-district groups in the data (40%). Some items exhibit bulk discounts in every district, such as maize, cooking oil, kerosene, and tea leaves. Other items, including sweet bananas, cooking bananas, onions, salt, sugar, and dried sardines, have downward-sloping price schedules in three or more districts. Cigarettes, beans, rice, cassava, and matches only exhibit discounts in 1 or 2 districts.<sup>13</sup> A natural concern with price schedules estimated from observational data is that unobserved quality variation could be misinterpreted as bulk discounts, if higher quality versions of each item are disproportionately purchased in smaller quantities, and unit prices factor in quality. There are three reasons to believe that this is not the case here. First, as described in Section 3, we are able to use the item descriptions in the diaries to create highly standardized item groups. This mitigates unobserved variation from different product types being grouped together. Second, there is no quality variation across quantities in the market survey price data, because enumerators asked vendors to provide prices for different quantities of the exact same item. Yet, we see clear evidence of bulk discounts in those data (Table 3, columns 1-3), and there is no clear pattern as to whether the market price data or the survey data exhibit larger discounts (4 out of 10 coefficients in column 3 of Table 3 are larger in magnitude than their counterparts in column 5). Finally, while nearly half of observed purchases take place exactly at a focal point, the other half are priced above or below the estimated price schedule. One might believe that some of this variation reflects unobserved quality, and, if that is true, that wealthier households may systematically pay prices above the price schedule while poorer households pay prices below it (because demand for quality is increasing in wealth). In Appendix S3 we show that deviations from the price

> 13Why discounts emerge for only some items, and why they persist despite apparently robust competition in retail markets, are open questions not addressed in this paper. See Attanasio and Pastorino (2015).

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schedule are not correlated with wealth. This is indirect evidence that the steps we took to homogenize the items were successful.<sup>14</sup>

# **The value of forgone consumption**

Recall from section 2 that the quantity of consumption forgone is given by _Qhi_ = _qhi_<sup>_∗−qhi_,</sup> where the first term is the inverse of the expenditure function evaluated at total adjusted expenditure _e_<sup>_∗_</sup> _hi_<sup>,andthesecondtermistotalobservedquantity.Likewise,thefinancialloss,</sup> ˆ or value of forgone consumption, is defined as _Lhi_ = _ehi − e_<sup>_∗_</sup> _hi_<sup>,where</sup><sup>_e_ˆ</sup><sup>_hi_istotaladjusted</sup> expenditure and _e_<sup>_∗_</sup> _hi_<sup>isthecostofbuying</sup><sup>_qhi_inasingletransaction.Summingacrossitems</sup> at the household level gives _Lh_ =<sup>�</sup> _i_<sup>_Lhi_.</sup> Columns 1–3 of Table 4 report the item-level means of total observed quantity, _qhi_ , counterfactual quantity, _qhi_<sup>_∗_, and the counterfactual percent increase in quantity,</sup><sup>_Q_ ̃</sup><sup>_hi_.Calcu-</sup> lations in this table are based on all households that purchase an item more than once. The results are striking: without changing total expenditure, households could increase quantity purchased by over 15% on average. Potential quantity increases are over 25% for kerosene, onions, cooking bananas, cooking oil, and tea leaves, and are almost 18% for dried sardines. These are staple goods: kerosene is the primary lighting fuel in much of Tanzania, cooking bananas are a staple carbohydrate in the two districts where they are commonly purchased, dried sardines are a key source of protein, cooking oil is the main source of cooking fat. Most households purchase one or more of these goods: 85% purchase kerosene, 78% purchase cooking oil, 70% purchase dried sardines, and 22% purchase cooking bananas (Table 2). The consumption losses implied by columns 1–3 of Table 4 are substantial at face value.

The money-metric measures of loss tell a similar story. In columns 5–7 of Table 4 we report summary statistics for _e_ ˆ _hi_ , _Lhi_ , and _L_<sup> ̃</sup> _hi_ . Items are listed by decreasing values of column 7, so that high loss items are at the top (from now on we will usually display items in that order.) On average, losses represent 8.7% of total expenditure at the householditem level. For a number of frequently purchased items – kerosene, onions, cooking bananas,

> 14In Appendix S3 we also argue that bulk discounts cannot be the manifestation social capital or buyerseller relationships, because the prices collected by enumerators in the market price surveys also reflect bulk discounts.

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cooking oil and tea leaves – losses represent more than 15% of expenditure. In columns 5–7 of the lower panel of Table 4 we report summary statistics for all households represented in the upper part of the table, divided into those above/below median _Lh_ . We calculate householdlevel means by first summing adjusted expenditure (ˆ _eh_ =<sup>�</sup> _i_<sup>_e_ˆ</sup><sup>_hi_)atthehouseholdlevel,</sup> ˆ then averaging. We define the household-level percentage loss measure, _L_<sup> ̃</sup> _h_ , as _L_<sup> ̃</sup> _h_ = _Lh/eh_ . Not surprisingly, losses vary substantially across households. The overall household-level average is 751 TZS, or 6.7% of expenditure. Financial losses among the above median group represent 8.9% of total expenditure, on average.

Figure 3 shows histograms and kernel density estimates for the distributions of _Lh_ (left panel) and _L_<sup> ̃</sup> _h_ (right panel) among multi-purchase household-item pairs. Items with flat price schedules are not dropped, so as not to bias the estimates toward large losses. There is substantial between-household variation in losses. Approximately 9% of households incur zero losses (with our conservative approach to estimation). Yet, nearly a quarter (24%) incur losses above 10% of expenditure.

To characterize the substantial between-household variation in financial losses, we estimate household-level descriptive regressions of _Lh_ and _L_<sup> ̃</sup> _h_ on a vector of household characteristics. Results are shown in Table 5. These regressions make use of a wealth index based on the first principal component of a vector of household assets (Filmer and Pritchett, 2001; Sahn and Stifel, 2003).<sup>15</sup> Columns 1 and 2 report the estimates with _Lh_ as the dependent variable. In both columns we see that the poorest quartile of households (the excluded category) have lower losses than the other three quarters of households. The age, gender, and education level of the household head do not meaningfully co-move with losses. Larger households exhibit slightly greater losses, a result we discuss further in the below subsection on coordination costs.

