Intertemporal Choice and Income Regularity: Non-Fungibility in the Timing of Income among Kenyan Farmers

Abstract The optimal design of informal contracts in agricultural value chains depends on when farmers prefer to be paid for their output. While the evidence from time preference experiments suggests a preference for early payments, field studies often indicate that farmers will defer regular payments if given the opportunity. In this study, we explicitly test whether farmers are more patient regarding regular, earned income than regarding experimental windfall payments. We asked farmers in a dairy cooperative in Kenya to allocate both their milk income and a one-time gift between an early and a deferred payment date. We find that a large majority of participants deferred their milk payments, while rarely choosing to defer the gift. Participants’ survey responses suggest that we observe this difference because of mental accounting: participants earmarked their regular milk payments, but not the gift, to save for bulky expenditures. We conclude that deferred payments can provide value to producers by functioning as a savings device, even when decisions over windfall income suggest a preference for early payments.


Introduction
Aggregators such as cooperatives and outgrower schemes help improve smallholder farmers' access to markets. These institutions generate economies of scale by bulking output from many small producers, which can improve prices, stability, and access to inputs (Reardon, Barrett, Berdegué, & Swinnen, 2009). However, they typically rely on informal contracts that are difficult to enforce, making side-selling of produce a major challenge (Minot & Sawyer, 2016). Farmers in need of cash may side-selleven at prices below the contract pricebecause aggregators tend to defer payments instead of paying upon delivery (Geng, Kramer, & Janssens, 2017). At the same time, farmers with limited access to sound savings devices may prefer deferred payments (Casaburi & Macchiavello, 2019). The optimal design of informal contracts with smallholders will hence depend not only on how much farmers are paid but also on when they prefer to be paid.
The evidence on when farmers would prefer being paid is ambiguous: economic theory predicts that discounters of future income prefer being paid early, and indeed, time preference experiments reveal a high demand for earlier (and smaller) as opposed to later (but larger) payments. However, attributes of regular versus irregular income types, including for instance the recipient, front-end delays and interest rates. In our experiment, we can control for these potential confounds.
Second, we shed light on the stability of intertemporal allocations of income. Several studies (for example Chuang & Schechter, 2015;Halevy, 2015;Janssens, Kramer, & Swart, 2017;Meier & Sprenger, 2015) analyse discounting of experimental windfalls for the same individuals at different points in time. Time preferences vary over time, in part due to random noise in decision making and in part due to liquidity constraints. Time preferences also depend on the commodity in which income is paid (Ubfal, 2016) and allocations of money earned through a physical effort task in the lab are more patient than allocations of experimental windfalls (Hvide, Lee, & Odean, 2018). We generalise this finding to regular income earned outside of a laboratory environment in a context of recurring earnings from a dairy cooperative, and highlight how elicited preferences depend on whether inference is based on allocations of windfalls versus regular income.
Third, we contribute to the literature on linkages between rural output and financial markets. For a different dairy cooperative in Kenya, Geng et al. (2017) suggest that deferring payments increases side-selling during periods in which farmers need cash. Neglecting this demand for liquidity puts at risk the farmer's loyalty to the cooperative and thereby also possible side benefits of collective marketing (Minot & Sawyer, 2016). At the same time, farmers may face savings constraints: Brune, Giné, Goldberg, and Yang (2016) find that channeling crop sale proceeds into personal bank accounts instead of paying in cash facilitates saving for agricultural inputs; Brune, Chyn, and Kerwin (2018) find a high demand for deferred wages at zero interest among agricultural employees in Malawi; and Casaburi and Macchiavello (2019) argue that Kenyan farmers sell to a cooperative, even at belowmarket prices, because they value deferred payments as a savings device.
The strong preference for deferred milk payments in our experiment corroborates their findings. In addition to replicating the results of Casaburi and Macchiavello (2019)using distinct methods and procedures in a separate context, strengthening the credibility of their experimental results (Duvendack, Palmer-Jones, & Reed, 2017) -, we show that this finding is source-dependent; it does not generalise to irregular windfalls. Hence, it is not driven by a selection into cooperatives of farmers with unusually low discount rates (or an unusually high demand for commitments to save) across income types.

