Abstract: Gini index is a widely used measure of economic inequality. This article develops a theory and methodology for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width without assuming any specific distribution of the data. Fixed sample size methods cannot simultaneously achieve both specified confidence coefficient and fixed width. We develop a purely sequential procedure for interval estimation of Gini index with a specified confidence coefficient and a specified margin of error. Optimality properties of the proposed method, namely first order asymptotic efficiency and asymptotic consistency properties are proved under mild moment assumptions of the distribution of the data.
Abstract: The Ramsey regression equation specification error test (RESET) furnishes a diagnostic for omitted variables in a linear regression model specification (i.e., the null hypothesis is no omitted variables). Integer powers of fitted values from a regression analysis are introduced as additional covariates in a second regression analysis. The former regression model can be considered restricted, whereas the latter model can be considered unrestricted; this first model is nested within this second model. A RESET significance test is conducted with an F-test using the error sums of squares and the degrees of freedom for the two models. For georeferenced data, eigenvectors can be extracted from a modified spatial weights matrix, and included in a linear regression model specification to account for the presence of nonzero spatial autocorrelation. The intuition underlying this methodology is that these synthetic variates function as surrogates for omitted variables. Accordingly, a restricted regression model without eigenvectors should indicate an omitted variables problem, whereas an unrestricted regression model with eigenvectors should result in a failure to reject the RESET null hypothesis. This paper furnishes eleven empirical examples, covering a wide range of spatial attribute data types, that illustrate the effectiveness of eigenvector spatial filtering in addressing the omitted variables problem for georeferenced data as measured by the RESET.
Abstract: This paper improves a kernel-smoothed test of symmetry through combining it with a new class of asymmetric kernels called the generalized gamma kernels. It is demonstrated that the improved test statistic has a normal limit under the null of symmetry and is consistent under the alternative. A test-oriented smoothing parameter selection method is also proposed to implement the test. Monte Carlo simulations indicate superior finite-sample performance of the test statistic. It is worth emphasizing that the performance is grounded on the first-order normal limit and a small number of observations, despite a nonparametric convergence rate and a sample-splitting procedure of the test.
Abstract: We develop a procedure for removing four major specification errors from the usual formulation of binary choice models. The model that results from this procedure is different from the conventional probit and logit models. This difference arises as a direct consequence of our relaxation of the usual assumption that omitted regressors constituting the error term of a latent linear regression model do not introduce omitted regressor biases into the coefficients of the included regressors.
Abstract: Using high-frequency data, we decompose the time-varying beta for stocks into beta for continuous systematic risk and beta for discontinuous systematic risk. Estimated discontinuous betas for S&P500 constituents between 2003 and 2011 generally exceed the corresponding continuous betas. We demonstrate how continuous and discontinuous betas decrease with portfolio diversification. Using an equiweighted broad market index, we assess the speed of convergence of continuous and discontinuous betas in portfolios of stocks as the number of holdings increase. We show that discontinuous risk dissipates faster with fewer stocks in a portfolio compared to its continuous counterpart.
Abstract: A fast method for estimating the parameters of a stable-APARCH not requiring likelihood or iteration is proposed. Several powerful tests for the (asymmetric) stable Paretian distribution with tail index are used for assessing the appropriateness of the stable assumption as the innovations process in stable-GARCH-type models for daily stock returns. Overall, there is strong evidence against the stable as the correct innovations assumption for all stocks and time periods, though for many stocks and windows of data, the stable hypothesis is not rejected.