Columns 3 and 4 of Table 5 report the results of the same specifications, with _L_<sup> ̃</sup> _h_ as the dependent variable. Households in the first three wealth quartiles have similar mean percentage losses, but percentage losses are substantially lower for those in the wealthiest quartile. The estimated coefficients on head of household characteristics, in column 4, are too

> 15 We use assets to characterize wealth because, unlike expenditure, it is not endogenous to consumer prices—an important distinction for a study of choice in the face of nonlinear prices.

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small in magnitude to be of importance. Distance from the market is statistically significantly associated with lower normalized losses, but the magnitude is inconsequential.

Perhaps the most interesting results in Table 5 are those related to wealth. When using levels (columns 1-2), losses appear to be positively related to wealth. When using percentages (columns 3-4), losses are negatively related to wealth. This pattern suggests that there may be different types of loss-prone households—wealthy households that suffer large losses in levels but small losses as a percentage of total spending, and poor households that suffer small losses in levels but large losses as a percentage of total spending. In some of the analysis to follow we distinguish between households that are loss-prone in levels only, percentiages only, both, and neither, where a household is “loss-prone” if it is in the highest quartile of losses. Section S4 in the Appendix contains more details on this categorization.

# **5 What explains the observed purchasing patterns?**

We now turn to hypotheses about what might lead households to engage in financially inefficient purchasing by foregoing bulk discounts. We consider a number of possibilities: binding liquidity constraints, utility from frequent shopping, transport costs, storage costs, ignorance of bulk discounts, purchasing in small quantities as a form of self- or other-control, avoidance of social taxation, and coordination costs within the household. These hypotheses arose from three sources: discussions with individuals and focus groups in Tanzania (described in Section 3), our own hypothesizing based on the literature or our knowledge of the context, and suggestions from colleagues or seminar participants.

Our analysis uses observational data, so it is not possible to say that a mechanism is relevant or irrelevant for all households. Rather, we assess which mechanisms do or do not seem to have a substantial impact on the losses that we observe. Our findings provide an important check on certain hypotheses, and should be especially useful as a guide to steer future research.

Because it is important for assessing some mechanisms, it is worth reiterating what it means to buy in bulk in our data. Bulk purchasing in developed countries typically connotes buying several weeks’ or months’ worth of an item at once. In our setting, bulk purchases 18
represent only a few days to a couple weeks’ worth of consumption. One way to see this is to compare average total 2-week purchase quantities with _qmin_<sup>_∗_,theminimumquantity</sup> required to pay the lowest unit price. Because price schedules are estimated at the district level, there are up to seven possible values of _qmin_<sup>_∗_(andtheassociatedexpendiurelevel,</sup> _e_<sup>_∗_</sup> _min_<sup>)foreachitem.Table6showsthemean,minimum,andmaximumvaluesofthesetwo</sup> statistics, across the seven districts. In columns 3, 4, 6, and 7 we see substantial spatial variation in the minimum and maximum of _qmin_<sup>_∗_and</sup><sup>_e∗_</sup> _min_<sup>—whatitmeansto“buyinbulk”</sup> varies across districts. Column 1 shows the mean quantity purchased over 2 weeks. Among households that purchase each item, the mean quantity purchased substantially exceeds the average value of _qmin_<sup>_∗_.</sup> To estimate the number of days’ worth of consumption represented by _qmin_<sup>_∗_, we divide</sup> _qmin_<sup>_∗_by the average total quantity purchased (at the district level), and multiply by 14.Figure</sup> 4 shows the histogram of results for the item-district pairs that exhibit bulk discounts (if we include the other items the distribution shifts significantly left). The median is 8.51 days. In half of cases, “bulk purchasing” involves buying roughly a week’s or less worth of consumption. The 75th and 90th percentiles are at roughly 2 and 3 weeks’ worth of consumption. Hence, even though the data are from 2-week transaction diaries, for most items the relevant time frame for storing and consuming a bulk purchase is substantially shorter. Bulk purchasing in this setting involves avoidance of very small quantities, rather than stocking up on several weeks’ or months’ worth of an item.

# **Liquidity constraints**

A natural hypothesis for the financial losses in our data is that people would like to take advantage of bulk discounts, but they lack the liquidity to do so. Prior work has argued that poor households may pay higher unit prices than wealthy households because binding liquidity constraints prevent the poor from buying in bulk. This is an intuitive idea. Credit constraints are well understood to be an important barrier to investment in low-income countries, so it is reasonable to wonder whether they are a binding constraint here.

For a liquidity constraint to drive small-quantity purchasing, a household must be unable to gather the cash needed to buy _qmin_<sup>_∗_,theminimumquantityrequiredtobuyat</sup> 19
the lowest unit price. Moreover, this constraint must apply both backwards and forwards in time. That is because if liquidity is the issue, the extra effort to save for _qmin_<sup>_∗_needonly</sup> be made once. After that, the household could always consume more and/or spend less by eating down its stock, saving, and buying in bulk again, rather than purchasing smaller quantities at higher unit prices.

