University of Southern California Dissertations and Theses

Essays on macroeconomics of health and labor

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Essays on macroeconomics of health and labor

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Content ESSAYSONMACROECONOMICSOF HEALTHANDLABOR by Osman Furkan Abbaso glu A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) August 2013 Copyright 2013 Osman Furkan Abbaso glu Dedication to my mother Mualla, my father Nurettin, my sisters S aziye and Tuba, my nieces Berra and Sena, my nephew Yunus Emre, and to my dear anc e, and soon to be my wife Zeynep and also to everyone I love... ii Acknowledgments I would like to thank my advisor, Ay se _ Imrohoro glu for her invaluable guidance, support and encouragement throughout the whole process. Without her, I would not be able to complete this dissertation. I would also like to thank Guillaume Vandenbroucke for his guidance and comments, especially his contribution to what I now know about quantitative macroeconomics. I am also thankful to Professors Vincenzo Quadrini, Julie Zissimopoulos, Robert Dekle and S elale T uzel for their comments and support. I am also grateful to my dear friend Ali G une s, with whom I had many fruitful discussions over what I have written in my dissertation. My all six years in graduate school would not have been as bearable if it were not for my dear friends in the department: Saurabh Singhal, James Ng, Arya Gaduh, Danilo Beteto, Vlad Radoias and all others. I am also grateful to Young Miller, Mor- gan Ponder and Christopher Frias, who have eased all the administrative processes. Last, but not the least, I would like to thank my family for supporting me during my graduate studies thousand of miles away from home. All remaining errors are my own. iii Table of Contents Acknowledgments iii List of Tables viii List of Figures x Abstract xi Chapter 1: Life-Cycle Analysis with an Increasing Wage Prole 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Empirical Life-Cycle Proles . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Demographics . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.2 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.3 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.4 Social Security . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.5 Market structure . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.6 Households' Problem . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.7 Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . 9 1.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4.1 Dierent Utility Functions . . . . . . . . . . . . . . . . . . . . 16 1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 iv Chapter 2: Risky Health Behaviors and Medical Expenditures: The Role of Policy 20 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.1 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Empirical Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2.1 Medical Expenditures . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.2 Health Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.3 Risky Health Behaviors . . . . . . . . . . . . . . . . . . . . . . 30 2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.1 Simple Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.2 Extended Full Model . . . . . . . . . . . . . . . . . . . . . . . 34 2.3.2.1 Demographics . . . . . . . . . . . . . . . . . . . . . . . 34 2.3.2.2 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3.2.3 Health Production . . . . . . . . . . . . . . . . . . . . . 35 2.3.2.4 Health Depreciation . . . . . . . . . . . . . . . . . . . . 37 2.3.2.5 Survival Probability . . . . . . . . . . . . . . . . . . . . 37 2.3.2.6 Health Care System . . . . . . . . . . . . . . . . . . . . 37 2.3.2.7 Social Security . . . . . . . . . . . . . . . . . . . . . . . 38 2.3.2.8 Individual's Dynamic Problem . . . . . . . . . . . . . . 38 2.3.2.9 Government Budget Constraint . . . . . . . . . . . . . 39 2.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.4.1 Benchmark Model . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.5.1 Policy exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.5.1.1 Coinsurance rate changes . . . . . . . . . . . . . . . . . 45 2.5.1.2 Welfare Analysis . . . . . . . . . . . . . . . . . . . . . . 49 v 2.5.2 Excise tax rate changes . . . . . . . . . . . . . . . . . . . . . . 53 2.5.3 Excise tax goes up and coinsurance goes down . . . . . . . . . 56 2.5.4 Redistribution via lump sum transfers . . . . . . . . . . . . . . 58 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Appendices 2.A Computation algorithm for stationary equilibrium . . . . . . . . . . . 69 2.B Additional Tables and Figures . . . . . . . . . . . . . . . . . . . . . . 70 Chapter 3: Optimal Health Insurance in the Presence of Risky Health Behaviors 79 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.1.1 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.2.1 Demographics . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.2.2 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.2.3 Health Production . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.2.4 Health Depreciation . . . . . . . . . . . . . . . . . . . . . . . . 82 3.2.5 Survival Probability . . . . . . . . . . . . . . . . . . . . . . . . 82 3.2.6 Health Care System . . . . . . . . . . . . . . . . . . . . . . . . 83 3.2.7 Social Security . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.2.8 Individuals' Dynamic Problem . . . . . . . . . . . . . . . . . . 83 3.2.9 Government Budget Constraint . . . . . . . . . . . . . . . . . . 84 3.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 vi 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.4.1 Policy Exercise: Eects of dierent co-insurance rates in the presence of bad consumption . . . . . . . . . . . . . . . . . . . 88 3.4.2 Model without bad consumption . . . . . . . . . . . . . . . . . 90 3.4.2.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.4.2.2 Policy Exercise: Eects of dierent co-insurance without bad consumption . . . . . . . . . . . . . . . . . 92 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Chapter 4: Conclusion 95 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Comprehensive bibliography 98 vii List of Tables 1.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Parameters for non-separable utility . . . . . . . . . . . . . . . . . . . 16 2.1 Perceived health status (Percentage of population) . . . . . . . . . . . 29 2.2 Weight Categories by BMI (Percentage of population) . . . . . . . . . 30 2.3 Smoking prevalence (Percentage of population) . . . . . . . . . . . . . 31 2.4 Smoking prevalence(Percentage of population) . . . . . . . . . . . . . 32 2.5 Fixed Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.6 Calibrated Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.7 Tax and coinsurance rates in benchmark calibration . . . . . . . . . . 44 2.8 Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.9 Eects of dierent coinsurance rates with ! r = 0%. . . . . . . . . . . 48 2.10 M/Y (%) with dierent coinsurance rates . . . . . . . . . . . . . . . . 49 2.11 % of smokers with dierent coinsurance rates . . . . . . . . . . . . . . 49 2.12 Welfare for dierent health states with dierent coinsurance rates . 51 2.13 Welfare Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.14 Eects of dierent excise tax rates with ! r = 0% and ! w = 10%. . . . 55 2.15 Welfare Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.16 Welfare for dierent health states with dierent excise tax rates . . 56 2.17 Coinsurance decreases and excise tax increases . . . . . . . . . . . . . 58 2.18 Eects of dierent coinsurance rates with ! r = 0% and lump sum transfers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 viii 2.19 Medical Expenditures as a percentage of Income (MEPS) . . . . . . . 70 2.20 Medical Expenditures . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.21 Perceived health status for ages 15-24 (Percentage of population) . . . 71 2.22 Average medical expenditures by health status . . . . . . . . . . . . . 71 2.23 Some Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.24 Eects of dierent coinsurance rates with ! r = 5%. . . . . . . . . . . 73 2.25 Eects of dierent coinsurance rates with ! r = 10%. . . . . . . . . . . 74 2.26 Excise taxes on tobacco . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.27 Smoking prevalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.1 Fixed Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.2 Probability of Health Shocks . . . . . . . . . . . . . . . . . . . . . . . 86 3.3 Calibrated Paremeters . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.4 Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.5 Policy exercise with dierent co-insurance rates . . . . . . . . . . . . 89 3.6 Welfare change with dierent co-insurance rates . . . . . . . . . . . . 90 3.7 Calibrated Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.8 Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.9 Policy exercise with dierent co-insurance rates (without bad consumption) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.10 Welfare change with dierent co-insurance rates (without bad consumption) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 ix List of Figures 1.1 Using Method 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Using Method 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Fitted Values using NLS . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Eciency Proles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Survival Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6 Simulated Hours vs. Data . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.7 Increasing vs. Hump-shaped Eciency . . . . . . . . . . . . . . . . . . 15 1.8 Simulated Hours vs. Data (Non-Separable Utility) . . . . . . . . . . . 17 2.1 Medical Expenditures as a percentage of GDP (Source:OECD) . . . . 27 2.2 Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.3 Change in Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.4 Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 2.5 M/Y over the life cycle with dierent coinsurance rates . . . . . . . . . 78 2.6 Change in Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.1 Medical Expenditures to Income Ratio: Model vs. Data . . . . . . . . 88 3.2 Medical Expenditures to Income Ratio: Model vs. Data . . . . . . . . 91 x Abstract This dissertation consists of three essays on quantitative macroeconomics that study labor and health. The rst essay uses data from Panel Study of Income Dynamics (PSID) to document a non-decreasing wage prole as reported by Rupert and Zanella (2010) and compares the implications of this prole on the life cycle hours allocation of households to the widely used hump-shaped wage prole. Results suggest that even using the non-decreasing wage-eciency prole, the income eect dominates the substitution eect coming from higher wages, hence after making a peak at prime ages, hours worked start declining far before reaching retirement. These results are robust to dierent intertemporal elasticities of substitution for labor and dierent utility functions. The second essay makes use of the wage-eciency prole generated in the rst essay and develops an overlapping generations model that incorporates bad behaviors (such as smoking and unhealthy eating habits that lead to obesity) to investigate the equilibrium eects of dierent cost sharing mechanisms and excise taxation on bad behaviors and medical expenditures. I show that higher cost sharing may induce individuals to refrain from bad behaviors. For example, if coinsurance rate is increased by 10 percentage points, smoking prevalence goes down by about 2 percentage points and medical expenditures to GDP ratio slightly declines. Welfare analysis of dierent policies shows that although higher cost sharing increases the overall welfare in the economy, unhealthy individuals are either worse o or have much less welfare gains compared to healthy individuals. The quantitative implications of the model are consistent with the variation in smoking prevalence and excise taxes across tobacco xi and non-tobacco states. The third essay builds upon the second essay and examines the insurer aspect of the health policy by introducing an age-dependent health shock. Inclusion of this aspect addresses two functions of health insurance: insurance against controllable health outcomes which stem from risky health behaviors and uncontrollable outcomes that randomly hit individuals. By comparing two settings with and without risky health behaviors, I look for the optimal co-pay mechanism that maximizes welfare and nd that in the presence of risky health behaviors, 10% co-pay is optimal while when risky health behaviors are absent, 0% co-pay is optimal. This result is consistent with the notion that some risk sharing mechanism is needed when moral hazard exists because of risky health behaviors. xii Chapter 1 Life-Cycle Analysis with an Increasing Wage Prole 1.1 Introduction This chapter aims to investigate the eects of an increasing labor eciency over the life cycle on hours worked and explain why households decrease their hours of work sharply towards retirement. Life-cycle proles of wages, hours and earnings have been extensively discussed in the macro-labor literature, and a hump-shaped earnings pro- le is common in the literature. This is mostly attributed to life-cycle wage prole being hump-shaped, especially in the human capital models, where the wage rate is dened as the return on one's human capital (Ben-Porath (1967); Heckman (1976)). French (2005) and Manovskii and Kambourov (2005) use Panel Study of Income Dy- namics (PSID) data in their empirical work and come up with a hump-shaped wage prole as in the human capital literature. Hansen (1993) constructs an eciency units prole using BLS data, and nds that returns to unit labor form a hump-shape over the life-cycle too. While the studies mentioned above documents the evolution of wages over the life cycle, other studies look at how hours worked respond to changes in wages. Pencavel (1986) asserts that individuals supply more hours when their wage rate is the highest in their life cycle. In another paper, Pencavel (2002) estimates the intertemporal sub- 1 stitution elasticity with respect to wage which measures the response of work hours to evolutionary changes in wages throughout the life cycle, and nds that the elasticity changes between 0:15 and 0:28 whereas Macurdy (1981) estimates it as being between 0:1 and 0:23. Devereux (2003), on the other hand, estimates the same elasticities, and conclude that wage eects on labor supply are too small to explain the variations in labor supply. In their working paper, Rupert and Zanella (2010) uses PSID data to show that the wage prole is actually not decreasing over the life-cycle. They generate a hump- shaped earnings prole, which is driven by a sharp decrease in the hours worked after mid 50's. This chapter aims to investigate the life-cycle proles of hours worked in a general equilibrium framework taking the increasing wage prole from PSID data as exogenously given, and explain the sharp decrease in hours worked towards retirement. 1.2 Empirical Life-Cycle Proles To get the life-cycle proles for wages, earnings and hours worked, I closely follow Rupert and Zanella (2010). PSID data identies each household and individual with a unique interview ID each year. This feature of the data enables us to follow a set individuals throughout almost all their working lives. The cohort I follow is the 23 year-old cohort, as in Rupert and Zanella (2010). Only the male head of households who work for someone else are observed for this purpose. This gives us a more ho- mogenous group. The proles are generated using averages of individuals at each age using the PSID sample weights. Using these weights makes the data more repre- sentative of the U.S. population. Here I follow two dierent strategies to follow the 2 individuals over their life-cycle. First, I take all individuals who are 23 years old and entered the market in 1967. PSID data starts in 1968, but since the individuals report their incomes, hours worked and wages from the previous year, 1967 is the rst year we observe. Following Rupert and Zanella (2010) again, I take 5-year bins for each age such that age 23 reports values for individuals who were aged between 21 and 25. So for each year, I use the middle value of the 5 year bin to represent the age of the individual. This method gives us more observations as the sample size is small otherwise, and decreases over time as age increases. Then I follow these individuals throughout their life cycles. As I mentioned above, the sample size drops over time, due to death or other reasons. And among those, I take the averages of individuals who supplied positive work hours. Figure 1.1 illustrates the life-cycle proles of the 23 year-old cohort. All nominal values are converted to real by using CPI-U, taking 1982 1984 = 100. The bottom-right graph in Figure 1.1 depicts the percentage of respondents who answered the question \Do you have any physical or nervous condi- tion that limits the type of work or the amount of work that you can do?" with yes in the PSID family surveys. 3 Figure 1.1: Using Method 1 As a second method, I follow those households who are present in all the survey years between 1968 and 2007. Using the same selection criteria as in the rst method, and applying the 5-year bins, there are 106 such individuals who are present in all years. The proles for this method are shown in Figure 1.2. 