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Aggregation Without Separability: A Generalized Composite Commodity Theorem

Arthur Lewbel
American Economic Review 1996 86(3), 524-543
This paper provides general conditions for aggregating commodities without separable utility. These conditions impose weaker and more empirically plausible restrictions on price movements than the currently existing alternative to separability, the Hicks-Leontief composite commodity theorem. The idea is to allow departures from Hicks-Leontief that take the form of well behaved error terms. Utility functions that permit generalized composite commodity aggregation include the AIDS model, the translog, all homothetic utility functions, and any utility function when demands are aggregated to two groups of goods. Implications of empirical nonstationarity of relative prices for aggregation and demand estimation are considered.

Aggregation and Simple Dynamics

Arthur Lewbel
American Economic Review 1994 84(4), 905-918
The koyck (geometric) lag or AR(1) specification is a commonly proposed behavioral model, sometimes after differencing. The distribution of koyck lag or AR(1) coefficients across agents in an economy is shown to be completely identified just from the dynamic behavior of aggregate (macroeconomic) data. Aggregate testable implications of an economy composed of agents having koyck lags or AR(1) models are provided. Extensions to higher-order and time-varying lags are discussed. Aggregate U.S. consumption data are shown to support the hypothesis that some consumers have random-walk consumption, while the rest have ARIMA(1,1,0) consumption with widely varying AR coefficients.

Demand Systems With and Without Errors

Arthur Lewbel
American Economic Review 2001 91(3), 611-618
Revealed preference theory assumes that each consumer has demands that are rational, meaning that they arise from the maximization of his or her own utility function. In contrast, econometric or statistical demand models assume that each consumer's demands equal a rational systematic component derived from a common utility function, plus an individual-specific, additive error term. This paper reconciles these differences, by providing necessary and sufficient conditions for rationality of statistical demand models given individual consumer rationality.

Aggregation without Separability: A Generalized Composite Commodity Theorem

Arthur Lewbel
American Economic Review 1996
This paper provides general conditions for aggregating commodities without separable utility. These conditions impose weaker and more empirically plausible restrictions on price movements than the currently existing alternative to separability, the Hicks-Leontief composite commodity theorem. The idea is to allow departures from Hicks-Leontief that take the form of well-behaved error terms. Utility functions that permit generalized composite commodity aggregation include the AIDS model, the translog, all homothetic utility functions, and any utility function when demands are aggregated to two groups of goods. Implications of empirical nonstationarity of relative prices for aggregation and demand estimation are considered.

Aggregation and simple dynamics

Arthur Lewbel
American Economic Review 1994
The koyck (geometric) lag or AR(1) specification is a commonly proposed behavioral model, sometimes after differencing. The distribution of koyck lag or AR(1) coefficients across agents in an economy is shown to be completely identified just from the dynamic behavior of aggregate (macroeconomic) data. Aggregate testable implications of an economy composed of agents having koyck lags or AR(1) models are provided. Extensions to higher-order and time-varying lags are discussed. Aggregate U.S. consumption data are shown to support the hypothesis that some consumers have random-walk consumption, while the rest have ARIMA (1, 1, 0) consumption with widely varying AR coefficients.

Tricks with Hicks: The EASI Demand System

Arthur Lewbel; Krishna Pendakur
American Economic Review 2009 99(3), 827-863
We invent Implicit Marshallian demands, which combine desirable features of Hicksian and Marshallian demands. We propose and estimate the Exact Affine Stone Index (EASI) implicit Marshallian demand system. Like the Almost Ideal Demand (AID) system, EASI budget shares are linear in parameters given real expenditures. However, unlike the AID, EASI demands can have any rank and its Engel curves can have any shape over real expenditures. EASI error terms equal random utility parameters to account for unobserved preference heterogeneity. EASI demand functions can be estimated using GMM or three stage least squares, and, like AID, an approximate EASI model can be estimated by linear regression.

Children's Resources in Collective Households: Identification, Estimation, and an Application to Child Poverty in Malawi

Geoffrey R. Dunbar; Arthur Lewbel; Krishna Pendakur
American Economic Review 2013 103(1), 438-471
The share of household resources devoted to children is hard to identify because consumption is measured at the household level and goods can be shared. Using semiparametric restrictions on individual preferences within a collective model, we identify how total household resources are divided up among household members by observing how each family member's expenditures on a single private good like clothing vary with income and family size. Using data from Malawi we show how resources devoted to wives and children vary by family size and structure, and we find that standard poverty indices understate the incidence of child poverty.