Nonparametric estimation of a polarization measure

Abstract

This paper develops methodology for nonparametric estimation of a polarization measure due to Anderson (2004) and Anderson, Ge, and Leo (2006) based on kernel estimation techniques. We give the asymptotic distribution theory of our estimator, which in some cases is nonstandard due to a boundary value problem. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate the …nite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years.Some key words: Kernel Estimation; Inequality; Overlap coe¢ cient; Poissonization JEL Classi…cation Number: C12, C13, C14.Thanks to David Mason for helpful comments and providing us with copies of his work. GAUSS programs that carry out the computations in this paper are available from the web site http://personal.lse.ac.uk/lintono/Software.htm. We thank Sorawoot Srisuma for helpful research assistance.

A polarization-cohesion perspective on cross-country convergence

“…The distribution of this measure has been fully developed in Anderson et al (2009), where the contact set, its complements and corresponding probabilities are defined respectively as:…”

Institutions and Economic Outcomes: A Dominance-Based Analysis

“…Note that n and 2 0 are bias correction factors in the mean and variance calculations respectively, details of which are also available in Anderson et al (2009). In the politygrowth application, the slight wrinkle for OV is that z is a mixture of discrete and continuous variables.…”

“…Moreover, even without the appropriate counterfactuals for a causal analysis, we can measure degrees of dependence. Given theoretical support for both the "polity causes growth"and "growth causes polity"hypotheses, we argue that they should not be treated as alternatives and instead focus on identifying the dominant hypothesis by adapting the overlap index proposed by Anderson et al (2009Anderson et al ( , 2010 for use with a mixture of discrete and continuous variables. The basic premise is that the joint density of two independent variables overlaps the product of their marginal densities at every point of support so, if institutions do indeed determine economic outcomes more than economic outcomes determine institutions, the joint density of earlier institutions and later outcomes should be systematically further away from independence than that of earlier outcomes and later institutions.…”

Boats and Tides and 'Trickle Down' Theories: What Economists Presume About Wellbeing When They Employ Stochastic Process Theory in Modeling Behavior

“…Essentially the interval contains those people who got a bad draw from the rich distribution and those people who got a good draw from the poor distribution. The overlap of the two weighted distributions, a measure of the extent of polarization of the two groups (Anderson, Linton and Wang (2009)), is given by ∫min((w p f p (x),(1-w p )),f r (x))dx and here corresponds to a measure of the potential for the lack of point identification. Suppose we could estimate the mixture distribution and by so doing identify w p , f p ( ), f r ( ), a and b then we could identify some of the rich and some of the poor.…”

“…In both cases the fits are extremely good and correspond to a more than adequate description of the data. The poor group has enjoyed zero economic growth and the rich group has enjoyed a steady one percent annual .82250730} * Tests are based on the trapezoid measure being asymptotically normally distributed with a variance ≈ (f(x1m)+f(x2m)) 2 (f(x1m)/[f''(x1m)] 2 +f(x2m)/[f''(x2m)] 2 )||K'|| 2 2 where xmj j = 1,2 are the modes of the respective distributions, where f() is the normal and K is the Gaussian kernel (Anderson, Linton and Wang (2009)). …”