Limited impact of business development programs on profitability in the presence of ambiguity aversion

Shapiro, Dmitry Working Paper Limited impact of business development programs on profitability in the presence of ambiguity aversion ADB Economics Working Paper Series, No. 614 Provided in Cooperation with: Asian Development Bank (ADB), Manila Suggested Citation: Shapiro, Dmitry (2020) : Limited impact of business development programs on profitability in the presence of ambiguity aversion, ADB Economics Working Paper Series, No. 614, Asian Development Bank (ADB), Manila, https://doi.org/10.22617/WPS200130-2 This Version is available at: https://hdl.handle.net/10419/230367 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/3.0/igo/ ASIAN DEVELOPMENT BANK ASIAN DEVELOPMENT BANK 6 ADB Avenue, Mandaluyong City 1550 Metro Manila, Philippines www.adb.org Limited Impact of Business Development Programs on Profitability in the Presence of Ambiguity Aversion There has been an emerging empirical literature on the use of business development programs (BDPs) to improve business knowledge, management practices, and overall profitability of microentrepreneurs in developing countries. However, the effect of such programs is mixed. In this paper, the author develops a theoretical framework aimed at understanding the mixed effect of business training. In his framework, entrepreneurs are ambiguity averse and have multiple sources of income (e.g., business and wage incomes). The author shows that a mismatch between a BDP’s narrow focus on business-promoting strategies and the wider context in which microentrepreneurs operate can limit the impact of business training. About the Asian Development Bank ADB is committed to achieving a prosperous, inclusive, resilient, and sustainable Asia and the Pacific, while sustaining its efforts to eradicate extreme poverty. Established in 1966, it is owned by 68 members —49 from the region. Its main instruments for helping its developing member countries are policy dialogue, loans, equity investments, guarantees, grants, and technical assistance. LIMITED IMPACT OF BUSINESS DEVELOPMENT PROGRAMS ON PROFITABILITY IN THE PRESENCE OF AMBIGUITY AVERSION Dmitry Shapiro ADB ECONOMICS WORKING PAPER SERIES NO. 614 April 2020 ASIAN DEVELOPMENT BANK ADB Economics Working Paper Series Limited Impact of Business Development Programs on Profitability in the Presence of Ambiguity Aversion Dmitry Shapiro No. 614 | April 2020 Dmitry Shapiro (dmitry[email protected]) is an associate professor in the Department of Economics and SNU Institute of Economic Research, College of Social Sciences, Seoul National University, Republic of Korea. I am grateful to Chris Ahlin, Suresh de Mel, David Dicks, Kevin Donovan, Dean Karlan, Xavier Gine, Antoinette Schoar, Tavneet Suri, Hebe Verrest, Chris Udry, and attendants of various economic seminars for their feedback and comments. Financial support from the Center for National Competitiveness in the Institute of Economic Research of Seoul National University is gratefully acknowledged. This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2018S1A5A8027545). Creative Commons Attribution 3.0 IGO license (CC BY 3.0 IGO) © 2020 Asian Development Bank 6 ADB Avenue, Mandaluyong City, 1550 Metro Manila, Philippines Tel +63 2 8632 4444; Fax +63 2 8636 2444 www.adb.org Some rights reserved. Published in 2020. ISSN 2313-6537 (print), 2313-6545 (electronic) Publication Stock No. WPS200130-2 DOI: http://dx.doi.org/10.22617/WPS200130-2 The views expressed in this publication are those of the authors and do not necessarily reflect the views and policies ofthe Asian Development Bank (ADB) or its Board of Governors or the governments they represent. ADB does not guarantee the accuracy of the data included in this publication and accepts no responsibility for any consequence of their use. 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Since papers in this series are intended for quick and easy dissemination, the content may or may not be fully edited and may later be modified for final publication. CONTENTS FIGURES iv ABSTRACT v I. INTRODUCTION 1 II. BASIC SETUP 4 III. BUSINESS TRAINING 7 A. Effect of Business Training on Profit: A Special Case 9 B. Business Training: A General Case 11 IV. CONCLUDING REMARKS 17 APPENDIX 19 REFERENCES 29 FIGURES 1 Pretraining and Posttraining Income Functions 15 2 Posttraining Decline of Expected Income 15 3 Capital Adjustment Effect ( λ , η ) 16 4 Capital Adjustment Effect ( λ , p) 17 ABSTRACT This paper develops a theoretical framework to explain the limited effect of business development programs (BDPs) on entrepreneurs’ profits. We argue that a mismatch between a BDP’s narrow focus on business-promoting strategies and the wider context in which microentrepreneurs operate can limit the impact of business training. In our framework, entrepreneurs are ambiguity averse and have multiple sources of income (e.g., business and wage incomes). We show that for a sufficiently ambiguity-averse entrepreneur with multiple income sources, efficient training can result in a decline in expected profit. Notably, when the wider context (multiple income sources, ambiguity aversion) is considered, the business training impact is limited and can result in a posttraining expected profit decline. This limited impact is caused by the diversifying role that the business income plays in household finances. Keywords: ambiguity aversion, business development programs, microentrepreneurship JEL codes: D10, O12, O16 I. INTRODUCTION Muhammad Yunus, in his “Banker to the Poor,” argued that teaching microentrepreneurs is a waste (Yunus 1999). One cannot improve loan use since borrowers already use loans efficiently. Indeed, the fact that the poor are alive despite all the adversity they face is the best proof of their innate ability. Recent research, however, questions the scope of the “poor but rational” view. Karlan and Valdivia (2011) tested whether microentrepreneurs maximize their profit given constraints and found