Background
The experiment was conducted with dairy farmers who supply milk to Metkei Dairies Limited, a farmer-owned dairy hub in the Rift Valley region in western Kenya. Metkei collects milk from 1,000 to 1,500 dairy farmers, stores the milk in two cooling centers, and sells it to larger processing companies. Metkei receives milk twice per day: once in the morning and once in the afternoon. In the morning, farmers can either deliver the milk themselves to one of the two cooling plants or deliver through a Metkei transporter who collects milk at the farmgate for a small deduction from the milk price. In the afternoon, no central transport is available, making afternoon delivery feasible only for farmers who live close enough to a cooling plant to deliver the milk themselves. Farmers have no cooling facilities and cannot store milk produced in the afternoon for the next morning's milk collection. Metkei prices vary from month to month.
Outside Metkei, farmers can sell their milk to other cooperatives that operate similarly as Metkei, serving formal milk markets, and to neighbors and traders who serve local (informal) markets. 1 It is common to send the morning milk to Metkei and keep afternoon milk for consumption or local marketing. Buyers in the local market tend to pay cash on deliveryat prices that can potentially vary from day to dayto any household member selling the milk. In contrast, Metkei (like other cooperatives) pays only the supplier registered with Metkei (often the male household head), and payments are typically deferred until the eleventh of the next month (which is when the monthly payment from the processing company is on the way).
Farmers can purchase veterinary services, animal feed, fertilisers, and other inputs from Metkei. They can choose to pay for these services in kind, meaning that costs are deducted from the next milk payment, free of charge. Prior to our study, 43 per cent of participants planned to use their milk account for such services in the next eight weeks. Farmers can also request advance payments for up to 50 per cent of the milk delivered in a given month from the 21st of that month onwards. These cash advances are costly: in order be paid three weeks before the regular payment date, farmers are charged a 7.5 per cent interest rate. 2 Despite these large fees, 35 per cent of all Metkei farmers took out an advance at least once in the nine months before our study, and for those who did, advance payments accounted for more than 30 per cent of the total monthly milk payment (or 60 % of the amount that farmers could take out as an advance). Hence, the demand for liquidity is high.

Experimental tasks
Recognising the cash constraints faced by their members, and looking for ways to improve its services and attract more milk, Metkei was interested in measuring farmers' demand for early milk payments. To that end, we elicited study participants' preferred allocations of milk payments between an earlier and a later date. We also asked farmers to allocate an irregular gift between an earlier and a later date. By eliciting preferences for these two types of income, we experimentally induced within-subject variation in preferences for when to be paid. 3 In total, we interviewed 355 participants (see Appendix A).

Allocation of milk payments.
We asked study participants to make the following decision, for each of the four weeks after the interview: 'For milk delivered between Friday … [start date] and Thursday … [end date], which is … [one, two, three, or four] weeks from now, for how many kilograms of milk do you prefer to be paid at the end of that week?' Thus, farmers indicated for how much of the milk delivered between Friday and Thursday they preferred to receive a payment on the subsequent Friday. The remainder would be paid on the later, standard payment date, with both early and later payments maintaining the Metkei milk price prevailing at the time of delivery. Appendix Figure A1 illustrates a timeline for January 30 as an example interview date. In this example, the participant allocated milk delivered in the week of February 1 (and the weeks of 8 February 2015, and 22) between an early payment on February 8 (and 15 February 2022, and 29) and a later payment on March 11.
Metkei handled both payments. To reduce transaction costs associated with receiving an extra (early) payment, participants could choose to receive this payment through mobile money or at the collection point, whichever was more convenient for the participant. All participants had access to an account with M-Pesa, the largest mobile money provider in Kenya, and the study paid for any fees associated with sending the money into their account. Farmers were used to receiving their monthly (later) payments through the collection point or transporter. We did not deviate from this approach.
