Essays on Entropy-based Robust Inference with Applications in Finance and Economics Open Access

Wu, Ke (2015)

Permanent URL: https://etd.library.emory.edu/concern/etds/dj52w484n?locale=en
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Abstract

The dissertation consists of three essays that center around entropy-based robust inference and its applications in the fields of asset pricing and labor economics.

In the first essay, I propose to use a metric entropy to measure asymmetric dependence in asset returns, i.e. the tendency that stocks co-move with the market more strongly during the market downturn than during the upside market. Using the entropy measure, I construct a model-free test for asymmetric dependence in stock returns, which is shown to have greater power than the existing correlation-based test proposed by Hong, Tu, and Zhou (2007). In stock portfolios sorted by size, book-to-market ratio and momentum, based on this new test I find statistically significant asymmetric dependence is much more pervasive than previously thought.

The second essay is an empirical extension to my first chapter, which examines how asymmetric dependence between stock return and the market return is priced in the cross-section of expected stock returns. Motivated by Ang, Chen, and Xing (2006), I construct proxies for the dependence with downside and upside market separately based on non-parametric kernel estimated joint return distributions. Empirically, I find a risk premium (discount) for stocks with high downside (upside) dependence. Moreover, downside dependence premium is almost twice as large as downside beta premium. Asymmetric dependence leaning toward the downside also earns a premium. The findings suggest that investors' aversion to downside losses are stronger than their attraction to the upside gains.

The third essay examines distributional wage gap between incumbents and newly hired workers in the US labor market from 1996 to 2012 based on metric entropy distances. We decompose the wage gap to structural and composition effects by identifying several counterfactual distributions using propensity score reweighting method as discussed in Firpo (2007). We consider weak uniform ranking of these counterfactual wage outcomes based on statistical tests for stochastic dominance as proposed in Linton, Maasoumi, and Whang (2005). Empirically, we find incumbent workers enjoy a better wage distribution, but the attribution of the gap to structural wage inequality and human capital characteristics varies among quantiles of the distribution.

Table of Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Asymmetric Dependence in Stock Returns: a Robust Entropy-Based Test 10 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2 Tests of Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.1 Asymmetric Correlation . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.2 Asymmetric Dependence . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.2.3 An Entropy Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2.4 Non-parametric Estimation . . . . . . . . . . . . . . . . . . . . . . . 19 1.2.5 Distribution of the Test Statistic . . . . . . . . . . . . . . . . . . . . 20 1.3 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.3.1 Modeling Dependence with Copulas . . . . . . . . . . . . . . . . . . 23 1.3.2 Simulation with Copula-GARCH Model . . . . . . . . . . . . . . . . 25 1.4 Is Asymmetry Rare? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.4.2 Empirical Testing Results . . . . . . . . . . . . . . . . . . . . . . . . 29 1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.A Appendix: Tawn (1988) Theorem . . . . . . . . . . . . . . . . . . . . . . . . 33 1.B Appendix: Additional Tables . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2 Asymmetric Dependence and the Cross-section of Stock Returns 50 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.2 Measuring Asymmetric Dependence . . . . . . . . . . . . . . . . . . . . . . 54 2.2.1 Downside Asymmetric Dependence . . . . . . . . . . . . . . . . . . . 54 2.2.2 Non-parametric estimation . . . . . . . . . . . . . . . . . . . . . . . 56 2.3 Data and Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.3.1 Data and Research Design . . . . . . . . . . . . . . . . . . . . . . . . 57 2.3.2 Portfolio Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.3.3 Fama-Macbeth Regressions . . . . . . . . . . . . . . . . . . . . . . . 72 2.3.4 Robustness Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.4 Past Downside Asymmetric Dependence and Future Returns . . . . . . . . 76 2.4.1 Determinants of Downside Asymmetric Dependence . . . . . . . . . 77 2.4.2 Trading Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.A Appendix: Variable Denitions . . . . . . . . . . . . . . . . . . . . . . 82 3 The Gap Between the Conditional Wage Distributions of Incumbents and the Newly Hired Employees: Decomposition and Uniform Ordering 99 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.2 The Decomposition Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3.2.1 Decomposition with General Distributional Function . . . . . . . . . 104 3.2.2 Oaxaca-Blinder Decomposition as a Special Case . . . . . . . . . . . 105 3.3 Empirical Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.3.1 A Metric Entropy Measure of the Wage Gap . . . . . . . . . . . . . 107 3.3.2 Stochastic Dominance . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.3.3 Identication of the Counterfactual Distributions . . . . . . . . . . . 109 3.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.5.1 Baseline Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.5.2 Counterfactual Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.5.3 Counterfactual Analysis of Dierent Wage Groups . . . . . . . . . . 118 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

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