that “... [many microentrepreneurs’] activities prove to be generating an economic loss” (p. 510). De Mel, McKenzie, and Woodruff (2008) found that real returns on capital vary with borrowers’ entrepreneurial ability, indicating that not everyone has the innate ability to do the best with what he or she has. Finally, there is no a priori reason why the “poor but rational” view would be true, as the poor lack the human capital and connections that help to build successful businesses (Banerjee 2013). One well-recognized way to make loan use more efficient is the use of business training programs to improve microentrepreneurs’ business knowledge (Prediger and Gut 2014). However, the effect of business training programs is mixed. Meta studies have shown that, while entrepreneurship programs do have a positive impact on business knowledge and practice, they have no impact on business expansion or income (Cho and Honorati 2014). To make matters worse, some studies have documented negative effects of business training on profits. Karlan and Valdivia (2011) reported that the training of female entrepreneurs in Peru led to a noticeable improvement in “bad months” and less noticeable improvement or even a decline in good months. Karlan, Knight and Udry (2012) studied the effect of training on a group of tailors in Ghana. While the business literacy of the tailors in their sample increased, their profits declined. Bruhn and Zia (2011) trained 445 clients in Bosnia and Herzegovina. They found that while basic financial knowledge improved, there was no improvement in the survival rate of business start-ups. Additionally, they find that profit declines, though insignificantly. Finally, Drexler, Fischer, and Schoar (2014) reported that only simplistic training—which consists mostly of basic rules of thumb—improves profits, while complex training does not. An immediate explanation, which is that training programs are too complicated for microentrepreneurs to comprehend, is not supported by the evidence. Most papers report noticeable increases in business literacy after training. Giné and Mansuri (2014) specifically noted that “business training did lead to an increase in business knowledge, so lack of understanding is not the issue” (p. 19). This limited impact of training does not appear to be due to improved accounting. For example, Drexler, Fischer, and Schoar (2014) found that although there was a reduction in mistakes and more consistency across measures of how people calculate profits or sales, it did not affect the main results. Further, de Mel, McKenzie, and Woodruff (2014) compared self-reported profits to revenue and cost figures and controlled for detailed measures of accounting practices as a further robustness check. They found no significant evidence that training changes reporting. McKenzie and Woodruff (2014) argued that issues such as sample size and sample heterogeneity make it harder to detect the effect of training on profitability. In a follow-up paper, de Mel, McKenzie, and Woodruff (2014) addressed those issues using a large and homogeneous sample of 1,252 female entrepreneurs in Sri Lanka. The authors found no training’s impact on the profitability of existing businesses but a positive impact on the profitability of new businesses and concluded that “the lack of impacts in most of the existing literature … may not be just due to power issues” (p. 200). They further conjectured that business training programs might be less effective than previously thought. 2 ADB Economics Working Paper Series No. 614 Finally, another explanation suggested in the empirical literature is that one reason for the weakness of BDPs and the business training they provide is related to their narrow focus on businesspromoting strategies, which ignores the wider economic context in which microfinance clients operate. First, many microfinance clients are neither interested nor “...particularly good at growing [their] businesses” (Banerjee 2013, p. 512). In a survey conducted in India, 80% of parents hoped their children would get government jobs, while 0% hoped their children would build successful businesses (Banerjee and Duflo 2011). Verrest (2013) argued that BDPs “are relevant to only a minority of entrepreneurs” due to variations in household vulnerability or a lack of business ambition (p. 58). Second, microentrepreneurs do not view their business activities solely as a way to bring in more money. Instead, they consider them as a valuable diversification tool for dealing with irregularities in income sources (Krishna 2004); as a way to reduce the household’s vulnerability to negative shocks, such as job loss or illness (Ellis 2000); or as a strategy for consumption and income smoothing (Bateman and Chang 2009, Banerjee and Duflo 2011). The goal of this paper is to develop a theoretical model that shows how a mismatch between BDPs’ narrow focus on business-promoting goals and the complex reality in which microentrepreneurs run their businesses can be responsible for a limited, or even negative, impact of business training on microentrepreneurs’ profits. To capture the wider context in which microentrepreneurs operate, we introduce two assumptions. Our first assumption is that the microentrepreneur has multiple sources of income. One source of income is profit from the business activity. This depends on the amount of capital invested and the state of nature. Other income sources can include farming, wage employment, temporary migration or income from informal risk-sharing arrangements. Nonbusiness income does not depend on the capital investment but can depend on the state of nature. It is well documented in the literature that households commonly rely on multiple income sources,1 yet this assumption is rarely used in the theoretical microfinance literature, where nonbusiness incomes are typically normalized to 0.2 As we show in this paper, disregarding multiple sources of income results in a loss of generality. The effectiveness of training differs depending on