University of Wisconsin-Madison

About: University of Wisconsin-Madison is a education organization based out in Madison, Wisconsin, United States. It is known for research contribution in the topics: Population & Gene. The organization has 108707 authors who have published 237594 publications receiving 11883575 citations.

Sample Splitting and Threshold Estimation

Abstract: .Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuously-distributed variable such as firm size. In addition, threshold models may be used as a parsimonious strategy for nonparametric function estimation. For example, the threshold autoregressive model .TAR is popular in the nonlinear time series literature. Threshold models also emerge as special cases of more complex statistical frameworks, such as mixture models, switching models, Markov switching models, and smooth transition threshold models. It may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures. Despite the large number of potential applications, the statistical theory of threshold estimation is undeveloped. It is known that threshold estimates are super-consistent, but a distribution theory useful for testing and inference has yet to be provided. This paper develops a statistical theory for threshold estimation in the regression context. We allow for either cross-section or time series observations. Least squares estimation of the regression parameters is considered. An asymptotic distribution theory . for the regression estimates the threshold and the regression slopes is developed. It is found that the distribution of the threshold estimate is nonstandard. A method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic. It is shown that this yields asymptotically conservative confidence regions. Monte Carlo simulations are presented to assess the accuracy of the asymptotic approximations. The empirical relevance of the theory is illustrated through an application to the multiple . equilibria growth model of Durlauf and Johnson 1995 .

Identity as an analytic lens for research in education

Abstract: n today's fast changing and interconnected global world, researchers in a variety of areas have come to see identity as an important analytic tool for understanding schools and society. A focus on the contextually specific ways in which people act out and recognize identities allows a more dynamic approach than the sometimes overly general and static trio of "race, class, and gender." However, the term identity has taken on a great many different meanings in the literature. Rather than survey this large literature, I will sketch out but one approach that draws on one consistent strand of that literature. This is not to deny that other, equally useful approaches are possible, based on different selections from the literature.