In our setting, the magnitudes in question are small enough that the liquidity constraint mechanism seems unlikely. To show this, we ask the following: based on household _h_ ’s observed time path of expenditures on item _i_ , for how many days would _h_ have to delay purchasing _i_ in order to save enough to buy it at the lowest available unit price? In other words, for how long would _h_ need to forego consumption in order to overcome a liquidˆ ity constraint? Let _ahi_ = _ehi/_ 14 be the average daily expenditure on item _i_ by household _h_ , and recall that _e_<sup>_∗_</sup> _min_<sup>istheminimumexpenditurerequiredtobuyitem</sup><sup>_i_atthelowest</sup> focal unit price. The answer to this question can be calculated as _dhi_ = _e_<sup>_∗_</sup> _min_<sup>_/ahi_.Ifwe</sup> allow the household to cross-subsidize its savings by also delaying its purchase of a few nonnecessities—tea leaves, salt, sugar, and cigarettes—we arrive at the measure _d_<sup> ̃</sup> _hi_ = _e_<sup>_∗_</sup> _min_<sup>_/a_ ̃</sup><sup>_hi_,</sup> ̃ where _ahi_ =<sup>�</sup> _j∈D_<sup>_e_ˆ</sup><sup>_hj/_14, and</sup><sup>_D_is a set including item</sup><sup>_i_and the non-necessities.We calcu-</sup> late _d_<sup> ̃</sup> _hi_ , the self-financed purchasing delay, for all household-item pairs consisting of at least one transaction.<sup>16</sup> The magnitudes of the self-financed purchasing delays give us insight into the possible role of binding liquidity constraints.

Table 7 shows the item-level median values of _d_<sup> ̃</sup> _hi_ for all households (column 1), by wealth quartile (columns 2–5), and for the three groups of loss-prone households (columns 6–8). The median delays are remarkably short, even for the high-loss items at the top of the table. The overall median is 1.2 days. There is only slight variation across wealth subgroups: the median delay for the poorest quartile is 1.5 days, and for the wealthiest quartile it is 1.0 days. The “Percentage-only” loss-prone households have the longest delays, at a median of 2.9 days (column 6). This group must wait roughly a week to purchase some of the higher-loss items in bulk: kerosene, cooking bananas, and cooking oil. Yet, losses by these

> 16This follows the spirit of an exercise in Mullainathan and Shafir (2013). They investigate a related question for roadside vendors in Chennai, India (p. 123-124). Those vendors lose roughly half of their daily earnings to interest payments on short-term loans, and yet still buy a daily cup of tea. The authors calculate that by foregoing tea for 50 days, the average vendor could save enough to permanently avoid short term borrowing, resulting in a doubling of take-home pay (and more tea consumption, in perpetuity).

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households on these items represent only 5.4% of total financial losses in the data. In other words, to find a household-item subgroup that would have to forego purchasing for a week or more in order to buy an item in bulk, we need to ignore 95% of the losses.

This approach is conservative in at least four ways. First, we have assumed no crosssubsidization between goods, other than for the least essential items. A liquidity-constrained household seeking to buy in bulk could surely rearrange other purchases so as to buy one item in bulk on day 1, another item in bulk on day 2, and so on. This would substantially reduce _d_<sup> ̃</sup> _hi_ . Second, we have assumed no access to additional sources of finance, treating the observed expenditure path as the only source of funds to be saved toward a bulk purchase. Access to any additional borrowing, windfall income, or other positive liquidity shock would reduce _d_<sup> ̃</sup> _hi_ . Third, we have described a scenario in which households forego consumption of an item for consecutive days. However, a household could also reach the financially efficient purchasing path by foregoing consumption for a single meal or a single day at a time, smoothing the consumption sacrifice over weeks or months by purchasing quantities smaller than _qmin_<sup>_∗_but greater than those at the highest unit prices.Fourth, we have implicitly treated</sup> _d_ ̃ _hi_ calculated over the observation window as the best case scenario for the household. If at any point in its lifetime the household commands more financial resources than during the study window, _d_<sup> ̃</sup> _hi_ would fall. Hence, the results in Table 7 are upper bounds.

# **Transport costs**

In wealthy countries, transport costs may constrain bulk purchasing (Griffith et al., 2009). A household cannot buy a carton of paper towels at a big-box store if it has no way to transport such a large item. The analogous concern in Tanzania is that shoppers that carry their purchases home from the market on foot, or by bicycle, may have difficulty transporting bulk purchases.

If transport costs impede bulk purchasing, then other things equal we expect households that live further from markets to incur larger losses. Table 5 reports the estimates from regressing bulking losses on distance from the community center and distance to market, as well as controls for wealth, household size, and various measures of human capital. There we see that bulking losses are slightly _decreasing_ in both distance measures (columns 2 and 21
4). This is not evidence that transport never matters for any household. But it suggests that transport costs are not a key driver of small-quantity purchasing.

One reason that transport may not play an important role is that over the support of the data, the minimum quantities required to reach the lowest unit price are relatively small. Consider the staple items that are purchased by most households and that are responsible for the largest share of losses: kerosene, cooking oil, onions, and dried sardines. In Table 6 we see that the maximum value (across the seven districts) of _qmin_<sup>_∗_is1literforkerosene,1</sup> liter for cooking oil, 0.4 kg for sardines, and 1.4 kg for onions (column 4). For households in the other 6 districts, the minimum quantities are even smaller. The large majority of bulk purchases are of a size that can be carried easily in a single trip.

To show this even more clearly, we calculate at the household level the total kilogram and liter quantities of _qmin_<sup>_∗_onallitemsforwhichthehouseholdincursaloss.</sup> This is the minimum aggregate shopping bundle associated with buying all loss-inducing items at their lowest unit price. The average size of this bundle, totaled across all items, is 4.3 Kg and 0.8 liters.<sup>17</sup> These quantities are not large relative to total purchases. The average sample household purchases a total of 31.4 Kg and 1.6 liters over the two-week study period. Furthermore, household shop frequently—the mean household reports at least one purchase on 11 out of 14 days (median = 12)—so the purchase of this bundle could be spread across multiple days if desired.

If there is an exception to the arguments presented here, it could be for cooking bananas, in the districts where _qmin_<sup>_∗_is over 20 kilograms.For these purchases, which represent</sup> only a small fraction of losses in the data, transport costs may be important. If we exclude cooking bananas from the calculation in the previous paragraph, the average size of the aggregate _qmin_ bundle falls by 25%, to 3.0 Kg.