whether the microentrepreneur has one or multiple sources of income available. In particular, only in a setting with multiple income sources can the posttraining expected profit decline. Our second assumption is that the microentrepreneur has two objectives. The first is to maximize expected income. We will refer to this as the business-oriented ambition. The second objective is to maximize the “rainy day” income or, more formally, the worst-case income. We will refer to this as the livelihoods-oriented ambition. We model the microentrepreneur’s utility as a weighted average of the two objectives: business-oriented ambition (maximizing expected income) and livelihoods-oriented ambition (maximizing worst-case income). Mathematically, our setup follows the 1 For example, a survey of households in Masaka district, Uganda, showed that for an average household, 64% of its income came from farm income, 20% from business profits, and 10.6% from wages (Ellis 2000, Table 3.1). A survey of households in Mamone, a poor community in South Africa, showed that the primary income source was remittances and other transfers (63.4%), wages accounted for 9.1%, business activities for 6.3% and farming activities for 12.8% (Ellis 2000, Table 3.2). In Botswana, wage employment accounted for 21.5% of household income portfolio; crop and livestock farming for 45.8%; and other activities (beer brewing, basket weaving, carpentry) for 18.5% (Valentine 1993). 2 The focus on the business part of the household’s income is a common assumption, starting from classical papers such as Besley and Coate (1995) and Ghosh and Ray (2001) and extending to more recent papers, including Chowdhury (2005); Ahlin and Waters (2014); de Quidt, Fetzer, and Ghatak (2016); and Shapiro (2015). Limited Impact of Business Development Programs on Profitability in the Presence of Ambiguity Aversion 9 of new business practices or a new technology. Unlike the profit improvement effect, the capital adjustment effect can be either positive or negative. If 𝐾∗ >𝐾∗, then it is positive. Otherwise, it is negative. Whenever the capital adjustment effect is negative, it means that the microentrepreneur does not take advantage of improved profitability but instead adjusts her investment in such a way that it hurts her expected profit. In our model, the business training will have stronger effect in higher states; so, in order to take full advantage of it, one needs to invest more than before the training. However, because of the microentrepreneur’s ambiguity aversion and availability of income from nonbusiness activities, the microentrepreneur might do the exact opposite and invest less, thereby limiting the training’s effect. A. Effect of Business Training on Profit: A Special Case In this subsection, we consider a special case where the business training improves profitability by a fixed factor. We will consider a more general specification in the next subsection. • (BT5-I) Nonnegativity: 𝜋(𝑠,𝐾)≥0 for every 𝑠 and every 𝐾∈(0,𝐾∗(𝑛)]. • (BT5-II) 𝜆-improvement: 𝜋(𝑠,𝐾)=𝜆𝜋(𝑠,𝐾), where 1<𝜆<⋯<𝜆. Assumption (BT5-I) is imposed to ensure that (BT4) is satisfied. Assumption (BT5-II) states that the training increases the profit in state 𝑠 by a fixed factor, 𝜆. (BT5-II) greatly simplifies the proofs due to its property that 𝐾∗(𝑠)=𝐾∗(𝑠); however, as the next section shows, it is not necessary for the main message of the paper. Condition 1<𝜆<⋯<𝜆, and its generalization in the next subsection, are imposed so that the effect of training is stronger in higher states, which are the states where capital is more profitable. An example of this would be if trainees learn how to find cheaper suppliers or become more efficient at inventory management, which will have a stronger effect during good states when sales are higher.9 We begin the analysis of business training on expected profit with two benchmarks. The first is when the microentrepreneur has only business-oriented ambition. The second benchmark is when the microentrepreneur’s only income source is the business income. As the next proposition shows, in both benchmarks, the capital adjustment effect is greater than or equal to 0. Given that the profit improvement effect is always positive, this means that the total effect is also positive. Proposition 4. Assume that the training satisfies (BT5-I) and (BT5-II). The capital adjustment effect is nonnegative if either: (i) 𝜂=0, or (ii) the microentrepreneur’s only source of income is the business income. 9 Brooks, Donovan, and Johnson (2018) empirically studied the effect of training using two treatments. The first is a standard business training program used throughout Kenya. The second treatment is the so-called, mentor condition, where the entrepreneur is being mentored by a more experienced entrepreneur from the community. In the study, only the mentor treatment had a positive effect on the entrepreneurs’ profit. As anecdotal evidence of why it worked, Brooks, Donovan, and Johnson (2018) mentioned Prudence, who was a participant of one of the mentor treatments, and who used to purchase inventory from suppliers at the entrance of a market area. After training, she started to purchase at stalls deeper into the market and only after comparing prices. Her cost dropped from 250 Kenyan shillings to 100 Kenyan shillings as a result, while she kept her sales price exactly the same. Relating this to our paper and (BT5-II), if training results in a posttraining reduction in marginal cost, it will have a stronger effect in states that are favorable to the business activity. 