A Nonparametric Examination of Capital-Skill Complementarity

This paper uses nonparametric kernel methods to construct observation-specific elasticities of substitution for a balanced panel of 73 developed and developing countries to examine the capital-skill complementarity hypothesis. The exercise shows some support for capital-skill complementarity, but the strength of the evidence depends upon the definition of skilled labor and the elasticity of substitution measure being used. The added flexibility of the nonparametric procedure is also able to uncover that the elasticities of substitution vary across countries, groups of countries and time periods.capital-skill complementarity, elasticity of substitution, nonparametric kernel, stochastic dominance

A Test for Multimodality of Regression Derivatives with an Application to Nonparametric Growth Regressions

This paper presents a method to test for multimodality of an estimated kernel density of parameter estimates from a local-linear least-squares regression derivative. The procedure is laid out in seven simple steps and a suggestion for implementation is proposed. A Monte Carlo exercise is used to examine the finite sample properties of the test along with those from a calibrated version of it which corrects for the conservative nature of Silverman-type tests. The test is included in a study on nonparametric growth regressions. The results show that in the estimation of unconditional β-convergence, the distribution of the parameter estimates is multimodal with one mode in the negative region (primarily OECD economies) and possibly two modes in the positive region (primarily non-OECD economies) of the parameter estimates. The results for conditional β-convergence show that the density is predominantly negative and unimodal. Finally, the application attempts to determine why particular observations posess positive marginal effects on initial income in both the unconditional and conditional frameworks.Nonparametric Kernel; Convergence; Modality Tests

Are We Wasting Our Children's Time by Giving Them More Homework?

Following an identification strategy that allows us to largely eliminate unobserved student and teacher traits, we examine the effect of homework on math, science, English and history test scores for eighth grade students in the United States. Noting that failure to control for these effects yields selection biases on the estimated effect of homework, we find that math homework has a large and statistically meaningful effect on math test scores throughout our sample. However, additional homework in science, English and history are shown to have little to no impact on their respective test scores.first differencing, unobserved traits, instrumental variable, selection bias, homework

Canonical Higher-Order Kernels for Density Derivative Estimation

In this note we present r th order kernel density derivative estimators using canonical higher-order kernels. These canonical rescalings uncouple the choice of kernel and scale factor. This approach is useful for selection of the order of the kernel in a data-driven procedure as well as for visual comparison of kernel estimates.Derivative Estimation, AMISE

Normal Reference Bandwidths for the General Order, Multivariate Kernel Density Derivative Estimator

This note derives the general form of the approximate mean integrated squared error for the q-variate, th-order kernel density r th derivative estimator. This formula allows for normal reference rule-of-thumb bandwidths to be derived. We give tables for some of the most common cases in the literature.Derivative Estimation, Smoothing, AMISE

Imposing Economic Constraints in Nonparametric Regression: Survey, Implementation and Extension

Economic conditions such as convexity, homogeneity, homotheticity, and monotonicity are all important assumptions or consequences of assumptions of economic functionals to be estimated. Recent research has seen a renewed interest in imposing constraints in nonparametric regression. We survey the available methods in the literature, discuss the challenges that present themselves when empirically implementing these methods and extend an existing method to handle general nonlinear constraints. A heuristic discussion on the empirical implementation for methods that use sequential quadratic programming is provided for the reader and simulated and empirical evidence on the distinction between constrained and unconstrained nonparametric regression surfaces is covered.identification, concavity, Hessian, constraint weighted bootstrapping, earnings function

Heterogeneity in Schooling Rates of Return

This paper relaxes the assumption of homogeneous rates of return to schooling by employing nonparametric kernel regression. This approach allows us to examine the differences in rates of return to education both across and within groups. Similar to previous studies we find that on average blacks have higher returns to education than whites, natives have higher returns than immigrants and younger workers have higher returns than older workers. Contrary to previous studies we find that the average gap of the rate of return between white and black workers is larger than previously thought and the gap is smaller between immigrants and natives. We also uncover significant heterogeneity, the extent of which differs both across and within groups. The estimated densities of returns vary across groups and time periods and are often skewed. For example, during the period 1950-1990, at least 5% of whites have negative returns. Finally, we uncover the characteristics common amongst those with the smallest and largest returns to education. For example, we find that immigrants, aged 50-59, are most likely to have rates of return in the bottom 5% of the population.nonparametric, Mincer regressions, rate of return to education

Are any growth theories linear? Why we should care about what the evidence tells us

Recent research on macroeconomic growth has been focused on resolving several key issues, two of which, specification uncertainty of the growth process and variable uncertainty, have received much attention in the recent literature. The standard procedure has been to assume a linear growth process and then to proceed with investigating the relevant variables that determine growth across countries. However, a more appropriate approach would be to recognize that a misspecified model may lead one to conclude that a variable is relevant when in fact it is not. This paper takes a step in this direction by considering conditional variable uncertainty with full blown specification uncertainty. We use recently developed nonparametric model selection techniques to deal with nonlinearities and competing growth theories. We show how one can interpret our results and use them to motivate more intriguing specifications within the traditional studies that use Bayesian Model Averaging or other model selection criteria. We find that the inclusion of nonlinearities is necessary for determining the empirically relevant variables that dictate growth and that nonlinearities are especially important in uncovering key mechanism of the growth process.Growth Nonlinearities, Irrelevant Variables, Least Squares Cross Validation, Bayesian Model Averaging, Parameter Heterogeneity

When, where and how to perform efficiency estimation

In this paper we compare two flexible estimators of technical efficiency in a cross-sectional setting: the nonparametric kernel SFA estimator of Fan, Li and Weersink (1996) to the nonparametric bias corrected DEA estimator of Kneip, Simar andWilson (2008). We assess the finite sample performance of each estimator via Monte Carlo simulations and empirical examples. We find that the reliability of efficiency scores critically hinges upon the ratio of the variation in efficiency to the variation in noise. These results should be a valuable resource to both academic researchers and practitioners.Bootstrap; Nonparametric kernel; Technical efficiency

When, Where and How to Perform Efficiency Estimation

In this paper we compare two flexible estimators of technical efficiency in a cross-sectional setting: the nonparametric kernel SFA estimator of Fan, Li and Weersink (1996) to the nonparametric bias corrected DEA estimator of Kneip, Simar and Wilson (2008). We assess the finite sample performance of each estimator via Monte Carlo simulations and empirical examples. We find that the reliability of efficiency scores critically hinges upon the ratio of the variation in efficiency to the variation in noise. These results should be a valuable resource to both academic researchers and practitioners.nonparametric kernel, technical efficiency, bootstrap