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In this chapter we demonstrate the construction of inverse test confidence intervals for the turning-points in estimated nonlinear relationships by the use of the marginal or first derivative function. First, we outline the inverse test confidence interval approach. Then we examine the relationship between the traditional confidence intervals based on the Wald test for the turning-points for a cubic, a quartic, and fractional polynomials estimated via regression analysis and the inverse test intervals. We show that the confidence interval plots of the marginal function can be used to estimate confidence intervals for the turning-points that are equivalent to the inverse test. We also provide a method for the interpretation of the confidence intervals for the second derivative function to draw inferences for the characteristics of the turning-point.

This method is applied to the examination of the turning-points found when estimating a quartic and a fractional polynomial from data used for the estimation of an Environmental Kuznets Curve. The Stata do files used to generate these examples are listed in Appendix A along with the data.

Conditional cash transfers (CCT) have been adopted in many countries over the last two decades. Although the impacts of these programs have been studied extensively, understanding of the economic mechanisms through which cash and conditions affect household decisions remains incomplete. In particular, relatively little is known about the effects of these programs on intra-household allocation decisions. This chapter uses evidence from a program in Cambodia, where eligibility varied substantially among siblings in the same household, to illustrate these effects. A simple model of schooling decisions highlights three different effects of a child-specific CCT: an income effect, a substitution effect, and a displacement effect. The model predicts that such a CCT should unambiguously increase enrollment for eligible children, but have an ambiguous effect on ineligible siblings. The ambiguity arises from the interaction of a positive income effect with a negative displacement effect. These predictions are shown to be consistent with evidence from Cambodia, where the CESSP Scholarship Program (CSP) makes modest transfers, conditional on school enrollment for children of middle-school age. Scholarship recipients were more than 20 percentage points more likely to be enrolled in school, and 10 percentage points less likely to work for pay. However, the school enrollment and work of ineligible siblings was largely unaffected by the program. A possible fourth effect, operating through non-pecuniary spillovers of the intervention among siblings, remains largely outside the scope of the analysis, although there is some tentative evidence to suggest that it might also be at work.

We consider conditional distribution and conditional density functionals in the space of generalized functions. The approach follows Phillips (1985, 1991, 1995) who employed generalized functions to overcome non-differentiability in order to develop expansions. We obtain the limit of the kernel estimators for weakly dependent data, even under non-differentiability of the distribution function; the limit Gaussian process is characterized as a stochastic random functional (random generalized function) on the suitable function space. An alternative simple to compute estimator based on the empirical distribution function is proposed for the generalized random functional. For test statistics based on this estimator, limit properties are established. A Monte Carlo experiment demonstrates good finite sample performance of the statistics for testing logit and probit specification in binary choice models.

Economists and sociologists have proposed arguments for why there can exist wage penalties for work involving helping and caring for others, penalties borne disproportionately by women. Evidence on wage penalties is neither abundant nor compelling. We examine wage differentials associated with caring jobs using multiple years of Current Population Survey (CPS) earnings files matched to O*NET job descriptors that provide continuous measures of “assisting & caring” and “concern” for others across all occupations. This approach differs from prior studies that assume occupations either do or do not require a high level of caring. Cross-section and longitudinal analyses are used to examine wage differences associated with the level of caring, conditioned on worker, location, and job attributes. Wage level estimates suggest substantive caring penalties, particularly among men. Longitudinal estimates based on wage changes among job switchers indicate smaller wage penalties, our preferred estimate being a 2% wage penalty resulting from a one standard deviation increase in our caring index. We find little difference in caring wage gaps across the earnings distribution. Measuring mean levels of caring across the U.S. labor market over nearly thirty years, we find a steady upward trend, but overall changes are small and there is no evidence of convergence between women and men.

The changes in women’s and men’s work lives have been considerable in recent decades. Yet much of the recent research on gender differences in employment and earnings has been of a more snapshot nature rather than taking a longer comparative look at evolving patterns. In this paper, we use 50 years (1964–2013) of US Census Annual Demographic Files (March Current Population Survey) to track the changing returns to human capital (measured as both educational attainment and potential work experience), estimating comparable earnings equations by gender at each point in time. We consider the effects of sample selection over time for both women and men and show the rising effect of selection for women in recent years. Returns to education diverge for women and men over this period in the selection-adjusted results but converge in the OLS results, while returns to potential experience converge in both sets of results. We also create annual calculations of synthetic lifetime labor force participation, hours, and earnings that indicate convergence by gender in worklife patterns, but less convergence in recent years in lifetime earnings. Thus, while some convergence has indeed occurred, the underlying mechanisms causing convergence differ for women and men, reflecting continued fundamental differences in women’s and men’s life experiences.

In the spirit of Polachek (1975) and the later work of Becker (1985) on the role of specialization within the family, we examine the relationship between fringe benefits and the division of labor within a married household. The provision of fringe benefits is complicated by their non-additive nature within the household, as well as IRS regulations that stipulate that they be offered in a non-discriminatory manner in order to maintain their tax-exempt status. We model family decisions within a framework in which one spouse specializes in childcare and as a result experiences a reduction in market productive capacity. Our model predicts that the forces toward specialization become stronger as the number of children increase, so that the spouse specializing in childcare will have some combination of lower wages, hours worked, and fringe benefits. We demonstrate that to the extent that labor markets are incomplete, the family is less likely to obtain health insurance from the employer of the spouse that specializes in childcare. Using data from the April 1993 CPS we find evidence consistent with our model.

A common feature of certain kinds of data is a high level of statistical dependence across space and time. This spatial and temporal dependence contains useful information that can be exploited to significantly reduce the uncertainty surrounding local distributions. This chapter develops a methodology for inferring local distributions that incorporates these dependencies. The approach accommodates active learning over space and time, and from aggregate data and distributions to disaggregate individual data and distributions. We combine data sets on Kansas winter wheat yields – annual county-level yields over the period from 1947 through 2000 for all 105 counties in the state of Kansas, and 20,720 individual farm-level sample moments, based on ten years of the reported actual production histories for the winter wheat yields of farmers participating in the United States Department of Agriculture Federal Crop Insurance Corporation Multiple Peril Crop Insurance Program in each of the years 1991–2000. We derive a learning rule that combines statewide, county, and local farm-level data using Bayes’ rule to estimate the moments of individual farm-level crop yield distributions. Information theory and the maximum entropy criterion are used to estimate farm-level crop yield densities from these moments. These posterior densities are found to substantially reduce the bias and volatility of crop insurance premium rates.