10 ADB Economics Working Paper Series No. 614 Corollary 1. If the conditions of Proposition 4 are satisfied, then the business training has a positive total effect on expected profit. Intuitively, BDPs are designed to promote business-oriented strategies, such as business growth or production strengthening (Verrest 2013). When 𝜂=0, the microentrepreneur’s only objective is to maximize her expected income, which is equivalent to maximizing her expected profit. The training’s focus on improving profit from the business activities matches the microentrepreneur’s objective, and posttraining expected profit goes up. When profit is the only source of income, there is nothing to supplement the microentrepreneur’s income in the worst-case state when the profit is low. As Proposition 4 shows, the best available option to maximize the worst-case income is to increase capital investment, which will result in a higher expected profit. Consider now the case of a microentrepreneur who has multiple income sources and whose objective differs from maximizing her expected income, 𝜂≠0. When 𝜂≠0, the microentrepreneur puts the positive weight on income in the worst-case state. When business income is the only income source, state 1 is the worst-case state for every 𝐾. With multiple income sources, however, state 1 is not necessarily the worst-case state, as nonbusiness income sources (e.g., an informal risk-sharing arrangement) can supplement the low income from business activities in state 1. This changes how the microentrepreneur responds to the business training. Let 𝑠 (𝐾∗) be the highest worst-case state before the training. If, because of the nonbusiness income sources, 𝑠 (𝐾∗)>1 then 𝑠 (𝐾∗)<𝑠 (𝐾∗), that is, new worst-case state(s) are strictly lower. By the complementarity, lower states need lower capital investment, which puts a downward pressure on the optimal posttraining capital level and can result in the negative capital adjustment effect. Proposition 5 formalizes the intuition above for the case of 𝜂=1. It imposes two conditions. First, 𝐾∗(1)<𝐾. By Proposition 1, 𝐾∗(1)≠𝐾 means there is state 𝑠≠1 that is a worst-case state given 𝐾. That is, as discussed above, nonbusiness income in state 1, ℎ(1), is high enough so that 𝜋(1,𝐾∗(1))+ℎ(1)≥𝜋(𝑠,𝐾∗(1))+ℎ(𝑠). The second condition is that 𝐾<𝐾∗ (i.e., the microentrepreneur was underinvesting prior to the training). Proposition 5 shows that, on the one hand, 𝐾∗<𝐾∗. To maximize expected income, one needs to invest more after the training. On the other hand, 𝐾  <𝐾. To maximize the worst-case income, one should invest less after the training. When 𝜂=1, the microentrepreneur maximizes her worst-case income, and so the capital adjustment effect is negative. Proposition 5. Assume that the training satisfies (BT5-I) and (BT5-II). Let 𝜂=1. If 𝐾∗(1)≠𝐾 and 𝐾<𝐾∗, then the capital adjustment effect is negative. We conclude this section by looking at the effect of BDPs on expected profit when 0<𝜂<1. Proposition 4 has shown that when 𝜂=0, the capital adjustment effect is always positive. Proposition 5 has shown that if 𝜂=1 and 𝐾∗(1)<𝐾<𝐾∗, then the capital adjustment effect is negative. A natural conjecture would be that, when 𝐾∗(1)<𝐾<𝐾∗, the capital adjustment effect is a decreasing function of 𝜂, and there exists 𝜂 such that it is positive when 𝜂<𝜂 and negative when 𝜂>𝜂. Similarly, one could conjecture that the total profit effect is also a decreasing function of 𝜂. It turns out that neither is correct. Proposition 6 shows that the capital adjustment effect is not a decreasing function of 𝜂, and the total effect is not necessarily a decreasing function of 𝜂. A consequence is that, even for this simple form of profit improvement, not much can be said about the signs of the capital adjustment effect and the total effect for intermediate values of 𝜂. Limited Impact of Business Development Programs on Profitability in the Presence of Ambiguity Aversion 11 To see why the capital adjustment effect is not a decreasing function of 𝜂, consider its derivative with respect to 𝜂, (𝐸𝜋(𝑠,𝐾∗)−𝐸𝜋(𝑠,𝐾∗))′, when 𝜂=0. Term (𝐸𝜋(𝑠,𝐾∗))′=0 when 𝜂=0 because 𝐾∗ =𝐾∗ and 𝐸𝜋 (𝑠,𝐾∗)=0. Term (𝐸𝜋(𝑠,𝐾∗))′, as we show, is negative when 𝜂=0 so that the sign of the derivative is positive. That is, when 𝜂 is sufficiently close to 0, the capital adjustment effect is an increasing function of 𝜂. When 𝜂 is sufficiently close to 1, on the other hand, the capital adjustment effect is a decreasing function of 𝜂. Therefore, it is a nonmonotone function of 𝜂. With the total effect, the situation is slightly different. First, similarly to the capital adjustment effect, it can be an increasing function of 𝜂 when 𝜂 is sufficiently close to 0. To see how, consider the limit case when 𝜆=⋯=𝜆=1 and 𝜆=∞. Then, the posttraining choice of capital is not sensitive to changes in 𝜂, so 𝐾∗=𝐾∗(𝑛) and the posttraining expected profit does not change. The pretraining expected profit, however, is a decreasing function of 𝜂. Then, the total effect of the training, 𝐸𝜋(𝑠,𝐾∗)−𝐸𝜋(𝑠,𝐾∗), is an increasing function of 𝜂. Second, also similarly to the capital adjustment effect, the total effect is a decreasing function of 𝜂 when 𝜂 is sufficiently close to 1. Third, differently from the capital adjustment effect, the total effect can be a decreasing function of 𝜂 for every 𝜂∈[0,1]. For example, as long as 𝜆/𝜆 is not too large, so that the extreme example above is not applicable, the total effect is a decreasing function of 𝜂. Proposition 6. Assume that the training satisfies (BT5-I) and (BT5-II). Assume also that 𝐾<𝐾∗. Then, the capital adjustment effect is (i) an increasing function of 𝜂 for any 𝜂 sufficiently close to 0, (ii) a decreasing function of 𝜂 for any 𝜂 sufficiently close to 1. The total effect of training on expected profit (iii) can be an increasing function of 𝜂 when 𝜂 is sufficiently close to 0; (iv) is a decreasing function of 𝜂 for any 𝜂 sufficiently close to 1; (v) there exists 𝛬>1 such that, if 𝜆/𝜆<𝛬, the total effect is a decreasing function of 𝜂. B. Business Training: A General Case In the previous subsection, we assumed a specific functional form of profit improvement, 𝜋(𝑠,𝐾)=𝜆𝜋(𝑠,𝐾). In this subsection, we extend the analysis to more general functional forms of profit improvement. We will refer to them as additive and multiplicative improvements. • (BTA) Additive improvement: The posttraining state-profit functions satisfy (BT1)–(BT4) and are such that (𝜋(𝑡,𝐾)−𝜋(𝑡,𝐾))′≥(𝜋(𝑠,𝐾) − 𝜋(𝑠,𝐾))′≥0when 𝑡>𝑠, (6) and 𝜋(𝑡,0)−𝜋(𝑡,0)≥𝜋(𝑠,0)−𝜋(𝑠,0)≥0 when 𝑡>𝑠. Under an additive improvement, 𝜋(𝑠,𝐾)>𝜋(𝑠,𝐾) for every 𝑠 and every 𝐾, so it is stronger than what is required by (BT4). Also, notice that by definition, the training with an additive improvement has a stronger effect in higher states (the first inequality in [6]) and for higher levels of 𝐾 (the second inequality in [6]). 