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Public Debt, High Inflation and Economic Depression: a Survival Analysis Approach Minjie Guo

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Public Debt, High Inflation and Economic Depression: a Survival Analysis Approach Minjie Guo CORE Metadata, citation and similar papers at core.ac.uk Provided by Scholar Commons - Institutional Repository of the University of South Carolina University of South Carolina Scholar Commons Theses and Dissertations Spring 2019 Public Debt, High Inflation and Economic Depression: A Survival Analysis Approach Minjie Guo Follow this and additional works at: https://scholarcommons.sc.edu/etd Part of the Economics Commons Recommended Citation Guo, M.(2019). Public Debt, High Inflation and Economic Depression: A Survival Analysis Approach. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/5279 This Open Access Dissertation is brought to you by Scholar Commons. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Public Debt, High Inflation and Economic Depression: A Survival Analysis Approach by Minjie Guo Bachelor of Arts Fujian Agriculture and Forestry University, 2007 Master of Arts University of Texas at Arlington, 2011 Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Economics Darla Moore School of Business University of South Carolina 2019 Accepted by: John McDermott, Major Professor Janice Bass, Committee Member William Hauk, Committee Member Warren Weber, Committee Member Cheryl L. Addy, Vice Provost and Dean of the Graduate School c Copyright by Minjie Guo, 2019 All Rights Reserved. ii Dedication To my parents and grandparents. iii Acknowledgments I would like to express my sincere gratitude to Dr. John McDermott for his support during my Ph.D study. His guidance and encouragement during the dissertation process were invaluable. He assisted in overcoming many difficulties and ensuring I learned more than anticipated during the previous five years. For his zeal for perfection and earnest attitude toward research I will be forever indebted throughout my life time. I also would like to thank Dr. Bass, Dr. Hauk and Dr. Weber for providing insightful discussion and suggestions about my research. My sincere thanks also go to Mr. Ron and Mrs. Marianne Parker. They have been my family and supported me during my Ph.D study. Last but not the least, I would like to thank all the professors and the graduate students in the Economics department. Special thanks to Liwen, Eunson and Pulkit. Together we had tons of fun and spent days and nights. I also would like to thank my friend TJ Skaff, who encouraged me to keep on going whenever I felt frustrated; Keping Xie, who helped me editing my dissertation. iv Abstract This dissertation investigates the association between public debt, high inflation and economics depression by using the survival analysis approach. In the first chapter, I use non-parametric survival analysis to check the association between high debt episodes and high inflation episodes. Both the Kaplan-Meier estimate and the Nelson-Aelon analysis indicate that the existence of an overlapping high inflation episode is correlated with longer duration of high debt episodes. The reverse is also true: the existence of a high debt episode overlap is associated with longer duration of high inflation episodes. Whether or not the country is a member of the OECD does not matter for the survival experience. In the second chapter, I use the Cox PH model, the exponential model and the Weibull model to analyze the survival experience of high debt episodes and high inflation episodes. I first consider the duration of high debt episodes (HDEs). Across all specifications, HDE duration depends on two variables: (1) the existence of an overlap with a high inflation episode; (2) the growth rate of GDP. These effects are not independent. At high GDP growth, an HIF overlap is associated with a shorter HDE. At low GDP growth, however, an HIF overlap is associated with a longer HDE. I also examine the duration of HIFs, using HDE overlap and GDP growth as regressors. Interestingly, the results are mixed and there is no evidence of interaction between HDE overlap and GDP growth. Debt of the public sector has been associated with low, or even negative, growth. This position is most closely associated with Reinhart and Rogoff (2010). In the third chapter, we analyze the duration of economic crises, in the form of depressions, to see v if there is an association with consecutive years of high public-debt-to-GDP ratios. We find that high debt is positively correlated with the duration of depressions while inflation is negatively correlated with such duration. The last chapter uses parametric survival analysis to analyze the duration of eco- nomic crises to see if they have an association with the occurrence of consecutive years of high public-debt-to-GDP ratios. By comparing the results from five para- metric models, including the exponential, the Weibull, the log-normal, the log-logistic, and the generalized gamma regression, all of which have the accelerated failure time (AFT) metric, I find that there is a positive association between high debt episodes and the length of economic crises. All of the results are consistent with each other throughout the models. The main results were not refuted by adding covariates including economic factors, political factors, cultural factors and financial crises as controls. vi Table of Contents Dedication .................................. iii Acknowledgments ............................. iv Abstract ................................... v List of Tables ................................ xi List of Figures ............................... xiv Chapter 1 Survival Analysis of Episode of High Debt and High Inflation: A Non-parametric Approach . 1 1.1 Introduction . 1 1.2 Literature Review . 2 1.3 Data . 4 1.4 Survival Analysis . 8 1.5 Survival Experience of High Debt Episode . 9 1.6 Survival Experience for High Inflation Episode . 17 1.7 Conclusion . 20 Chapter 2 High Debt and High Inflation: A Semi-Parametric and Parametric Approach . 35 2.1 Introduction . 35 vii 2.2 Data . 37 2.3 Semi-Parametric Analysis for High Debt Episodes . 38 2.4 Parametric Analysis for High Debt Episodes . 49 2.5 Survival Experience for High Inflation Episode . 57 2.6 Conclusion . 61 Chapter 3 Negative Growth and High Debt: A Survival Anal- ysis Approach ........................ 72 3.1 Introduction . 72 3.2 Literature Review . 73 3.3 Data . 76 3.4 Survival Analysis . 79 3.5 Non-Parametric Analysis . 80 3.6 the Cox Proportional Hazards Model . 86 3.7 Parametric Analysis . 92 3.8 Conclusion . 95 Chapter 4 Negative Growth and High Debt: An AFT Para- metric Survival Analysis Approach . 103 4.1 Introduction . 103 4.2 Data . 104 4.3 Parametric Models: AFT Metric . 105 4.4 More Covariates in the Log-normal Regression Model . 111 4.5 Other Threshold Value for HDE . 117 4.6 Conclusion . 118 viii Bibliography ................................ 124 Appendix A Terminology for Survival Analysis . 129 A.1 Survival Function and Hazard Function . 129 A.2 Median and Mean . 131 Appendix B Results for HDE90 with HIF10 . 133 Appendix C Log-Rank Test and Wilcoxon Test . 138 Appendix D Computation of Survival Analysis . 140 D.1 Maximum Likelihood . 140 D.2 Proportional Hazards Models-Likelihood Calculation . 141 Appendix E Handling Tied Data . 143 Appendix F Computation of Schoenfeld Residuals . 147 Appendix G Testing the PH Assumption . 150 Appendix H Goodness of Fit . 153 Appendix I Alternative Thresholds for Defining High-Debt Episodes . 155 Appendix J The Five AFT Parametric Models . 157 J.1 Exponential Model . 157 J.2 Weibull Model . 158 J.3 Log-normal Regression . 158 ix J.4 Log-logistic Regression . 158 J.5 Generalized Gamma Regression . 159 Appendix K Odds Ratio . 160 x List of Tables Table 1.1 Overlapping Episode . 21 Table 1.2 HIF First . 21 Table 1.3 HDE First . 21 Table 1.4 Simultaneous . 23 Table 1.5 Summary of Statistics for HDE50 . 23 Table 1.6 Summary of Statistics for HIF10 ................... 23 Table 1.7 Kaplan-Meier Output for HDE50 ................... 24 Table 1.8 KM Output for HDE50 Comparison Between YHIF . 25 Table 1.9 The Median Survival Time for HDE50 . 25 Table 1.10 The Mean Survival Time For HDE50 . 27 Table 1.11 Log Rank Test for Equality of Survivor Functions . 28 Table 1.12 The Wilcoxon Test for Equality of Survivor Functions . 28 Table 1.13 Nelson-Aalen Estimate for HDE50 . 29 Table 1.14 Log-Rank Test for HIF10 ....................... 32 Table 1.15 Wilcoxon Test for HIF10 ....................... 32 Table 1.16 The Median Survival Time for HIF10 . 33 Table 1.17 The Mean Survival Time for HIF10 . 33 Table 2.1 The Cox Proportional Hazards Model-HDE50 Exact Marginal . 62 Table 2.2 Estimated HR for YHIF with Fixed GDP Growth Rate . 63 xi Table 2.3 The Cox Model Using Different Approximation . 63 Table 2.4 Cutoff GDP Growth Rate . 63 Table 2.5 Score Test and p−values for the Test of Proportional Hazards Assumption for HDE50 ........................ 65 Table 2.6 Exponential Model for HDE50-Hazard Ratio . 67 Table 2.7 Exponential Model for HDE50-AFT . 67 Table 2.8 Weibull Model for HDE50-Hazard Ratio . 68 Table 2.9 Weibull Model for HDE50-AFT . 68 Table 2.10 The Cox Proportional Hazards Model-HIF10 . 69 Table 2.11 Exponential Model for HIF10-Hazard Ratio . 69 Table 2.12 Exponential Model for HIF10-AFT . 70 Table 2.13 Weibull Model for HIF10-Hazard Ratio . 70 Table 2.14 Weibull Model for HIF10-AFT . 71 Table 3.1 Kaplan-Meier Estimate for NGE . 97 Table 3.2 Median and Mean Survival Times . 100 Table 3.3 Significance Tests for Equality of Survivor Function . 101 Table 3.4 The Cox Proportional Hazard Model . 102 Table 3.5 Parametric Regression Models . 102 Table 4.1 Parametric Regression Model-AFT Metric . 119 Table 4.2 Acceleration Parameter for the Lognormal Model . 120 Table 4.3 Log-Normal Regression with Economic Factors .
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