Essays on Entropy-based Robust Inference with Applications in Finance and Economics Público
Wu, Ke (2015)
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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