MUE

Estimating demand for many goods usually means estimating many cross-price effects. We show that low-rank cross-price structure is equivalent to a small number of "price aggregators," and characterize the preferences behind them. Download Paper Abstract Estimating consumer demands is a bread-and-butter undertaking in applied economics. In general, demand for each good depends on the prices of all goods and services, but for most applications it is impractical to estimate models of such high dimension. In this paper, we consider consumer demand with a low rank of the matrix of cross-price effects, a property implicitly assumed in most empirical settings. First, we show that imposing a low rank is equivalent to introducing functions that we call “aggregators”, where each aggregator maps information from an arbitrarily large vector of prices (and perhaps income) into a scalar. We then provide a complete characterization of the preferences that rationalize demand systems with such aggregators. These results can be used to derive new and flexible forms of demand that can be tailored to applications in various fields of economics. Most commonly-used demand systems (including directly-additive, indirectly-additive, non-homothetic CES and Kimball preferences) can be described with one or two aggregators where the price index may coincide with one of the aggregators. Nested and mixed logit require as many aggregators as nests or consumer types. Aggregators can also be naturally expressed as a function of observed product attributes. Using barcode data on purchases of ready-to-eat cereals, we illustrate how to estimate a simple yet flexible specification of such a demand system with K aggregators, with or without using information on product attributes. ...

The agricultural season naturally induces seasonal variation to prices for things like maize. Is it possible to make money by timing this market? Download Paper Abstract Consumption expenditures in rural areas of low-income countries are highly variable across seasons, yet the literature still lacks a standard framework for asking whether seasonal poverty reflects local credit market failure or poor integration with the broader economy. We develop an intertemporal model of farmers’ portfolio choices under seasonal price risk and borrowing constraints, and derive a sign diagnostic: The amount a farmer is willing to pay for a small risk-free bond (call this price q) must rise in response to a positive income shock if credit constraints bind, but fall if precautionary motives dominate. We apply this framework to a randomized post-harvest loan program in Gombe, Nigeria, and supplement the experiment by also collecting high-frequency data on prices, stocks, and expenditures. The loan sharply reduces the marginal utility of expenditure around delivery, but q never rises over the full follow-up. Precautionary savings, not credit constraints, govern the intertemporal allocation. Receipt of the loan leads to a portfolio rebalancing, as farmers adjust their grain stores, and increase investment. But maize prices increase little after harvest and season-average consumption expenditure effects are small, though the MUE—a more sensitive welfare measure—detects a large and significant improvement around delivery that expenditures miss. We fail to reject the null of well-functioning local financial markets. The binding constraint is poor spatial integration rather than inefficient local allocation—promoting market integration may improve lean-season welfare more than would the local provision of credit. ...

"Covariate" shocks such as droughts or floods may affect everyone, but not everyone is affected equally. We devise ways to test the extent to which the effects of these shocks are shared. Download Paper Abstract Efficient risk-sharing implies a simple factor structure for marginal utilities of expenditure (MUEs): Pareto weights divided by a common price. The standard approach infers MUEs from total expenditures, implicitly assuming homothetic preferences, unitary income elasticities, and identical price elasticities. Risk-sharing tests using total expenditures work for idiosyncratic shocks (budgets change, but not prices), but not ``covariate’’ shocks (prices change). We describe all preferences which permit one to infer MUEs from expenditures, and estimate nonhomothetic MUEs to test whether covariate shocks are shared efficiently in Uganda. This delivers sensible results; the standard approach suggests that droughts, floods, and pests are beneficial. ...

How well do social protection programs reach the poorest? We assess Ghana's LEAP program and show that community-based targeting may outperform proxy-based methods when evaluated against a marginal-utility benchmark. Download Paper Abstract We propose an alternative benchmark for evaluating the targeting accuracy of social protection programs based on the marginal utility of expenditure. Using this benchmark, we assess the targeting performance of Ghana’s Livelihood Empowerment Against Poverty (LEAP) program. We find that community-based targeting may yield more accurate targeting outcomes than proxy-based methods under a marginal-utility benchmark, because the latter better captures the welfare losses from poverty that standard consumption-based measures can miss. ...

Can we save money on surveys by measuring poverty with a few goods instead of full consumption? Theory says only if all Engel curves are linear; data from East Africa confirm this shortcut fails in practice. Download Paper Abstract Frequent measurement of poverty is challenging because measurement often relies on complex and expensive expenditure surveys that try to measure expenditures on a comprehensive consumption aggregate. This paper investigates the use of consumption subaggregates instead. The use of consumption subaggregates is theoretically justified if and only if all Engel curves are linear for any realization of prices. This is very stringent. However, it may be possible to empirically identify certain goods that happen to have linear Engel curves given prevailing prices, and when the effect of price changes is small, such a subaggregate might work in practice. We construct such linear subaggregates using data from Rwanda, Tanzania, and Uganda. Our findings show that using subaggregates is ill advised in practice as well as in theory. ...

Frisch demands that are separable in the budget multiplier \(\lambda\) turn out to have a surprisingly simple structure. We give a complete characterization: quantities are $λ$-separable iff utility is additively separable. Download Paper Abstract Frisch demands depend on prices and a multiplier \(\lambda\) associated with the consumer’s budget constraint. Subject only to standard, modest, regularity conditions, we provide a complete characterization of all Frisch demand systems and of the utility functions that rationalize these demand systems when either quantities demanded or consumption expenditures are separable in \(\lambda\). Quantities demanded are $λ$-separable if and only if the rationalizing utility function is additively separable in these quantities. In contrast, expenditures are $λ$-separable if and only if marginal utilities for these expenditures belong to one of two simple parametric families. ...

Many applied demand models assume $λ$-separability without checking that a rationalizing utility function exists. We provide closed-form utility functions for several common families. Download Paper Abstract Many commonly used demand systems in applied economics assume that demands are separable in the multiplier \(\lambda\) on the consumer’s budget constraint. We provide closed-form expressions for the utility functions that rationalize several important families of $λ$-separable Frisch demand systems, including demands that are affine in \(\lambda\) and demands with constant expenditure elasticities. ...