12 ADB Economics Working Paper Series No. 614 One example of the business training that satisfies (BTA) is 𝜋(𝑠,𝐾)=𝜆+𝜋(𝑠,𝐾), where 𝜆≥⋯≥𝜆≥0. For another example, assume that the pretraining profit function is given by 𝜋(𝑠,𝐾)=𝐹(𝑠,𝐾)−𝑅𝐾, where 𝐹(𝑠,𝐾) is a standard production function such that 𝐹>0,𝐹 <0 and 𝐹(𝑡,𝐾)>𝐹(𝑠,𝐾) when 𝑡>𝑠. The posttraining profit function is 𝜋(𝑠,𝐾)=𝜆𝐹(𝑠,𝐾)−𝑅𝐾. In this case, condition (6) becomes (𝜆−1)𝐹′(𝑡,𝐾)≥(𝜆−1)𝐹′(𝑠,𝐾)≥0. It is satisfied if 𝜆≥⋯≥𝜆≥1. The second requirement of (BTA) is trivially satisfied. • (BTM-I) Nonnegativity: 𝜋(𝑠,𝐾)≥0 for every 𝑠∈{1,…,𝑛} and every 𝐾∈[0,𝐾∗(𝑛)]. • (BTM-II) Multiplicative improvement: The posttraining state-profit functions satisfy (BT1)– (BT4) and are such that 𝜋(𝑠,𝐾) 𝜋(𝑠,𝐾) =𝑔(𝑠)𝜋(1,𝐾) 𝜋(1,𝐾) , (7) where 𝑔(𝑠)≥1 is a weakly increasing function of 𝑠. (,) (,) >1 and is a weakly increasing function of 𝐾 when 𝐾∈[0,𝐾∗(𝑛)]. By design, the business training is weakly more efficient in higher states because 𝑔(𝑠) is an increasing function of 𝑠. From equation (7), it follows that 𝜋(𝑠,𝐾)/𝜋(𝑠,𝐾) is an increasing function of 𝐾 when 𝐾∈[0,𝐾∗(𝑛)], so in that domain, the training has a stronger effect for higher 𝐾. We impose (BTMI) for the same reason as we imposed (BT5-I). The multiplicative improvement improves the profit function by multiplying it by some factor. To ensure that it is an improvement, the pretraining profit function needs to be positive. It is straightforward to verify that under multiplicative improvement 𝐾∗(𝑛)≥𝐾∗(𝑛), which means that that multiplicative training satisfies (BT4). An example of the multiplicative improvement is 𝜋(𝑠,𝐾)=𝜆𝜋(𝑠,𝐾), where 𝜆≥1. The requirement that 𝑔(𝑠) is a weakly increasing function of 𝑠 is satisfied if 𝜆≥⋯≥𝜆. It turns out that when the posttraining profit function satisfies either (BTA) or the two (BTM) assumptions, then the equivalent of Proposition 4 holds. When the microentrepreneur is risk neutral or has only one source of income, the training will have a positive effect on expected profit. The proof of Proposition 7, while more technical, follows the same steps as that of Proposition 4. Proposition 7. Assume that the training satisfies either (BTA) or (BTM-I) and (BTM-II). The capital adjustment effect is nonnegative if one of the two conditions hold: (i) 𝜂=0, or (ii) the microentrepreneur’s only source of income is the business income. Corollary 2. If conditions of Proposition 7 are satisfied, then the business training has a positive total effect on expected profit. Finally, we derive sufficient conditions for the capital adjustment effect to be negative, which is a generalization of Proposition 5. Just like in Proposition 5, it is necessary that 𝐾∗(1)<𝐾. Nonbusiness income sources must provide sufficient cushion to the business income in state 1. However, in a more general setting of this subsection, an additional condition is needed. Since Limited Impact of Business Development Programs on Profitability in the Presence of Ambiguity Aversion 13 𝐾∗(𝑠) is not necessarily equal to 𝐾∗(𝑠), it is possible to have a training so efficient at improving the marginal profitability of capital that it results in 𝐾∗(𝑠)>𝐾 for every 𝑠 so that 𝐾  >𝐾. Then, the capital adjustment effect is positive. Thus, we need to impose a restriction on how much the training can improve capital’s marginal profitability. Finally, the last condition of Proposition 8 is analogous to the assumption 𝜆<⋯<𝜆 from the previous subsection. Proposition 8. Let 𝜂=1 and 𝐾∗(1)<𝐾<𝐾∗. Let 𝑠 be the lowest pretraining worst-case state given 𝐾, and let 𝐾∗(𝑠)<𝐾. If (BTA) is satisfied and all inequalities in (6) are strict, then the capital adjustment effect is negative. Similarly, if (BTM-I) and (BTM-II) are satisfied and 𝑔(𝑠) is a strictly increasing function of 𝑠, then the capital adjustment effect is negative. C. Example of Posttraining Profit Decline As we discussed earlier, whenever the capital adjustment effect is negative, it undermines the effectiveness of the business training. Instead of taking advantage of improved profitability and expanding her business by investing more, the microentrepreneur finds it safer to invest less, thereby limiting the training’s impact. In fact, the negativity of the capital adjustment effect can be large enough to outweigh the positive profit improvement effect and result in a lower posttraining expected income and expected profit. Consider the following example. There are six states, each of which is equally likely, 𝑝=1/6. The microentrepreneur has three income sources: business profit, employment income, and income from informal risk-sharing arrangements. The microentrepreneur has the endowment of labor normalized to 1. Labor can be used for business activities and for employment. The microentrepreneur has no endowment of capital but can borrow it at rate 𝑅. Capital can be used for business activities only. Income from risk-sharing arrangements does not require any inputs. The timing is as follows. First, the microentrepreneur decides how much capital to invest into her business. Second, the state of nature, 𝑠, is realized. Given 𝑠, the microentrepreneur decides how to divide her labor endowment between business activities and employment. Finally, the microentrepreneur earns employment income and business profit according to her capital choice and labor allocation. She also receives income from her risk-sharing arrangements. Note that the choice of labor allocation is flexible and can be adjusted to the state of nature. The capital investment, on the other hand, cannot, as it is made before the uncertainty is realized. If the microentrepreneur splits the labor between employment and business activities as (1−𝐿,𝐿) and makes capital investment, 𝐾, then her