4 Figure 1.2: Using Method 2 As we can clearly see, methods 1 and 2 give almost the same life cycle proles. I am going to continue with the proles obtained from method 2 from this point on. As seen in Figure 1.2, real annual earnings exhibit a hump-shape, rapidly increasing during the rst 10 years of the working life, staying constant until 50's, and declining thereafter. We cannot observe such a decline in the real hourly earnings over the life cycle though. The prole for real hourly earnings is increasing with age, with diminishing returns. When we look at the prole for annual hours worked, we see a more or less stable patter until 50's, but then hours worked decline sharply. And lastly the ratio of people whose work hours are limited due to a physical or nervous condition 5 steadily increases with age as seen in the last panel. One might ask whether this self- reported measure of health status re ects the true health status of an individual or not. Benitez-Silva et al. (2004) show that self-reported health status is a good indicator of the true health status of an individual, and it aects the labor force participation of the individual. Cai (2010) also nds that health has a positive and signicant eect on labor supply, meaning that healthier people supply more labor. Stern (1989) shows that disability of the worker adversely aects his/her labor force participation too. 1.3 Model 1.3.1 Demographics The economy is populated by overlapping generations of individuals of age j = 1; 2;:::;J. J R is the mandatory retirement age. One model period is equivalent to one year. Population growth rate is assumed to be zero. Conditional probability of surviving from age j 1 to age j is denoted by j , with 1 = 1 and J = 0. Co- hort shares are constant and equal to j . Given the sequence of conditional survival probabilities,f j g J j=1 , time invariant cohort shares,f j g J j=1 can be determined by: j+1 = j+1 j (1.1) And since P J j=1 j = 1, 1 can be determined by using this and (1.1). Since we are interested in steady states, all time subscripts are omitted below. 6 1.3.2 Preferences Households maximize the following lifetime utility: J X j=1 j1 j Y k=1 k ! u(c j ;h j ) (1.2) where is the subjective time discount factor, c j and h j are consumption and hours worked by the age j household. The utility function is assumed to be separable for the benchmark model, and is of the following form: u(c j ;h j ) = c 1 j 1 h 1+ 1 j 1 + 1 (1.3) where is the coecient of relative risk aversion, captures the intertemporal elas- ticity of substitution in labor, and is the weight on disutiliy from work. Households are endowed with one unit of time each period, which can be allocated between work and leisure until retirement. h j is zero after the mandatory retirement age. Households' earnings are given by w j h j for j = 1; 2;:::J R 1 where w is the market wage rate, and j is the age specic eciency unit of labor. Forj =J R ;:::;J, households simply earn a xed benet, b. Accidental bequests due to death are re- distributed to all living households in a lump-sump manner at the amount T . 1.3.3 Technology There is a representative rm that has access to a constant returns to scale, Cobb- Douglas production function of the form Y = BK N 1 , with B > 0, and the capital's share of output, 2 (0; 1). Capital depreciates at a constant rate, 2 (0; 1). Firm rents capital and hires labor from households, paying them the marginal 7 products of capital and labor: r =B K N 1 (1.4) w = (1)B K N (1.5) 1.3.4 Social Security There is a pay-as-you-go social security system, where households are taxed by the rate ss on their labor income, and the benets that the retired households get are fully funded by these tax revenues. Following Imrohoroglu et al. (1995), the benets that the retired households get are are dened as a proportion of their average lifetime earnings from working, which is given as: b = P J R 1 j=1 w j h j J R 1 (1.6) where is the replacement ratio. 1.3.5 Market structure Households cannot insure against the mortality risk, thus the markets are incom- plete. However, they are allowed to hold one-period riskless bonds, a j+1 . There are borrowing constraints in the economy, so a j+1 0 for all j. 1.3.6 Households' Problem Households are heterogeneous in their ages and asset holdings. The optimal alloca- tions of the household is computed by solving the following dynamic problem recur- 8 sively. V (a j ) = max c j ;h j ;a j+1 u(c j ;h j ) + j V (a j+1 ) (1.7) subject to c j +a j+1 = (1 +r)a j + (1 ss )w j h j +T forj = 1; 2;:::;J R 1 (1.8) c j +a j+1 = (1 +r)a j +b +T forj =J R ;:::;J (1.9) a j+1 0 (1.10) 1.3.7 Competitive Equilibrium For given demographic parametersf j g J j=1 , a stationary competitive equilibrium con- sists of households' decision rulesfc j ;h j ;a j+1 g J j=1 , factor prices w and r, social se- curity tax rate ss , accidental bequests T , and constant cohort sharesf j g J j=1 that satisfy that following conditions: 1. Households' decision rules solve (1.7) subject to (1.8), (1.9) and (1.10). 2. Factor prices are determined competitively: r =B K N 1 w = (1)B K N 3. Lump-sum transfers of accidental bequests is equal to the amount of assets left by the dead: T = J X j=1 j (1 j )a j 9 4. The labor and capital markets clear: K t = J X j=1 j a j N t = J R 1 X j=1 j j h j 1.4 Calibration First, we obtain the eciency prole of labor using the PSID real hourly earnings prole, and compare it with the hump-shaped prole of eciency of labor from Hansen (1993) and Hansen and Imrohoroglu (2009). Eciency prole using PSID data is smoothed by using nonlinear least squares and predicting the tted values. Figure 1.3 shows the t, and Figure 1.4 shows the eciency proles of Hansen (1993) and PSID. Figure 1.3: Fitted Values using NLS 10 (a) Hansen's Efficiency Profile (b) Efficiency profile from PSID Figure 1.4: Efficiency Profiles Conditional survival probabilities for men are taken from National Vital Statistics Reports 2010. Proles for conditional probability of surviving from age j 1 to age j and cumulative probability of surviving to age j are given in Figure 1.5 Figure 1.5: Survival Probabilities 11 Throughout the calibrations, an average hours worked ratio of around 0.38 was targeted to match the prole obtained from PSID data. And a capital-output ratio of around 3 was targeted to match the U.S. capital-output ratio. Mandatory retirement age was set as 65, and maximum lifetime possible is set to 80. Since we start the model at age 23, 65 corresponds to J R = 44, and 80 corresponds to J = 58. The calibration process takes place as follows: I rst choose values for parameters for the coecient of relative risk aversion, intertemporal elasticity of substitution in labor, capital's share of output, depreciation rate of capital and social security replacement ratio from the literature. Then I calibrate the subjective time discount factor and the weight on disutility from work to match the targets. Initial guesses for wage, interest rate, social security tax rate, social security benets and accidental bequests are given, and the quantitative model is iterated until these variables converge. I used two dierent values for the intertemporal elasticity of substitution in labor. Table 1.1 shows the choice of parameters, and calibrated parameters. Table 1.1: Parameters Preference Parameters Explanation Value Capital's share of output 0.36 Depreciation rate of capital 0.06 Social security replacement ratio 0.44 Coecient of relative risk aversion 1 (log utility) IES 0.1,0.5 Calibrated Parameters IES=0.1 IES=0.5 Subjective time discount factor 0.965 0.965 Weight on disutility from labor 35000 17 Figure 1.6 shows the results. We can see that the hours prole generated by the model with = 0:1 is relatively at, with little change of hours over the life cycle, whereas the prole generated by the model with = 0:5 is above the prole with 12 = 0:1 until mid 40's, and below thereafter. And also we can see that the variation in hours with = 0:5 is considerably more than the other one. Notice that both simulated hours proles are unable to match the data in the sense that hours do not exhibit a sharp decrease after 50's. With = 0:5, even though the eciency prole is an increasing one, income eect dominates the substitution eect due to higher labor earnings, and hours begin to decline after the rst 10 years of the life cycle. Figure 1.6: Simulated Hours vs. Data Next we use the hump-shaped eciency prole from Hansen (1993) to see how that eects the proles for hours worked over the life cycle. Parameters remain same as in Table 1.1. And results are shown in Figure 1.7. We can see that the hours prole generated using the hump-shaped eciency prole is more humped relative to the one generated using the increasing eciency prole, which means compared to a hours prole with increasing eciency of labor, households work less in the rst few 13 years of their life cycles, then work more until about mid 40's, and then work less again for the remaining part of their life cycles when they have a hump-shaped labor eciency prole. The picture is qualitatively the same for dierent values of , but we can see from the top and the bottom panel of Fifgure 1.7 that the hours proles become more humped when increases. 14 (a) = 0:1 (b) = 0:5 Figure 1.7: Increasing vs. Hump-shaped Efficiency 15 1.4.1 Dierent Utility Functions So far we have assumed that the utility function is separable in consumption and leisure. This section investigates the eects of using a non-separable utility function on the life cycle prole of hours worked. We consider the following non-separable utility function. u(c j ;h j ) = [c j (1h j ) 1 ] 1 1 (1.11) where still represents the coecient of relative risk aversion, and represents the weight of consumption in utility. Notice that for = 1 we have a log utility. Table 1.2 shows the calibrated parameters and Figure 1.8 displays the results of the model generated hours. Table 1.2: Parameters for non-separable utility Preference Parameters Explanation Value Capital's share of output 0.36 Depreciation rate of capital 0.06 Social security replacement ratio 0.44 Coecient of relative risk aversion 1 (log utility) Calibrated Parameters Subjective time discount factor 0.9705 Utility weight on consumption 0.41 We can see that using a non-separable utility function generated a more humped prole compared to those with a separable utility function. Qualitatively the results remain the same though: An increasing eciency prole induces households to work more in the rst few years and after late 40's-early 50's compared to a hump-shaped eciency prole. 16 Figure 1.8: Simulated Hours vs. Data (Non-Separable Utility) 1.5 Conclusion In this chapter, I examine how life cycle prole for hours worked behaved when the eciency units of labor increased steadily over the life cycle. Whether I use a separable or non-separable utility function, the life cycle hours worked proles I get have a hump-shape, where households start decreasing their work hours in the earlier periods of their life cycles, due to income eect. On the other hand, the proles generated by the model in this study show that in all cases, using an increasing eciency prole makes the hours worked proles less humped. Lower values of intertemporal elasticity of substitution for labor generate less humps in the hours worked prole. 17 Bibliography Ben-Porath, Yoram, \The production of human capital and the life cycle of earn- ings," Journal of Political Economy, 1967, 75, 1{18. Benitez-Silva, Hugo, Moshe Buchinsky, Hui Man Chan, Soa Cheidvasser, and John Rust, \How large is the bias in self-reported disability?," Journal of Applied Econometrics, 2004, 19, 649{670. Cai, Lixin, \The relationship between health and labour force participation: Evi- dence from a panel data simultaneous equation model," Labour Economics, 2010, 17, 77{90. Devereux, Paul J., \Changes in male labor supply and wages," Industrial & Labor Relations Review, 2003, 56 (3). French, Eric, \The eects of health, weatlh, and wages on labour supply and retire- ment behaviour," Review of Economic Studies, 2005, 72, 395{427. 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Pencavel, John, \Labor supply of men: A survey," Handbook of Labor Economics: Chapter 1, 1986, 1. , \A cohort analysis of the association between work hours and wages among men," Journal of Human Resources, 2002, 37 (2), 251{274. Rupert, Peter and Giulio Zanella, \Revisiting wage, earnings, and hours pro- les," Working Paper, 2010. Stern, Steven, \Measuring the eect of disability on labor force participation," Journal of Human Resources, 1989, 24, 361{395. 19 Chapter 2 Risky Health Behaviors and Medical Expenditures: The Role of Policy 2.1 Introduction The eect of health insurance on the demand for medical care is well examined in the literature. Generous health insurance policies decrease people's sensitivity to the cost of care, inducing people to spend more on health (e.g. Zweifel and Manning 2000, Newhouse 1993). That is why high coinsurance rates are usually associated with low medical expenditures and vice versa. This chapter highlights another aspect of cost sharing mechanisms in medical care, which is the moral hazard problem stemming from risky health behaviors (bad consumption) such as smoking and poor diet. Bad consumption increases the likelihood of getting severe health shocks that are accompanied by high medical costs. For example, Rice et al. (1986) estimate the total direct costs of smoking to be about 23 percent of total personal health care expenditures. Finkelstein et al. (2009) nd that obese people spend about 42 percent more on health care than normal weight people. Risky health behaviors also lead to increased morbidity. Danaei et al. (2009) estimate that in 2005, 19 percent of all deaths in the U.S. were attributable to tobacco use. Overweight/obesity, poor diet, physical inactivity and alcohol use accounted for 8.8, 26, 7.8 and 2.5 percent of all deaths in the same year respectively. Individuals are more likely to smoke and eat unhealthy food if they don't share 20 the cost of getting medical treatment since the extra cost generated by those bad behaviors are borne by the insurance provider. Higher coinsurance rates, on the other hand, would mean that the cost of bad behavior is partly paid by the individual too. In an environment where medical expenditures are nanced by taxes collected from households, these costs are paid by everyone in the economy regardless of engaging in risky health behaviors or not. So, higher coinsurance rates would yield lower tax rates which leave individuals with more disposable income. But bad consumption behaviors also generate utility. Hence whether people become better or worse o by the implementation of dierent insurance policies requires a quantitative analysis. This study develops a macroeconomic model with bad consumption in order to investigate the equilibrium eects of aforementioned policy changes. The main con- tribution of this study to the literature is the explicit modeling of bad consumption behaviors and the mechanism through which these behaviors interact with medical expenditures as well as policy. To be able to do that, I calibrate an overlapping generations (OLG) model to match the prominent features of the U.S. economy and examine the eects of changes in coinsurance rates and excise tax rates on the bad consumption behavior of individuals and their medical expenditures. I also examine how individuals with dierent health levels respond to policy changes and how their welfare changes subsequently. Results show that higher coinsurance rates lower the medical expenditures to GDP ratio as well as the prevalence of smoking. When coinsurance rate is increased from 10% to 30%, medical expenditure to GDP ratio goes down by almost 1 percentage point and percentage of smokers goes down by about 2 percentage points. People who start life with a poor health stock become worse o as a result of higher cost sharing, as medical treatment is more costly for them, but the overall welfare in the economy increases due to the high share of healthy people who spend less on medical care. 21 This result is mainly driven by the fact that higher cost sharing leads to less taxes paid to nance health spending, leaving people with more income to spend on good consumption, thus making them better o. In this environment, optimal coinsurance rate turns out to be 100%, which means all medical expenditures are out-of-pocket. Overall, higher coinsurance rates are welfare enhancing for the economy. 2.1.1 Related Literature Macro models have been used to explain health related questions and evaluate health policy outcomes. In most of those models, health status is treated as a stock of capital, a la Grossman (1972), where individuals can invest on health by making medical expenditures. Hall and Jones (2007) explain how increasing spending on health can be justied by higher longevity using a macro model. In other words, more health spending buys health. Their model incorporates a utility function where individuals value the quality of their lives, which is measured by their health status, as well as the quantity of life, i.e. the value of being alive. A similar utility function is used in this chapter too. Some studies in the literature look at the relationship between savings and medical expenditures. Scholz and Seshadri (2010) examine the link between lifetime income and health using a life cycle model where individuals in the model economy dier in their lifetime incomes. They employ a health production function where individuals can produce health by using time and medical expenditures. They nd that elimi- nating Medicare leads households to do more buer stock savings and high income households can do more so. De Nardi et al. (2010) nd that medical expenditures are important in explaining the observed savings of the elderly and especially the richer ones. Palumbo (1999) also nds that a model with uncertain medical expenses better 22 predict saving and consumption motives of the elderly. Health status is important in macro models for a number of reasons. First, it delivers direct utility to individuals, which is named as the quality of life by Hall and Jones (2007) as mentioned above. Second, it aects the probability of surviving to the next period along with other things. And lastly, it aects the available amount of time allocatable to market activities and leisure. Halliday et al. (2011) investigates the roles of consumption motive and investment motive in generating the medical expenditures over the life cycle. Consumption motive drives people to be more healthy because better health leads to more utility, and investment motive makes people invest on health because better health means more time allocatable to market and leisure activities. They nd that consumption motive is the main channel that drives medical expenditures over the life cycle. Ozkan (2011) makes a distinction between preventive and curative medical expenditures. He uses two kinds of health capital in his model: Physical and preventive. The utility is obtained from the physical health capital and it also determines the probability of survival, whereas the preventive health capital governs the distribution of health shocks to the physical health capital. So the higher the preventive health capital is, the less likely that an individual will be hit by a health shock. He nds that higher-income individuals spend more on preventive health in the earlier phases of their lives so they can avoid higher expenditures midway through their lives. Using similar life cycle models, Feng (2009) and Jung and Tran (2010) analyze the macroeconomic outcomes of dierent health care reforms. Feng (2009) examines the eects of dierent health coverage policies such as Medicaid and Medicare and tax subsidy on macroeconomic aggregates such as the insurance coverage ratio, hours worked and welfare. He nds that universal health coverage can be achieved by ex- panding Medicare and enforcing individual insurance whereas removing tax subsidies 23 for private insurance leads to lower coverage ratios. Jung and Tran (2010) examine the eects of the 2010 health care reform proposed by the Obama administration using a dynamic general equilibrium OLG model and nd that these reforms lead to almost universal coverage as well as an increase in total medical expenditures due to newly insured people under the new reform. Jeske and Kitao (2009), on the other hand, investigate the eects of a regressive tax policy on health insurance on insurance coverage and welfare using a dynamic general equilibrium framework. He and Huang (2011) try to explain the dierence in medical expenditure-output ratio between the U.S. and Europe by the dierence in income taxes. They use a neoclassical growth model where health production occurs by spending on health and having leisure time and nd that the dierence in tax rates can explain about half of the dierence in health expenditures, as higher income taxes lead people in Europe to work less and have more leisure time to produce more health. In a similar study, He et al. (2011) argue that recessions help improve the overall health status in the economy since people can allocate more time to health producing activities and medical expenditures are pro-cyclical. In their appendix, they let bad consumption aect the period depreciation of health. I use a similar idea in this chapter about bad consumption, but my model incorporates bad consumption in a way that its eects are carried over throughout the life cycle. The rest of the chapter is organized as follows: Section 2.2 summarizes some aspects of health care data in the U.S., Section 2.3 introduces the model, Section 2.4 discusses the calibration of the model. In Section 2.5, I discuss my ndings from the policy experiments and I conclude in Section 2.6. 