# **Storage costs and concerns about depreciation**

Perhaps households do not buy in bulk because it is too costly to store bulk quantities? In this subsection, we exmaine two components of storage costs: space constraints, and concerns

> 17We exclude cigarettes and matches for this calculation, because they were measured in alternative units. These items are unlikely to impede transport.

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about depreciation. Other storage-related concerns, due to self-control problems or social taxation, are examined below.

As we argued with transport costs, the small quantities represented by the _qmin_<sup>_∗_make</sup> it unlikely that space constraints are the main driver of bulking losses. Table 6 shows that “bulk” purchases in our data are relatively small. The technologies to store small quantities of goods securely for a short period—plastic bins with sealed lids, used jerry cans with screw tops, used plastic water bottles with screw tops—are widely available and inexpensive. If bulk purchasing required a household to store its purchases in a 20 liter drum, or a 100 kg bag, then space constraints could be a more plausible concern.

The above argument also makes it unlikely that concerns about depreciation during storage prevent households from bulk purchasing. Figure 4 plots the distribution of the average number of days worth of consumption represented by _qmin_<sup>_∗_,whichisalsoanindication</sup> of the average required storage duration for a bulk purchase. Half of the storage periods are a week or less; 75% are less than two weeks; 95% are less than a month. If depreciation is the concern, depreciation rates for stored items would need to be exceedingly high. Yet, there is little reason to believe that they are. Some of the study items—kerosene, cooking oil—are essentially free from depreciation related to moisture or pest exposure, which are the primary concerns. For the other items, we look to the existing evidence on post-consumer storage losses. A 2011 FAO report indicates that post-consumer losses in sub-Saharan Africa for a wide range of commodities—grains, roots, tubers, pulses, fruit, vegetables, meat, and seafood—are the lowest in the world, ranging from 0–2% (Gustavsson et al., 2011). Other work looking at the depreciation rate of crops stored by farmers post-harvest finds depreciation rates of 1-5% over periods of 6 months or longer in Ghana, Malawi, Tanzania, and Uganda (Kaminski and Christiaensen (2014); University of Ghana (2008), as cited in Zorya et al. (2011)).

If there is an exception to this argument it is likely to be for bananas. For a small number of banana-purchasing households, _qmin_<sup>_∗_isover20kgforcookingbananas,andover</sup> 8 kg for sweet bananas. We cannot rule out that these households avoid bulk purchasing because of concerns about depreciation. Yet, this would explain only a tiny fraction of financial losses from not buying in bulk.

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# **Utility from shopping**

Perhaps people make frequent, small-quantity purchases because there is a utility value from shopping—e.g., from the socializing and community engagement that one enjoys in the market. An obvious problem with this hypothesis is that people can visit shops and markets without making purchases, and do so frequently. That said, if one believes in a very specific social contract that relies on frequent purchasing in small quantities, that could generate the observed patterns in the SHWALITA data.

It is straightforward to show that the data contradict this hypothesis. Many households make purchases both above and below _qmin_<sup>_∗_.</sup> By rearranging purchases to always purchase exactly _qmin_<sup>_∗_, households could increase the total number of purchases while always</sup> buying in bulk.

To illustrate, define _Khi_<sup>_∗_=</sup><sup>_e_ˆ</sup><sup>_hi/e∗_</sup> _min_<sup>.Thisisthemaximumnumberoftransactions</sup> that household _h_ could make on item _i_ at the lowest available unit price, without changing total expenditure on the item. The actual number of transactions that household _h_ makes on item _i_ , _Khi_ , could be smaller or larger than _Khi_<sup>_∗_.Thevalue</sup><sup>_K_</sup> _h_<sup>_∗_=�</sup> _i_<sup>_K_</sup> _hi_<sup>_∗_tellsushow</sup> many purchases the household could make if its goal were to maximize total purchases—to shop as much as possible—while only buying at the lowest available unit prices.

Table 8 shows the mean values of _Khi_ , _Khi_<sup>_∗_, and the difference</sup><sup>_K_</sup> _hi_<sup>_∗−Khi_, as well as the</sup> same measures aggregated across items. The results in column 3 indicate that the average household in all four groups could shop at least as much, or more, than it does at present, while only buying in bulk. The average household could make 20.8 more purchases than at present. Households that are loss-prone in levels (only) could make 30.9 more transactions on average. The high percentage-loss group, who are relatively poor and tend to shop less, could make 0.1 more purchases. Finally, households that are in the 25% worst group in both levels and percentages could make 5.2 more purchases on average.

These counterfactual shopping patterns are unlikely to be optimal for a variety of reasons. However, this analysis demonstrates that the desire to shop frequently cannot explain the failure to take advantage of bulk discounts, because households could already do more of both.

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# **Ignorance of bulk discounts**

Is it possible that many people in Tanzania simply do not know of the available bulk discounts? We are doubtful. When we conducted informal interviews with individuals in the study area, everyone was well aware of bulk discounts for a wide range of consumption items. Furthermore, many households personally experience non-linear prices. Column 5 of Table 3 shows the results of item-level regressions of unit price on quantity, with household fixed effects. Even _within household_ , bulk discounts are present. The members of households that purchase items multiple times—exactly those that are foregoing potential consumption by not buying in bulk—are surely aware of the available discounts.

# **Rationing consumption**

Could it be that people avoid buying in bulk as a way to limit their consumption? A sophisticated but present-biased agent would forego bulk purchasing in order to prevent her future self from over-consuming (Laibson, 1997; O’Donoghue and Rabin, 1999). Relatedly, shoppers may not trust other household members to control their consumption, and so may limit stocks as a form of rationing. In focus-group discussions we heard numerous variations on this theme.<sup>18</sup> If rationing is present, it is most likely to occur on items that are “temptation goods”—goods which, if held in stock, are likely to be consumed too quickly relative to one’s _ex ante_ plan. Because temptation goods are culturally specific, we conducted a survey in Tanzania to measure the temptingness of the study items. We invited Tanzanian staff members from recent survey projects to rank the study items on a five-point scale (1 = not at all tempting; 5 = tempting for essentially everyone who consumes the item). These respondents implement consumption surveys and speak regularly with households about their economic choices—in essence, they constitute a panel of experts. We asked respondents to

> 18The story of one respondent in Bukoba can be paraphrased as follows: “We know that we need 1 kilogram of maize flour each evening. But if we buy a 50 kilogram bag, we may find that it is gone at the end of one month, because we use too much each day. So it is better to buy smaller amounts.” Despite this anecdote, in the forthcoming analysis maize was not deemed to be “temptation goods” in our survey (see next paragraph). This underscores the subjectivity of temptation and the importance of grounding any analysis of temptation in data sourced from more than one person.

