Two Applications of Infrequency of Purchase and Double Hurdle Models to the Study of Time Use
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TWO APPLICATIONS OF INFREQUENCY OF PURCHASE AND DOUBLE HURDLE MODELS TO THE STUDY OF TIME USE by James M. Payne A Dissertation Submitted to the Faculty of the College of Graduate Studies at Middle Tennessee State University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Economics Murfreesboro, TN August 2012 UMI Number: 3528673 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ttswWioft FtoMstfiriii UMI 3528673 Published by ProQuest LLC 2012. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 TWO APPLICATIONS OF INFREQUENCY OF PURCHASE AND DOUBLE HURDLE MODELS TO THE STUDY OF TIME USE JAMES M. PAYNE Approved: / \TA s Dr. Mark F. Owens, Committee Chair SLDrJB.Dr, E. AnthAn'thon ¥jf. Committee Member Dr. Steven G.}. Livingston, CCommittee Member Dr. Charles L. Baum, Chair, Economics and Finance Department Dr. Michael1D. T). Allen, Dean, CcCollege of Graduate Studies Copyright © 2012 James M. Payne All rights reserved ii TO MY MOTHER AND FATHER who, unable to attend college, ensured that I iii ACKNOWLEDGEMENTS Many thanks go to the faculty of Middle Tennessee State University, particularly Dr. Mark Owens, Dr. Anthon Eff, and Dr. Steven Livingston, for their advice, comments and inexhaustible patience. I thank my colleagues, particularly Derek Berry, for his helpful and clear-eyed comments, and Marsha Craig, for her invaluable technical assistance. I appreciate the resources made available by my college and my department which I used in my research. I thank Dr. Janice Louie and Meileen Acosta of the California Department of Public Health for explaining the idiosyncrasies of the H IN 1 data. Most of all, I am grateful to my wife, Nancy, and daughters, Peggy and Gracie, without whose encouragement, support, and endurance this project would not have been completed. All errors are my own. iv ABSTRACT Using a household production framework, these articles examine two important components of people's time allocation. Data from the American Time Use Survey (ATUS) for 2003 - 2010 are analyzed with infrequency of purchase and double hurdle models to account for the idiosyncrasies of the time diaries. The first article investigates parents' time allocation between direct and indirect child care for producing human capital in their children. Sources of the "time gap" between men and women are identified by decomposition. Endogeneity and selection bias are managed simultaneously with a multi-step estimation process. I use multiple imputation to handle missing data and an inverse hyperbolic sine transformation to correct for heteroskedasticity and nonormality of residuals. I find that mothers increase indirect child care time relative to direct child care as hourly earnings rise, evincing a substitution effect. This effect is stronger for whites, college graduates, and single parents. Greater amounts of both types of care are associated with higher incomes for mothers and fathers. Parent-students of both sexes devote less time to both types of care. More schooling is associated with sizable increases in both types of care for women. Longer work hours reduce child care time for men far more than women, suggesting that women reduce leisure or household work to preserve child care time. Rising earnings attenuates the time gap, while schooling increases it. Also, 1 find evidence of negative selection in reporting earnings for men in the ATUS. v Article two finds that Californians responded to the H1N1 pandemic of 2009 - 2010 by reducing work time to avoid catching the disease, again using infrequency of purchase and double hurdle models. ATUS data are combined with official mortality reports and local newspaper article counts. Modeling separately by region, sex, and age, 1 find evidence that some workers responded to reports of the pandemic in the news media but not to actual changes in mortality, with the most consistent effects for younger females in southern California and the Bay Area. The relative performance of multiple imputation and inverse probability weight methods are examined, with Ml showing some advantage in finding significant results. vi TABLE OF CONTENTS Page LIST OF TABLES ix LIST OF FIGURES xii INTRODUCTION 1 COPING WITH PROSPERITY: THE RESPONSE OF PARENTS' CHILD CARE TIME USE TO RISING EARNINGS 4 I. Introduction and Motivation 4 II. Literature Review 8 III. Theoretical Model 18 IV. Data 30 V. Empirical Results 38 VI. Conclusions and Suggestions for Further Research 65 