Empirical Applications of Entropy-based Inference Open Access

Zhu, Yifeng (2016)

Permanent URL: https://etd.library.emory.edu/concern/etds/sx61dm88b?locale=en
Published

Abstract

In the first chapter, I first propose two types of asymmetry measures which based on the tail distribution of the data instead of just the third moment-skewness for stock returns. With these new measures, greater tail asymmetries imply lower average returns in the cross section. In contrast, the relation between the skewness and the expected return is conditional. Then I discuss the relationship between asymmetries and several benchmark anomalies. Size and liquidity effects only appear among low upside asymmetry stocks, while momentum effect is getting stronger when upside asymmetry is increasing.

In the second chapter, we examine the potential effect of naturalization on the U.S. immigrants' earnings. We find the earning gap between naturalized citizens and non-citizens is positive over many years, with a tent shape across the wage distribution. We focus on a normalized metric entropy measure of the gap between distributions, and compare with conventional measures at the mean, median and other quantiles. In addition, we further examine the potential sources of the earning gap, the "wage structure" effect and the "composition" effect. Both of these sources contribute to the gap, but the composition effect, while diminishing somewhat after 2005, accounts for about 3/4 of the gap. The unconditional quantile regression and conditional quantile regressions confirm that naturalized citizens have generally higher wages, although the gap varies for different income groups.

In the last chapter, I propose linear and nonparametric models to predict crude oil price. Mainly, my forecast depends on three predictor variables, the change in crude oil inventories, its previous prices and product spread. By employing mean-squared prediction error (MSPE) and stochastic dominance (SD) tests, I find that the prediction result of our nonparametric models is significantly better than the random walk model, while the corresponding linear models' performance is better than the random walk model only for longer horizon forecasts (one to two years). And for the nonparametric model including all three predictors, I document MSPE reduction as high as 62.6% compared to the random walk model and the directional accuracy ratio as high as 77.5% at the two years horizon.