In order to ensure that farmers could still take out in-kind advances for other services, Metkei restricted the maximum weekly payment to 50 per cent of the total quantity delivered in a given week. This is consistent with the rule for regular cash advances that farmers were familiar with (although we emphasised that the weekly payments were free of charge, as opposed to the advance payments). Hence, our weekly payment to the farmer was either the amount that the farmer had asked to be paid early, or a payment for 50 per cent of the milk delivered throughout the previous week (whichever was lower, since otherwise the payment would exceed the maximum amount allowed to be paid in advance). 4 Intertemporal choice and income regularity 1051 2.2.2. Allocation of the gift. During the same interview, participants were also asked to allocate a gift of KSh 250, approximately US$ 2.50, or a third of the budget in the median farmer's milk payment allocation, between the Friday after the interview versus three weeks later (see the bottom row labeled 'Gift' in the example from Figure A1). Both payments were made through mobile money. Farmers received an extra KSh 65 on both dates regardless of their choice: 'In addition to the KSh 65 that we are sending you both … [early date] (this Friday) and … [later date] (Friday three weeks from now), how much out of KSh 250 do you prefer to receive this Friday?' Similar to the milk payment allocations, the gift allocation involved a linear budget, without return or penalty on deferred payments. Hence, a standard model with discounting of future income predicts that participants would prefer to receive both types of income on the early date. Further, the number of days between the early and the late payment date was 21 days, comparable to the median delay in the milk payment. 5 As was the case for milk payments, gift allocations were elicited by our enumerators, and payments on the earlier date were done through mobile money. Finally, because preferences were elicited from the same farmers during the same interview, any differences in allocations cannot be driven by differences in participant characteristics, changes in background wealth, liquidity constraints or time-varying preferences.
Choices also differed in a number of dimensions. In the Supplementary Materials (SM), we show that our findings are robust to controlling for differences in front-end delays (that is, the number of days between the moment that a participant decides and the early payment date), the magnitude of experimental stakes, and our definition of the milk budget (that is, 50 % of expected milk production in a given week); and that issues related to trust, transaction costs and order effects are unlikely explanations for our findings. Figure 1 presents the distribution of income allocations, that is, the share of the total payment under consideration (the 'budget') allocated to the early payment date. The figure presents the distribution of these shares separately for all four milk income allocations (in gray) and for the gift allocation (in white). For the milk payment, the budget to be allocated between the two dates is 50 per cent of the expected milk production. For the gift, the budget to be allocated between the two dates is KSh 250. Figure 1 reveals a stark difference between the allocations of milk payments and the gift: a large majority of participants chose to receive the entire gift on the early payment date, consistent with standard economic predictions for discounters of future income. In contrast, most participants chose to defer the receipt of the entire milk payment to the regular, later payment date, allocating none to the early payment date. Only very few allocations fell in the interior of the distribution, where some but not all money was allocated to the early payment date. Figure 1 treats every choice as one observation, meaning that for every participant, the figure includes four milk payment allocations: one for each week in the four-week period following the interview. Table 1 instead summarises the choices at the participant level, showing that 93 per cent of all participants selected no early milk payment for any of the four weeks, whereas only 7 per cent chose not to receive an early gift payment. At the same time, less than 1 per cent chose to receive the maximum possible milk payment early in every week as opposed to 83 per cent who chose to receive the entire gift on the early payment date. Conditional on choosing to receive payments on both the early and the later date (6.5 % for allocations of milk payments and 10.4 % for allocations of the gift), participants split the budget equally between the two dates, independent of the income type. After completing the allocation task for milk payments, the enumerator would ask the participant to state which factors influenced his or her decision (not) to choose a weekly milk payment, and which factor was the most important reason for doing so. Table 2 presents self-reported reasons for Notes: Histogram of income allocations between an early payment date and a late payment date, treating every choice as one observation (N ¼ 1; 770). The maximum amount of milk income that a participant could allocate to the early date in a given week is calculated as 50 per cent of the participant's expected milk production for that week, unless the participant is among the few who delivered only afternoon milk to Metkei, in which case we calculate the budget for milk income allocations as 100 per cent of the participant's expected milk production for that week. One participant allocated more than 50 per cent of expected milk production to the early payment date, although her budget was 50 per cent of expected milk production. For ease of presentation, we censor her share of income allocated to the early payment date such that this share cannot take on values greater than one. Notes: Overview of income allocations between an early payment date and a late payment date. Every respondent is treated as one observation, and the milk allocation figures correspond to the average of the four milk income allocations respondents made. The correlation in the second last row is insignificant, with a p-value of 0.29. Table 2. Reasons for rejecting weekly milk payments Did the following affect your decision to get none of your milk paid the same week?

