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.]

"July 1984, revised November 1985."

Bibliography: p. 38-40.

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.

This paper presents estimates of the distributional welfare impacts of the actual price rises of energy and nonenergy commodities during the 1970-80 decade in the United States. Measures of welfare change based on net compensating variations are computed for different types of families. These show that welfare differences due to changes in commodity prices are minor compared to welfare differences due to different income growth patterns over the decade.

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.

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.

Continuing rapid growth in U.S. gasoline consumption threatens to exacerbate environmental and congestion problems. We use flexible semiparametric and nonparametric methods to guide analysis of household gasoline consumption, and including this variable cuts the estimated income elasticity in half. Slower projected future growth in licensed drivers points to slower growth in gasoline consumption. A parsimonious representation of age, income, lifecycle and location effects is developed and tested. We show how flexible methods also helped reveal fundamental problems with the available price data.

June 1988, revised April 1992