24 2.2 Empirical Facts The linkage between risky health behaviors, health status, mortality, longevity and medical expenditures is well studied and documented in various studies in the eco- nomics and medical literature. Barendregt et al. (1997) nd that smokers incur 40 percent more health care costs than nonsmokers at a given age. Rice et al. (1986) estimate the direct and indirect costs of smoking and conclude that about 23 percent of lifetime medical expenditures are due to smoking. Sloan et al. (2004) survey a variety of studies about the economic cost of smoking and report substantial varia- tions in estimates due to reasons such as analytical approach in estimating the cost, methods for valuing health loss, data sources etc. Their own estimates report 8.5 years of gain in life for people who quit smoking at age 35 and they also report that smoking leads to an increase in medical expenditures of $3,800 per 24 year old female smoker and $2,600 for male smoker in 2000 dollars. Taylor Jr. et al. (2002) give similar estimates for the increase in life expectancy too. Miller et al. (1999) estimate the smoking attributable fraction of expenses to be 6.54 percent whereas Warner et al. (1999) say that annual medical costs of smoking may exceed 8 percent of total medical expenditures. Cawley and Meyerhoefer (2011) estimate the annual medical cost of obesity to be about $2,800 in 2005 dollars. Finkelstein et al. (2009) nd that obese people spend 42 percent more per capita on health and obesity accounts for about 9 percent of total medical expenditures in 2008. Peeters et al. (2003), van Ball et al. (2006) and Stewart et al. (2009) examine the individual and joint eects of obesity and smoking on death and years of life. Peeters et al. (2003), for example, nd that the dierence in life expectancy between an obese smoker and normal-weight smoker is about 7 years whereas the dierence between an obese smoker and a normal-weight nonsmoker is 25 about 13 years. A signicant portion of deaths can be linked to risky health behaviors. Danaei et al. (2009), McGinnis and Foege (1993), Mokdad et al. (2005a), Mokdad et al. (2005b), Peto et al. (1994) and Woloshin et al. (2008) estimate the amount of deaths attributable to dierent risk factors. About 19 percent of deaths were attributed to tobacco use in all these studies whereas less than 5 percent were attributed to alcohol use. Deaths attributable to poor diet are estimated to be 14 percent in McGinnis and Foege (1993), 15 percent in Mokdad et al. (2005a) and 26 percent in Danaei et al. (2009). Peto et al. (1994) estimate the fraction of deaths attributable to smoking to be 24 percent for males and 7 percent for females. In this section, I summarize some important facts about health care expenditures, measures of health and risky health behaviors in the U.S. that motivates this study. 2.2.1 Medical Expenditures Medical expenditures 1 in the U.S. have been attracting an increasing attention from researchers for various reasons. First, they constitute a very large portion of the Gross Domestic Product (GDP), which is about 17% in 2009. Second, they have been increasing steadily over the years. Total medical expenditures to GDP ratio was about 5% in 1960, and now total medical expenditures comprise more than three times of a larger portion of GDP. Third, while the share of health care expenditure have been increasing all over the world, the speed of growth is much larger in the U.S., which has been widening the gap between the U.S. and the rest of the world. Figure 2.1 summarizes these facts. 1 When I say medical expenditures throughout this chapter, I refer to total health care expendi- tures, including public, private and out of pocket medical expenditures. 26 1 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0 2 0 1 0 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 M e d ic a l E x p e n d itu re s a s a % o f G D P Y e a r U .S . U .K . S p a in Figure 2.1: Medical Expenditures as a percentage of GDP (Source:OECD) McKinsey Global Institute (2008) report on health care in the U.S. summarizes the reasons why medical expenditures have been so high and growing, including higher prices due to R&D and technological innovation in the health sector and people's insensitivity to those higher prices due to insurance policies, more tests and procedures asked by physicians due to increasing number of malpractice suits and higher incidence of chronic conditions. I use Medical Expenditures Panel Survey (MEPS) data to construct life cycle proles of medical expenditures. I use data from 2000 to 2009 to construct these proles. For each year for this interval, I calculate the average total medical expen- ditures, including out of pocket expenditures, medicare, medicaid, private insurance, veterans' administration and other federal, state and local sources by age categories. Medical expenditures and incomes of people younger than 20 are equally distributed 27 to each age category. Income data is acquired using the total income received by individuals during a particular year. The constructed data is provided in Table 2.19 and Table 2.20 in the appendix. 2.2.2 Health Status There is neither a single measure of health, nor a perfect one. As Strauss and Thomas (2008) argue, there are various dimensions of health such as physical and mental well being, and it is important to know what dierent health indicators measure. Mortality and life expectancy are referred as the \ultimate" measure of health by Strauss and Thomas (2008) and they are relatively easy to measure. Morbidity is another health indicator as it is critical to know what leads to death too. These measures are however more useful on the country level. When we want to measure the health status of an individual, we resort to indicators such as Body Mass Index (BMI), limitations in the activities of daily life (ADL), and self-assessed measure of health. Although it is likely to be correlated with socioeconomic status, Benitez-Silva et al. (2004) nd that self-reported health status is a good indicator of the true health status. MEPS provides us a self-reported health status, where individuals were asked to rate their health as excellent, very good, good, fair or poor. Respondents in MEPS were asked \In general, would you say your health is: Excellent, Very good, Good, Fair, Poor?" in three dierent rounds. Table 2.1 shows the percentage of all people reporting each dierent health status in the U.S between 2001 and 2009. About 88 percent of the respondents report a health status that is good, very good or excellent in all three rounds. Shares of people falling in dierent self reported health categories have remained fairly constant over time. Table 2.21 report the shares of respondents 28 falling into the health categories for ages 15-24. About 95 percent of respondents report to have good health or above in all three rounds. These numbers will be used as shares of initial population falling into dierent health states in the model later. Table 2.1: Perceived health status (Percentage of population) Round 1 Health Status 2001 2002 2003 2004 2005 2006 2007 2008 2009 Av. 1 - excellent 32.27 30.55 30.95 30.73 30.50 30.40 31.86 34.19 33.15 31.62 2 - very good 31.02 31.02 29.59 29.83 29.41 29.51 29.62 29.58 29.13 29.86 3 - good 24.76 26.22 26.17 26.40 26.76 26.60 25.79 24.18 24.97 25.76 4 - fair 8.77 9.01 9.86 9.56 9.78 10.00 9.55 9.05 9.80 9.49 5 - poor 3.19 3.20 3.42 3.47 3.55 3.49 3.19 3.00 2.94 3.27 Round 2 Health Status 2001 2002 2003 2004 2005 2006 2007 2008 2009 Av. 1 - excellent 29.71 29.91 30.09 30.87 30.00 29.92 30.40 30.54 30.18 30.18 2 - very good 32.99 32.84 31.28 30.31 31.45 30.71 31.81 31.58 31.07 31.56 3 - good 26.26 25.53 26.75 26.68 26.53 27.02 26.05 26.75 27.36 26.55 4 - fair 8.32 8.87 8.95 9.08 9.03 9.29 9.03 8.61 8.89 8.90 5 - poor 2.72 2.85 2.94 3.06 3.01 3.05 2.70 2.53 2.50 2.82 Round 3 Health Status 2001 2002 2003 2004 2005 2006 2007 2008 2009 Av. 1 - excellent 29.00 29.44 29.26 29.21 29.21 28.88 31.16 32.01 31.28 29.94 2 - very good 33.18 32.26 31.44 30.75 31.49 31.47 31.47 30.69 30.55 31.48 3 - good 26.86 26.66 27.57 28.18 27.43 27.68 26.21 25.90 26.78 27.03 4 - fair 8.29 8.65 8.69 8.87 8.87 8.97 8.48 8.86 8.86 8.73 5 - poor 2.67 2.99 3.04 2.99 3.01 3.00 2.68 2.54 2.54 2.83 Percentages of people in MEPS falling into dierent weight categories according to Body Mass Index are displayed in Table 2.2. Obese people comprise almost 30 percent of the population on average for 2000-2009 whereas share of normal and over- weight people are almost equal to each other. Looking at the rates for people aged 15-24, slightly more than half of the population fall into normal weight category and obesity is still prevalent. Unlike the perceived health status rates, the composition of 29 population according to BMI category seems to be changing over time where percent- age of normal weight people has been declining and prevalence of obesity has been increasing. Table 2.2: Weight Categories by BMI (Percentage of population) All population BMI category 2001 2002 2003 2004 2005 2006 2007 2008 2009 Av. Normal weight 37.19 36.03 35.77 34.90 34.45 33.77 34.24 33.45 32.83 34.74 Overweight 35.66 35.77 35.15 34.89 34.75 35.04 34.87 34.92 35.22 35.14 Obese 25.20 26.15 26.95 28.13 28.86 29.33 29.20 29.76 30.23 28.20 Ages 15-24 BMI category 2001 2002 2003 2004 2005 2006 2007 2008 2009 Av. Normal weight 54.14 51.65 51.36 50.02 50.38 51.04 51.45 51.25 49.32 51.18 Overweight 26.47 27.13 27.74 27.85 26.99 27.61 27.08 26.01 27.29 27.13 Obese 14.71 16.50 16.54 17.33 18.38 17.71 17.76 18.54 19.19 17.41 2.2.3 Risky Health Behaviors Table 2.3 shows the percentage of smokers by dierent characteristics for two dierent years: 2005 and 2010 (Morbidity and Mortality Weekly Report 2011). Smoking is more prevalent among males while the smoking rates are decreasing for both genders. There is not much dierence in smoking prevalence for ages 18-64 while the smoking rate declines sharply after 65. However the rates have declined over time for ages 18- 64 while they increased for 65 and older. Contrary to common belief, smoking rate among whites is higher than the U.S. average. 32 percent of American Indians and Alaska Natives smoke, which is the highest rate among all races/ethnicities. Asians experienced the largest decline in smoking percentage and they have the lowest rate of smoking. Years of schooling does not lead to lower rates of tobacco use until college. 30 College graduates and beyond have much lower smoking rates than others. Table 2.3: Smoking prevalence (Percentage of population) 2005 2010 Characteristics Males Females Total Males Females Total Age group 18-24 28.0 20.7 24.4 22.8 17.4 20.1 25-44 26.8 21.4 24.1 24.3 19.8 22.0 45-64 25.2 18.8 21.9 23.2 19.1 21.1 65+ 8.9 8.3 8.6 9.7 9.3 9.5 Race/Ethnicity White 24.0 20.0 21.9 22.6 19.6 21.0 Black 26.7 17.3 21.5 24.8 17.1 20.6 Hispanic 21.1 11.1 16.2 15.8 9.0 12.5 AI/AN 37.5 26.8 32.0 - 36.0 31.4 Asian 20.6 6.1 13.3 14.7 4.3 9.2 Multiple race 26.1 23.5 24.8 28.4 23.8 25.9 Education 0-12 29.5 21.9 25.5 28.5 21.8 25.1 GED 47.5 38.8 43.2 46.4 44.1 45.2 High school diploma 28.8 20.7 24.6 27.4 20.6 23.8 Some college (no degree) 26.2 19.5 22.5 25.1 21.6 23.2 Associate degree 16.1 17.1 20.9 21.8 16.4 18.8 Undergraduate degree 11.9 9.6 10.7 10.2 9.5 9.9 Graduate degree 6.9 7.4 7.1 7.1 5.4 6.3 Total 23.9 18.1 20.9 21.5 17.3 19.3 Table 2.4 shows smoking prevalence by perceived health status and BMI categories that are obtained from MEPS. On average between 2001 and 2009, about 32 percent of people who reported poor health status smoke whereas only 15 percent of people with excellent health status smoke. Healthy people have experienced a sharper decline in smoking rates compared to unhealthy people. On the other hand, although the dierence is not that large, normal weight people smoke more than obese people. 31 Table 2.4: Smoking prevalence(Percentage of population) Smoking by health status Health Status 2001 2002 2003 2004 2005 2006 2007 2008 2009 Av. 1 - excellent 18.51 16.84 15.71 15.34 14.89 13.85 14.65 14.50 12.81 15.23 2 - very good 20.50 20.05 20.02 19.61 18.45 17.67 17.91 17.23 16.66 18.68 3 - good 25.22 25.08 25.10 23.34 23.78 23.30 22.07 21.89 20.44 23.36 4 - fair 27.00 28.61 28.02 28.62 26.88 25.73 26.28 25.54 23.81 26.72 5 - poor 32.48 32.57 35.08 33.03 31.70 34.02 34.29 31.47 29.95 32.73 Smoking by BMI category BMI Category 2001 2002 2003 2004 2005 2006 2007 2008 2009 Av. Normal weight 25.36 24.81 24.54 23.32 22.36 21.77 21.19 20.95 19.00 22.59 Overweight 22.13 20.64 21.18 20.26 20.46 19.97 19.09 18.75 17.51 20.00 Obese 19.12 20.61 20.35 20.33 19.50 19.13 19.56 18.47 18.42 19.50 2.3 Model 2.3.1 Simple Model I rst start with a simple model to highlight some features of the environment used in this analysis. I use an overlapping generations (OLG) model with liquidity con- straints. Individuals get utility from regular consumption as well as bad consumption and from their health status. Health is accumulated by spending on medical goods and services and bad consumption adversely aects health. Health status in this model can be thought as a stock of capital and medical expenditures are investments in health. Individuals maximize their lifetime utility subject to a period budget con- straint. max c gj ;c bj ;m j ;a j+1 J X j=1 j1 u(c gj ;c bj ;h j ) (2.1) 32 subject to c gj + (1 + c b )c bj +!m j +a j+1 y j + (1 +r)a j (2.2) h j+1 = (1 h )h j +F (m j ;c bj ) (2.3) Utility function is assumed to be increasing in all of its arguments, and exhibits diminishing marginal utility (@u=@c g > 0, @u=@c b > 0, @u=@h > 0, @ 2 u=@c 2 g < 0, @ 2 u=@c 2 b < 0, @ 2 u=@h 2 < 0). Health stock depreciates at a rate, h and health pro- duction function is increasing in medical expenditures and decreasing in bad consump- tion, both of which exhibit diminishing marginal product (@F=@m> 0, @F=@c b < 0, @ 2 F=@m 2 < 0, @ 2 F=@c 2 b < 0). c b is the excise tax rate levied on bad consumption and! is the coinsurance rate, the amount of an individual's total medical expenditures that is paid out-of-pocket. Individuals can accumulate assets by saving a part of their exogenously given income at each age, y j . The rst order conditions of this problem imply: @F @m j = @u =@c gj @u =@h j+1 | {z } > 0 ! (2.4) @u =@c bj @u =@c gj = (1 + c b )! @F =@c bj @F =@m j | {z } < 0 (2.5) (2.4) implies that higher coinsurance rate leads to lower medical expenditures, all other things held constant, since @ 2 F=@m 2 < 0. The marginal rate of substitution between good and bad consumption is given by (2.5), which implies higher marginal rate of substitution when coinsurance rate or excise tax rate goes up. Since@ 2 u=@c 2 g < 33 0 and @ 2 u=@c 2 b < 0, higher marginal rate of substitution is either achieved by lower bad consumption or higher good consumption. (2.5) also implies that the joint eect of an increase in excise taxes and a decrease in coinsurance rate is ambiguous and we need a quantitative model to address that. Notice that the term @u=@c g > 0 also governs the income eect. When coin- surance rate goes up, less taxes are needed to nance the health care system, thus individuals are given subsidies as transfers, leading to higher income levels. So income eect coming from higher income due to higher coinsurance rate may dominate the substitution eect which make individuals substitute away from bad consumption when coinsurance rate is higher. Hence, this question also required a quantitative analysis. 2.3.2 Extended Full Model 2.3.2.1 Demographics Individuals in the model live for a maximum of J years, and dier by their initial health status, s2fs 1 ;s 2 ;:::;s 5 g. ' j (h j1 ; h;j1 ) is the probability of surviving from age j 1 to j, that depends on the health stock and the depreciation rate of health capital at age j 1. I am interested in steady-state properties of the model, hence drop the time subscripts. 