A factor
Most important in decision factor in decision Respondents were asked for each item below whether this was a factor in their Percentage Percentage decision (Column 1) and whether it was the most important factor (Column 2).
(1) never selecting the weekly milk payments. Among participants who never selected a weekly payment, nearly all -95 per centindicated a preference for setting their milk payments aside for lump-sum expenditures or emergencies, instead of facing the temptation to spend the money on something else. This was the most important reason for 78 per cent of the participants. Participants thereby self-reported a demand for commitment savings; they intended to save their milk payments for future expenditures, but feared that if paid out in cash at the end of the week, they would be tempted to spend it on something else. This finding is in line with prior evidence of demand for commitment devices (Bryan et al., 2010). Also the gift could be allocated to the later payment date as a commitment savings device, but very few participants selected this option. Moreover, the correlation between gift and milk payment allocations is very small and statistically insignificant (Table 1). Participants deferring (a larger share of) their milk payments were not more likely to also defer (a larger share of) their gift. This raises the question why participants did not also choose to defer the receipt of their gift. The next section explores potential explanations for this choice gap.

Mechanisms related to the regularity of milk payments
A key difference between both allocations is that milk payments are a regular type of income, whereas the gift is irregular in the sense of being an unexpected and one-time payment. This difference in income regularity could explain why participants preferred deferring milk payments but not the payment of their gift through the four mechanisms discussed below.
3.2.1. Timing of bulky expenditures and preference for lump-sum payments. First, participants may have arranged their finances so that bulky expenditures occur around the eleventh of a month, which is when they receive their regular milk payment, giving them more cash on hand. Participants may prefer deferring their milk payments because they need the money to pay for planned expenditures around the eleventh of the month. Deferred gift payments cannot be used in the same way as they do not always occur around the eleventh of the month.
To explore this mechanism, we first analyse when farmers planned to spend money on large and predictable expenditures that occur at most once a month. Participants reported during the survey for each of the four weeks following the interview whether they were expecting any large expenditures in that week. In Table S4 in the Supplementary Materials, we regress this variablemeasured at the participant-week levelon a dummy variable for whether that week includes the eleventh of the month. Bulky agricultural expenditures were indeed significantly more often planned for around the eleventh of the month (p < 0:01).
In Table 3, we analyse whether this could explain participants' preferences for deferred milk payments. This table explores heterogeneity in income allocations for different subgroups, indicated in the column headers. Each column presents the coefficients estimated through a regression of the share of income allocated to the early payment date in a given choice on a dummy variable 'Milk payment', which indicates whether that choice involves one of the four weekly milk payments (using the allocation of the gift as the choice for the base category), on a dummy variable 'Subgroup', which indicates that the participant belongs to the subgroup indicated in the table header (for instance whether the participant expected bulky expenses around the eleventh of the month in the first column), and on an interaction between these milk payment and subgroup indicators.
Column 1 tests whether the gap in the share of milk payments versus the gift allocated to the earlier payment date is significantly different for participants who expected a bulky expenditure in the week with the eleventh of the next month. If this gap was driven by the timing of bulky expenditures, we would expect a more pronounced gap among this sample of participants. However, the coefficient for the interaction of 'Milk payment' and 'Subgroup' (a variable indicating that the participant expects bulky expenses around the eleventh of the next month) is small and statistically insignificant, meaning that the choice gap did not differ for such participants. 6 Thus, we do not find stronger Intertemporal choice and income regularity 1055 Milk payment Notes: Estimated using ordinary least squares with standard errors (in parentheses) clustered at the respondent level. Each column presents the result of a separate regression of the share of the respondent's budget allocated to the early payment date in a given choice on a dummy variable indicating whether that choice involves a milk payment ('Milk payment'), on a variable indicating the 'subgroup', that is an indicator variable for the group of respondents defined by the column label, and on an interaction of these two variables. Controls: Budget size, number of days to the early payment, number of days between early and late payments, and self-reported share of milk consumed yesterday. Column 1 excludes one respondent for whom data on expected income and expenditures are missing. Column 3 excludes respondents who stated that they had not delivered milk to the cooperative on the day prior to the interview, as well as three respondents for whom data about the use of milk income are missing. The other columns contain one gift allocation and a maximum of four milk allocations per respondent, resulting in a maximum of 1,775 allocations. Since a few respondents expected their cows to be dry in some of the weeks, they made less than four milk income allocations, decreasing