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.

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.

Over two dozen different terms for identification appear in the econometrics literature, including set identification, causal identification, local identification, generic identification, weak identification, identification at infinity, and many more. This survey: (i) gives a new framework unifying existing definitions of point identification; (ii) summarizes and compares the zooful of different terms associated with identification that appear in the literature; and (iii) discusses concepts closely related to identification, such as normalizations and the differences in identification between structural models and causal, reduced form models.

When economic theory suggests a log-linear specification for individual agents, e.g., Cobb-Douglas production, it is common to estimate the same log-linear model with aggregate data, invoking a representative agent assumption and thereby assuming away aggregation errors. This paper gives necessary and sufficient restrictions on the distribution of agents in an economy for log-linear agent models to aggregate into log-linear macro models, and discusses the aggregation bias resulting from violation of these restrictions. Theorems, tests, economic rationales, and empirical results are given. Included are connections to random walks and to cointegration. Analogous results for log-level models are derived.

This paper shows that most methods of incorporating demographic variation into separable models can be represented in a form that is identical to Barten equivalence scales, except that the scales themselves depend on the exact mix of goods that comprise each group, as well as on demographic variables. This generalization of Barten scales is shown to be more plausible than ordinary scales; can be used to increase the efficiency of demand system estimation; and can overcome J. Muellbauer's underidentification result for cross-sectional estimation of equivalence scales.

"A general method of introducing demographic effects into any demand system, using modifying functions, is described which permits complicated interactions of demographic variables with prices and expeditures. Theorems give properties the modifying functions must have to ensure integrability of the resulting system. Demand equations of the new system are given explicitly as functions of the original demand equations and the modifying functions. The procedure is interpreted as altering a household's technology, and is shown to encompass adult equivalent scales and related methods. Examples of modifying functions are derived and applications of the technique to uses other than demographic variation are considered."

Journal Article Exact Aggregation and a Representative Consumer Get access Arthur Lewbel Arthur Lewbel Brandeis Uuniversity Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 104, Issue 3, August 1989, Pages 621–633, https://doi.org/10.2307/2937813 Published: 01 August 1989