Testing Linearity Using Power Transforms of Regressors

Journal of Econometrics

Sul³

2019

The concept of relative convergence, which requires the ratio of two time series to converge to unity in the long run, explains convergent behavior when series share commonly divergent stochastic or deterministic trend components. Relative convergence of this type does not necessarily hold when series share common time decay patterns measured by evaporating rather than divergent trend behavior. To capture convergent behavior in panel data that do not involve stochastic or divergent deterministic trends, we introduce the notion of weak-convergence, whereby cross section variation in the panel decreases over time. The paper formalizes this concept and proposes a simple-to-implement linear trend regression test of the null of noconvergence. Asymptotic properties for the test are developed under general regularity conditions and various data generating processes. Simulations show that the test has good size control and discriminatory power. The method is applied to examine whether the idiosyncratic components of 90 disaggregate personal consumption expenditure (PCE) price index itemsconverge over time. We …nd strong evidence of weak-convergence in the period after 1992, which implies that cross sectional dependence has strenthened over the last two decades. In a second application, the method is used to test whether experimental data in ultimatum games converge over successive rounds, again …nding evidence in favor of weak-convergence. A third application studies convergence and divergence in US States unemployment data over the period 2001-2016.

Section: Further Uses and Empirical Applicationsmentioning

confidence: 80%

Weakσ-convergence: Theory and applications

Kong

Journal of Econometrics

Sul³

2019

“…Although we consider only a linear trend for D t in what follows, the method and theory developed in this section are readily extendable to polynomial trends. But general power trends such as t α with unknown power parameter α involve further complications of asymptotic singularity -see Phillips (2007) and Baek, Cho and Phillips (2015), which are not pursued here.…”

Section: Kernel Estimation With Stochastic and Deterministic Trendsmentioning

confidence: 99%

Kernel-based Inference in Time-Varying Coefficient Cointegrating Regression

Journal of Econometrics

Gao

2020

This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated and to embody a mixture of stochastic and deterministic trends, complications which result in asymptotic degeneracy of the kernel-weighted signal matrix. To address these complications new local and global rotation techniques are introduced to transform the covariate space to accommodate multiple scenarios of induced degeneracy. Under certain regularity conditions we derive asymptotic results that differ substantially from existing kernel regression asymptotics, leading to new limit theory under multiple convergence rates. For the practically important case of endogenous nonstationary regressors we propose a fully-modified kernel estimator whose limit distribution theory corresponds to the prototypical pure (i.e., exogenous covariate) cointegration case, thereby facilitating inference using a generalized Wald-type test statistic. These results substantially generalize econometric estimation and testing techniques in the cointegration literature to accommodate time variation and complications of co-moving regressors. Finally an empirical illustration to aggregate US data on consumption, income, and interest rates is provided.

“…This shortcoming in coverage is restrictive because power function regression is a commonly used model in many empirical applications. An area of application where such regression has been found particularly useful is in testing the validity and order of polynomial regression (Baek, Cho and Phillips, 2015;Cho and Phillips, 2018. ) One goal of the present paper is to address this omission in coverage.…”

Section: Introductionmentioning

confidence: 99%

“…The functional limit theorems for the process Z n (γ) appearing in Theorems 3.2 and 3.5 are useful in testing linearity or polynomial regression using power transformations of regressors. See, for example,Baek et al (2015) andCho and Phillips (2018).Further, in models like (2.8) we may be interested in testing β = 0. In such inference problems, the unknown power parameter γ is identified (or semi-identified) only under the alternative (local alternative) hypothesis and is unidentified under the null.…”

mentioning

confidence: 99%

Nonlinear Cointegrating Power Function Regression with Endogeneity

Wang

2019

SSRN Journal

Self Cite

This paper develops an asymptotic theory for nonlinear cointegrating power function regression. The framework extends earlier work on the deterministic trend case and allows for both endogeneity and heteroskedasticity, which makes the models and inferential methods relevant to many empirical economic and financial applications, including predictive regression. Accompanying the asymptotic theory of nonlinear regression, the paper establishes some new results on weak convergence to stochastic integrals that go beyond the usual semi-martingale structure and considerably extend existing limit theory, complementing other recent findings on stochastic integral asymptotics. The paper also provides a general framework for extremum estimation limit theory that encompasses stochastically nonstationary time series and should be of wide applicability.