2.3.2.2 Preferences Individuals get utility from good consumption, bad consumption and their health stocks. They maximize the lifetime utility: max J X j=1 j1 j Y k=1 ' k (h k1 ; h;k1 ) ! u(c gj ;c bj ;h j ) (2.6) 34 The period utility is dened as in Hall and Jones (2007) and Ozkan (2011), with the addition of bad consumption. u(c gj ;c bj ;h j ) =b + c 1 gj 1 + h 1 j 1 + c 1 bj 1 (2.7) b represents the value of being alive, and is set to be positive, so that individuals get utility from an extra year of life. c g represents good consumption and c b represents bad consumption. and are quality of life parameters. is the weight on utility from bad consumption and and are coecients of relative risk aversion for good and bad consumption respectively. 2.3.2.3 Health Production Following the idea of health capital introduced by Grossman (1972), I use a health production function where the stock of health depreciates at a rate that changes with age and bad consumption behavior, and individuals can invest into health by spending on medical goods and services, m j . Similar health production functions were used in Feng (2009), Jung and Tran (2010), Scholz and Seshadri (2010), Halliday et al. (2011) and Ozkan (2011). Some of these studies use a health production function where leisure time, or time spent in health producing activities such as exercise, enter into the production function too, whereas some like Ozkan (2011) use a two- step health capital accumulation: Physical and preventive. The health production function I use in this chapter is: h j+1 = (1 h;j h j )h j +Bm j (2.8) Individuals are endowed with an initial health capital, s, which may dier from 35 one individual to another. Health capital depreciates at a rate which depends on age and history of bad consumption, and individuals can accumulate health capital by investing on health, i.e. by making medical expenditures, m j . This process is irreversible, i.e., an individual can only invest as much as to recover from the current depreciation. B and are scale and curvature parameters for health production respectively. Unlike many previous studies, here I use an adjustment mechanism through which people with lower health capital have to make higher investment on health to recover, which is governed by . To see this, let's assume that there is no adjustment cost, hence health is accumulated according to the following health production function: h j+1 = (1 h;j )h j +Bm j (2.9) If an individual wants to preserve his health status, i.e. he wants to chooseh j+1 =h j , then the amount of medical expenditure needed will be h;j h j =Bm j (2.10) m j = h;j h j B !1 (2.11) Thus, sinceB and are positive,m j will be higher for higher values ofh j . Table 2.22 shows the average medical expenditures at all ages for dierent self-reported health states obtained from MEPS. We can clearly see that people with worse health spend signicantly more than those with better health. Thus I introduce an adjustment cost parameter to the health production function, where the depreciation rate is divided by h , so the eective depreciation becomes h;j =h j . 36 2.3.2.4 Health Depreciation The mechanism through which risky health behaviors (i.e. bad consumtion) aects health is the way in which the depreciation of health evolves over time. denotes the incremental change in the depreciation rate of health. I c bj is the indicator function for bad consumption where I c bj 2f0; 1g. Aging increases depreciation of health by and bad consumption increases it by 2 in one period. h;j+1 = h;j +(1 +I c bj ) (2.12) 2.3.2.5 Survival Probability The probability of survival from age j to age j + 1 is a function of the health status and rate of health depreciation at agej and is denoted by'(h j ; h;j ). Following Feng (2009) and Scholz and Seshadri (2010), the survival probability function is governed by the cumulative Weibull distribution function. But here the survival probability depends on health capital net of depreciation and before health investment and can be thought as a health shock. and are parameters in the cumulative Weibull distribution. '(h j ; h;j ) = 1exp( h (1 h;j h j )h j i ) (2.13) 2.3.2.6 Health Care System There is a single-payer health care system where the government is the provider of health insurance. Working age population pays! w of their medical expenses whereas retired population pays ! r of them. These expenditures are nanced by taxes on good consumption, bad consumption, capital and labor income. 37 2.3.2.7 Social Security Following Imrohoroglu et al. (1995), the benets that the retired households get are dened as a proportion of their average lifetime earnings from working, which is given as: ssb =& P J R 1 j=1 w j J R 1 (2.14) where & is the replacement ratio. 2.3.2.8 Individual's Dynamic Problem We can denote the individual's life time maximization problem at (2.6) as a discrete time dynamic programming problem and maximize the following value function: V (a j ;h j ; h;j ) = max c gj ;Ic bj ;m j ;a j+1 u(c gj ;c bj ;h j ) +' j+1 (h j ; h;j )V (a j+1 ;h j+1 ; h;j+1 ) (2.15) subject to (1 + cg )c gj + (1 + c b )c bj +! w m j +a j+1 =(1 + (1 k )r)a j + (1 n )w j forj = 1; 2;:::;J R 1 (2.16) (1 + cg )c gj + (1 + c b )c bj +! r m j +a j+1 =(1 + (1 k )r)a j +ssb forj =J R ;:::;J (2.17) c bj =I c bj (2.18) h j+1 = (1 h;j h j )h j +Bm j (2.19) h;j+1 = h;j +(1 +I c bj ) (2.20) 38 '(h j ) = 1exp( h (1 h;j h j )h j i ) (2.21) where cg and c b are tax rates on good and bad consumption respectively, m j is the amount of medical expenditures at age j, a j+1 is the saving for the next period. Individuals supply labor inelastically in the market and earn an income of w j where w is the market wage rate and j is the age specic eciency rate of labor. n and k are labor income capital income tax rates respectively. ssb denotes the social security benets received by the retired. r is the market interest rate on risk-free bonds. denotes the amount of income spent on bad consumption if the individual chooses to consume those goods. h;j is the depreciation rate of health capital, h j . 2.3.2.9 Government Budget Constraint Revenues from taxes on good consumption, excise taxes from bad consumption, cap- ital and labor income taxes and assets left by the deceased are collected by the central government and are used to nance health care expenditures, discretionary government spending and social security benets. Labor income tax, n is set to clear the government budget constraint. Let's dene s;j as the measure of age j individuals with initial health status s alive in a given period. Let's further dene J W =f1; 2;:::;J R1 g,J R =fJ R ;J R + 1;:::;Jg andJ =f1; 2;:::;Jg. AndH is the set of possible initial health states. So the following budget constraint has to clear. T cg +T c b +T n +T k +A =G +SSB + (1!)M (2.22) T cg = cg X s2H X j2J sj c g;sj (2.23) 39 T c b = c b X s2H X j2J sj c b;sj (2.24) T n = n w X s2H X j2J W sj j (2.25) T k = k r X s2H X j2J sj a j (2.26) A = X s2H X j2J (1' sj ) sj a j (2.27) SSB =ssb X s2H X j2J R sj (2.28) M = X s2H X j2J sj m sj (2.29) G =%Y (2.30) where ! is the coinsurance rate and % is the xed portion of income spent for dis- cretionary government spending. T cg andT c b are total taxes collected from good and bad consumption goods. T n andT k are total labor and capital income taxes collected from individuals. A is the savings left by the deceased in the economy. G is the dis- cretionary government spending on goods and services,SSB is total expenditures on social security benets andM is the aggregate medical expenditures in the economy. 2.4 Calibration Although the model is designed for any type of bad consumption, in the quantitative exercise I focus on smoking as the bad consumption good since it is easier to quantify in data. There are two sets of parameters in the model. First set of parameters are picked from real data and literature and the second set of parameters are calibrated to match the relevant features of the U.S. data in the benchmark calibration. I start by by setting one model year to 5 years, where individuals start their life 40 cycles at age 20, retire at 65 and die with certainty at age 100, which coincides to J = 15 and J R = 10 in the model. Since I do not have the production side of the economy, wage, interest rate and the discount factor are exogenously given. Time discount factor, , is set to 0.98 and interest rate, r, is set to 2:5% annually. Wage rate,w, is arbitrarily set to 1.2. Eciency prole for labor, j , is obtained from Panel Study of Income Dynamics (PSID) data, following Rupert and Zanella (2010) and Chapter 1. There are two dierent parameters for the coecient of relative risk aversion, for good consumption and for bad consumption. is set to 2, as widely used in the literature and is set to 0.6 to avoid negative innity since bad consumption can take the value of zero. Capital income tax rate is taken from Chen and Imrohoroglu (2012), which is equal to 34.3% on average between 2000-2009. Average sales tax rate in the U.S. is obtained from McDaniel (2007) for years 2000-2003 and average excise tax rate on tobacco is obtained from Orzechowski and Walker (2011) for years 2000-2009. Both sales tax and excise tax rates are state averages, since sales taxes are imposed by states and excise taxes on cigarettes are a combination of federal and state taxes (See Table 2.26) in the U.S. Hence cg is taken as 7.42% and cb is taken as 29.68%. Table 2.5 summarizes the xed parameters of the model. I choose the rest of the parameters to minimize the distance between model gen- erated moments and target moments from the U.S. data. Let be the vector of parameters to be calibrated: = (b;; ;;; ;;B;;) (2.31) I nd by minimizing the following objective function: 41 Table 2.5: Fixed Parameters Parameter Explanation Value J Life time 15 J R Retirement age 10 k Capital income tax rate 34.3% cg Sales tax rate 7.42% cb Excise tax rate 29.68% Time discount factor 0.98 yearly w Wage rate 1.2 r Interest rate 2.5% yearly CRRA coecient for c g 2 CRRA coecient for c b 0.6 min n M X i=1 MM i TM i 2 (2.32) where MM i refers to model generated moments and TM i refers to target moments from data. n M denotes the number of calibrated parameters. I perform the calibration in two steps: First, I calibrate the survival probability parameters, and , using grids for health stock and depreciation. Specically, I target two dierent paths of survival proles: Never smoker and always smoker. Sur- vival dierentials from Peeters et al. (2003) were used to calibrate these parameters. In the second step, I calibrate the rest of the parameters to match the targets from data. I chooseb such that an extra year of life gives positive utility. Values for and are chosen in accordance with Ozkan (2011). is chosen such that the percentage of smokers in the model matches its data counterpart and is chosen to match the ratio of tobacco use in total consumption, which is obtained from NIPA accounts. B and are pinned down to match medical expenditure to GDP ratio for the total population and the working population respectively. And nally, is chosen to cap- 42 ture the medical expenditure dierentials between healthy and unhealthy people by perceived health status. Table 2.6 shows the calibrated parameters of the model. Table 2.6: Calibrated Parameters Parameter Explanation Value b Value of being alive 2.5 ; Quality of life parameters 0.2,1.2 ; Parameters in survival probability 6,1.2 Weight on c b 0.0853 Amount of c b 0.3055 B;; Parameters on health production function 0.215,0.1876,1.8306 2.4.1 Benchmark Model Tax and coinsurance rates used in the benchmark calibration are given in Table 2.7. Coinsurance rate for the working population is set to 10 percent and all retired peo- ple are covered with medicare, for which the coinsurance rate is set to 0 percent 2 . Labor income tax is chosen such that it clears the government budget. Computation algorithm is provided in the appendix. Table 2.8 displays results from the benchmark calibration. There is a good t of the model in terms of the medical expenditure to GDP ratio, ratio of smoking in total 2 I assume a very simple health care system in the model where there are no insurance premiums and deductibles. Instead, labor income tax is adjusted to balance the health care system. Thus, higher coverage is associated with higher taxes. One can think of this mechanism as a premium or copayment through taxes. In the U.S., depending on the coverage scheme, Medicare may involve premiums, deductibles and copayments depending on the duration and the provider of care. For example, under Medicare Part A, there is $0 cost for home and hospital care and there is no deductible, but one has to pay 20 percent of durable medical equipment. Also, hospital inpatient stays require some deductible depending on the duration of stay. Under Medicare Part B, there is a monthly premium which depends on the income of the individual. 43 Table 2.7: Tax and coinsurance rates in benchmark calibration Parameter Explanation Value cg Sales tax on good consumption 7.42% c b Excise tax on bad consumption 29.68% k Capital income tax 34.3% ! w Insurance co-payment rate 10% ! r Medicare co-payment rate 0% consumption and percentage of population that smokes. Life cycle prole of medical expenditures generated by the benchmark model also matches the prole from data as shown in Figure 2.2. Figure 2.4 shows medical expenditures and medical expenditure- income ratio for dierent health states from both data and the model. Both in the data and benchmark simulation unhealthy people smoke more than healthy people. Table 2.8: Model Fit Target Data Model Medical expenditure-output ratio 15.6% 15.1% Bad consumption-total consumption ratio 1.6% 3.3% % of population that smokes 21.1% 22.9% 44 2 0 -2 4 3 0 -3 4 4 0 -4 4 5 0 -5 4 6 0 -6 4 7 0 -7 4 8 0 -8 4 0 .0 5 0 .1 0 0 .1 5 0 .2 0 0 .2 5 0 .3 0 0 .3 5 0 .4 0 0 .4 5 M /Y (% ) A g e D a ta B e n c h m a rk Figure 2.2: Model Fit 2.5 Results In this section, I perform several policy experiments to investigate the responses of medical expenditures and bad behaviors to dierent coinsurance and excise tax rates. I also observe the changes in welfare due to policy changes and evaluate the welfare implications of dierent policies. 2.5.1 Policy exercises 2.5.1.1 Coinsurance rate changes Table 2.9 displays the results from changing the coinsurance rates for the working population,! w while the coinsurance for the retired,! r is held constant at 0 percent. Increasing the coinsurance rate for the working population leads to a reduced medical 45 expenditure to GDP ratio, denoted byM=Y . The decrease in this ratio is monotonic unless the coinsurance rate is too high. But even for 100 percent coinsurance, where all medical expenditures are out-of-pocket, medical expenditures to GDP ratio remains below the benchmark case by about 0.1 percentage points. In a system where all medical expenditures are funded by the government, medical expenditures to GDP ratio goes up by about 0.5 percentage points. Going from 10 percent to 30 percent coinsurance leads to a less than 1 percentage point decrease in medical expenditures to GDP ratio. These results are in accordance with the ndings of Zweifel and Manning (2000) and Newhouse (1993) as higher cost sharing reduces the medical expenditures. Smoking prevalence also goes down by higher coinsurance rates since with higher cost sharing people bear more of the cost of their risky health behaviors, which makes them refrain from those bad behaviors. Increasing the coinsurance rate from 10 percent to 30 percent leads to about 2 percentage points decrease in smoking prevalence. Notice that with 40 percent or more coinsurance, ratio of smokers increase although cost sharing is higher. This is due to the fact that with higher coinsurance rates, the labor income tax rate clearing the government budget declines, giving people more income to spend on both good and bad consumption. Ratio of smokers by health status given in Table 2.9 shows how smoking behaviors of people in dierent health categories change with dierent coinsurance rates. Since it is not as costly for people who have good health to recover from health depreciation, they substantially increase smoking when coinsurance rate is 100 percent. In other words, people with good health status prefers making their medical expenditures themselves rather than getting taxed to be insured. I test this by keeping the labor income tax rate constant at its benchmark level of 26.31 percent so that higher coinsurance rates will not yield any income eect. Under this setting, 40 percent coinsurance rate yields 12.91 percent of medical expenditures to GDP ratio and 8.36 percent of smoking prevalence. Only 46 people with very good or excellent health states smoke in this case. Increasing the coinsurance rate further to 100 percent leads to 11.85 percent medical expenditures to GDP ratio and nobody smokes in this case. Table 2.24 and Table 2.25 show the results when coinsurance rate for the retired is 5 percent and 10 percent respectively. The qualitative implications of the model are similar with the case where ! r = 0%, except for the smoking prevalence which goes up when ! r = 10%. Since medical expenditure are higher at older ages, increasing the coinsurance rate for the retired leads to a larger decrease in the labor income tax rate that clears the government budget, hence a bigger income eect. Tables 2.10 and 2.11 show the medical expenditures to GDP ratios and smoking prevalences with dierent coinsurance rates for the working and retired population. We can see from Table 2.10 that going horizontally along the rows, the reduction in medical expenditures to GDP ratio is larger when compared to going vertically along the columns, which means increasing! r has a bigger impact on medical expenditures to GDP ratio than increasing! w since most of the medical expenditures are incurred at older ages. Table 2.11 shows that although increasing ! w for every ! r leads to reduced smoking ratios, increasing! r might yield to more smoking due to high income eect. 47 Table 2.9: Effects of different coinsurance rates with ! r = 0%. (! w ) Data Benchmark(! w = 10%) 0% 5% 15% 20% 25% 30% 35% 40% 100% M/Y (%) 15.60 15.19 15.63 15.55 15.06 14.97 14.48 14.42 14.23 14.22 14.94 % of smokers 21.10 22.92 22.94 22.95 22.66 22.64 20.75 20.75 20.49 23.33 72.08 Labor income tax(%) 26.80 26.31 28.56 28.09 25.80 25.16 24.29 23.87 22.96 21.51 2.10 % of smokers (! w ) Health Status Data Benchmark(! w = 10%) 0% 5% 15% 20% 25% 30% 35% 40% 100% Poor 32.50 27.14 34.14 35.28 26.99 27.23 26.98 26.90 26.91 19.14 10.43 Fair 27.12 24.45 24.30 24.33 16.89 16.66 16.65 16.66 8.64 8.60 25.15 Good 23.23 23.00 22.97 23.01 22.99 22.93 15.05 15.05 15.03 15.53 45.00 Very good 