Table of Contents

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Stock Return Asymmetry and Anomalies 7 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Asymmetry Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Continuous Data Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . 14 1.4 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4.2 Stock Level Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.3 Portfolio Level Results . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.4.4 Asymmetry Conditional on Sentiment . . . . . . . . . . . . . . . . . 23 1.4.5 Asymmetry Conditional on VIX . . . . . . . . . . . . . . . . . . . . 25 1.4.6 Asymmetry Conditional on Aggregate Stock Market Liquidity . . . 26 1.4.7 Asymmetry Conditional on Capital Gains Overhang . . . . . . . . . 26 1.5 Benchmark Anomalies and Asymmetry . . . . . . . . . . . . . . . . . . . . . 28 1.5.1 Short Term Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.5.2 Benchmark Anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.5.3 Benchmark Anomalies and Short Term Asymmetry . . . . . . . . . . 32 1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2 The Wage Premium of Naturalized Citizenship 135 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 2.2 Empirical Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 2.2.1 Basic Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 2.2.2 Decision-Theoretics: Entropy as a Distributional Measure of the Earnings Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 2.2.3 Stochastic Dominance . . . . . . . . . . . . . . . . . . . . . . . . . . 141 2.2.4 Counterfactual Distributions . . . . . . . . . . . . . . . . . . . . . . 142 2.2.5 Decomposition of the Distributional Statistics . . . . . . . . . . . . . 144 2.2.6 Unconditional Quantile Partial Eects (UQPE) . . . . . . . . . . . . 144 2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 2.4 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 2.4.1 Distributional Comparison and Analysis . . . . . . . . . . . . . . . . 147 2.4.2 Counterfactual Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 148 2.4.3 Decomposition of the Gap in Conditional Means and Quantiles . . . 150 2.4.4 the Unconditional Quantile Partial Eect (UQPE) and the Conditional Quantile Partial Eect (CQPE) of Citizenship . . . . . . . . . 150 2.5 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 151 3 Crude Oil Price Prediction: A Nonparametric Approach 179 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 3.2 Data and One Month Ahead Predictive Models . . . . . . . . . . . . . . . . 185 3.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 3.2.2 Unit Root Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 3.2.3 Predictive Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 3.3 The Predictability and Model Comparison for One Month Ahead . . . . . . 189 3.4 The Models for Longer Horizon Forecasts . . . . . . . . . . . . . . . . . . . 191 3.5 Robustness Check-Stochastic Dominance . . . . . . . . . . . . . . . . . . . . 193 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 List of Figures
1.1 Asymmetric Distribution with skewness=0 . . . . . . . . . . . . . . . . . . . 55
1.2 Dierent Asymmetry, skewness=1 . . . . . . . . . . . . . . . . . . . . . . . 56
1.3 Recursive Gamma in the front of Idiosyncratic Asymmetry Proxies . . . . . 57
1.4 Recursive Idiosyncratic Asymmetry Portfolio10-1 Excess Return Dierence(%) 58
2.1 CDF Comparisons of Naturalized Citizen and Non-citizen . . . . . . . . . . 156
2.2 The Time Trend of Citizenship Wage Gap . . . . . . . . . . . . . . . . . . . 157
2.3 CDF Comparisons of Non-citizen Counterfactual # 1 and Non-citizen . . . 158
2.4 CDF Comparisons of Non-citizen Counterfactual # 2 and Non-citizen . . . 159
2.5 Unconditional and Conditional Quantile Regression Estimates of the Eect
of Citizenship Status on Log Wages . . . . . . . . . . . . . . . . . . . . . . . 160
IA.1 CDF Comparisons of Naturalized Citizen and Non-citizen (1994-2012) . . . 171
IA.2 CDF Comparisons of Non-citizen Counterfactual # 1 and Non-citizen (1994-
2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
IA.3 CDF Comparisons of Non-citizen Counterfactual # 2 and Non-citizen (1994-
2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
IA.4 Unconditional and Conditional Quantile Regression Estimates of the Eect
of Citizenship Status on Log Wages (1994-2012) . . . . . . . . . . . . . . . . 177
3.1 Nominal and Real Spot Prices . . . . . . . . . . . . . . . . . . . . . . . . . . 205
3.2 WTI One-month-ahead Out-of-sample's Predictions . . . . . . . . . . . . . 206
3.3 WTI One-month-ahead Out-of-sample's Predictions . . . . . . . . . . . . . 207
3.4 Forecast Errors for One Month's Ahead Prediction(in US Dollars) . . . . . 208
3.5 Recursive MSPE ratio for One Month's Ahead Prediction . . . . . . . . . . 209
3.6 Recursive MSPE ratio for 3, and 6 Months Ahead Prediction(in US Dollars) 210
3.7 Recursive MSPE ratio for 12, and 18 Months Ahead Prediction(in US Dollars)211
3.8 Recursive MSPE ratio for 2 Years Ahead Prediction(in US Dollars) . . . . . 212
3.9 3, 6, and 12 Months' Predictions by Linear Models . . . . . . . . . . . . . . 213
3.10 18 and 24 Months' Predictions by Linear Models . . . . . . . . . . . . . . . 214
3.11 3, 6, and 12 Months' Predictions by Nonparametric Models . . . . . . . . . 215
3.12 18, and 24 Months' Predictions by Nonparametric Models . . . . . . . . . . 216
3.13 Forecast Errors for 3, and 6 Months Ahead Prediction(in US Dollars) . . . 217
3.14 Forecast Errors for 12, and 18 Months Ahead Prediction(in US Dollars) . . 218
3.15 Forecast Errors for 2 Years Ahead Prediction(in US Dollars) . . . . . . . . . 219
3.16 CDF Comparisons of the Negative Absolute Forecast Error (1995.1-2015.4) 220
3.17 CDF Comparisons of the Negative Absolute Forecast Error (1995.1-2015.4) 221