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answer for a typical household in a typical village, not to self-assess their own temptations. The survey was conducted online in June-July 2016. Across the 43 responses that we received, we assign each item its average score on the 5-point scale, and classify the top third (6 items) as the temptation goods in the study. These are: sugar, rice, cooking oil, soap, cigarettes, and sweet bananas.<sup>19</sup> For this analysis, household fixed effects are identified, so we can examine a specific behavior associated with not buying in bulk, rather than base tests on variation in losses. The primary outcome of interest is _Khi_ , the number of purchases of item _i_ by household _h_ . We first examine whether households make fewer purchases when bulk discounts are present, a response that indicates at least some attending to bulk discounts. We then test the hypothesis that households ration their stocks of temptation goods by purchasing them more frequently than non-temptation goods. Finally, we estimate the joint effects of temptingness and bulk discounts on _Khi_ , and test for differential responses between high- and low-loss households. Identification in these regressions is from three sources: household fixed effects control for average purchasing behavior; the temptation survey provides an objective, exogenous measure of the temptingness of a good; and the fact that households face some flat and some non-flat unit price schedules in their local markets provides exogenous withinhousehold variation in the presence of bulk discounts.<sup>20</sup> We include item fixed effects, when Regression results are in Table 9. Column 1 shows that after controlling for both household and item fixed effects, the average effect of a bulk discount is to induce fewer purchases. The average household does react to bulk discounts, to some degree. Column 2 shows that this result does not hold without the item fixed effects. Households also react to the temptingess of the good, but in the opposite direction (column 3). Households make 0.65 more purchases on temptation goods than non-temptation goods. This is indicative of consumption rationing for tempting items. When variables for bulk discounts and temptation

> 19The full ranking and average scores from the temptation survey are shown in Appendix S5. There is little correlation between a good having bulk discounts and being a temptation good. The correlation between the temptation dummy and the indicator for bulk discounts is _−_ 0 _._ 07, and it is not statistically different from zero. The relationship is unchanged if we control for district fixed effects.

> 20For the average study household, 56% of observed purchases are of items with bulk discounts, and 44% are of items with flat price schedules.

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are both included (column 4), the desire to ration a temptation good is actually stronger for goods that exhibit bulk discounts. This is not what we would expect to find if shopping choices were purely reflective of the tension between buying in bulk and rationing. Nonetheless, the key takeaway is that on average, the desire to ration temptation goods outweighs the financial incentive to buy in bulk.

In column 5 we repeat the analysis of column 4, allowing for heterogeneity by whether or not the household is loss-prone. We consider a household loss-prone if it is in the highest quartile of losses measured in levels and/or percentages. The first three coefficients in column 5 of Table 9 sum to 0.16, with a p-value = 0.16. This indicates that for non-loss-prone households, the net effect of bulk discounts and temptation is effectively zero. In contrast, for loss-prone households the net effect is a significant increase in the number of purchases. The marginal effect is 1.42 more purchases (p-value = 0.000). This heterogeneity analysis is a characterization, not a causal model. We cannot be certain that the difference between loss-prone and non-loss-prone households reflects differences in temptation or the desire to ration. But the finding is consistent with such an interpretation.

On balance, we take the finding that all types of households tend to purchase tempting goods more frequently than other goods, and that this response overwhelms any tendency to make fewer purchases when an item has bulk discounts, as evidence that consumption rationing is an important factor in inducing households to forego bulk discounts and purchase in small quantities. The heterogeneity analysis by loss-prone type is further evidence that rationing is partly responsible for the financial losses from small quantity purchasing.

# **Social taxation**

In much of sub-Saharan Africa, requests by non-household members for gifts, shared meals, or loans—which we refer to as “social taxes”—are commonplace (Platteau, 2014). Recent experimental work has shown that participants’ willingness to share windfall gains with others is related in part to the visibility of those gains, suggesting social pressure in favor of redistribution (Goldberg, 2016; Jakiela and Ozier, 2016). Baland, Guirkinger and Mali (2011) find that 1 in 5 savings-group participants in Cameroon are willing to pay to signal poverty to their social network, to deter requests. De Weerdt, Genicot and Mesnard (2015) 27
show that a transfer recipient’s _perception_ of a donor’s wealth affects the value of the transfer between them, conditional on the donor’s actual wealth. Social pressure is clearly a factor in determining patterns of redistribution, and buying small quantities may be a useful way to deter requests from one’s social network.

A particular feature of the data allows us to estimate a proxy for household-specific social tax rates and test whether buying in bulk is associated with higher social taxes. In addition to recording purchases, diary keepers also recorded the item description, quantity, unit, and estimated value of items sold or given away.<sup>21</sup> These disposal events are recorded on the household’s daily transaction log, in the same manner as the purchases. To estimate a proxy for the household-level social tax rate, we sum the total value of items outgoing over the two-week study period, and divide by the total value of items incoming. Because we are calculating a proxy for a household-level variable, we use every row of the transaction diaries for this calculation, not just the rows associated with the 19 items that are the focus of the rest of this paper. To our knowledge, this is the first accounting measure of social taxes—one based on diary records from a large sample of households—in the literature.