18.71 21.43 21.45 21.44 21.43 21.46 21.41 21.42 21.44 21.47 66.35 Excellent 15.22 20.70 20.69 20.70 20.70 20.67 20.66 20.66 20.69 27.32 86.75 48 Table 2.10: M/Y (%) with different coinsurance rates H H H H H H ! w ! r 0% 5% 10% 20% 0% 15.63 15.19 14.10 13.72 5% 15.55 15.10 14.39 13.30 10% 15.18 14.99 14.28 13.22 20% 14.96 14.73 13.85 13.09 Table 2.11: % of smokers with different coinsurance rates H H H H H H ! w ! r 0% 5% 10% 20% 0% 22.94 22.94 28.62 33.23 5% 22.95 22.92 28.39 39.93 10% 22.92 22.66 28.37 31.21 20% 22.64 22.70 28.06 31.15 2.5.1.2 Welfare Analysis So far we have seen how changing the coinsurance rate aected risky behaviors as well as medical expenditures. But since risky behaviors also generate utility, we need a welfare analysis to see if reducing smoking makes people better or worse o. To be able to do that, I calculate the total welfare under each coinsurance rate and the consumption compensation required to make people in the benchmark economy as well o as people under dierent coinsurance rate regimes. I examine required consumption compensation for the whole economy as well as for each health status separately. I start by dening the discounted life time utility of a newborn individual 49 for policy as W = 5 X s=1 15 X j=1 j1 sj u c g;sj ;c b;sj ;h sj (2.33) W s = 15 X j=1 j1 sj u c g;sj ;c b;sj ;h sj ; s = 1; 2;:::; 5 (2.34) So the consumption compensation,x, required for people in the benchmark econ- omy, denoted by 0 , to make them as well o as under policy is calculated as: 5 X s=1 15 X j=1 j1 sj u (1 +x)c 0 g;sj ;c 0 b;sj ;h 0 sj = 5 X s=1 15 X j=1 j1 sj u c g;sj ;c b;sj ;h sj (2.35) 15 X j=1 j1 sj u (1 +x s )c 0 g;sj ;c 0 b;sj ;h 0 sj = 15 X j=1 j1 sj u c g;sj ;c b;sj ;h sj ; s = 1; 2;:::; 5 (2.36) Table 2.12 displays thex's calculated from the above equations. A coinsurance rate below 10 percent decreases the welfare of everyone in the economy. Higher coinsurance rates are welfare enhancing for the economy although unhealthy people become worse o because the majority of the population is comprised of health people. Welfare gains from higher coinsurance rates are larger for healthy people. For example, 1.21 percent consumption compensation is required for a newborn individual in the benchmark economy so that he has the same life time utility as if he lived in an economy with 30 percent coinsurance rate. Individuals with poor health in the same economy are worse o as they have to give up 1.57 percent of their consumption to live in an economy with 30 percent coinsurance. Figure 2.3 shows the life time prole of welfare changes for dierent coinsurance rates. To get these proles, I divide the welfare of people at each age in an economy with a certain coinsurance rate to the welfare of people with the same age in the benchmark economy. Any number above one means 50 a welfare gain whereas numbers below zero means w welfare loss. We can see that young individuals are the ones who are most aected by the changes in policy. With 40 percent coinsurance, for example, individuals aged 20-24 become about 15 percent better o compared to the benchmark economy. Only people who are in the 40-50 range become slightly worse o with higher coinsurance rates, mainly because they are the ones giving up smoking. Table 2.12: Welfare for different health states with different coinsurance rates (! w ) 0% 5% 15% 20% 25% 30% 35% 40% 100% Health Status Poor -0.17 % -0.77 % -0.52 % -0.87 % -0.92 % -1.57 % -1.56 % -1.16 % 10.07 % Fair -1.22 % -1.43 % -0.22 % -0.20 % 0.12 % -0.13 % 0.28 % 1.30 % 16.28 % Good -1.64 % -1.64 % 0.06 % 0.27 % 0.74 % 0.70 % 1.25 % 2.45 % 19.93 % Very Good -1.90 % -1.77 % 0.20 % 0.54 % 1.17 % 1.26 % 1.94 % 3.31 % 23.03 % Excellent -2.10 % -1.86 % 0.30 % 0.74 % 1.47 % 1.65 % 2.41 % 3.88 % 25.61 % Total -1.89 % -1.76 % 0.19 % 0.52 % 1.14 % 1.21 % 1.88 % 3.23 % 22.93 % Table 2.13 shows the total welfare under each coinsurance rate. In this envi- ronment, 100 percent coinsurance rate is the optimal policy. As I discussed earlier, since healthy people incur much less health care expenditures, they prefer paying less taxes and paying for their own medical expenditures, the case where all medical expenditures are out-of-pocket yields the maximum welfare for this economy. 51 2 0 -2 4 3 0 -3 4 4 0 -4 4 5 0 -5 4 6 0 -6 4 7 0 -7 4 8 0 -8 4 9 0 -9 4 0 .9 0 0 .9 5 1 .0 0 1 .0 5 1 .1 0 1 .1 5 ΔW e lfa re A g e 0 % c o p a y 2 0 % c o p a y 3 0 % c o p a y 4 0 % c o p a y Figure 2.3: Change in Welfare Table 2.13: Welfare Analysis ! w % of smokers M/Y(%) Welfare 0% 22.94 15.63 1041395 5% 22.95 15.55 1042180 10% 22.91 15.18 1058740 15% 22.66 15.05 1060187 20% 22.64 14.96 1062949 25% 20.74 14.48 1068482 30% 20.74 14.42 1068868 35% 20.48 14.22 1074761 40% 23.33 14.22 1086669 100% 72.08 14.94 1236046 52 2.5.2 Excise tax rate changes Next, I examine the eects of dierent excise tax rates on medical expenditures and smoking. I choose a range from 16 percent to 42 percent for two reasons: First, the average excise tax rate between 2000-2009 for the six major tobacco states 3 is about 16 percent. And second, a major excise tax increase occurred in 2009 in the U.S., after which the national average of excise taxes on tobacco became about 42 percent. Remember that in the benchmark economy excise taxes are about 30 percent. Table 2.14 shows results for dierent excise tax rates. Higher excise taxes mono- tonically reduce the medical expenditures to GDP ratio. Higher excise taxes do not aect the smoking prevalence among people with excellent and poor health up to 42 percent, but leads to a reduction in smoking for people with a health status in between those. Overall, the increased taxation after 2009 is expected to reduce smok- ing prevalence by more than 4 percentage points and reduce health care spending by about 1 percentage points. The average excise tax in the 2000s in tobacco states have been 16.79 percent and for the other states it has been 29.21 percent. While 23.71 percent of people smoked in the tobacco states, 20.87 percent did in others. Table 2.26 and 2.27 gives yearly excise tax rates and smoking prevalence in each state in the U.S.. I examine whether the model can capture the dierence in smoking prevalence by reducing the excise tax rate to 16 percent. Results show that the percentage of smokers goes up to 25.78 percent with 16 percent excise taxes, overpredicting the eect of excise taxes by about 2 percentage points. A similar welfare analysis is carried out as in the previous section too. Table 2.16 and Table 2.15 show the welfare analysis for dierent excise tax rates. Higher taxes 3 Tobacco states are Georgia, Kentucky, North Carolina, South Carolina, Tennessee and Virginia. 53 are associated with higher welfare while lower taxes yield lower welfare. 42 percent excise tax is the welfare maximizing level among the examined and the consumption compensation required for a newborn in the benchmark economy to make him as well of as in the economy with 42 percent excise tax is 2.26 percent. Similarly, a newborn to the benchmark economy has to give up 6.56 percent of his consumption to be as well o as in an economy with 16 percent excise taxes. 54 Table 2.14: Effects of different excise tax rates with ! r = 0% and ! w = 10%. ( c b ) 16% 18% 20% 22% 24% 26% 28% 30% 32% 34% 36% 38% 40% 42% M/Y (%) 16.75 16.54 16.33 16.08 16.04 15.54 15.49 15.19 15.11 15.06 14.64 14.58 14.46 14.06 % of smokers 25.78 25.52 25.78 25.78 25.78 22.95 22.92 22.92 22.67 22.67 20.05 20.77 20.77 18.16 Labor Income Tax (%) 31.94 31.24 30.09 28.98 28.71 27.99 27.77 26.31 26.10 25.85 25.55 25.02 24.36 24.18 % of smokers ( c b ) Health Status 16% 18% 20% 22% 24% 26% 28% 30% 32% 34% 36% 38% 40% 42% Poor 35.28 35.28 35.28 35.28 35.28 35.28 28.31 28.31 28.31 28.31 28.31 28.31 28.31 28.31 Fair 24.33 16.72 24.33 24.33 24.33 24.33 24.33 24.33 16.72 16.72 16.72 16.72 16.72 16.72 Good 23.01 23.01 23.01 23.01 23.01 23.01 23.01 23.01 23.01 23.01 23.01 15.03 15.03 15.03 Very good 21.44 21.44 21.44 21.44 21.44 21.44 21.44 21.44 21.44 21.44 14.38 21.44 21.44 14.38 Excellent 27.51 27.51 27.51 27.51 27.51 20.70 20.70 20.70 20.70 20.70 20.70 20.70 20.70 20.70 55 Table 2.15: Welfare Analysis c b % of smokers M/Y (%) Welfare 16% 25.78 16.75 993954 18% 25.52 16.54 1002512 20% 25.78 16.33 1016717 22% 25.78 16.08 1029902 24% 25.78 16.04 1032029 26% 22.95 15.54 1040189 28% 22.92 15.49 1041998 30% 22.92 15.19 1058740 32% 22.67 15.11 1060392 34% 22.67 15.06 1062756 36% 20.05 14.64 1065161 38% 20.77 14.58 1070391 40% 20.77 14.46 1077299 42% 18.16 14.06 1078667 Table 2.16: Welfare for different health states with different excise tax rates ( cb ) 16% 18% 20% 22% 24% 26% 28% 32% 34% 36% 38% 40% 42% Health Status Poor -6.87 % -5.97 % -4.45 % -2.99 % -2.68 % -1.76 % -1.91 % 0.23 % 0.52 % 0.87 % 1.53 % 2.37 % 2.56 % Fair -6.77 % -5.99 % -4.52 % -3.16 % -2.87 % -2.01 % -1.78 % 0.13 % 0.41 % 0.75 % 1.37 % 2.16 % 2.35 % Good -6.63 % -5.81 % -4.43 % -3.10 % -2.82 % -1.99 % -1.77 % 0.20 % 0.46 % 0.76 % 1.34 % 2.11 % 2.28 % Very Good -6.53 % -5.73 % -4.37 % -3.06 % -2.79 % -1.97 % -1.76 % 0.19 % 0.44 % 0.73 % 1.33 % 2.09 % 2.24 % Excellent -6.52 % -5.72 % -4.35 % -3.04 % -2.78 % -1.96 % -1.75 % 0.19 % 0.44 % 0.74 % 1.33 % 2.08 % 2.24 % Total -6.56 % -5.76 % -4.38 % -3.07 % -2.79 % -1.97 % -1.76 % 0.19 % 0.44 % 0.74 % 1.33 % 2.10 % 2.26 % 2.5.3 Excise tax goes up and coinsurance goes down In this section I analyze the joint eect of two opposing policies. Patient Protection and Aordable Care Act (PPACA) passed by the Obama administration aims to provide universal health care and legislation at the federal and state level increased 56 the excise taxes on tobacco in 2009. So I examine an economy where coinsurance rate is reduced to 0 percent while excise taxe on tobacco is raised to 42 percent. Results are displayed in Table 2.17. The joint eect of the two policies are shown in the last column. The eect of the decrease in the coinsurance rate is dominated by the eect of the increase in excise taxes, leading to lower smoking and medical expenditure to GDP ratio compared to the benchmark economy. There is a welfare gain equivalent to 0.86 percent more consumption. People with poor health gain more in term of welfare and as health status increases, the gains in welfare declines. This is because the decline in welfare is larger for healthy people with 0 percent coinsurance while the gain in welfare due to higher excise tax does not dier much by health status. 57 Table 2.17: Coinsurance decreases and excise tax increases Benchmark ! w # c b " c b " and ! w # M/Y (%) 15.19 15.63 14.06 14.71 % of smokers 22.92 22.94 18.16 20.07 Labor Income Tax(%) 26.31 28.56 24.18 26.06 % of smokers Health Status Benchmark ! w # c b " c b " and ! w # Poor 27.14 34.14 28.31 35.28 Fair 24.45 24.30 16.72 16.72 Good 23.00 22.97 15.03 23.01 Very good 21.43 21.45 14.38 14.38 Excellent 20.70 20.69 20.70 20.70 Welfare Health Status ! w # c b " c b " and ! w # Poor -0.17 % 2.56 % 2.89 % Fair -1.22 % 2.35 % 1.57 % Good -1.64 % 2.28 % 1.14 % Very good -1.90 % 2.24 % 0.83 % Excellent -2.10 % 2.24 % 0.63 % Total -1.89 % 2.26 % 0.86 % 2.5.4 Redistribution via lump sum transfers Here I redene the mechanism through which the government budget clears. Instead of adjusting the labor income tax rate to clear the budget, I redistribute income 58 through lump sum transfers. So the individual's budget constraints now look like: (1 + cg )c gj + (1 + c b )c bj +! w m j +a j+1 =(1 + (1 k )r)a j + (1 n )w j +Tr forj = 1; 2;:::;J R 1 (2.37) (1 + cg )c gj + (1 + c b )c bj +! r m j +a j+1 =(1 + (1 k )r)a j +ssb +Tr forj =J R ;:::;J (2.38) where Tr is the lump sum transfers to clear the following government budget: T cg +T c b +T n +T k +A =G +SSB + (1!)M +TR (2.39) where TR =Tr P s2H P j2J sj m sj . This way the transfers clearing the government budget not only aects the income of the working population but also the income of the retired population. In other words, health care costs are shared by the whole population under lump sum transfers. The benchmark economy is recalibrated with transfers. Labor income tax is set to its value in data, which is 26.8 percent. Table 2.18 reports the results of then benchmark economy as well as policy exercises. With lump sum transfers in eect, higher coinsurance rates lead to sharper de- clines in medical expenditures to GDP ratio and smoking prevalence. For example, increasing the coinsurance rate from 10 percent to 30 percent leads to about 1.5 per- centage points decline in medical expenditures to output ratio with lump sum trans- fers whereas the decline under the labor tax rate clearing scenario is about half of this decrease. Similarly, the decline is much sharper with transfers, which is about 6.5 percentage points while with labor income tax clearing, it is only about 2 percentage points. Notice that while under the rst redistribution scenario where labor income 59 taxes clears the government budget, 100 percent coinsurance leads to a substantial increase in smoking prevalence, when lump sum transfers clear the government bud- get, people with poor or fair health completely give up smoking and overall smoking prevalence only increases by about 2 percentage points. We can conclude that with lump sum transfers, higher coinsurance makes people give up smoking faster since now the budget surplus is redistributed to the entire population instead of only the workers. Table 2.18 also shows the welfare analysis in terms of the consumption compensation needed to make people in the benchmark economy as well of as in the economies with dierent coinsurance rates. Welfare gains are much less compared to the case where labor income tax clears the market, but even in the case where coin- surance rate declines, there are welfare gains. Only people with poor health become slightly worse o under 30-40 percent coinsurance rates. 60 Table 2.18: Effects of different coinsurance rates with ! r = 0% and lump sum transfers. (! w ) Data Benchmark(! w = 10%) 0% 5% 15% 20% 25% 30% 35% 40% 100% M/Y (%) 15.60 15.32 16.51 15.35 15.11 14.67 14.21 13.85 13.73 13.73 12.18 % of smokers 21.10 22.66 30.06 22.94 22.66 20.75 18.16 16.07 16.04 16.03 24.87 Transfers -0.012 -0.021 -0.010 0.016 0.032 0.045 0.049 0.068 0.071 0.298 % of smokers (! w ) Health Status Data Benchmark(! w = 10%) 0% 5% 15% 20% 25% 30% 35% 40% 100% Poor 32.5 26.85 32.94 34.35 27.11 27.08 27.37 16.43 9.17 8.46 0 Fair 27.12 16.71 24.21 24.24 16.88 16.65 16.76 8.59 8.62 8.58 0 Good 23.23 22.99 30.21 22.99 22.99 15.06 15.02 7.62 7.62 7.62 6.42 Very good 18.71 21.45 28.4 21.45 21.43 21.43 14.39 14.39 14.38 14.38 26.04 Excellent 15.22 20.69 27.48 20.69 20.7 20.65 20.69 20.69 20.69 20.69 33.13 Welfare (! w ) Health Status 0% 5% 15% 20% 25% 30% 35% 40% 100% Poor 2.26 % 1.78 % 0.88 % 0.88 % 0.62 % -0.60 % -0.24 % -1.15 % 1.51 % Fair 1.22 % 1.10 % 1.16 % 1.46 % 1.52 % 1.02 % 1.45 % 0.89 % 6.47 % Good 0.65 % 0.71 % 1.18 % 1.58 % 1.82 % 1.48 % 2.06 % 1.72 % 8.72 % Very good 0.37 % 0.55 % 1.26 % 1.79 % 2.13 % 1.93 % 2.60 % 2.35 % 10.47 % Excellent 0.17 % 0.45 % 1.34 % 1.97 % 2.40 % 2.28 % 3.03 % 2.85 % 11.90 % Total 0.40 % 0.58 % 1.27 % 1.80 % 2.13 % 1.91 % 2.58 % 2.33 % 10.40 % 61 2.6 Conclusion Risky health behaviors such as smoking are utility generating activities with external costs. The direct cost of those risky behaviors is higher medical expenditures due to increased health conditions. There are also indirect costs of risky health behaviors in an economy where health care expenditures are nanced by taxes. This chapter develops a macroeconomic model of risky health behaviors, named as bad consumption goods, to examine how policy aects those risky behaviors as well as medical expenditures in an equilibrium framework. I calibrate an OLG model where individuals engage in utility generating bad consumption that has a negative externality on health. People in the model start life with a given health stock, which may dier from an individual to the other, and that health stock depreciates. There are two mechanisms through which depreciation of health stock increases: First one is aging, and the second one is bad consumption, something that people have control over. In an economy where government is the provider of a single payer health care system, taxes are used to nance medical expenditures. Individuals pay a certain portion of their health care bills, which is called the coinsurance rate. I examine the implications of dierent coinsurance rates and excise taxes on risky health behaviors and medical expenditures. Results suggest that both increasing the coinsurance rate and the excise tax rate are welfare enhancing for the economy, which are associated with lower medical ex- penditure to GDP ratios. As the coinsurance rate increases, people bear a larger share of the cost of their risky behaviors, leading to lower risky behaviors. At the same time, higher coinsurance rates are associated with lower taxes, thus higher in- comes, which enables people to consume more goods. Since healthier people, who 62 comprise the majority of the population, incur less health care costs, higher coinsur- ance rates are benecial for the economy overall although unhealthy people become worse o by having to pay a larger portion of their health care bills. Overall, higher coinsurance rates reduce the moral hazard problem among unhealthy people whose bad consumption behaviors are riskier. The model also does a good job in explaining the dierences in smoking prevalence between the U.S. states where excise taxes dier by a great deal. Although higher excise taxes are associated with lower smoking rates, welfare of the economy as a whole increases due to higher incomes. Finally the joint eect of higher taxes and lower coinsurance rates is examined. With both policies in eect, smoking prevalence and medical expenditures to GDP ratio declines and people become better o. 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Manning, \Moral hazard and consumer incentives in health care," Handbook of Health Economics, 2000, Volume 1, 409{459. 68 Appendix 2.A Computation algorithm for station- ary equilibrium Given the xed parameters of the model, I compute the stationary equilibrium in the following steps: Step 1: Discretize the state space for assets, health stock and depreciation rate of health stock. H =fs 1 ;s 2 ;s 3 ;s 4 ;s 5 g D =fd 1 ;d 2 ;:::;d 29 g A =fa 1 ;a 2 ;:::;a 100 g Step 2: Start with an arbitrary value for the labor income tax rate, n and other parameters, . Step 3: Find the decision rules for assets, health stock, good consumption, bad con- sumption and the law of motion for the depreciation rate of health stock by backward induction. Step 4: Simulate the economy for 100,000 people, diering in their initial health stocks. Step 5: Compute the aggregates from the simulation. Step 6: Compute 0 n that clears the government budget. Step 7: Iterate on until the distance between model and target moments are min- imized. Step 8: Repeat steps 5 and 6 until n and converges. 