This paper proposes nonparametric tests of additive constraints on the first and second derivatives of a model E(y|x) = g(x), where the true function g is unknown. Such constraints are illustrated by the economic restrictions of homogeneity and symmetry, and the functional form restrictions of additivity and linearity. The proposed tests are based on estimates of regression coefficients, that statistically characterize the departures from the constraint exhibited by the data. The coefficients are based on weighted-average derivatives, that are reformulated in terms of derivatives of the density of x. Coefficient estimators are proposed that use nonparametric kernel estimators of the density and its derivatives. These statistics are shown to be √N consistent and asymptotically normal, and thus are comparable to estimators based on a (correctly specified) parametric model of g(x).

[In this paper several results are established which provide for the consistent estimation of macroeconomic effects using cross-section data, for general assumptions on the movement of the population distribution over time. We show that macroeconomic effects are always consistently estimated by linear instrumental variables coefficients, where the instruments are determined by the form of distribution movement. This leads to a natural way to assess the biases in OLS coefficients as estimators of macroeconomic effects, provides a nonparametric macroeconomic interpretation of linear instrumental variables coefficients when the true microeconomic behavioral model is unknown, and gives a nonparametric interpretation of standard regression decomposition statistics such as R extasciicircum2 relative to the information costs of nonlinearities in aggregation. All of the results are valid without imposing any testable restrictions on the cross-section data.]

This paper presents estimates of the distributional welfare impacts ofthe actual price rises of energy and nonenergy commodities during the1970-80 decade in the United States. Measures of welfare changes basedon net compensating variations are computed for families that differ with respect to demographic characteristics, initial total expenditurelevels, and total expenditure growth profiles over the decade. For comparison, measures of welfare change based solely on the changes inenergy prices are computed. The author shows that welfare differencesdue to initial expenditure levels or demographic profiles are minor incomparison to welfare differences due to different expenditure growthprofiles.

The presence of distributional effects in macroeconomic equations is shown to coincide with nonlinearity in micro behavioral relationships. Parameters estimated with aggregate data, as in representative agent models, contain distributional biases that are not measurable using aggregate data alone. Tests for distributional effects and other measures of the extent of aggregation problems are derived using distributional data observed over time. Significant distributional effects are noted for a model of annual aggregate U.S. commodity expenditure data. A static model that accommodates individual heterogeneity is found to be statistically equivalent to a simply dynamic model that accommodates first-order autocorrelation.

This survey covers recent solutions to aggregation problems in three application areas, consumer demand analysis, consumption growth and wealth, and labor participation and wages. Each area involves treatment of heterogeneity and nonlinearity at the individual level. Three types of heterogeneity are highlighted: heterogeneity in individual tastes, heterogeneity in income and wealth risks and heterogeneity in market participation. Work in each area is illustrated using results from empirical data. The overall aim is to show how concerns faced by empirical researchers regarding aggregation can be addressed.

Emissions of carbon dioxide from the combustion of fossil fuels, which may contribute to long-term climate change, are projected through 2050 using reduced-form models estimated with national-level panel data for the period of 1950–1990. Using the same set of income and population growth assumptions as the Intergovernmental Panel on Climate Change (IPCC), we find that the IPCC's widely used emissions growth projections exhibit significant and substantial departures from the implications of historical experience. Our model employs a flexible form for income effects, along with fixed time and country effects, and we handle forecast uncertainty explicitly. We find clear evidence of an “inverse U” relation with a within-sample peak between carbon dioxide emissions (and energy use) per capita and per-capita income.

This paper gives a solution to the problem of estimating coefficients of index models, through the estimation of the density-weighted average derivative of a general regression function. A normalized version of the density-weighted average derivative can be estimated by certain linear instrumental variables coefficients. The estimators, based on sample analogies of the product moment representation of the average derivative, are constructed using nonparametric kernel estimators of the density of the regressors. Consistent estimators of the asymptotic variance-covariance matrices of the estimators are given, and a limited Monte Carlo simulation is used to study the practical performance of the procedures.

A new and easily implementable framework for the empirical analysis of the relationship between aggregate and individual wages is developed. Aggregate real wages are shown to contain three important bias terms: one associated with the dispersion of individual wages, a second deriving from compositional changes in the (selected) sample of workers, and a third reflecting the distribution of working hours. Their importance for interpreting the path of aggregate wages and of the returns to education for recent experience in Britain is highlighted. A close correspondence between the estimated biases and the patterns of differences shown by aggregate wages is established.

new econometric model of aggregate consumer behavior in the United States and to apply this model to the analysis of impacts of alternative economic policies on the welfare of individual consuming units. The model incorporates time-series data on quantities consumed, prices, the level and distribution of income, and demographic characteristics of the population. It also incorporates cross-section data on the allocation of consumer expenditures for households with different demographic characteristics. Our econometric model is based on the theory of exact aggregation developed by Lau (1977a, c). This theory makes it possible to dispense with the notion of a representative consumer in constructing models of aggregate consumer behavior. One of the most remarkable implications of Lau's theory of exact aggregation is that systems of demand functions for individuals with common demographic characteristics can be recovered uniquely from the system of aggregate demand functions. Using the individual demand functions we can analyze the impact of economic policy on consumer welfare.