Econometrics

Econometrics, Volume 2, Issue 3 (September 2014) – 2 articles , Pages 123-150

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Open AccessArticle

Two-Part Models for Fractional Responses Defined as Ratios of Integers

by Harald Oberhofer and Michael Pfaffermayr

Econometrics 2014, 2(3), 123-144; https://doi.org/10.3390/econometrics2030123 - 19 Sep 2014

Cited by 2 | Viewed by 5434

Abstract

This paper discusses two alternative two-part models for fractional response variables that are defined as ratios of integers. The first two-part model assumes a Binomial distribution and known group size. It nests the one-part fractional response model proposed by Papke and Wooldridge (1996) and, thus, allows one to apply Wald, LM and/or LR tests in order to discriminate between the two models. The second model extends the first one by allowing for overdispersion in the data. We demonstrate the usefulness of the proposed two-part models for data on the 401(k) pension plan participation rates used in Papke and Wooldridge (1996). Full article

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161 KiB

Open AccessArticle

Asymmetry and Leverage in Conditional Volatility Models

by Michael McAleer

Econometrics 2014, 2(3), 145-150; https://doi.org/10.3390/econometrics2030145 - 24 Sep 2014

Cited by 55 | Viewed by 9134

Abstract

The three most popular univariate conditional volatility models are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). The underlying stochastic specification to obtain GARCH was demonstrated by Tsay (1987), and that of EGARCH was shown recently in McAleer and Hafner (2014). These models are important in estimating and forecasting volatility, as well as in capturing asymmetry, which is the different effects on conditional volatility of positive and negative effects of equal magnitude, and purportedly in capturing leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. As there seems to be some confusion in the literature between asymmetry and leverage, as well as which asymmetric models are purported to be able to capture leverage, the purpose of the paper is three-fold, namely, (1) to derive the GJR model from a random coefficient autoregressive process, with appropriate regularity conditions; (2) to show that leverage is not possible in the GJR and EGARCH models; and (3) to present the interpretation of the parameters of the three popular univariate conditional volatility models in a unified manner. Full article

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Econometrics, Volume 2, Issue 3 (September 2014) – 2 articles , Pages 123-150

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