3.18 CDF Comparisons of the Negative Absolute Forecast Error (1995.1-2015.4) 222
3.19 CDF Comparisons of the Negative Absolute Forecast Error (1995.1-2015.4) 223 List of Tables
1.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
1.2 Correlations of Asymmetry Measures and Volatility . . . . . . . . . . . . . . 60
1.3 The Characteristics of ISKEW, IS', and IE' . . . . . . . . . . . . . . . . 61
1.4 Firm-Level Cross-Sectional Return Regressions . . . . . . . . . . . . . . . . 62
1.5 Equal-Weighted Average Monthly Returns of Decile Portfolios Based on
ISKEW, IS'1 and IE'1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
1.6 Cross-Section Regressions on Idiosyncratic Asymmetry During High and Low
Sentiment Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1.7 Idiosyncratic Asymmetry Proxies Performance Conditional on the Sentiment 70
1.8 Fama-MacBeth Regressions on Idiosyncratic Asymmetry in VIX Regimes . 71
1.9 Fama-MacBeth Regressions on Idiosyncratic Asymmetry in ALIQ Regimes 74
1.10 Cross-Section Regressions with Interaction Terms of Idiosyncratic Asymmetry
Proxies and CGO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
1.11 Double-Sorted Portfolio Returns by CGO and Idiosyncratic Asymmetry Proxies 80
1.12 Equal-Weighted Average Monthly Returns of Portfolios Based on Anomalies 81
1.13 Cross-Section Regressions with Interaction Terms of Asymmetry Proxies and
SIZE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
1.14 Cross-Section Regressions with Interaction Terms of Asymmetry Proxies and
MOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
1.15 Cross-Section Regressions with Interaction Terms of Asymmetry Proxies and
ILLIQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
1.16 Equal-Weighted Bivariate Dependent Sort Portfolio Analysis-SIZE and Asymmetry
Proxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
1.17 Equal-Weighted Bivariate Dependent Sort Portfolio Analysis-MOM and Asymmetry
Proxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
1.18 Equal-Weighted Bivariate Dependent Sort Portfolio Analysis-ILLIQ and
Asymmetry Proxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
IA.1 The Characteristics of the S', E' and SKEW . . . . . . . . . . . . . . . . 95
IA.2 Firm-Level Cross-Sectional Return Regressions . . . . . . . . . . . . . . . . 96
IA.3 Firm-Level Cross-Sectional Return Regressions with 24 Newey-West Lags . 99
IA.4 Firm-Level Cross-Sectional Return Regressions with IS'1, IE'1 and ISKEW
Based on 6 Months Daily Returns . . . . . . . . . . . . . . . . . . . . . . . 101
IA.5 Firm-Level Cross-Sectional Return Regressions Using E(ISKEW) . . . . . 103
IA.6 Cross-Section Regressions on Skewness During High and Low Sentiment Period105
IA.7 Cross-Section Regressions on Idiosyncratic Asymmetry During High and Low
Sentiment Period when Excess Return is the Dependent Variable . . . . . . 106
IA.8 Asymmetry Proxies Performance Conditional on the Sentiment . . . . . . . 109
IA.9 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
IA.10Summary Statistics for Decile Portfolios of Stocks Sorted by E'2 and SKEW 111
IA.11Summary Statistics for Decile Portfolios of Stocks Sorted by IE'2 and ISKEW112
IA.12The Characteristics of the E'2 and SKEW . . . . . . . . . . . . . . . . . . 113
IA.13Firm-Level Cross-Sectional Return Regressions with E'2 and SKEW . . . 114
IA.14Firm-Level Cross-Sectional Return Regressions with E'2 with 24 Newey-
West Lags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
IA.15Firm-Level Cross-Sectional Return Regressions with IE'2 and ISKEW . . 118
IA.16Equal-Weighted Average Monthly Returns of Portfolios Based on Realized
E'2 and SKEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
IA.17Equal-Weighted Average Monthly Returns of Decile Portfolios Based on Realized
IE'2 and ISKEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
IA.18Cross-Section Regressions with Interaction Terms of Idiosyncratic Asymmetry
Proxies and SIZE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
IA.19Cross-Section Regressions with Interaction Terms of Idiosyncratic Asymmetry
Proxies and MOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
IA.20Cross-Section Regressions with Interaction Terms of Idiosyncratic Asymmetry
Proxies and ILLIQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
IA.21Equal-Weighted Bivariate Dependent Sort Portfolio Analysis-SIZE and Idiosyncratic
Asymmetry Proxies . . . . . . . . . . . . . . . . . . . . . . . . . 128
IA.22Equal-Weighted Bivariate Dependent Sort Portfolio Analysis-MOM and Idiosyncratic
Asymmetry Proxies . . . . . . . . . . . . . . . . . . . . . . . . . 130
IA.23Equal-Weighted Bivariate Dependent Sort Portfolio Analysis-ILLIQ and Idiosyncratic
Asymmetry Proxies . . . . . . . . . . . . . . . . . . . . . . . . . 132
IA.24Cross Section Correlations of Short Term Asymmetry, Volatility, and Anomalies134
2.1 Critical Values for Testing of H0 : S = 0 . . . . . . . . . . . . . . . . . . . . 161
2.2 NATURALIZED CITIZEN V.S. NON-CITIZEN WAGE DISTRIBUTIONS 162
2.3 NON-CITIZEN COUNTERFACTUAL #1 V.S NON-CITIZEN Distributions 164
2.4 NON-CITIZEN COUNTERFACTUAL #2 V.S NON-CITIZEN Distributions 166
2.5 Wage Gap Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
2.6 Comparing OLS, Unconditional Quantile Regressions (UQR), and Conditional
Quantile Regressions (CQR) :Citizenship Status Eect . . . . . . . . . . 170
3.1 Out-of-sample One Month Ahead Forecast Performance . . . . . . . . . . . 224
3.2 Out-of-sample 3, 6, 12, 18 and 24 Months Ahead Forecast Performance . . . 225
3.3 Stochastic Dominance Test Results . . . . . . . . . . . . . . . . . . . . . . . 228
IA.25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
IA.26Estimated Coecients for One Month Ahead in Sample Model . . . . . . . 230
IA.27Estimated Coecients for 3, 6, 12, 18 and 24 Months Ahead in Sample Model231

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