the sample size to 1,770 in the remaining columns. y p < 0:10, Ã p < 0:05, ÃÃ p < 0:01. differences between milk payment and gift allocations among participants who will have larger cash needs around the eleventh of the month. For a further check, we can also use the fact that for 81 participants, the late gift payment was scheduled for the eleventh of March, hence coinciding with the day of a regular milk payment. If there was a preference to receive payments around that time due to a preference for lump-sum payments, independent of the source of income, we would expect these participants to allocate a larger share of the gift to the late payment date. Column 2 explores this hypothesis, testing for heterogeneity in the difference between gift and milk payment allocations for these 81 participants versus the remainder of the sample. We find no difference in allocations when focusing on gift allocations with a late payment date on the eleventh, and their milk payment allocations do not differ either. 7 3.2.2. Income accounting. Regularity also allows farmers to engage in income accounting. To analyse this channel, Table 4 presents planned income use for milk sold on the day before the interview, distinguishing between morning versus afternoon milk, and milk sold to Metkei versus another buyer. Table 4 summarises the percentage of participants planning to use their milk income for the main categories that participants listed: food and daily expenditures, school fees, and dairy and crop expenditures. Dairy income from morning milk sold to the cooperative was often used for bulky expenditures such as school fees (62.6%) and agricultural inputs (65.2%), whereas income from selling afternoon milk to other buyers was generally used for food and other daily expenditures (89.8%), and less often for school fees (6.8%) or agricultural inputs (12.5%). Even afternoon milk income from the cooperative was more likely to be spent on food and other daily expenditures. Columns 5-6 show that this was the case even among the 15 participants who had delivered both morning and afternoon milk to the cooperative on the day before the interview, and for whom morning and afternoon milk income would hence be paid out together.
This suggests that participants earmarked milk income from the cooperative (and in particular, income from selling morning milk) to save for bulky expenditures such as school fees, agricultural investments, and emergencies. In the taxonomy of income accounts proposed by Thaler (1990), farmers may assign the cooperative milk payment to a 'future income account', while assigning the gift to a 'current income account'. They may then perceive the offer of more frequent milk payments as an offer to use the future income account for liquidity purposesand therefore reject it. This is consistent with farmers reporting to reject weekly payments because they have earmarked their morning milk income for savings (Table 2). Conversely, spending rules of the current income Notes: Responses of participants who stated selling AM or PM milk to the respective buyer on the day before the interview. Percentages do not add up to 100 because participants could select up to two spending categories. Other buyers are mostly neighbors and shops/vendors, and we exclude 5 responses of farmers that stated delivering to another cooperative on the day before the interview. The data on intended use of milk income is missing for 3 respondents. account, as well as standard discounting, predict a preference for the early payment option in the gift allocation.
To explore this hypothesis, the third column of Table 3 estimates the allocation gap separately for participants who were planning to use the income from milk delivered to the cooperative for lumpsum expenditures (the reference category) versus those planning to use it for food and other small purchases. The latter category of participants allocated less to the early payment date in allocations of the gift (p < 0:10), and the interaction term for milk payments and planning to use milk payments for daily expenses is positive and significant (p < 0:05). Thus, controlling for gift allocations, these participants were more likely to choose early milk payments, suggesting ceteris paribus a stronger demand for liquidity from the cooperative. Column 4 shows that demand for liquidity is also stronger for participants who deliver afternoon milk to Metkeialbeit not significantly so, suggesting that the morning versus afternoon distinction matters primarily because participants tend to associate morning milk with bulky expenditures, and afternoon milk with smaller and more frequent purchases.

3.2.3.
Habit formation, reference dependence and status quo bias. Another strand of potential mechanisms relates to habit formation (cf. Duesenberry, 1952), reference dependence and status quo bias (Kahneman, Knetsch, & Thaler, 1991). Farmers may prefer to defer milk payments from the cooperative primarily because they are used to this, or because their reference points for consumption are built on the expectation that income arrives around the eleventh of the next month. In theory, when reference points are based on expectations held before consumption, the marginal propensity to consume for windfall gains (for example, an irregular gift for survey participants) is higher than the propensity to consume for anticipated income (for example, a milk payment) (Kőszegi and Rabin, 2009). Because the participants were already expecting milk payments on the eleventh of the next month, a reallocation would result in lower future consumption than expected. A loss-averse participant will weigh the associated utility loss more heavily than the corresponding utility gain from consuming more in the present, inducing the participant to maintain the status quo and reject weekly milk payments. By contrast, there is no habit, reference point or status quo for gift payments, and thus, standard time preferences prevail.
