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We propose a nonparametric estimator of the Lorenz curve that satisfies its theoretical properties, including monotonicity and convexity. We adopt a transformation approach that transforms a constrained estimation problem into an unconstrained one, which is estimated nonparametrically. We utilize the splines to facilitate the numerical implementation of our estimator and to provide a parametric representation of the constructed Lorenz curve. We conduct Monte Carlo simulations to demonstrate the superior performance of the proposed estimator. We apply our method to estimate the Lorenz curve of the U.S. household income distribution and calculate the Gini index based on the estimated Lorenz curve.

The lack of a satisfactory theory of personal income distribution is a problem that economists have pondered for most of the twentieth century. In 1912 Irving Fisher wrote:

Enterprise diversification is a self‐insuring strategy used by farmers to protect against risk. This study examines the impact of various farm, operator, and household characteristics on the level of onfarm enterprise diversification. Evidence exists that larger farms are more specialized. Also, farmers who participate in off‐farm work, farms located near urban areas, or farms with higher debt‐to‐asset ratios are less likely to be diversified. In contrast, evidence suggests there is a significant positive relationship between diversification and whether the farm business has crop insurance, is organized as a sole proprietorship, or receives any direct payments from current farm commodity programs.

This chapter presents an exposition of the Generalized Fechner–Thurstone (GFT) direct utility function, the system of demand functions derived from it, other systems of demand functions from which it can be derived, and its purpose and the econometric circumstances that motivated its original development. Its use in econometrics is demonstrated by an application to household consumer survey data which explores the relationship between prices, on the one hand, and expected exogenous preference changers such as household size, schooling of heads of household, and other social factors, on the other.