profit in state 𝑠 is 𝑠𝐹(𝐾,𝐿)−𝑅𝐾=𝑠(√𝐾+ √𝐿)−𝑅𝐾. Her employment income in state 𝑠 is 𝑤(1−𝐿). We assumed that 𝑤=𝑤 such that wages are neither positively nor negatively correlated with the state of nature.10 Her income from a risksharing arrangement in state 𝑠 is 𝐴. We assume that the income from the risk-sharing arrangement 10 Depending on circumstances, employment and business incomes can be positively or negatively correlated. For example, own-farm production and agricultural wage labor will exhibit a high correlation. At the same time, Verrest (2013) showed that many households use business activities as a diversification tool against possible negative labor shocks: “They [homebased economic activities] may provide savings in the form of cash or kind as ‘an apple for a rainy day’ when other incomes disappear because jobs are lost or people fall ill.” (p. 64). Thus, in the example section, we do not take either side and simply assume that there is no correlation between labor and business incomes. By continuity, our example will continue to hold for small values of positive and negative correlation between wages and business incomes. 14 ADB Economics Working Paper Series No. 614 has an expected payment of 0, 𝐸𝐴=0. Specifically, we assume that 𝐴=𝐴>0 when 𝑠≤3, and 𝐴=−𝐴<0 when 𝑠≥4.11 Conditional on realized state 𝑠, the microentrepreneur’s objective is to maximize her total income max 𝑠(√𝐾+𝐿)−𝑅𝐾+𝑤(1−𝐿)+𝐴, so that 𝐿 ∗=min{ ,1}. The objective is total income and not utility because this decision is made after the uncertainty (i.e., the state of nature) is realized so that the microentrepreneur no longer faces any risk. The state-income function 𝐼(𝑠,𝐾), therefore, is 𝐼(𝑠,𝐾)=𝑠(√𝐾+𝐿 ∗)−𝑅𝐾 󰆄 󰆈 󰆈 󰆈 󰆈 󰆈 󰆅 󰆈 󰆈 󰆈 󰆈 󰆈 󰆆 (,) +𝑤(1−𝐿 ∗)+ 𝐴  󰆄 󰆈 󰆈 󰆈 󰆈 󰆅 󰆈 󰆈 󰆈 󰆈 󰆆 () . (8) Before the state of nature is realized, the microentrepreneur chooses capital to maximize her utility 𝑈(𝐾)=(1−𝜂)𝐸𝐼(𝑠,𝐾)+𝜂min 𝐼(𝑠,𝐾), which is the same as (1). Consider an additive improvement where the posttraining profit is given by 𝑠𝜆(√𝐾+√𝐿)− 𝑅𝐾, where 1≤𝜆…≤𝜆. We use the following numerical example. Let 𝑅=0.7, 𝑤=1, 𝐴=3, and the values of 𝜆’s are such that 𝜆=1, 𝜆=1.02, 𝜆=1.05, 𝜆=1.15, 𝜆=1.16 and 𝜆=1.17. One can verify that when 𝜂=1, then not only is the capital adjustment effect negative, but, most importantly, the posttraining expected income and posttraining expected profit are also lower than pretraining expected income and pretraining expected profit, respectively. Figures 1 and 2 visualize the example.12 When 𝜂=1, then only income in the worst-case states matter, which are states 1 and 4. States 2, 3, 5, and 6 are never worst-case states. Thus, in order to keep Figure 1 tractable, we plot 𝐼(𝑠,𝐾) and 𝐼(𝑠,𝐾) in state 2 only but not in states 3, 5, and 6. As Figure 1 shows, training makes state 4 more profitable but results in the negative capital adjustment effect, as 𝐾  ≈0.54<𝐾≈1.17. The negative capital adjustment effect dominates the profit improvement effect. Posttraining expected income 𝐸𝐼(𝑠,𝐾 )≈6.49<𝐸𝐼(𝑠,𝐾)≈6.51. Posttraining expected profit is lower as well: 𝐸𝜋(𝑠,𝐾 )≈6.37<𝐸𝜋(𝑠,𝐾)≈6.39. 11 An implicit assumption here is that informal insurance payments cannot be used for investment, which is generally consistent with the empirical evidence showing that the most common reason for accepting such payments is to meet immediate consumption needs rather than for investment purposes. Only 3.8% of all gifts and 18.4% of informal loans are used for investment purposes (Fafchamps and Lund 2003). 12 For both figures, 𝐾 is on the horizontal axis and income is on the vertical axis. In both figures, the values of 𝐾 are from interval [0,3]. The values on the vertical axis are from [2.2,7.5] for Figure 1 and [2.2,8.5] for Figure 2. The numbers are picked merely for illustrative purposes. Limited Impact of Business Development Programs on Profitability in the Presence of Ambiguity Aversion 15 Figure 1: Pretraining and Posttraining Income Functions Notes: Thin dashed and solid curves are income functions in different states that are labeled using the vertical axis. Solid lines are posttraining income functions, while dashed lines are pretraining income functions. Since (1, ) (1, ) new IK I K=, the dashed line is used for both. The solid line above (2, )IK is (2, ) new IK . The thick dashed line is ()min{(1,),(4,)} w IK I KI K=, the thick solid line is ()min{ (1,), (4,)} new new new w IK I KI K=. Source: Author’s calculations. Figure 2: Posttraining Decline of Expected Income Notes: Thin lines are expected incomes before and after the training. Thick lines are the worst-case incomes before and after the training. Dashed lines are for the pretraining expected income and worst-case income functions. Solid lines are for the posttraining expected income and worst-case incomes. When 1η=, the microentrepreneur’s choice of capital changes from w K to new w K. New expected income is lower. Source: Author’s calculations. I(,K) I(,K) Inew(,K) I(,K) Kw new IwIw new KwK Old income New income K w K K w new 16 ADB Economics Working Paper Series No. 614 Figures 3 and 4 are plotted to study how robust the example above is to perturbations in parameters. In total, there are 13 parameters: {𝑝}  and {𝜆}  and 𝜂. For the purpose of visualization, we parameterize {𝑝} and {𝜆} to make them functions of one-dimensional variables 𝑝 and 𝜆, respectively. We set the probability of state 1 to be equal to 𝑝 and the probabilities of states 2 through 6 equal to (1−𝑝)/5. When 𝑝=1/6, all states are equally likely. We define the effect in state 𝑠 as 𝜆󰆹=1+(𝜆−1)(𝜆−1), where {𝜆} are parameters used to build Figures 1 and 2. When 𝜆=1, then the training has no effect, 𝜆󰆹=1. When 𝜆=2, then 𝜆󰆹=𝜆. Figure 3 shows that a high degree of ambiguity aversion is needed in order to have the negative capital adjustment effect: for the total effect to be negative, one needs to have a very high 𝜂 and an intermediate range of 𝜆. When 𝜂 is set equal to 1, as on Figure 4, the capital adjustment effect is negative for almost all parameter values. When 𝑝 gets close to 1, then 𝐾∗→𝐾∗(1) so that the condition 𝐾<𝐾∗ in Proposition 8 is no longer satisfied, and the capital adjustment effect can be positive. The total effect is negative for low values of 𝑝, and intermediate values of 𝜆. When 𝜆 is high, then the profit improvement effect is also high and outweighs the capital adjustment effect. When 𝜆 is low, the capital adjustment effect is too small to outweigh the profit improvement effect. Thus, the total effect can be negative only for intermediate values of 𝜆. Figure 3: Capital Adjustment Effect (λ,η) Notes: The figure is built for 1/6p=. ‘x’ signs correspond to (,) λ η values where the posttraining expected profit declines; ‘.’ signs correspond to (,) λ η values where the capital adjustment effect is negative but the total effect is positive; ‘+’ signs correspond to (,) λ η where values the capital adjustment is positive. Source: Author’s calculations. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 λ 1.0 1.5 2.0 2.5 η 0.3 0.2 0.1 0 Limited Impact of Business Development Programs on Profitability in the Presence of Ambiguity Aversion 17 Figure 4: Capital Adjustment Effect (λ,p) Notes: The figure is built for 1.η= ‘x’ signs correspond to (,) λ p values where the posttraining expected profit declines; ‘.’ signs correspond to (,) λ p values where the capital adjustment effect is negative but the total effect is positive; ‘+’ signs correspond to (,) λ p where values the capital adjustment is positive. Source: Author’s calculations. IV. CONCLUDING REMARKS This paper provides a theoretical framework to understand the mixed impact of business training. We rely on a holistic view of a microentrepreneur as someone whose livelihood and goals are more complex than just being an entrepreneur. We model it using two assumptions. First, the microentrepreneur has several sources of income in addition to income from business activities. Second, the microentrepreneur has other ambitions in addition to maximizing business income. The impact of the training varies depending on the microentrepreneurs’ ambitions and the environment in which they operate. This is consistent with the observation that “BDPs have been more successful for some entrepreneurs than the others” (Verrest, 2013, p. 58). We further show that the reason behind the limited effect of business training is that BDPs’ focus on growing microentrepreneurs’ businesses ignores the nonbusiness aspects of microentrepreneurs’ livelihoods. For microentrepreneurs who have a strong business-oriented ambition or whose only income source is profit from business activities, the training effect is always positive. When the microentrepreneur has other goals beyond profit maximization and other income sources beyond business activities, the training impact can be limited and even negative. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 p 0.3 0.2 0.1 0 1.0 1.5 2.0 2.5 18 ADB Economics Working Paper Series No. 614 There are several limitations of our approach that are left for future research. First, we focus on one factor that could be responsible for the posttraining expected profit decline. However, there are other factors that could lead to the same outcome (e.g., inefficiency of the training). Second, our framework cannot be used to explain the success of some of the training treatments studied in the literature. Drexler, Fischer, and Schoar (2014) showed that a simplistic rule-of-thumb training worked better than the more complex one that is commonly used by BDPs. Brooks, Donovan, and Johnson (2018) introduced the mentor treatment as an alternative to a standard business training program, where trainees were mentored by a more experienced entrepreneur from the community. They showed that the mentor treatment, and only the mentor treatment, had a positive effect on the profit. Finally, our model is static and thus cannot be used to explain some dynamic phenomena documented in the literature. For instance, Karlan, Knight, and Udry (2012) reported that Ghana tailors switched to a new practice after the training but then abandoned it 1 year after the training stopped. The static framework in our paper could not be used to explain this short-run switch and the medium-run reversal. Appendix 25 profit function, it would immediately follow from complementarity. But posttraining profit function does not necessarily satisfy complementarity, which is why it has to be proved. First, we consider an additive improvement. From (6) follows (𝜋(𝑠,𝐾)−𝜋(𝑠,𝐾))′≥(𝜋(𝑠,𝐾)−𝜋(𝑠,𝐾))′. By complementarity of the pretraining state-profit functions (𝜋(𝑠,𝐾)−𝜋(𝑠,𝐾))′>0, and 𝜋′(𝑠,𝐾)≥0 by the assumption. Thus, 𝜋 (𝑠,𝐾)>0. In the case of a multiplicative improvement 𝜋 (𝑠,𝐾) = 𝑔(𝑠) 𝑔(𝑠)󰇧𝜋(𝑠,𝐾)󰇧𝜋(𝑠,𝐾) 𝜋(𝑠,𝐾) 󰇨′+𝜋(𝑠,𝐾)𝜋(𝑠,𝐾) 𝜋(𝑠,𝐾) 󰇨 >𝑔(𝑠) 𝑔(𝑠)󰇧𝜋(𝑠,𝐾)󰇧𝜋(𝑠,𝐾) 𝜋(𝑠,𝐾) 󰇨′+𝜋(𝑠,𝐾)𝜋(𝑠,𝐾) 𝜋(𝑠,𝐾) 󰇨 =𝑔(𝑠) 𝑔(𝑠)󰇧𝜋(𝑠,𝐾)󰇧𝜋(𝑠,𝐾) 𝜋(𝑠,𝐾) 󰇨′+𝜋(𝑠,𝐾)𝜋(𝑠,𝐾) 𝜋(𝑠,𝐾) 󰇨+ + 𝑔(𝑠) 𝑔(𝑠)(𝜋(𝑠,𝐾)−𝜋(𝑠,𝐾))󰇧𝜋(𝑠,𝐾) 𝜋(𝑠,𝐾) 󰇨′≥0. The first inequality holds because 𝜋(𝑠,𝐾)>𝜋(𝑠,𝐾), which is the complementarity assumption, and because profit functions are positive. The last inequality follows from two facts: the third line is nonnegative because it is equal to 𝜋 (𝑠,𝐾) which, by assumption, is greater or equal than 0. The last line is nonnegative because state 𝑠 is the pretraining worst-case state given 𝐾, and the derivative of 𝜋(𝑠,𝐾)/𝜋(𝑠,𝐾) is nonnegative. State 1 is the worst posttraining case and, therefore, from 𝜋 (1,𝐾∗(1))=0 follows that 𝜋 (𝑠,𝐾∗(1))>0 for every s . Plugging 𝐾=𝐾∗(1) into the FOC we get (1−𝜂)𝐸𝜋(𝑠,𝐾∗(1))+𝜂𝜋(1,𝐾∗(1))>0 when 𝜂<1. Thus, by concavity 𝐾∗ > 𝐾∗(1) when 𝜂<1. Now, we prove that 𝐾∗≤𝐾∗. To do that, we take the derivative of the posttraining utility function at 𝐾∗ and show that it is nonnegative. Concavity then would imply 𝐾∗≤𝐾∗. Consider an additive improvement. The derivative of the posttraining utility function is (𝑈(𝐾∗))′ = (𝑈(𝐾∗)−𝑈(𝐾∗))′+𝑈(𝐾∗)′=(𝑈(𝐾∗)−𝑈(𝐾∗))′= = (1−𝜂)𝐸(𝜋(𝑠,𝐾∗)−𝜋(𝑠,𝐾∗))+𝜂(𝜋(1,𝐾∗)−𝜋(1,𝐾∗))′≥0. Here we took into account that 𝐾∗ is optimal for pretraining utility and the last inequality is by the definition of the additive improvement. In the case of a multiplicative improvement, the posttraining utility can be written as (1−𝜂)𝐸𝜋(𝑠,𝐾∗)+𝜂𝜋(1,𝐾∗)=𝜋(1,𝐾∗) 𝜋(1,𝐾∗)((1−𝜂)𝐸𝑔(𝑠)𝜋(𝑠,𝐾∗)+𝜂𝜋(1,𝐾∗)). 