Table 10 shows descriptive statistics for the social tax estimates. The uppermost panel shows the value of resources outgoing in the form of sales or gifts, divided into subcategories. The most important group is “meals and snacks,” which accounts for 40% of outgoing resource flows. The largest share of entries under “meals and snacks” are those for “full meals”—guests at the household table (see Appendix section S6 for details about the item categorization). The lower part of the table shows the value of incoming resources. The mean tax rate is 14.4% (s.d. = 26.5%).<sup>22</sup> It is clear both that redistribution is widespread, and that there is significant heterogeneity between households in the implied social tax rate.

How does the existence of social taxes affect a household’s incentives to purchase in

> 21It is not possible to determine whether an item was sold or given away. This could be problematic if many households re-sell consumer items. That does not appear to be the case. Other households in the study villages—not the households that filled out consumption diaries—were randomly selected to participate in a survey experiment dealing with measurement of labor supply. These households were able to indicate their sectors of work, with varying degrees of detail. The share of respondents that indicated “buying and selling” as their primary sector of work ranged from 5–8% across survey modules. Hence, even if every purchase made by such households was for the purpose of re-selling—which is surely not the case—for the vast majority of disposal events it is still reasonable to assume that items “sold or given away” are in fact “given away.”

> 22A small number of estimated tax rates are over 100%. All results are robust to winsorizing by replacing rates above 60% with 60%.

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bulk? Let _τ_ ( _q_ ) _∈_ [0 _,_ 1) indicate the tax rate levied on transaction quantity _q_ , and define _s_ ( _q_ ) = 1 _− τ_ ( _q_ ). A household purchasing quantity _q_ is able to retain quantity _s_ ( _q_ ) _q_ , while _τ_ ( _q_ ) _q_ flows out of the household. The intuition from the prior literature suggests that _τ_ ( _q_ ) is increasing in _q_ , because larger quantities are more visible to non-household members, and thus lead to more requests to share. If social taxes take this form, then they would indeed push households to take less advantage of bulk discounts.

Identifying the shape of _τ_ ( _q_ ) is complicated by the fact that the transaction quantities we observe are in part driven by reactions to the shape of _τ_ ( _q_ ). However, those transaction quantities are also driven in part by the existence of bulk discounts, which creates an incentive to purchase larger quantities. The effective unit price in the face of social taxes—the price paid per unit consumed by household members—depends on both the price schedule and the social tax schedule. How a household adjusts transaction quantities in the face of these countervailing forces depends on the relative magnitudes of these forces, budget constraints, and preferences.<sup>23</sup> As long as there is sufficient variation so that it is optimal for some households to make purchases that expose them to variable social taxes, _τ_<sup>_′_</sup> _>_ 0 will generate a positive correlation between transaction quantities and social tax rates in our data.

Suppose instead that the social tax rate is independent of transaction quantity, so _τ_ ( _q_ ) = _τ_ ̄ for some _τ_ ̄ _∈_ [0 _,_ 1). This tax has the effect of shifting up the price schedule by <u>1</u> factor 1 _−τ_ ̄<sup>.Thereisnoclearreasontoexpectadirecteffectofthesetaxesontheincentive</sup> to buy in bulk.<sup>24</sup> Whether one buys quantity _q_ every day, or quantity 5 _q_ every five days, the total social taxes paid is the same. However, between-household variation in _τ_ ̄ may indirectly affect the tendency to purchase in bulk, if _τ_ ̄ is correlated with other factors that determine transaction quantities. If this is what drives an empirical relationship between social tax rates and transaction quantities, we expect that relationship to be attenuated once

> 23Formally: at transaction quantity _q_ , the effective unit price is decreasing if the elasticity _ηps_ =<sup>_<u>p</u>_</sup> _p_<sup>_′_</sup> (<sup><u>(</u></sup> _q_<sup>_<u>q</u>_</sup> )<sup><u>)</u></sup><sup>_/ s_</sup> _s_<sup>_′_</sup> (<sup><u>(</u></sup> _q_<sup>_<u>q</u>_</sup> )<sup><u>)</u></sup> is greater than 1, and increasing otherwise. To see this, note that the effective unit price on retained quantity ˆ ˆ ˆ ˆ _q_ , _p_ (ˆ _q_ ), is calculated as expenditure divided by quantity retained, i.e., _p_ (ˆ _q_ ) = _p_ ( _s_ ( _q_ ) _q_ ) =<sup>_<u>p</u>_</sup> _s_ (<sup><u>(</u></sup> _q_<sup>_<u>q</u>_</sup> )<sup><u>)</u></sup> _q_<sup>_<u>q</u>_=</sup><sup>_<u>p</u>_</sup> _s_ (<sup><u>(</u></sup> _q_<sup>_<u>q</u>_</sup> )<sup><u>)</u>.On</sup> ˆ ˆ the margin, to increase _q_ the household must increase _q_ . Hence _p_<sup>_′_</sup> (ˆ _q_ ) =<sup>_<u>p</u>_</sup> _s_<sup>_′−_</sup> _s_<sup>_<u>p</u>_2</sup><sup>_s′_, which is zero when</sup><sup>_ηps_= 1.</sup>

> 24Because the tax acts like a price increase, it is tempting to assume that demand for taxed items is decreasing in _τ_  ̄. This would predict a negative correlation between tax rates and transaction quantities, the opposite of the variable tax case. However, the conditions under which the law of demand applies to items with bulk discounts are not understood, in part because it is not possible to derive demand functions in the face of nonlinear prices (Beatty, 2010).

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we control for observable factors that are likely to account for some of the heterogeneity in tax rates, such as wealth, age, and household size.