69 Appendix 2.B Additional Tables and Figures Table 2.19: Medical Expenditures as a percentage of Income (MEPS) Age 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Average 20-24 8.00 10.22 10.59 11.94 10.84 12.31 12.18 12.47 13.46 15.95 11.80 25-29 6.08 5.76 6.92 8.02 8.06 8.47 7.71 8.24 8.42 10.13 7.78 30-34 6.15 6.90 6.63 6.56 7.19 7.62 7.36 7.55 7.52 8.65 7.21 35-39 5.22 5.99 6.34 6.40 6.86 7.46 6.93 6.57 7.68 8.26 6.77 40-44 6.16 5.98 7.21 9.17 8.33 9.21 7.12 7.61 8.07 9.64 7.85 45-49 7.51 7.42 8.75 7.90 8.83 9.19 8.63 9.77 9.45 11.59 8.91 50-54 8.17 9.15 9.16 11.32 11.20 11.06 12.43 12.15 10.61 12.26 10.75 55-59 11.71 13.16 13.45 15.06 14.19 15.76 14.01 16.62 13.99 16.04 14.40 60-64 14.84 18.00 16.54 18.39 23.03 18.26 17.83 18.22 20.28 20.95 18.63 65-69 23.71 21.51 22.57 25.58 26.63 23.33 23.58 23.12 26.30 22.81 23.91 70-74 28.77 31.12 35.46 39.87 38.46 36.19 32.34 34.04 30.99 36.57 34.38 75-79 30.61 39.65 41.33 39.43 43.50 45.47 38.66 36.02 39.81 47.14 40.16 80-84 46.69 39.46 41.08 51.44 47.34 48.10 49.97 49.49 46.59 47.38 46.75 85+ 43.84 57.67 51.87 43.29 62.96 53.40 50.38 51.71 51.21 62.22 52.86 Table 2.20: Total Medical Expenditures (MEPS) (in millions) 4 Age 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 20-24 21,063 28,875 28,207 31,874 31,715 37,427 39,007 37,554 40,074 48,878 25-29 27,911 28,737 35,300 44,104 41,762 46,569 45,089 50,978 54,495 59,753 30-34 37,464 43,392 43,465 43,305 51,176 51,063 53,317 52,795 50,196 59,594 35-39 42,619 46,605 46,307 46,356 50,027 56,983 56,781 57,983 63,517 65,665 40-44 46,962 48,993 63,175 81,380 71,930 81,551 64,679 65,367 74,021 82,429 45-49 54,970 56,434 69,617 62,580 78,854 82,468 79,122 92,109 82,283 101,720 50-54 54,946 67,814 67,993 83,899 83,059 90,919 105,942 108,893 101,320 115,996 55-59 51,838 66,869 76,405 91,816 94,677 109,025 109,675 137,143 116,587 134,261 60-64 45,349 59,569 65,748 78,573 98,103 86,986 93,185 112,038 139,083 132,113 65-69 53,314 53,415 58,820 73,405 76,947 74,406 87,789 86,594 101,967 96,016 70-74 52,468 59,421 69,383 80,619 79,103 81,604 70,175 87,179 82,338 95,780 75-79 44,136 56,401 67,108 65,680 73,671 81,429 73,900 77,579 79,404 82,451 80-84 31,870 41,699 48,886 54,680 53,857 61,387 63,206 62,211 62,720 71,355 85+ 27,271 36,295 35,603 34,277 48,122 43,900 49,009 61,471 62,832 74,720 70 Table 2.21: Perceived health status for ages 15-24 (Percentage of population) Round 1 Health Status 2001 2002 2003 2004 2005 2006 2007 2008 2009 Av. 1 - excellent 39.33 40.02 39.62 38.83 39.17 40.30 42.62 45.30 45.04 41.14 2 - very good 32.48 31.63 30.19 30.68 30.98 30.49 29.99 29.44 30.31 30.69 3 - good 22.36 23.26 24.40 24.75 23.90 23.78 22.30 20.16 20.22 22.79 4 - fair 4.90 4.56 4.94 4.91 5.09 4.68 4.32 4.40 3.93 4.64 5 - poor 0.92 0.53 0.85 0.83 0.86 0.76 0.78 0.70 0.51 0.75 Round 2 Health Status 2001 2002 2003 2004 2005 2006 2007 2008 2009 Av. 1 - excellent 36.89 38.46 38.42 38.89 38.11 40.32 39.72 38.08 38.93 38.65 2 - very good 35.21 33.88 31.59 31.54 32.68 30.81 33.18 33.52 33.16 32.84 3 - good 23.19 23.20 24.82 24.59 24.54 24.27 22.45 23.63 23.24 23.77 4 - fair 4.18 3.86 4.44 4.30 3.94 3.93 3.96 4.25 4.11 4.11 5 - poor 0.55 0.59 0.73 0.69 0.73 0.68 0.70 0.52 0.55 0.64 Round 3 Health Status 2001 2002 2003 2004 2005 2006 2007 2008 2009 Av. 1 - excellent 35.76 38.47 37.57 37.34 37.05 37.42 40.13 41.99 41.07 38.53 2 - very good 34.19 32.98 31.55 31.03 32.89 32.81 33.00 32.25 31.02 32.42 3 - good 24.63 23.86 26.00 26.13 25.46 24.88 21.76 20.50 23.23 24.05 4 - fair 4.93 4.02 4.20 4.73 4.05 4.04 4.21 4.74 4.11 4.34 5 - poor 0.47 0.67 0.68 0.77 0.54 0.85 0.91 0.53 0.56 0.67 Table 2.22: Average medical expenditures by health status Health Status 2001 2002 2003 2004 2005 2006 2007 2008 2009 1 - excellent $1,110 $1,162 $1,271 $1,356 $1,382 $1,429 $1,616 $1,649 $1,788 2 - very good $1,789 $1,902 $2,257 $2,337 $2,382 $2,505 $2,511 $2,741 $2,838 3 - good $2,839 $3,245 $3,484 $3,905 $3,955 $3,991 $4,460 $4,230 $4,832 4 - fair $6,223 $6,931 $7,653 $7,841 $8,542 $8,646 $9,098 $8,848 $10,227 5 - poor $13,709 $15,246 $17,123 $16,832 $19,205 $15,725 $13,709 $20,365 $20,129 4 Medical Expenditures are denoted in nominal terms for each year. 71 Table 2.23: Some Moments % of smokers Health Status Data Model Poor 32.5 27.14 Fair 27.12 24.45 Good 23.23 23.00 Very good 18.71 21.43 Excellent 15.22 20.70 72 Table 2.24: Effects of different coinsurance rates with ! r = 5%. (! w ) Data Benchmark(! r = 0%) 0% 5% 10% 15% 20% 25% 30% 35% 40% M/Y (%) 15.60 15.19 15.20 15.10 14.99 14.93 14.73 14.32 14.20 14.31 13.96 % of smokers 21.10 22.92 22.94 22.92 22.66 22.65 22.70 20.89 20.61 23.44 23.33 Labor Income Tax(%) 26.80 26.31 26.75 26.10 25.40 25.02 24.00 23.07 22.58 21.45 20.02 % of smokers (! w ) Health Status Data Benchmark(! r = 0%) 0% 5% 10% 15% 20% 25% 30% 35% 40% Poor 32.50 27.14 26.34 25.73 26.99 26.37 27.23 27.74 26.79 26.91 19.66 Fair 27.12 24.45 25.30 25.11 16.69 16.57 16.72 16.74 8.65 8.70 8.68 Good 23.23 23.00 23.01 22.95 22.99 23.04 23.12 15.54 15.54 15.55 15.55 Very good 18.71 21.43 21.43 21.45 21.45 21.43 21.48 21.44 21.44 21.42 21.42 Excellent 15.22 20.70 20.70 20.66 20.69 20.67 20.69 20.69 20.69 27.51 27.32 73 Table 2.25: Effects of different coinsurance rates with ! r = 10%. (! w ) Data Benchmark(! r = 0%) 0% 5% 10% 15% 20% 25% 30% 35% 40% M/Y (%) 15.60 15.19 14.10 14.39 14.28 13.74 13.85 13.61 13.60 13.54 13.01 % of smokers 21.10 22.92 28.62 28.39 28.37 25.49 28.06 25.46 28.06 28.02 33.41 Labor Income Tax(%) 26.80 26.31 25.43 24.07 23.38 22.36 21.10 21.28 19.42 19.03 17.12 % of smokers (! w ) Health Status Data Benchmark(! r = 0%) 0% 5% 10% 15% 20% 25% 30% 35% 40% Poor 32.50 27.14 20.65 21.41 20.58 20.80 21.12 20.67 20.07 14.85 14.94 Fair 27.12 24.45 25.57 19.91 19.86 12.74 12.77 12.65 12.68 12.75 12.75 Good 23.23 23.00 22.08 22.13 22.08 22.10 22.13 22.06 22.10 22.08 22.08 Very good 18.71 21.43 28.05 30.12 30.15 22.75 30.12 22.78 30.18 30.15 27.68 Excellent 15.22 20.70 29.33 27.51 27.50 27.51 27.51 27.47 27.50 27.50 43.54 74 Table 2.26: Excise taxes on tobacco State 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Alabama 25.6 24.2 22.4 20.7 15 17.5 15.6 16.9 17.2 22.8 22.9 23.1 21.7 21.7 31.6 Alaska 24.9 24.2 41.8 37.9 30.6 30.5 30.2 30.3 31.5 27.6 35.5 37.6 37.6 35.7 39.6 Arizona 39.4 36.9 35.5 32.8 25.8 26.6 25.5 40.8 38.9 39.6 37.8 36.1 45.9 43.7 48 Arkansas 33.2 30.6 29.6 26.8 19.9 22.2 19.8 30.9 27.3 27.7 27.8 26.4 25.6 24.9 40.8 California 30.8 30.5 29.4 40.3 31.6 33.1 30.4 30.9 31.9 32.8 31.9 31.9 30 29.4 37 Colorado 25.9 25.2 23.7 21.5 15.6 18.4 17.6 18.1 18.4 17.2 30.5 30.6 29.2 29.3 36.4 Connecticut 35.9 35.5 34 31.3 23.7 26.3 23.7 34.7 40.6 40.4 40.1 40.7 44.6 42.8 53.7 Delaware 28.4 27.9 26.8 24.2 17.4 20.1 18.3 19.5 26.6 27.6 27 26.4 36.3 36.5 48.8 District of Columbia 38.2 38.6 37.6 35.1 27.5 27.9 26.7 27.3 33.9 33.1 32.7 32.8 32.3 46.9 52.2 Florida 32.2 31.7 30.2 26.9 20.2 22.5 20.4 21.5 22 22.5 21.2 21.2 20.2 20.4 42.9 Georgia 23.1 22.7 21.3 19.1 14 16 15 16.2 23 22.6 21.8 21.7 20.8 20.9 30.5 Hawaii 36.3 34.6 40 41.1 33.2 33.1 32.3 35 35.8 35.5 35.9 37.8 38.2 40.8 32.1 Idaho 29.5 28.2 27.8 24.7 18.8 21.3 20.3 21.1 26.3 27.4 26.6 26.3 25.2 24.9 34.6 Illinois 36 34.2 33.6 34.1 26.2 28.4 26.4 33.9 33.8 31.5 29.7 28.4 27.5 27.7 35.3 Indiana 26.7 25.3 23.7 20.8 15.2 18.3 16.4 26.4 26.9 27.4 26.9 27.1 33.5 33.8 41.6 Iowa 32.6 31.7 31 28.2 21 23.4 21.9 22.6 22.5 22.9 22.3 22.3 38.5 38.8 44.5 Kansas 28.6 28 26 23.2 17.7 19.7 19.3 29.3 30.5 31.5 31.6 26.9 28.7 28.9 37.9 Kentucky 19.3 18.5 17.3 15.1 11.1 14.3 12.6 14.1 13.5 14 20.9 20.8 19.9 19.8 35.2 Louisiana 26.6 26.4 23.7 21.2 15.6 19.7 18.6 22.5 22 22 22 21.4 20.8 20 30.4 Maine 32.6 32.1 44.6 36.6 29.7 30.6 34.1 34.7 32.5 34.3 45.8 45.3 43.3 42.6 48.2 Maryland 33.7 31.5 30.4 27.3 28.6 29 27 34.7 33.9 34.6 34.9 33.8 32.5 43.3 48.4 Massachusetts 36.1 40.9 38.7 35.4 28.4 28.6 27.5 39.2 36.9 37.8 37.6 38 37 45.6 48.5 Michigan 43.2 42.3 40.7 37.9 29.7 31.5 28.7 37.7 37.8 47 46.9 45.2 44.7 44.2 49 Minnesota 34.5 33.2 32.7 31.7 23.7 25.7 23.6 24.7 25.4 24.8 42 41 40.8 39.1 44.3 Mississippi 26.1 24.9 23.9 21.1 15.4 18.6 16.8 17.9 17.7 17.8 17.9 17.7 16.6 16.5 37.3 Missouri 25.7 25.1 23.6 20.8 15.8 18.1 16.8 18.2 17.7 18.1 17.6 17.2 16.7 16.4 29.2 Montana 26.8 25.5 23.9 21.4 16.1 19.2 16.8 17.7 28.4 27.7 43.4 42.5 42.1 41.7 47 Nebraska 33 31.4 29.8 27 20 22 20.7 26.6 27.2 28.5 28.2 27.7 27.4 27.3 35.2 Nevada 30.3 29.7 29.4 26.1 19.4 21.7 21.4 22.4 31.6 31.1 31.7 31.5 29.6 29.5 36.4 New Hampshire 29.1 27.7 31 27.4 24.2 26.7 24.4 25.4 25.5 25.9 31.9 31.6 34.7 38 47.5 New Jersey 32.9 32.9 30.7 38.1 30.6 31.3 30 40.8 44.6 49.7 49.7 49.5 48.7 47.7 51.9 New Mexico 26.3 25.6 24.5 22.3 16.1 18.9 17.2 17.9 34.3 33.5 34.1 34 32 31 37.6 New York 37.3 36 34.9 31.5 24.5 36.4 33.6 33.3 34.1 34.5 34.6 34.7 34.5 46.6 49.4 North Carolina 19.9 19.1 17.3 15.5 11.3 14.1 13.4 14.3 14.1 14.5 21 21 20 19.9 32.4 North Dakota 37.2 35 33.1 30.4 22.9 25.4 23.1 23 23.5 24.4 24.8 24.7 23.4 23.5 34.6 Ohio 30.1 28.8 27.8 24.8 18.1 20.8 18.7 26.2 26.2 26.9 40 39.1 37.2 36.6 42.1 Oklahoma 28.9 27.3 25.6 23.1 17.2 19.6 18.2 19.3 19.2 19.2 35.5 35.2 34.6 33.9 39.2 Oregon 32.5 31.4 39.3 35.6 28.4 29.5 28.2 41.3 39.4 37.9 37.1 37.3 36.6 36.6 42.9 Pennsylvania 32.5 31.2 28.8 26.8 19.6 22.3 20.3 35 44.5 40.4 40.2 40.5 39.6 39.4 47.8 Rhode Island 39.6 39.2 40.9 37.7 29.4 31 34.6 38.7 43.7 52.3 50.6 49.9 49.3 49.1 57.8 South Carolina 20.7 20.1 18.8 17.3 12.1 14.7 13.6 14.8 14.5 14.7 14.6 14.9 14.1 13.9 27.2 South Dakota 33.3 31.4 29.6 27.4 20.9 22 20.5 21.1 26.4 26.2 26 26.3 43.7 41.9 46.7 Tennessee 23.7 23 22.1 19.5 14.2 16.7 15.3 18 18.5 18.5 18.1 18.2 27 26.9 35.1 Texas 34.5 34.2 32.2 28.9 22.2 24.1 23 22.7 22.9 23.8 23.7 24 40.4 39.6 43.8 Utah 28.9 27.1 33.9 31 24.1 25.8 25.5 28.5 29.3 28.9 28.8 29.2 27.9 26.9 36.5 Vermont 34.6 33.7 31.8 29.1 22.6 24.1 22 33.8 36.3 35.6 35.3 44.9 42.8 42.7 48.8 Virginia 16.6 16.6 16.3 14.4 10.5 13.3 12.4 13.5 12.9 18 19.6 19.7 19.2 18.9 34.6 Washington 42.7 40.2 39.1 37.1 29.6 30.5 29.5 38 38.9 38.4 45.7 44.7 43.8 42.5 51 West Virginia 26.1 25.5 24 21.3 16.2 18.5 17.3 18.4 27.1 27.9 27.7 27 26.4 25.4 34.6 Wisconsin 33.9 33.9 39.4 34.1 26.5 28.1 28.9 29.4 30.4 30.8 30.7 30 28.3 43 51 Wyoming 22.2 21.9 21.3 19 13.5 15.8 14.8 16.2 27.8 27.3 27.1 26.6 26.5 25.5 34.4 75 Table 2.27: Smoking prevalence State 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Alabama 22.4 24.6 24.6 23.5 25.2 23.8 24.4 25.3 24.9 24.8 23.2 22.5 22.1 22.5 21.9 Alaska 27.7 26.5 26.1 27.3 25 26.2 29.3 26.2 24.8 24.9 24 22.2 21.5 20.6 20.4 Arizona 23.7 21.1 21.8 20.1 18.6 21.5 23.4 20.8 18.5 20.2 18.2 19.8 15.9 16.1 15 Arkansas 25.3 28.4 25.9 27.2 25.1 25.5 26.3 24.8 25.6 23.5 23.7 22.4 22.3 21.5 22.9 California 18.6 18.4 19.2 18.7 17.2 17.2 16.4 16.8 14.8 15.2 14.9 14.3 14 12.9 12.1 Colorado 22.8 22.5 22.8 22.5 20 22.3 20.4 18.6 20 19.8 17.9 18.7 17.6 17.1 16 Connecticut 21.8 21.6 20.9 22.8 19.9 20.6 19.4 18.6 18.1 16.5 17 15.4 15.9 15.4 13.2 Delaware 24.2 26.6 24.5 25.4 22.9 25 24.7 21.9 24.4 20.6 21.7 18.9 17.8 18.3 17.3 District of Columbia 20.5 18.8 21.6 20.6 20.9 20.8 20.4 22 20.9 20 17.9 17.2 16.2 15.3 15.6 Florida 21.8 23.6 22 20.6 23.2 22.4 22 23.9 20.2 21.7 21 19.3 17.5 17.1 17.1 Georgia 20.3 22.4 23.6 23.7 23.5 23.7 23.2 22.8 20 22.1 19.9 19.4 19.5 17.7 17.6 Hawaii 22.2 18.7 19.5 18.5 19.7 20.5 21 17.2 n/a 17 17.5 17 15.4 15.4 14.5 Idaho 21.1 19.9 20.3 21.5 22.3 19.6 20.6 19 17.4 17.9 16.8 19.1 16.9 16.3 15.7 Illinois 24.8 23.2 23.1 24.2 22.3 23.7 22.8 23.4 22.2 19.9 20.5 20.1 21.3 18.6 16.9 Indiana 28.6 26.4 26 27 26.9 27.4 27.6 26.1 24.9 27.3 24.1 24.1 26 23.1 21.2 Iowa 23.6 23.1 23.4 23.5 23.2 22.1 23.2 21.7 20.8 20.4 21.4 19.8 18.8 17.2 16.1 Kansas 22.1 22.6 21.1 21 21 22.2 22.1 20.4 19.8 17.8 20 17.9 17.9 17.8 17 Kentucky 31.7 30.7 30.8 29.7 30.5 30.9 32.6 30.8 27.5 28.7 28.5 28.2 25.2 25.6 24.8 Louisiana 25.9 24.5 25.5 23.5 24.1 24.6 23.9 26.5 23.5 22.6 23.4 22.6 20.5 22.1 22.1 Maine 25.3 22.7 22.4 23.3 23.8 23.9 23.6 23.7 21 20.8 20.9 20.2 18.2 17.3 18.2 Maryland 20.9 20.4 22.4 20.3 20.5 21.1 21.9 20.1 19.5 18.9 17.7 17.1 14.9 15.2 15.2 Massachusetts 23.4 20.5 20.9 19.3 19.9 19.5 18.9 19.1 18.5 18.1 17.8 16.4 16.1 15 14.1 Michigan 25.6 26 27.4 25.1 24.1 25.6 24.2 26.1 23.3 22 22.4 21.1 20.5 19.6 18.9 Minnesota 20.6 21.8 18 19.5 19.8 22.2 21.7 21.1 20.7 20 18.3 16.5 17.6 16.8 14.9 Mississippi 23.2 23.1 24.1 22.9 23.5 25.3 27.3 25.6 24.5 23.6 25.1 23.9 22.7 23.3 22.9 Missouri 27.8 28.6 26.4 27.1 27.2 25.9 26.5 27.2 24.1 23.4 23.2 24.5 25 23.1 21.1 Montana 21.7 20.5 21.4 20.2 18.8 21.9 21.2 20 20.4 19.2 18.9 19.5 18.5 16.8 18.8 Nebraska 22.1 22.1 22 23.2 21.2 20.2 22.7 21.2 20.3 21.3 18.7 19.9 18.4 16.7 17.2 Nevada 28.2 28 30.3 31.5 29 26.9 26 25.2 23.2 23.1 22.2 21.5 22.2 22 21.3 New Hampshire 24.8 24.7 23.3 22.3 25.3 24.1 23.2 21.2 21.7 20.4 18.7 19.3 17.1 15.8 16.9 New Jersey 22.7 21.4 19.1 20.6 21 21.1 19 19.4 18.8 18 18 17.1 14.8 15.8 14.4 New Mexico 22.8 22.1 22.5 22.4 23.6 23.8 21.2 22 20.3 21.5 20.1 20.8 19.4 17.9 18.5 New York 23.2 23.1 24.1 21.8 21.6 23.2 22.3 21.6 19.9 20.5 18.2 18.9 16.8 18 15.5 North Carolina 25.7 25.8 24.6 25.1 26.1 25.7 26.3 24.8 23.1 22.6 22.1 22.9 20.9 20.3 19.8 North Dakota 23.4 22.3 20 22.1 23.2 22.1 21.5 20.5 19.9 20.1 19.5 20.9 18.1 18.6 17.4 Ohio 28.4 25.1 26.1 27.6 26.2 27.6 26.6 25.2 25.9 22.3 22.4 23.1 20.1 20.3 22.5 Oklahoma 24.1 24.6 23.9 25.2 23.3 28.7 26.6 25.1 26.1 25.1 25.1 25.8 24.7 25.5 23.7 Oregon 23.4 20.7 21.1 21.4 20.7 20.5 22.4 20.9 20 18.5 18.5 16.9 16.3 17.9 15.1 Pennsylvania 24.5 24.2 23.8 23.1 24.3 24.5 24.5 25.4 22.7 23.6 21.5 21 21.3 20.2 18.4 Rhode Island 22.5 24.3 22.6 22.3 23.4 23.9 22.4 22.4 21.3 19.8 19.2 17 17.4 15.1 15.7 South Carolina 24.5 23.4 24.7 23.6 24.9 26 26.6 25.5 24.3 22.5 22.3 21.9 20 20.4 21 South Dakota 20.7 24.3 27.2 22.5 21.9 22.3 22.6 22.7 20.3 19.8 20.3 19.8 17.5 17.5 15.4 Tennessee 28 26.9 26 24.8 25.7 24.4 27.7 25.6 26.2 26.7 22.6 24.3 23.1 22 20.1 Texas 22.9 22.5 21.9 22.4 21.9 22.4 22.9 22.1 20.5 20 17.9 19.3 18.5 17.9 15.8 Utah 15.9 13.8 14.2 14 12.9 13.2 12.8 11.9 10.5 11.5 9.8 11.7 9.3 9.8 9.1 Vermont 24.1 23.3 22.3 21.7 21.5 22.4 21.1 19.5 20 19.3 18 17.6 16.8 17.1 15.4 Virginia 24.8 24.4 22.9 21.4 21.4 22.5 24.6 22 20.8 20.6 19.3 18.5 16.4 19 18.5 Washington 23.4 23.8 21.4 22.4 20.7 22.5 21.5 19.5 19.2 17.6 17.1 16.8 15.7 14.9 15.2 West Virginia 26.6 27.4 27.9 27.1 26.1 28.2 28.4 27.3 26.9 26.7 25.7 26.9 26.5 25.6 26.8 Wisconsin 24.9 23.2 23.4 23.7 24.1 23.6 23.3 22 21.9 20.7 20.8 19.6 19.9 18.8 19.1 Wyoming 24.6 24 22.8 23.9 23.8 22.2 23.7 24.6 21.7 21.3 21.6 22.1 19.4 19.9 19.5 76 2 0 -2 4 3 0 -3 4 4 0 -4 4 5 0 -5 4 6 0 -6 4 7 0 -7 4 8 0 -8 4 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 2 0 -2 4 3 0 -3 4 4 0 -4 4 5 0 -5 4 6 0 -6 4 7 0 -7 4 8 0 -8 4 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 2 0 -2 4 3 0 -3 4 4 0 -4 4 5 0 -5 4 6 0 -6 4 7 0 -7 4 8 0 -8 4 0 .0 0 .2 0 .4 0 .6 0 .8 1 .0 1 .2 1 .4 2 0 -2 4 3 0 -3 4 4 0 -4 4 5 0 -5 4 6 0 -6 4 7 0 -7 4 8 0 -8 4 0 .0 0 .2 0 .4 0 .6 0 .8 1 .0 1 .2 1 .4 M e d ic a l E x p e n d itu re s (D a ta ) A g e p o o r fa ir g o o d v e ry g o o d e x c e lle n t M /Y (D a ta ) A g e p o o r fa ir g o o d v e ry g o o d e x c e lle n t M e d ic a l E x p e n d itu re s (M o d e l) A g e p o o r fa ir g o o d v e ry g o o d e x c e lle n t M /Y (M o d e l) A g e p o o r fa ir g o o d v e ry g o o d e x c e lle n t Figure 2.4: Model Fit 77 2 0 -2 4 3 0 -3 4 4 0 -4 4 5 0 -5 4 6 0 -6 4 7 0 -7 4 8 0 -8 4 0 .0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 M /Y A g e B e n c h m a rk 0 % c o p a y 2 0 % c o p a y 3 0 % c o p a y 4 0 % c o p a y 1 0 0 % c o p a y Figure 2.5: M/Y over the life cycle with different coinsurance rates 2 0 -2 4 3 0 -3 4 4 0 -4 4 5 0 -5 4 6 0 -6 4 7 0 -7 4 8 0 -8 4 9 0 -9 4 0 .5 5 0 .6 0 0 .6 5 0 .7 0 0 .7 5 0 .8 0 0 .8 5 0 .9 0 0 .9 5 1 .0 0 1 .0 5 1 .1 0 1 .1 5 ΔW e lfa re A g e 1 6 % 2 4 % 3 4 % 4 2 % Figure 2.6: Change in Welfare 78 Chapter 3 Optimal Health Insurance in the Presence of Risky Health Behaviors 3.1 Introduction This chapter builds on the framework that has been set up in Chapter 2. In addition to the medical expenditures that stem from individuals' behaviors, it is important to consider medical shocks that may hit anyone regardless of risky health behaviors. Hence, I address the two aspects of health insurance in this chapter. First, health insurance covers medical expenditures resulting from controllable behaviors such as smoking and dietary activities. Second, it provides insurance for health shocks, mostly catastrophic ones. As to what may be considered catastrophic is usually decided by looking at the ratio of medical expenditures to total expenditures or total income of the individual. As I discussed in Chapter 2 too, risky health behaviors raise the problem of moral hazard and higher co-insurance rates induce people to refrain from risky health behav- iors. In the light of this argument, it is expected to have a lower optimal co-insurance rate in the absence of risky health behaviors. Pauly (2000) states that when moral hazard exists, positive cost-sharing is optimal, but the magnitude depends on many other things regarding demand and supply of medical services. Here I consider two scenarios where risky health behaviors aect and do not aect individual's health cap- ital, hence medical expenditures and in investigate the optimality of dierent health 79 insurance systems in the presence and absence of risky health behaviors. My results show that in the absence of risky health behaviors, zero co-payment is optimal, i.e. no cost-sharing is needed. However, when risky health behaviors aect medical expenditures, ten percent co-payment rate is found to be optimal. 