26 Appendix Here we use that 𝐾∗≤ 𝐾∗(𝑛)≤𝐾∗(𝑛) so that state 1 is the worst-case state. Its derivative is 󰇧𝜋(1,𝐾∗) 𝜋(1,𝐾∗)󰇨′((1−𝜂)𝐸𝑔(𝑠)𝜋(𝑠,𝐾∗)+𝜂𝜋(1,𝐾∗))+𝜋(1,𝐾∗) 𝜋(1,𝐾∗)((1−𝜂)𝐸𝑔(𝑠)𝜋(𝑠,𝐾∗)+𝜂𝜋(1,𝐾∗))′. The first term is positive because multiplicative improvement requires that 𝜋(1,𝐾)/𝜋(1,𝐾) is an increasing function of 𝐾. Since 𝐾∗ maximizes the pretraining utility the second term is equal to 𝜋(1,𝐾∗) 𝜋(1,𝐾∗)((1−𝜂)𝐸𝑔(𝑠)𝜋(𝑠,𝐾∗)+𝜂𝜋(1,𝐾∗))′=𝜋(1,𝐾∗) 𝜋(1,𝐾∗)((1−𝜂)𝐸(𝑔(𝑠)−1)𝜋(𝑠,𝐾∗))′. We will show that expression in parenthesis is positive whenever 𝜂<1. Let 𝜏 be the lowest state such that 𝜋(𝜏,𝐾∗)≥0. The pretraining profit function satisfies complementarity and, therefore, ( 𝑔(𝑠)−1)𝐸𝜋(𝑠,𝐾∗)′ = (  𝑔(𝑠)−1)𝑝𝜋(𝑠,𝐾∗)+(  𝑔(𝑠)−1)𝑝𝜋(𝑠,𝐾∗)> >(𝑔(𝜏)−1)𝑝   𝜋(𝑠,𝐾∗)+(𝑔(𝜏)−1)𝑝  𝜋(𝑠,𝐾∗)= =(𝑔(𝜏)−1)𝐸 𝜋(𝑠,𝐾∗)≥0. The last inequality follows from the earlier established fact that 𝐾∗<𝐾∗ and that from the definition of the multiplicative improvement follows that 𝑔(𝜏)≥1. Thus, 𝐾∗<𝐾∗ when 𝜂<1 and by continuity, 𝐾∗≤𝐾∗ when 𝜂≤1. This completes the proof since 𝐾∗≤𝐾∗ ≤𝐾∗ implies that the capital adjustment effect is nonnegative. Proof of Proposition 8: Because of the concavity of the utility function, to show that the capital adjustment effect is negative, it is sufficient to show that 𝐾  <𝐾 and 𝐾∗<𝐾∗. First, we prove that 𝐾  <𝐾. Since 𝐾≠𝐾∗(1), it follows from Proposition 1 that there exist two states, 𝑠<𝑠′, such that 𝐼(𝑠,𝐾)=𝐼(𝑠′,𝐾)≤𝐼(𝑡,𝐾) for all other states 𝑡, and 𝐼′(𝑠,𝐾)< 0<𝐼′(𝑠′,𝐾). Let 𝑠 and 𝑠  be the lowest worst states given 𝐾 before and after the training, respectively. By Lemma 5.3 𝑠≥𝑠 . Proposition 8 requires that 𝐾∗(𝑠)<𝐾. One can show that from 𝐾∗(𝑠)<𝐾 follows that 𝐾∗(𝑠 )<𝐾. In the case of an additive improvement, it directly follows from the definition. Indeed, since 𝑠≥𝑠  we have (𝐼(𝑠,𝐾)−𝐼(𝑠 ,𝐾))′≥(𝐼(𝑠,𝐾)−𝐼(𝑠 ,𝐾))′≥0. From 𝐾>𝐾∗(𝑠), it follows that 𝐼 (𝑠,𝐾)<0, which combined with the inequality above implies that 𝐼 (𝑠 ,𝐾)<0 and, therefore, 𝐾∗(𝑠 )<𝐾. In the case of a multiplicative improvement, we use the states-ranking assumption. If 𝑠=𝑠  then we are done. The case 𝑠>𝑠  is impossible. Indeed, if 𝑠>𝑠  then 𝐼(𝑠,𝐾∗(𝑠))>𝐼(𝑠 ,𝐾∗(𝑠 ))> 𝐼(𝑠 ,𝐾∗(𝑠)). The first inequality is by the states-ranking assumption. The second inequality follows from the fact that 𝐾∗(𝑠 ) is optimal in 𝑠 . By definition of 𝑠, 𝐼′(𝑠,𝐾)<0 and, therefore, Appendix 27 𝐾>𝐾∗(𝑠). One can then use complementarity to conclude that 𝐼(𝑠,𝐾)>𝐼(𝑠 ,𝐾). But then 𝑠 cannot be the worst-case state given 𝐾, which is a contradiction. From 𝐾∗(𝑠 )<𝐾 follows that 𝐾>𝐾 cannot be the new optimal worst-case capital: 𝐼 (𝐾)=min𝐼(𝑡,𝐾)≤𝐼(𝑠 ,𝐾) < 𝐼(𝑠 ,𝐾)=min𝐼(𝑡,𝐾)=𝐼 (𝐾). The first inequality comes from the fact that the lowest income given 𝐾 is less or equal than the income at state 𝑠 . The second inequality comes from the fact that 𝐼(𝑠 ,⋅) declines when 𝐾>𝐾. Thus, 𝐾  ≤𝐾. Furthermore, 𝐾 is no longer the optimal worst-case capital either. By definition of 𝑠, 𝐼(𝑠,𝐾)≤𝐼(𝑡,𝐾) for every 𝑡, including 𝑡>𝑠. By the proposition’s assumption, all inequalities in (6) are strict in the case of the additive improvement, and 𝑔(𝑠) is strictly increasing in the case of the multiplicative improvement. Therefore, 𝐼(𝑡,𝐾)>𝐼(𝑠,𝐾) for any 𝑡>𝑠. Then, it must be the case that all worst states for 𝐾 are less than or equal to 𝑠.15 Take any posttraining worst-case state given 𝐾, and denote it as 𝑠 . We know that 𝑠  ≤𝑠. Then 𝐾∗(𝑠 )<𝐾 by the exact same reasoning as in the beginning of the proof of Proposition 8. Thus, all state functions that correspond to the worst-case states are strictly decreasing at 𝐾. But then, 𝐾 slightly below 𝐾 will give strictly higher worst-case income, and 𝐾 is no longer optimal. That proves that 𝐾  <𝐾. Now we need to show that 𝐾∗<𝐾∗. In the proof of Proposition 7, it was established that 𝐾∗≤𝐾∗ for any 𝜂<1. When all inequalities in (6) are strict, in the case of the additive improvement, or 𝑔(𝑠) is strictly increasing in the case of multiplicative improvement, it is trivial to show that 𝐾∗<𝐾∗ for every 𝜂<1. In particular, the inequality holds for 𝜂=0, which means that 𝐾∗<𝐾∗. 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Verrest, Hebe. 2013. “Rethinking Microentrepreneurship and Business Development Programs: Vulnerability and Ambition in Low-Income Urban Caribbean Households.” World Development 47: 58–70. Yunus, Muhammad. 1999. Banker to the Poor. New York: Public Affairs. ASIAN DEVELOPMENT BANK ASIAN DEVELOPMENT BANK 6 ADB Avenue, Mandaluyong City 1550 Metro Manila, Philippines www.adb.org Limited Impact of Business Development Programs on Profitability in the Presence of Ambiguity Aversion There has been an emerging empirical literature on the use of business development programs (BDPs) to improve business knowledge, management practices, and overall profitability of microentrepreneurs in developing countries. However, the effect of such programs is mixed. In this paper, the author develops a theoretical framework aimed at understanding the mixed effect of business training. In his framework, entrepreneurs are ambiguity averse and have multiple sources of income (e.g., business and wage incomes). The author shows that a mismatch between a BDP’s narrow focus on business-promoting strategies and the wider context in which microentrepreneurs operate can limit the impact of business training. About the Asian Development Bank ADB is committed to achieving a prosperous, inclusive, resilient, and sustainable Asia and the Pacific, while sustaining its efforts to eradicate extreme poverty. Established in 1966, it is owned by 68 members —49 from the region. Its main instruments for helping its developing member countries are policy dialogue, loans, equity investments, guarantees, grants, and technical assistance. LIMITED IMPACT OF BUSINESS DEVELOPMENT PROGRAMS ON PROFITABILITY IN THE PRESENCE OF AMBIGUITY AVERSION Dmitry Shapiro ADB ECONOMICS WORKING PAPER SERIES NO. 614 April 2020