A practical challenge to identifying the shape of _τ_ ( _q_ ) is that we cannot match most flows of outgoing resources to specific transactions. Hence, instead of estimating _τ_ ( _q_ ), we regress the estimated household-level social tax rates over two weeks on a measure of household tendencies to buy in bulk. Specifically, we regress the estimated social tax rate on _q_ ̃ _h_ , the average of the within-district percentile of transaction quantities on the items purchased by household _h_ . Households that tend to make larger purchases than others in their district ̃ will have higher values of _qh_ . If social tax rates are responsive to bulk purchasing, we should find a positive correlation between _q_ ̃ _h_ and the household’s social tax rate. For robustness we also regress social tax rates on ( _i_ ) the alternative _q_ ̃ _h_<sup>_w_,whichistheweightedaverageofthe</sup> percentiles, where the weights are the shares of household expenditure on each item; and ( _ii_ ) the two loss measures, _Lh_ and _L_<sup> ̃</sup> _h_ , which proxies for _not_ buying in bulk.<sup>25</sup> Column 1 of Table 11 shows the baseline estimate. The coefficient on _q_ ̃ _h_ is statistically significant and in the hypothesized direction: households that make larger purchases are also those that face higher rates of social taxes. The magnitude is economically significant: a one standard deviation increase in _q_ ̃ _h_ (0.15 for the estimation sample) is associated with a tax rate change of 1.4 percentage points, or 9.7% of the mean. In column 2 we add controls for covariates that are likely to vary with exposure to social taxes, if there are indeed fixed differences in tax rates. Rather than being attenuated, the relationship between transaction quantities and social taxes becomes stronger. Surprisingly, social tax rates do not meaningfully co-move with wealth or human capital of the household. The only other statistically significant coefficient is the distance from market.

There is of course still the possibility of correlated heterogeneity that is completely unobserved in our data. While we cannot fully rule out such unobserved heterogeneity, we do address one natural possibility. By chance, some households may have hosted a wedding,

> 25To construct _q_  ̃ _h_ we first sort the observed transaction quantities at the item-district level, then assign the percentile value _n/N_ to the _n_ th largest quantity (1 is the smallest), where _N_ is the number of item-district observations. When there are ties at the item-district-quantity level, we assign the average value of _n/N_ to the tied observations. We then calculate the average percentile at the household-item level, for the items purchased by the household. Finally, _q_  ̃ _h_ is the average across items within household. For _q_  ̃ _h_<sup>_w_,thefinal</sup> average is weighted by the share of household expenditure on each item. The mean (s.d.) of _q_  ̃ _h_ is 0.52 (0.15); the mean (s.d.) of _q_  ̃ _h_<sup>_w_is0.57(0.17).Theyarehighlycorrelated(</sup><sup>_ρ_= 0</sup><sup>_._89).</sup>

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funeral, dinner party, or similar event during the study period. If these households bought items in bulk, in preparation, this could generate a correlation between outgoing resources and purchase quantities that is purely idiosyncratic.<sup>26</sup> We address this possibility in two ways. First, we look for evidence of large events. Patterns in the data suggest that such events are rare. We find that 94% of households never host seven or more guests on a single day, and a further 4% host seven or more people on just one day.<sup>27</sup> Second, we repeat the analysis in columns 1–2 of Table 11 after first recalculating social tax rates without including “meals and snacks” in the value of outgoing resources.<sup>28</sup> Columns 3–4 of Table 11 show the results using this alternative measure. The findings are effectively unchanged. If anything, the relationship between social taxes and transaction quantities is stronger.

In Appendix S6 we subject these results to a variety of robustness checks. These include: using the alternative average percentile measure _q_ ̃ _h_<sup>_w_as the key independent variable;</sup> using _Lh_ as the key independent variable; using _L_<sup> ̃</sup> _h_ as the key independent variable; and winsorizing tax rates at 60%. In all cases we repeat the analysis in all 4 columns of Table 11, and the findings are qualitatively and quantitatively similar to those reported here.

From these findings, we conclude that there is clear evidence that households face social taxes that are increasing in transaction quantities. The remaining question is whether households react to these social taxes by taking less advantage of bulk discounts. In theory, they ought to. The prior research cited above suggests that people react this way in other contexts. Moreover, in our focus groups, we regularly heard, without prompting, anecdotes suggesting a connection between small-quantity purchasing and social taxation. As one interviewee put it: “If I buy 5 kilograms of sugar, everyone will take their tea at my house.” Unfortunately, our cross-sectional data do not permit a direct test of how households react to variable social tax rates in this setting.

> 26Note that one might naturally expect the propensity to host such events would depend on household characteristics such as wealth, age, and household size. Hence, the fact that controlling for these variables does not alter the basic relationship between social tax rates and measures of buying in bulk casts some doubt on this hypothesis.

> 27To make these estimates, we calculate that the average value of a full meal for an outside guest is 630 TZS, based on the value of outside meals provided on days with only one guest. We then divide the total value of meals and snacks given away to outside guests by 630, to estimate the number of guests at the household-day level.

> 28The implied social tax rate without “meals and snacks” is 9.2% (Table 10). The correlation between the two tax rates is just below 0.8.

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# **Coordination costs within the household**

Finally, we examine the possibility that the purchase of financially inefficient small quantities could be driven by the costs associated with coordinating purchases between household members. In Table 5 we see that losses are increasing in household size, hinting at the possibility of coordination difficulties. Coordination failures would manifest as multiple household members buying the same item in small quantities, rather than aggregating into a single purchase so as to pay a lower unit price. Studying this phenomenon requires data on individual- rather than household-level purchases, so we restrict this analysis to the 500 households that were randomly assigned to complete personal rather than household diaries. The modal household in this group has 2 personal diary keepers (54% of observations); the mean number of diary keepers is 2.1, and the maximum is 7.

To proxy for uncoordinated shopping, we calculate _dmult_ , the number of days on which multiple household members purchase the same item. We then regress _Lh_ or _L_<sup> ̃</sup> _h_ on _dmult_ and an extensive set of household control variables. We also control for the total number of itemdays on which any purchase is made. This focuses on the behavior of interest: controlling for the household’s tendency to make purchases at the item-day level, do we see that losses are increasing in the number of times that multiple household members buy the same item on the same day? The hypothesized link between coordination costs and bulking losses would show up as a positive and statistically significant coefficient on _dmult_ .