3.1.1 Related Literature Following from Chapter 2, health insurance system in the model economy will be nanced by taxes on income. Blomqvist and Horn (1984) argue that a public health system nanced by taxes contributes to an optimal redistribution policy. Manning and Marquis (1996) state that regarding the optimal health insurance, there is a trade of between the decrease in risk at higher co-insurance (or lower cost-sharing) systems and increase in deadweight loss due to moral hazard in those systems. They nd that 30 percent coinsurance rate is close to optimal. Chernew et al. (2000) dierentiate between high and low cost treatment and nd that it is optimal to charge a co-pay to the patients taking the former and subsidize the patients with latter, which decreases the moral hazard too. However the optimal rate varies with the elasticity of demand for medical services. Eggleston (2000) analyzes demand and supply side cost-sharing, and a mix of both and argues that rather than being discriminated against by insurance providers, people prefer to share their medical costs. The rest of this chapter is organized as follows: Section 3.2 builds on the model presented in Chapter 2 and presents the model using in this chapter, section 3.3 gives the details of the calibration, section 3.4 presents the results of the policy experiments and section 3.5 concludes. 80 3.2 Model Since the model used in this chapter is very close to the one in Chapter 2, I am going to skip some explanations regarding the specic functional forms and parameters that have already been explained in Chapter 2. 3.2.1 Demographics Individuals in the model live for a maximum of J years, and dier by their initial health status, s2fs 1 ;s 2 ;:::;s 5 g. '(h j1 ; h;j1 ;s j1 ) is the probability of surviving from age j 1 to j, that depends on the health stock, depreciation rate of health capital at age j 1 and health shock, s j1 at age j 1. 3.2.2 Preferences Individuals maximize the following lifetime utility: max J X j=1 j1 j Y k=1 ' k (h k1 ; h;k1 ;s k1 ) ! u(c gj ;c bj ;h j ) (3.1) Period utility function is the same as in Chapter 2. u(c gj ;c bj ;h j ) =b + c 1 gj 1 + h 1 j 1 + c 1 bj 1 (3.2) 81 3.2.3 Health Production Health stock is accumulated by m dj , i.e. the amount of medical expenditures needed to keep up with depreciation of health stock. h j+1 = (1 h;j h j )h j +Bm dj (3.3) 3.2.4 Health Depreciation The rate at which health stock depreciates evolves in the same way as in Chapter 2. h;j+1 = h;j +(1 +I c bj ) (3.4) 3.2.5 Survival Probability Notice that survival probability function now has a second component, # Im sj , which denotes that if the health shock denoted bys j hits, survival probability is only aected if the individual cannot eliminate the eects of the shock by spending on medical goods and services to revert the shock, m sj . That is, if the part of the medical expenditures to cure the health shock, (1!)m sj , is greater than individual's resources at j, y j , then I m sj = 1 and the survival probability is reduced by #. '(h j ; h;j ;s j ) = " 1exp( h (1 h;j h j )h j i ) # # Im sj (3.5) where I m sj = 8 > < > : 0 if (1!)m sj <y j 1 if (1!)m sj >y j (3.6) 82 3.2.6 Health Care System There is a single-payer health care system where the government is the provider of health insurance. Working age population pays! w of their medical expenses whereas retired population pays ! r of them. These expenditures are nanced by taxes on good consumption, bad consumption and labor income. 3.2.7 Social Security Following Imrohoroglu et al. (1995), the benets that the retired households get are dened as a proportion of their average lifetime earnings from working, which is given as: ssb =& P J R 1 j=1 w j J R 1 (3.7) where & is the replacement ratio. 3.2.8 Individuals' Dynamic Problem We can denote the individual's life time maximization problem at (3.1) as a discrete time dynamic programming problem and maximize the following value function: V (a j ;h j ; h;j ;s j ) = max c gj ;Ic bj ;m j ;a j+1 n u(c gj ;c bj ;h j ) +' j+1 (h j ; h;j ;s j ) h Pr(s j+1 = 0)V (a j+1 ;h j+1 ; h;j+1 ; 0) +Pr(s j+1 = 1)V (a j+1 ;h j+1 ; h;j+1 ; 1) io (3.8) subject to (1 + cg )c gj +(1 + c b )c bj +! w (m dj +I m sj m sj ) +a j+1 83 = (1 +r)a j + (1 n )w j j = 1; 2;:::;J R 1 (3.9) (1 + cg )c gj + (1 + c b )c bj +! r (m dj +I m sj m sj ) +a j+1 = (1 +r)a j +ssbj =J R ;:::;J (3.10) c bj =I c bj (3.11) m sj = 8 > < > : 0 if I sj = 0 y j if I sj = 1 (3.12) h j+1 = (1 h;j h j )h j +Bm dj (3.13) h;j+1 = h;j +(1 +I c bj ) (3.14) '(h j ; h;j ;s j ) = " 1exp( h (1 h;j h j )h j i ) # # Im sj (3.15) is the magnitude of health shocks as a share of income, which will be disciplined according to what is considered to be catastrophic health shock from the literature. I sj is an indicator function which takes the value of 1 if the health shock hits. Pr(s j+1 = 1) is the probability that the health shock will hit at age j + 1. This probability is age dependent. 3.2.9 Government Budget Constraint Government budget is similar to the one in Chapter 2. T cg +T c b +T n +A =G +SSB + (1!)M (3.16) T cg = cg X h2H X j2J hj c g;hj (3.17) 84 T c b = c b X h2H X j2J hj c b;hj (3.18) T n = n w X h2H X j2J W hj j (3.19) A = X h2H X j2J (1' hj ) hj a j (3.20) G =%Y (3.21) SSB =ssb X h2H X j2J R hj (3.22) M = X h2H X j2J hj m hj (3.23) 3.3 Calibration I still keep my focus on smoking as a form of bad consumption for the rest of this chapter too. Details about the choice of xed parameters and calibration of many parameters are already discussed in Section 2.4. # is chosen to be 0:5, so that if the health shock hits and it is not cured, survival probability will reduce by half. is the ratio of medical expenses needed to cure health shocks to individual's income at any age. Xu et al. (2003) denes catastrophic health expenditures as expenditures exceeding 40% of income. This is a lower bound for health shocks, and I take this ratio to be 50%. Values of the xed parameters are given in table 3.1. Age specic probabilities of getting hit by a health shock are generated using MEPS data. The probabilities are found by taking the ratio of people spending over a certain ratio of their incomes on medical goods and services. Values are shown in table 3.2. The remaining parameters are calibrated, and the values are shown in table 3.3. 85 Table 3.1: Fixed Parameters Parameter Explanation Value J Life time 15 J R Retirement age 10 cg Sales tax rate 7.42% cb Excise tax rate 29.68% Time discount factor 0.98 yearly w Wage rate 1.2 r Interest rate 2.5% yearly CRRA coecient for c g 2 CRRA coecient for c b 0.6 # Survival parameter 0.5 Medical shock parameter 0.5 Table 3.2: Probability of Health Shocks Age(j) Probability 1 0.23960539 2 0.16806345 3 0.16073077 4 0.15119961 5 0.14794292 6 0.15495435 7 0.18745806 8 0.21941187 9 0.25586015 10 0.26569608 11 0.31974537 12 0.34848484 13 0.38966942 14 0.41866093 15 0.41866093 Table 3.3: Calibrated Paremeters Parameter Explanation Value b Value of being alive 2.5 ; Quality of life parameters 0.2,1.2 ; Parameters in survival probability 6,1.2 Weight on c b 0.106 Amount of c b 0.2417 B;; Parameters on health production function 0.235,0.107,1.5 86 3.4 Results For the benchmark calibration, co-payment rate for workers is set to be 10% and for the retired it is set to be 0%. We can think of the co-payment for the retired as medicare. Tax rates on good and bad consumption goods are the same as in Chapter 2 benchmark calibration. Main targets and model generated moments for the benchmark economy are given in table 3.4 and the t of the model to data in terms of life cycle prole of medical expenditures to income ratio is shown in gure 3.1. Table 3.4: Model Fit Target Data Model Medical expenditure-output ratio 15.6% 15.30% Bad consumption-total consumption ratio 1.6% 3.6% % of population that smokes 21.1% 20.49% Although the life cycle prole of medical expenditures to income ratio seems to overshoot at earlier ages and undershoot at older ages, the model seems to have a fairly good t with data. 87 2 0 -2 4 3 0 -3 4 4 0 -4 4 5 0 -5 4 6 0 -6 4 7 0 -7 4 8 0 -8 4 0 .0 5 0 .1 0 0 .1 5 0 .2 0 0 .2 5 0 .3 0 0 .3 5 0 .4 0 0 .4 5 M /Y (% ) A g e D a ta B e n c h m a rk Figure 3.1: Medical Expenditures to Income Ratio: Model vs. Data 3.4.1 Policy Exercise: Eects of dierent co-insurance rates in the presence of bad consumption I start by experimenting with dierent co-payment rates for the workers, keeping the co-pay for the retired at 0%. For any co-pay, government budget is cleared by adjusting the labor income tax rate. Hence, since the health system is nanced through taxes, change in income tax can be thought of as a change in insurance premium. Table 3.5 shows the results of these policy experiments. Notice that the changes in the aggregate medical expenditures to output ratio and ratio of smokers in the economy are not monotonically increasing or decreasing when co-pay increases. 88 This is mainly due to the two opposing forces of the mechanism: substitution and income eects. Increasing the co-pay makes smoking more expensive since people have to bear a higher cost for that risky behavior but at the same time, higher co-pay translates into lower labor income tax rate (or premium) which leaves individuals with higher disposable income. This is why the ratio of smokers goes down rst, but goes back up for higher co-pays. Table 3.5: Policy exercise with different co-insurance rates (! w ) Data 0% 10% a 20% 30% 40% 50% 60% 70% 80% 90% 100% M/Y (%) 15.6 15.55 15.33 15.14 15.21 15.13 15.15 15.26 15.24 15.22 15.29 15.26 % of smokers 21.1 21.79 20.51 18.68 19.9 18.56 18.37 20.56 20.65 20.41 22.14 22.11 Premium(%) 26.8 40.83 40.16 39.55 39.12 38.51 37.91 37.39 36.83 36.14 35.6 34.94 a Benchmark We can see that between two economies with 0% and 100% co-pays, the dierence in premium is about 6% of income. The reduction in taxes (premiums) is consistent with the ratio of private insurance premiums paid as a percentage of GDP, which was about 5.7% 1 in 2010. Next I look at the welfare implications of these policies in terms of consump- tion compensation required to make individuals indierent between two dierent economies. Details about how these values are calculated are already discussed in Chapter 2. Table 3.6 shows these values compared to the benchmark economy with 10% co-pay. 1 Value is taken from National Health Expenditure Projections 2011-2021 report of Center for Medicare & Medicaid Services (CMS). The report can be accessed at: http: //www.cms.gov/Research-Statistics-Data-and-Systems/Statistics-Trends-and-Reports/ NationalHealthExpendData/Downloads/Proj2011PDF.pdf 89 Table 3.6: Welfare change with different co-insurance rates (! w ) Health Status 0% 10% a 20% 30% 40% 50% 60% 70% 80% 90% 100% Poor -0.68 0.00 -4.03 -6.22 -4.94 -7.25 -9.76 -12.38 -12.74 -16.08 -16.26 Fair 0.14 0.00 -0.56 -1.21 -3.16 -3.82 -3.45 -4.47 -5.31 -6.29 -6.83 Good -0.28 0.00 -0.38 -0.49 -1.15 -1.31 -1.41 -2.10 -2.50 -3.26 -3.58 Very Good -0.09 0.00 -0.15 -0.29 -0.45 -0.60 -0.52 -0.74 -1.23 -1.54 -1.68 Excellent -0.11 0.00 0.12 0.20 0.48 0.41 -0.07 -0.34 -0.45 -0.59 -0.70 Total -0.13 0.00 -0.13 -0.21 -0.37 -0.52 -0.70 -1.08 -1.42 -1.80 -1.99 a Benchmark Positive numbers in table 3.6 means higher welfare compared to the benchmark and negative numbers mean lower welfare in terms of consumption equivalent terms. Results show that although since their health is less expensive to maintain, individuals with excellent health status prefer to live in an economy with 40% co-pay, the optimal co-payment rate for the whole economy is 10%. 3.4.2 Model without bad consumption 3.4.2.1 Calibration Next, I recalibrate the model setting = 0, i.e. individuals do not get utility from bad consumption, hence they do not smoke, and repeat the policy experiments in this framework. Table 3.7 shows the recalibrated parameters of the model. Table 3.7: Calibrated Parameters Parameter Explanation Value b Value of being alive 2.5 ; Quality of life parameters 0.2,1.2 ; Parameters in survival probability 6,1.2 Weight on c b 0 B;; Parameters on health production function 0.232,0.107,1.5 90 Table 3.8 shows the t of the model in terms of medical expenditures to output ratio. The model closely ts the relevant moment from data. Figure 3.2 shows the t of the model in terms of life cycle prole of medical expenditures to income ratio. Table 3.8: Model Fit Target Data Model Medical expenditure-output ratio 15.6% 15.65% 2 0 -2 4 3 0 -3 4 4 0 -4 4 5 0 -5 4 6 0 -6 4 7 0 -7 4 8 0 -8 4 0 .0 5 0 .1 0 0 .1 5 0 .2 0 0 .2 5 0 .3 0 0 .3 5 0 .4 0 0 .4 5 M /Y (% ) A g e D a ta B e n c h m a rk Figure 3.2: Medical Expenditures to Income Ratio: Model vs. Data 91 3.4.2.2 Policy Exercise: Eects of dierent co-insurance without bad con- sumption Table 3.9 displays the results with dierent co-pays. Without bad consumption, medical expenditures to GDP ratio declines monotonically with increased co-pay but the total decrease in that ratio is less than 1% when co-pay is 100%, i.e. everything is out-of-pocket. And the reduction in income tax (premium) is slight less than the case with bad consumption since now the medical expenditures that need to be nances are lower. Table 3.9: Policy exercise with different co-insurance rates (without bad consumption) (! w ) Data 0% 10% a 20% 30% 40% 50% 60% 70% 80% 90% 100% M/Y 15.6 15.7 15.65 15.59 15.52 15.46 15.45 15.39 15.32 15.25 15.12 15.05 Premium(%) 26.8 41.6 40.95 40.5 39.84 39.25 38.67 38.05 37.37 36.81 36.09 35.47 a Benchmark Next I conduct welfare analysis to nd the optimal policy in the absence of bad consumption. Table 3.10 shows the results of the welfare analysis. It seems that 0% co-payment rate is the optimal policy under this scenario. This result implies that with decreased moral hazard due to the absence of bad consumption, a more generous health insurance policy is optimal. However, when moral hazard due to risky health behaviors exists, some level of risk sharing gets us to the optimal. 92 Table 3.10: Welfare change with different co-insurance rates (without bad consumption) (! w ) Health Status 0% 10% a 20% 30% 40% 50% 60% 70% 80% 90% 100% Poor -0.94 0.00 -5.92 -5.16 -4.56 -6.38 -8.12 -11.57 -12.06 -14.57 -17.88 Fair 0.14 0.00 -0.40 -1.82 -1.66 -2.86 -3.64 -4.74 -5.07 -6.39 -6.19 Good 0.40 0.00 -0.25 -0.60 -0.90 -1.54 -1.96 -2.10 -2.71 -2.90 -3.38 Very Good 0.14 0.00 -0.20 -0.39 -0.44 -0.94 -1.17 -1.18 -1.54 -1.87 -2.14 Excellent 0.33 0.00 -0.17 0.06 -0.17 -0.59 -0.73 -0.38 -0.89 -0.86 -1.33 Total 0.27 0.00 -0.23 -0.34 -0.51 -1.05 -1.31 -1.27 -1.75 -1.95 -2.35 a Benchmark 3.5 Conclusion In this chapter, I look for the optimal health insurance policy in the presence and absence of risky health behaviors. Risky health behaviors come with the moral hazard problem since the health system is nanced by everyone, and those who do not involve in risky health behaviors end up paying for the actions of those who involve in risky health behaviors. It is expected from economic theory that some level of risk sharing would be optimal for the case where moral hazard exists. Results show that while no risk sharing is needed when risky health behaviors are not assumed to aect medical expenditures and health status, 10% co-pay is found to be optimal when I let risky health behaviors aect health and medical expenditures. To sum up, risky health behaviors bring in moral hazard problem which can be alleviated by a higher cost sharing mechanism. Since the numerical exercise in this chapter is focused on only smoking, 10% may be thought as a lower bound for the level of risk sharing. The co-pay would probably be much higher when we include other types of risky health behaviors such as poor diet, which is left to future studies. 93 Bibliography Blomqvist, Ake and Henrik Horn, \Public health insurance and optimal income taxation," Journal of Public Economics, 1984, 24, 353{371. Chernew, Michael E., William E. Encinosa, and Richard A. Hirth, \Op- timal health insurance: the case of observable, severe illness," Journal of Health Economics, 2000, 19, 585{609. Eggleston, Karen, \Risk Selection and Optimal Health Insurance-Provider Pay- ment Systems," Journal of Risk and Insurance, 2000, 67 (2), 173{196. Imrohoroglu, Ayse, Selahattin Imrohoroglu, and Douglas H. Joines, \A life cycle analysis of social security," Economic Theory, 1995, 6, 83{114. Manning, Willard G. and M. Susan Marquis, \Health insurance: the tradeo between risk pooling and moral hazard," Journal of Health Economics, 1996, 15, 609{639. Pauly, Mark V., \Optimal health insurance," Geneva Papers on Risk and Insur- ance, 2000, 25 (1), 116{127. Xu, Ke, David B. Evans, Kei Kawabata, Riadh Zeramdini, Jan Klavus, and Christopher J. L. Murray, \Household catastrophic health expenditure: a multicountry analysis," Lancet, 2003, 362, 111{117. 94 Chapter 4 Conclusion This dissertation examines dierent aspects of labor and health in a macro setting making use of quantitative methods. Chapter 1 builds a model of consumption and leisure choice to investigate the implications of dierent wage-eciency proles on life cycle hours allocation of individuals. The hump shaped wage-eciency prole generated by Hansen (1993) is extensively used in the literature in similar models. I compare and contrast the implications of using a non-decreasing wage-eciency prole, which was rst documented by Rupert and Zanella (2010). The proles I generate from PSID using two dierent methods are consistent with what Rupert and Zanella (2010) nds. Results of the model simulations show that although the hours- worked prole becomes less steep by the use of the non-decreasing wage-eciency prole, the decline in hours-worked after prime ages is mainly driven by the income eect, and this result is robust to dierent utility specications as well as dierent elasticities of substitution between consumption and labor. In Chapter 2, I build an overlapping generations model with endogenous health capital accumulation and risky health behaviors to investigate the eects of dierent health insurance policies and excise taxation on risky health behaviors. In the frame- work used in this chapter, all health expenditures stem from controllable behaviors. Results imply that increasing the co-payment ratio leads to a decline in risky health behaviors, smoking in this case, and also a decline in medical expenditures to GDP ratio up to a certain level. Likewise, higher excise taxation leads to lower use of 95 tobacco and lower medical expenditures to GDP ratio and the outcomes of the model are consistent with the across-state variation in excise taxes and smoking prevalence in the U.S. Insurance raises the problem of moral hazard. The extent to which individuals care about the outcomes of their risky health behaviors partly depends on the gen- erosity of health insurance system. In Chapter 3, I examine the optimality of health insurance policies by introducing a health shock into the model used in Chapter 2. This allows me to address to the catastrophic health shocks that may arise regard- less of individuals' behaviors. 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Abstract (if available)