To the extent that habits are stronger among older or more experienced dairy farmers, we would expect them to defer milk payments the most. Column 5 of Table 3 shows that the allocation gap was indeed somewhat larger for participants with at least 30 years of experience in dairy farming (the top 10%). Thus, we cannot formally rule out that our findings are driven by either habit formation or reference dependence. Also mental accounting may however be stronger among more experienced participants and the self-reported reasons for rejecting weekly payments suggest that farmers value deferred milk payments because they facilitate saving for bulky expenditures, including agricultural spending. Such expenditures are durables or investments that do not directly generate consumption utility; their returns are consumed throughout a longer period of time. It is not clear to what extent consumption habits or reference-dependent consumption utility could drive preferences to save for those types of expenditures.
Moreover, in an initial pilot round of the experiment (see Appendix A.1 and Section S2 in the Supplementary Materials for details), we created unanticipated changes in milk payments by offering 2 KSh more per liter of milk allocated to the early payment date. Reference-dependent farmers should have reacted to this surprise income shock in their milk payment allocations by allocating more to the early date. Nonetheless, the elasticity of allocations with respect to an increase in the milk price was very low ( Figure S1 in the Supplementary Materials), suggesting that expectations-based reference points may not be as relevant as income accounting in our setting. 8 3.2.4. Visibility of income. Finally, regularity may matter due to the visibility of such income to others, for instance one's husband, who may be tempted to spend the money. A dairy farmer may not want to get some of the milk money paid at the end of the week out of concern that her husband, the household member registered with the cooperative and hence likely to collect milk payments from the cooperative, may spend it; by deferring the payment, the money is locked away with the cooperative. Conversely, she can hide irregular income, such as the experimental gift, and keep it with her for an emergency, because her husband will not know she received the money. In our context, we would expect this effect to be strongest for women because in the local Kalenjin culture, men are traditionally perceived to be in charge of household finances.
Column 6 of Table 3 therefore assesses whether the gap between milk payment and gift allocations is larger for female than for male dairy farmers. 9 In milk payment allocations, male suppliers allocated a significantly smaller portion to the early payment date than in gift allocations (83.9% points, p < 0:01). Among female suppliers, the share of the gift allocated to the early payment date is 2.3 per cent points higher than among male suppliers, but this difference is not significantly different. Men and women are also very comparable in the share of milk payments allocated to the early payment date. To further complement these findings, note that having to share weekly payments with family or friends was the main reason for rejecting payments for only 3.6 per cent of participants (Table 2). Thus, differences in the visibility of milk income and gifts do not appear to drive the gap in income allocations.
In summary, we explored four explanations for why allocations of regular income tend to be more patient than allocations of windfall payments. Although the experiment was not designed to formally distinguish these different mechanisms, income allocations and survey evidence suggest that the observed differences between intertemporal allocations cannot be accounted for by planned expenditures, habit formation, reference dependence or intra-household bargaining motives alone. Rather, our findings are consistent with the view that dairy farmers apply different mental accounts to different sources of income. Income from morning milk delivered to the cooperative is earmarked for lump-sum expenditures, whereas this does not apply to irregular windfalls and to income from selling afternoon milk.

Weekly payments versus advances
This final section explores the implications for the design of informal contracts in agricultural value chains, and in particular, whether our findings imply that aggregators should always defer payments. We were surprised by the low demand for weekly milk payments, given the high demand for costly advances described in Section 2.1. Partly, this may be because participants can cover at least small liquidity needs by side-selling milk to neighbors or traders; but it could also be that farmers could not predict their liquidity needs at the time of the experiment, and did not want to commit to receiving the payments early.
Consistent with the former conjecture, Column 7 of Table 3 shows that controlling for choices regarding the windfall, the demand for weekly milk payments was lower for participants who stated that they had also sold milk to buyers outside Metkei, that is participants with access to neighbors or traders who pay cash upon delivery to cover small liquidity needs. These may be the farmers who turn to Metkei mostly to satisfy their demand for commitment savings. In a setting with fewer side-selling opportunities, the demand for more frequent payments by the cooperative would potentially be greater.