Results with _Lh_ as the dependent variable are in columns 1 and 2 of Table 12. For both samples, the estimated coefficients on _dmult_ (“Number of item-days with 2+ purchasers”) are negative and statistically significant. This runs directly contrary to the coordination-cost hypothesis. Not surprisingly, the coefficient on the count of item-days with a purchase is positive and statistically significant. In columns 3 and 4 we repeat the analysis using percentage losses ( _L_<sup> ̃</sup> _h_ ) as the dependent variable. The signs and pattern of statistical significance are the same as for _Lh_ .

These findings do not support the hypothesis that coordination costs are responsible for the forgone bulk discounts in the SHWALITA data.

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# **6 Interactions between rationing and social taxation**

In the previous sections we separately investigate potential explanations for why households would forego bulk discounts. We find the strongest evidence for two hypotheses: rationing and social taxation. These mechanisms may be naturally confounded if social taxes are more likely to be levied on temptation goods. Also, the observational nature of the data introduces the concern that we could be detecting a single phenomenon through multiple channels. In this subsection we implement joint tests of these two mechanisms to shed light on whether they are operating independently.

The regressions in the Section 5 subsections on rationing/temptation and social taxes use different dependent variables and are conducted at different units of analysis. Some compromises must be made in order to design joint tests. We approach the problem from two directions. First, we test for heterogeneity by social tax rate in the effect of temptation on the number of purchases at the household-item level (as in Table 9). These regressions include household fixed effects, so the direct effect of the social tax rate on _Khi_ is not identified. Second, we calculate the sum of _Khi_ , the dependent variable in the rationing analysis, across the temptation goods, and include it along with the social tax rate and other controls in household-level regressions with _Lh_ and _L_<sup> ̃</sup> _h_ as the dependent variables. For this test we are regressing losses on the tax rate, instead of the other way around (as we do for the robustness checks in Appendix S6, where we use _Lh_ and _L_<sup> ̃</sup> _h_ as proxies for not buying in bulk). Hence, inference is based on the implied correlation rather than a causal link. The goal of this full set of regressions is to examine whether evidence consistent with each of the two mechanisms is robust to the inclusion of variables that account for the other.

Table 13 shows the results. In the upper panel we replicate the key specifications from Table 9, adding interactions between bulk discounts, temptation, and the household social tax rate. There is no evidence of heterogeneous effects by social tax rate: the interaction coefficients are far from statistically significant and trivial in magnitude. In contrast, the main effects of bulk discounts and temptation are largely unchanged from Table 9.

In the bottom panel of Table 13 we see that each mechanism has an independent association with losses, in the expected direction (negative for social taxes, positive for 33
temptation). Yet, the interaction between the social tax rate and the number of temptation goods purchased is small in magnitude and far from statistically significant.

The analysis in this subsection gives us little reason to suspect that household responses to temptation and to social taxes are manifestations of a single force. It appears that the tendency to forego bulk discounts is driven by multiple channels.

# **7 Discussion**

In this paper we have shown that some households in Tanzania incur substantial financial losses by purchasing staple items in very small quantities, frequently, rather than buying modestly larger quantities at lower unit prices. We test numerous hypotheses for why households would engage in this behavior, including the possibility of binding liquidity constraints. The evidence is consistent with households limiting stocks in order to ration their consumption of temptation goods, and to avoid social taxes. Other tested mechanisms seem not to have a major impact on the losses we observe.

The nature of the data prevents us from testing additional hypotheses that emerged in the literature or in our qualitative work. Two of these bear mention. The first is that, at the time of purchase, shoppers may simply not be attentive to the high cost of buying in small quantities. If so, then making the aggregate implications of bulk discounts more salient at the time of purchase could be a rewarding intervention for many households. The second proposed hypothesis is that husbands in Tanzania ration the spending of their wives by giving them daily allowances to purchase necessities—such as the components of the family meal—which prevents these women from buying in bulk. This mechanism alone would not be sufficient to generate losses, because the wife could potentially save some cash and delay purchasing certain items in order to buy goods in bulk. However, if such behavior would be perceived as a violation of the social contract between spouses, the personal cost to the woman could be too high to justify saving up in order to bulk purchase. Tests of these potential mechanisms, in Tanzania or elsewhere, are left to future work.

The two mechanisms highlighted by our analysis, social taxes and rationing, share a common feature. Both involve limiting the consumption of a future agent—one’s self, other 34
household members, or non-household members—by avoiding stocks. This raises the question: if stocking exposes households to leakage through social taxes or over-consumption, but some goods exhibit bulk discounts, what is the optimal purchasing pattern? There is a tension between the financial savings from buying in bulk and the degree of over-consumption. The optimal shopping pattern depends on household-specific preferences, shadow prices, and the specific manifestation of the pressures to over-consume within a given household.

Given this, we cannot be certain that the observed purchasing patterns are suboptimal for all households. It seems highly likely that some households could increase utility by buying in bulk. However, our calculation that the average household could increase consumption by almost 9% through bulk purchasing does not take into account the likelihood of higher social taxes or over-consumption. Revealed preference evidence, outside of our scope, is needed to conclude that utility would be higher overall with more buying in bulk.

That point notwithstanding, there may be some relatively benign but effective interventions suggested by our findings. For example, programs to coordinate bulk purchasing across households could be beneficial. Groups of households should be able to buy in bulk, pay lower unit prices, and still avoid stocking. Before leaping to advocate for such interventions, we would argue for additional research to understand why households do not already coordinate purchases in this manner, what effect changes in shopper behavior would have on sellers (many of whom are poor themselves), and whether the findings from Tanzania are broadly representative of those elsewhere.

One of the puzzles raised by our analysis is why bulk discounts persist in equilibrium despite apparently robust competition in retail markets. Do retailers impose high mark-ups on the smallest quantities, in order to take advantage of customer demand for rationing? The link between the demand-side factors examined in this paper and the related set of supply-side factors is a key area for future work.

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