The Average Is Not an Allocation Rule
Formal credit and small and medium-sized enterprise (SME) performance are the subject of this series. The opening question is deceptively simple: when firms receive more formal credit, do they perform better? The evidence says that they often do on average. But the more consequential question for a lender or policymaker is different: which firms benefit from a larger loan, under what conditions, and what happens when the same decision is made for firms that respond differently? The aim here is to build a way of reading credit evidence that can answer both questions without confusing them.
That distinction matters because an average can be true and still be inadequate for a decision. A credit program may raise performance in the population while producing large gains for some firms, little change for others, and costly outcomes for another group. If those responses are combined into one number, the number remains useful as a summary of the program. It simply cannot tell an allocator where the gains are.
Credit changes capacity—and exposure
A formal loan does more than add cash to a balance sheet. It can relax a financial constraint: a firm that could not previously fund an opportunity may now be able to expand. At the same time, the loan creates a repayment obligation and changes the consequences of a bad decision. The same increase in capacity can therefore be productive for one business and hazardous for another. That is not a moral distinction between “good” and “bad” entrepreneurs. It is a question of how a given firm’s opportunities, decisions, risks, and local market interact with the contract.
This is why “does credit work?” is an incomplete formulation. It treats credit as if it had one predictable effect, independent of the business receiving it and the program delivering it. A better formulation has at least three layers:
- The average effect: What happened to outcomes across the people or firms included in the evaluation?
- The distribution of effects: How widely did responses vary around that average?
- The allocation decision: Can the lender identify, before lending, where a larger or differently designed loan is more likely to create value?
The first layer is the natural starting point for impact evaluation. The second explains why the first may conceal important consequences. The third is where evidence becomes operational—and where overconfidence becomes expensive.
The diagram captures the central problem. The average is produced after different responses have been combined. An allocation decision has to be made before those outcomes are observed. Treating the average as if it identified the right recipients skips the most difficult link in the chain.
What the broad evidence establishes
The Inter-American Development Bank report Formal Credit and SME Performance: Reviewing Evidence from Impact Evaluations provides the broad starting point. Its abstract reports meta-analytic mean effects of formal loans that are economically meaningful: employment rises by about 12% on average, sales by about 18%, and profits by about 18%. Those figures make an important case for taking formal credit seriously. Relaxing a financial constraint can affect the scale and performance of an SME, not merely its access to a financial product.
The qualifiers are equally important. These are approximate means across an evidence base, not promises attached to an individual loan. The report emphasizes substantial heterogeneity across settings, programs, and outcome horizons. “About 18%” for profits does not mean that every firm’s profits rise by 18%, that sales and profits move together in every study, or that an effect measured soon after lending will persist. It means that, after the evidence is assembled into a population-level summary, the average movement is positive and economically meaningful.
The report also identifies conditions under which the mean changes. Effects are larger in some large-scale public interventions and in programs that explicitly target financially constrained firms. In other programs, effects are smaller or statistically indistinguishable from zero. The intervention is therefore not simply “credit.” It is credit delivered through a particular design, to a particular group, in a particular financial architecture, with outcomes measured over a particular horizon.
That context also prevents a narrow reading of benefit. The report warns that credit expansions are not automatically welfare improving. They can create distributional and competitive spillovers, and their consequences depend on targeting, program design, and local financial conditions. A loan may improve the recipient firm while changing competitive pressure on other firms. A program that explicitly targets constrained businesses may operate differently from a broad expansion, while a poorly targeted intervention may place capital where it adds little value. The average effect is thus a starting point for judgment about design, not a substitute for it.
The broad review leaves a question that its own summary cannot answer: even within a single lending program and a relatively defined group of applicants, are the firms receiving more credit responding in similar ways? To answer that, we need evidence that holds more of the surrounding context constant and examines variation within the treatment.
The focal case: larger loans in Egypt
The companion study by Gharad Bryan, Dean Karlan, and Adam Osman makes that allocation problem concrete. It experimentally studies relatively large enterprise loans in Egypt. The available study metadata identifies approved applicants to the Tamouh program at the Alexandria Business Association, and the online appendix explains that the researchers designed the randomization and evaluation while the lender designed and implemented the loans. Participants voluntarily applied for the larger loan and passed the lender’s ordinary approval process. The results therefore concern a real lending margin among eligible applicants, not every business in Egypt.