But the main distinction between weekly payments and the more popular advances in the eyes of the participants is the lack of flexibility of the former. Table 5 shows that 20 per cent of participants reported that they actually had taken cash advances during the eight weeks prior to the interview, mostly to pay for school fees and health expenditures or emergencies. More than half said they needed this money urgently and could not have obtained it elsewhere. Moreover, 22 per cent of participants who rejected weekly payments expected to take advances within the next four weeks. More than 85 per cent of them said they preferred this form of liquidity because the decision to take an advance could be made spontaneously and on any day of the week. These findings suggest that participants value advances as insurance against unexpected liquidity demands. Weekly milk payments do not provide this service, and are moreover perceived as putting at risk the participant's savings goals.

Intertemporal choice and income regularity 1059
Even for advances, participants' views are nuanced. On one hand, 87 per cent stated they would be better off if advances were available at a lower fee and 39 per cent stated having to side-sell milk in case of an emergency if advances were not available, suggesting a demand for deferred payments as a soft commitment device. On the other hand, less than half of participants thought it would be better for them if advances were available already in the first two weeks of a month, and only 27 per cent reported that they would benefit if advances could be taken against all milk delivered to Metkei (instead of allowing advances for up to 50 %) in a month. A sizeable minority of 24 per cent even stated that they would be better off without the possibility of taking advances, and 11 per cent indicated they would like the advances to be more expensive, suggesting a preference for stronger commitments to save.
Summarising, although we find limited heterogeneity in farmers' demand for the weekly milk payments, we find more heterogeneity in the demand for advances. Advances help farmers meet their liquidity demands without having to commit to early milk payments also in the absence of urgent cash needs. Advances are hence preferred over weekly payments, but there is substantial heterogeneity in the extent to which farmers prefer advances being more accessiblethat is, whether they prefer deferred milk payments to be a stronger versus softer commitment savings device.

Conclusion
We find that dairy farmers of a Kenyan cooperative preferred to defer their milk payments but chose to receive an experimental gift at the earlier of two possible payment dates. Potential confounding factors such as differences in stakes, front-end delays, trust, and transaction costs do not seem to account for this discrepancy. Our results are consistent with both the experimental literature, which generally finds a preference for early over late receipts of windfalls (compare Frederick et al., 2002), and with field evidence revealing lower discount rates for more regular income types and a demand for commitment savings or deferred payments (Ashraf et al., 2006;Bryan et al., 2010;Casaburi & Macchiavello, 2019).

Number of participants 355
Notes: Question about use of inkind advances in first row only included in the first round (368 respondents). See Appendix A for an introduction of the first round-interviews. Due to a software error, questions about advances were skipped for 3 respondents.
Our findings are not an artifact of the cooperative we chose to work with. In a comparable study in a different part of Kenya, 83 of 96 dairy farmers (86%) declined the offer to be paid for their milk upon delivery (Casaburi & Macchiavello, 2019), mirroring our 93 per cent of participants who never chose weekly payments. Moreover, 73 per cent of those farmers referred to self-control problems or the need to achieve savings targets as motivating their decisions, comparable to our 78 per cent. In both studies, farmers appeared to use the deferred milk payments as a commitment device to overcome limited access to sound savings instruments. In addition, we show that this finding is income source-dependent as we cannot replicate it for allocations of an experimental gift. This supports the conclusion by Cohen, Ericson, Laibson, and White (2016) that intertemporal choice over regular income does not always reflect domain-general time preferences.
We propose the timing of lump-sum expenditures, income accounting, habit formation and income visibility as four mechanisms through which the regularity of the income may matter for intertemporal choice. Although our experiment does not allow us to distinguish clearly between these mechanisms, survey evidence and heterogeneity in milk income allocations suggest that farmers assign milk income from the cooperative, but not gift income, to a mental savings account for bulky expenditures. An area for future research would be to investigate whether also in other settings, nonfungibility in intertemporal choice is driven by the regularity of the income source through one of the mechanisms highlighted in the present study, and whether non-fungibility in intertemporal choice is more likely to be observed in the presence of savings constraints.