References 71 Appendices 79 Appendix A: Definitions of Time Use Variables 80 Appendix B: Comparison of Estimation Methods for the Double Hurdle Truncated Normal Regression 81 Appendix C: Considerations in Selecting m for Multiple Imputation 84 Appendix D: Comparison of Multiple Imputation and Listwise Deletion Estimates 86 THE CALIFORNIA H1N1 PANDEMIC AND WORK TIME USE 92 I. Introduction and Motivation 92 vii Page II. Literature Review 96 III. Theoretical Model 101 IV. Data 113 V. Empirical Results 131 VI. Conclusions and Suggestions for Further Research 148 References 152 Appendices 160 Appendix E: Definition of Work Time Use Variable 161 Appendix F: Matching ATUS and CPS data 162 Appendix G: California Department of Public Health (CDPH) HlNl Incidence Data 165 CONCLUSION 168 References 170 Appendix 171 Appendix H: Definition of Real Hourly Earnings 172 viii LIST OF TABLES Page Table 1: Definitions of Variables 31 Table 2: Descriptive Statistics for Continuous Variables 32 Table 3: Frequency Distributions for Demographic Variables 33 Table 4: Infrequency of Purchase Model (IPM) Results; Dependent variable sinh'1 FACETIME for men and women 39 Table 5: Blinder-Oaxaca Decomposition for IPM; Dependent variable sinh'1 FACETIME 43 Table 6: Infrequency of Purchase Model (IPM) Results; Dependent variable sinh'1 BEHALF for men and women 45 Table 7: Blinder-Oaxaca Decomposition for IPM; Dependent variable sinh'BEHALF 46 Table 8: Double Hurdle Model Results; Dependent variable w FACETIME ( = 1 for nonzero values of FACETIME), men and women, first hurdle 48 Table 9: Fairlie Nonlinear Decomposition for Double Hurdle Model; Dependent variable w FACETIME ( = 1 for nonzero values of FACETIME?) 50 Table 10: Double Hurdle Model Results; Dependent variable wFACETIME ( = 1 for nonzero values of FACETIME), men and women, second hurdle 51 Table 11: Blinder-Oaxaca Decomposition for Double Hurdle Model; Dependent variable w FACETIME ( = 1 for nonzero values of FACETIME 52 Table 12: Double Hurdle Model Results; Dependent variable w BEHALF ( = 1 for nonzero values of BEHALF), men and women, first hurdle) 54 Table 13 Fairlie Nonlinear Decomposition for Double Hurdle Model; Dependent variable w BEHALF ( = 1 for nonzero values of BEHALF) 55 Table 14: Double Hurdle Model Results; Dependent variable w BEHALF ( = 1 for nonzero values of BEHALF) 57 ix Page Table 15: Blinder-Oaxaca Decomposition for Double Hurdle Model; Dependent variable w BEHALF ( = 1 for nonzero values of BEHALF) 58 Table 16: Bivariate Probit Model Results 60 Table 17: Ratios of Marginal Effects of Real Hourly Earnings, as MEBEHALF! MEPACETIME; Women, white college graduates 62 Table 18: Ratios of Marginal Effects of Real Hourly Earnings, as ME BEHALF! MEFACETIME', Women, by race and schooling 63 Table 19: Ratios of Marginal Effects of Real Hourly Earnings, as MEBEHALF /MEFACETIME', Women, by race and type of household, high school diploma only 64 Table 20: Definition of Child Care Variables, FACETIME and BEHALF 80 Table 21: Comparison of Maximum Likelihood and Ordinary Least Squares Results.... 83 Table 22 Infrequency of Purchase Model (IPM) Results; Listwise deletion 87 Table 23: Blinder-Oaxaca Decomposition for IPM; Listwise deletion 88 Table 24: Comparison of Multiple Imputation and Listwise Deletion Estimates 90 Table 25: First- and Second-order Autocorrelations of MDMA, by DMA 111 Table 26: Definitions of Variables 116 Table 27: ACNielsen Designated Market Area (DMA) Media Coverage 121 Table 28: Descriptive Statistics for Continuous Variables, by Sex and Region 127 Table 29: Frequency Distributions for Categorical Variables 128 Table 30: Frequency Distributions for Diary Day Variables 129 Table 31: Infrequency of purchase model (IPM) results for WORKTIME; Southern California women, age 40 and under 136 Table 32: Infrequency of purchase model (IPM) results for WORKTIME; Bay Area women, age 40 and under 137 x Page Table 33: Double Hurdle Model Results; Southern California women, age 40 and under 140 Table 34: Double Hurdle Model Results; Southern California men, age 40 and under 141 Table 35: Double Hurdle Model Results; Southern California women over age 40 143 Table 36: Double Hurdle Model Results; Central Valley men over age 40 145 Table 37: Double Hurdle Model Results; Comparison of listwise deletion, inverse probability weight, and multiple imputation models, first hurdle 146 Table 38: Double Hurdle Model Results; Comparison of listwise deletion, inverse probability weight, and multiple imputation models, second hurdle 147 Table 39: Definition of WORKT1ME 161 xi LIST OF FIGURES Page