The experiment’s headline is deliberately uncomfortable for a simple expansion story. Larger loans generate small average impacts. Yet the authors report that baseline psychometric information, analyzed with machine-learning methods, reveals large differences in predicted treatment effects: the group with the highest predicted gains substantially increases profits, while profits fall for the group with the poorest predicted response. The authors connect that contrast to aggregate income and argue that existing credit-allocation practice leads to substantial misallocation.
This does not mean that the experiment found a permanent category of winners and losers. “Top performers” and “poor performers” are labels for groups formed from predicted responses to the treatment being studied. They describe how firms in this sample were expected to respond to a larger loan; they do not describe an entrepreneur’s essence or guarantee what will happen in a different market, contract, or time period. The contrast is valuable precisely because it is conditional: the same loan-size change did not have the same consequence for everyone in the studied population.
The authors propose one explanation for the divergence. Some entrepreneurs, they argue, may be overoptimistic and take on too much risk when given the opportunity created by a larger loan. That mechanism is plausible within the study’s logic, but it should be kept as a proposed explanation rather than converted into a diagnosis. The experiment identifies the causal effect of changing loan size. The survey and prediction evidence helps describe who responds differently and suggests why; it does not, by itself, isolate one psychological trait as the cause of every poor outcome.
The case therefore separates two decisions that are often bundled together. The first is whether expanding formal credit can improve SME performance. The review suggests that it can, on average, and the experiment studies one such expansion margin. The second is how to allocate additional credit among eligible firms. That decision depends on the distribution of responses. A program can be worthwhile in the aggregate while still leaving value on the table—or exposing some borrowers to avoidable downside—if it treats conditional response as irrelevant.
The standard required to say “who benefits”
The allocation question cannot be answered by looking backward at which firms happened to do well after receiving a loan. An allocator needs information available before treatment and a way to test whether a ranking based on that information predicts actual differences in treatment response. That is why the Egyptian study’s use of psychometric, cognitive, risk, financial-literacy, and business data matters. It attempts to turn baseline information into a testable prediction rather than relying on a post hoc story about successful borrowers.
But prediction and explanation are not the same achievement. A model may rank firms with different responses without revealing the causal pathway that produced the ranking. A survey answer can be useful as a signal while remaining an imperfect proxy for opportunity, decision-making, risk tolerance, or some combination of factors. A predictive group can be statistically distinct without becoming a natural kind. And a ranking that works in one evaluation may lose accuracy when the loan contract, applicant pool, market, or economic conditions change.
The study’s design takes this problem seriously by separating the data used to build predictions from the data used to test them. That protects the test from simply rewarding a model for remembering the outcomes it saw during training. The later analysis also matters: the authors issued a corrigendum after identifying a coding error in part of the original machine-learning implementation. The corrected results continue to support meaningful heterogeneity and a strong difference between high- and low-predicted-benefit groups, while weakening the claim that the bottom group’s negative effect is individually statistically significant. In evidence about allocation, that is not a footnote. It is a reminder that the strength and shape of the conclusion depend on the integrity of the measurement process.
The practical judgment this series supports is consequently narrower—and more useful—than “give bigger loans to the winners.” Average credit effects tell us whether a program appears to move outcomes for its population. Heterogeneous-effect evidence asks whether the movement is uneven. Predictive analysis asks whether some of that unevenness can be recognized before lending. None of those steps alone supplies an optimal allocation rule, proves a mechanism, or removes the need to monitor borrowers and markets.
Before deciding what to do with the evidence from the Egyptian experiment, we need to examine what the broad credit average is actually averaging together. That means looking closely at how program design, targeting, setting, and time horizon turn the same apparent intervention into different economic outcomes. Only then can the experiment’s small mean and large conditional differences be read as parts of one subject: the performance consequences of formal credit, and the allocation choices that determine who receives its benefits.