These findings have implications for the design of informal contracts between farmers and aggregators in agricultural value chains such as cooperatives, producer groups and outgrower schemes. Farmers may value deferred payments from trustworthy institutions. In such contexts, aggregators should abstain from making more frequent payments the default, irrespective of whether discount rates elicited using experimenter money would suggest otherwise. We do, however, observe a strong demand for advance payments along with the low demand for early and more frequent payments. Instead of paying early, aggregators may want to provide more flexibility in the form of advance payments, which can be accessed if farmers need the money ex post, without having to commit to these payments ex ante.
Our results suggest that the optimal informal contract in such a setting needs to strike a delicate balance between providing sufficient liquidity to farmers in case of need, without depriving farmers of the ability to commit their income to saving for bulky expenditures. This is consistent with recent empirical work, which finds greater impacts of soft commitment savings devices with flexible rules compared to impacts of more binding alternatives (Dupas & Robinson, 2013;Karlan & Linden, 2017). Aligning the conditions of informal contracts with farmers' preference for when to be paid could help improve farmers' loyalty to such contracts. This, in turn, could allow aggregators to operate more effectively and realise economies of scale, an important consideration for increasing agricultural incomes and productivity (Bellemare, 2012;Ma & Abdulai, 2016;Verhofstadt & Maertens, 2014). introduced as a reward for participation, but only at the end of the survey, after an intentional break with survey questions.
The first interview round already included an allocation task for milk payments, but not for a gift. Instead, first-round allocations varied the return on deferring payments to be negative, positive, oras in the second roundzero, and we offered weekly payments for only two weeks versus a longer period of eight weeks. We included this variation because we were worried that the strong preference for deferred payments found in Casaburi and Macchiavello (2019) could be due to the short duration of their experiment (in the main experiment, farmers could receive early payments for a duration of two weeks, and in a robustness check, this was two months). We feared that participants would have informal contracts with buyers in the local market to deliver their milk to these buyers, so that providing early payments through the cooperative could improve upon these contracts only if offered for a long enough period.
Because of limited demand for weekly payments, irrespective of the return on deferring payments or offer duration, we simplified the second-round design, and included the allocation of a gift to assess whether the strong preference for deferred payments generalises to other, less regular, income types. The analyses focus on second-round allocations to maximise comparability of gift versus milk payment allocations. First-round and second-round allocations yield very similar results (see the Supplementary Materials).

A.2. Sampling and attrition
Participants were sampled using the following procedures. First, from all farmers to whom Metkei made a payment in September 2015, we omitted the 2 per cent who delivered, on average, more than 25 kilograms of milk per day. To implement the experiment in a confined geographic area, we then selected all 313 farmers who self-delivered to one of the collection points, and all 220 farmers who delivered through one of the three largest transporters to be approached for interviews. The enumerators were able to locate and conduct first interviews with 64 per cent of the self-deliverers and 74 per cent of the transporter deliverers, or 363 of the 533 selected households.
In the first round, we targeted the person responsible for the decision of where to sell milk and also interviewed 11 additional household members who were afternoon suppliers and interested in delivering this milk to Metkei, resulting in a sample of 374 first-round participants. In the second round, enumerators approached all first-round participants for interviews and were able to interview 338 participants or 90.4 per cent (Table S2 in the Supplementary Materials). They also interviewed an additional 28 suppliers from the same households who had not been included in the first round, yielding a second-round sample of 355 participants. Attrition was limited and cannot account for our main results: firstround participants who agreed to be re-surveyed during the second round made, on average, similar allocations as firstround participants who were not re-surveyed during the second round, and in analyses that include both first-and second-round allocations, findings are robust to the exclusion of participants who were not surveyed in both rounds (results available upon request). Figure A1. Timeline for experimental tasks. Notes: On the interview day, the participant allocates payments between an early ('E') and late ('L') payment date. Text in italics indicates the number of days between the early and late payment date. Participants make allocations for in total four milk delivery periods (indicated in yellow) and a gift. Regarding milk payments, the median delay between the two dates is 21 days, with front-end delays (number of days between the interview and the early payment) ranging between 7 and 35 days. Regarding the gift, the delay between the two dates is always 21 days, with a front-end delay between 1 and 7 days.