Abstract This dissertation consists of three essays on quantitative macroeconomics that study labor and health. The first essay uses data from Panel Study of Income Dynamics (PSID) to document a non-decreasing wage profile as reported by cite{rupert} and compares the implications of this profile on the life cycle hours allocation of households to the widely used hump-shaped wage profile. Results suggest that even using the non-decreasing wage-efficiency profile, the income effect dominates the substitution effect coming from higher wages, hence after making a peak at prime ages, hours worked start declining far before reaching retirement. These results are robust to different intertemporal elasticities of substitution for labor and different utility functions. ❧ The second essay makes use of the wage-efficiency profile generated in the first essay and develops an overlapping generations model that incorporates bad behaviors (such as smoking and unhealthy eating habits that lead to obesity) to investigate the equilibrium effects of different cost sharing mechanisms and excise taxation on bad behaviors and medical expenditures. I show that higher cost sharing may induce individuals to refrain from bad behaviors. For example, if coinsurance rate is increased by 10 percentage points, smoking prevalence goes down by about 2 percentage points and medical expenditures to GDP ratio slightly declines. Welfare analysis of different policies shows that although higher cost sharing increases the overall welfare in the economy, unhealthy individuals are either worse off or have much less welfare gains compared to healthy individuals. The quantitative implications of the model are consistent with the variation in smoking prevalence and excise taxes across tobacco and non-tobacco states. ❧ The third essay builds upon the second essay and examines the insurer aspect of the health policy by introducing an age-dependent health shock. Inclusion of this aspect addresses two functions of health insurance: insurance against controllable health outcomes which stem from risky health behaviors and uncontrollable outcomes that randomly hit individuals. By comparing two settings with and without risky health behaviors, I look for the optimal co-pay mechanism that maximizes welfare and find that in the presence of risky health behaviors, 10% co-pay is optimal while when risky health behaviors are absent, 0% co-pay is optimal. This result is consistent with the notion that some risk sharing mechanism is needed when moral hazard exists because of risky health behaviors.

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Creator Abbasoğlu, Osman Furkan (author)

Core Title Essays on macroeconomics of health and labor

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 07/23/2013

Defense Date 05/07/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag efficiency profile,health,health insurance,Labor,OAI-PMH Harvest,quantitative macroeconomics,risky health behaviors

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Imrohoroglu, Ayse (committee chair), Vandenbroucke, Guillaume (committee member), Zissimopoulos, Julie (committee member)

Creator Email abbasogl@usc.edu,ofurkan@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-297823

Unique identifier UC11294650

Identifier etd-AbbasogluO-1825.pdf (filename),usctheses-c3-297823 (legacy record id)

Legacy Identifier etd-AbbasogluO-1825.pdf

Dmrecord 297823

Document Type Dissertation

Format application/pdf (imt)

Rights Abbasoğlu, Osman Furkan; Abbasoglu, Osman Furkan

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA