## Frank A. Sloan and Hirschel Kasper

Print publication date: 2008

Print ISBN-13: 9780262195775

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262195775.001.0001

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# Health Capital: Theory and Empirical Evidence

Chapter:
(p.51) 3 Health Capital: Theory and Empirical Evidence
Source:
Incentives and Choice in Health Care
Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262195775.003.0003

# Abstract and Keywords

This chapter describes the Grossman health capital model and its theoretical extensions, including its incorporation of the effects of uncertainty and application to the study of health capital and the role of incentives. It considers the various empirical applications of the model, including empirical studies of demand for medical care and other inputs affecting health, such as diet, exercise, and tobacco and drug use. It also outlines structural models of household decision making about health and health care and considers the use of medical care and absences from work during episodes of acute illness. Furthermore, the chapter discusses some applications of the structural approach to modeling: the use of mental health services during childhood; choices of prescription drugs when the effects of the drug can only be learned by trying it; and an investigation of annual smoking, exercise, alcohol consumption, and medical care use decisions over a lifetime. Finally, it highlights many of the difficulties encountered in empirical research on health behavior.

This chapter focuses on a particular commodity that we as individuals are likely to produce and/or consume often. It is a sustainable product that frequently requires our deliberate attention and action, and one that influences many of our daily decisions. Economists call it human capital. Like the physical capital of a firm, human capital is essentially a stock of an asset that an individual owns, and to which that person can allocate time and resources as inputs for its continued development. The capital good also provides a flow of services for the stockholder. Economists have concerned themselves with two types of human capital: knowledge capital and health capital.

# What Is Health Capital?

Health capital, or health stock, is often measured by general levels of health or functioning, such as health status or the degree of difficulties with activities of daily living. Health flows describe the illness or morbidity conditions that an individual experiences over time. More specifically, an individual in excellent health (stock) may still get the flu or break leg (flow). In this chapter, I explore the economist’s understanding of health capital, its formation, maintenance, and deterioration. More to the point, I examine the economist’s understanding of individual health behavior since the evolution of health over one’s life cycle, while partially explained by random events beyond one’s control, is greatly influenced by a person’s own choices regarding medical care consumption, employment, education, and lifestyle. This understanding of individual decision making with regard to health reveals the role of incentives (e.g., the interaction of governmental or market policies with individual preferences, constraints, and beliefs) that affect behavior throughout one’s life.

(p.52) It is reasonable to assume that many policy recommendations are supported by statistical evidence. In fact, establishing evidence of a correlation between two variables of interest in health behavior is a topic of research among many health economists, health policy researchers, and physicians. Some well-known examples include the observed positive correlation between health and income or education.1 Statistical evidence can be found at the macroeconomic comparing aggregate measures of national income (e.g., the gross domestic product) and the health of a population (e.g., mortality or morbidity rates), and at the microeconomic with years of schooling and individual measures of health (e.g., self-reported health levels). Many other examples abound: a positive correlation between health insurance and medical care consumption, a negative correlation between exercise and heart disease, and debatable findings for the relationship between alcohol consumption and mortality. But most economists consider these observed statistical associations to be the spark that initiates further exploration into the individual behavior that generates such empirical links. That is, an economist seeks to understand the mechanisms through which such associations arise. It is only with this deeper understanding that policies—meant to provide, alter, or enhance incentives that affect individual alternatives and decision-making behavior—can be appropriately prescribed.

Modeling is a tool to help researchers understand the relationships between variables of interest. Comprehension of the causal relationships in physics may be facilitated with a model of the force at work. Computer models may be used to study and predict coastline erosion during hurricanes. Unfortunately for economists, there are no proven theories like Sir Isaac Newton’s laws of motion that explain human decision-making behavior. Nonetheless, we rely on models that attempt to capture or mimic how people make decisions using the economic concepts of preferences, constraints, technology, expectations, and uncertainty.

I begin the chapter by discussing the fundamentals of the economist’s model of health capital. The presentation is purposefully nontechnical, but conveys the rudiments of the theory so as to discuss the inferences about human behavior that follow from the model. Hypotheses derived from the model can be empirically tested in order to validate the theory. Extensions to the basic model are also touched on briefly. I continue the chapter by summarizing empirical research based on this theory of health capital. The empirical applications have been plentiful, and the (p.53) model has been applied in several dimensions of health behavior and medical care demand. Yet there have been few attempts to estimate the formal model itself and to use it to evaluate the role of incentives. I describe the policy alternatives examined by economists who solve and estimate models of health behavior that specify the preferences, constraints, and expectations of optimizing individuals. Finally, I highlight many of the difficulties encountered in the empirical investigation of health behavior, and address the importance of an accurate and complete understanding of health behavior for policy evaluation and implementation.

# Modeling the Demand for Health: The Grossman Model

The dissertation research of a young economics PhD student in the late 1960s has become the foundation on which most economists base their understanding of the individual’s demand for health and medical care. Building on the premise of household production theory that was introduced less than a decade earlier, Michael Grossman developed a theoretical model to explain the health behavior he observed among individuals.2 At the root of his model is the assumption that people do not necessarily enjoy consuming health care but rather receive happiness, or utility, from the services that health provides. An individual’s health stock at a particular age determines the flow of health services or the amount of healthy time that person receives.

This stock is not fully depleted each period. Instead, like a capital good such as a refrigerator or an automobile, it stays around, yields services, and depreciates each period. Different forms of health care, both medical care as well as lifestyle choices such as exercise (and smoking), are inputs that maintain or improve (or deteriorate) one’s stock of health.3 As both a consumption and an investment good, optimal health capital accumulation requires the decision making of its owner—the individual—who is also the consumer and the producer.

## Utility Maximization

In most economic models of individual behavior, a person seeks to maximize utility or happiness, which is characterized by a utility function, U(·). This function expresses the utility maximizer’s preferences about things he values. In Grossman’s model of health behavior, the (p.54) person cares about the amount of healthy time (ht) available to him. Healthy days are the benefits or services of that person’s health capital or stock of health (Ht). The individual also cares about other “nonhealth” commodities (zt) that one produces on one’s own by combining market goods and time inputs, much as a factory worker produces output in a factory. Examples of one’s output are a home-cooked meal, which requires the inputs of grocery items, a stove, and cooking time, or the entertainment activity of reading a book, which requires the inputs of a book, a chair, and time.4 Yet, individual utility U(ht,zt), which can be evaluated at each different combination of its arguments over one’s lifetime, is constrained by one’s available time for health production (e.g., visiting a physician), home production (e.g., preparing a meal), and income production (e.g., working for wages) as well as by one’s resulting income (Yt) used to purchase market goods (e.g., medical care, groceries, or a book). Economists label these as the time constraint and the budget constraint.

## Production Technologies and the Time and Budget Constraints

The person’s health stock determines the amount of time lost due to illness, and hence dictates the total amount of time available for allocation between health production, home production, and work in the marketplace.5 Each of the production activities is governed by the production technology that describes the conversion of inputs into outputs.

1. 1. Healthy time production. The health stock determines the flow of health services (i.e., healthy time) that provide utility each period:

$Display mathematics$

2. 2. Health stock production. Deterioration (δt) of the current health stock and health investment, using the inputs of medical care (mt) and time spent in health-producing activities $(TtH)$, determine future health:

$Display mathematics$

3. 3. Home good production. Production of the home good, like health investment, requires both market inputs (xt) and nonmarket inputs (e.g., time) $(TtZ)$:

$Display mathematics$

4. (p.55) 4. Income production. Income is a function of one’s wage (wt) and time spent working $(TtW)$:

$Display mathematics$

Individuals are endowed with a fixed amount of time, Ω, each period (e.g., 365 days per year). They lose time, $TtL$, if they are ill; $TtL=Ω−ht$. Nonsick time is allocated between health-, home-, and incomeproducing activities. The time constraint is

$Display mathematics$
(3.1)

A person’s initial assets (A0) and labor income dictate which combinations of the market inputs (mt and xt) are feasible at prices pmt and pxt. All future dollars are discounted using interest rate r to reflect their present values.6 The (lifetime) budget constraint is

$Display mathematics$
(3.2)

An individual’s choices regarding work time, time spent in healthand home- producing activities, and the purchase of medical care and other market inputs determine the end of life (T). Death occurs when the stock of health falls below a life-sustaining level. Maximizing utility with respect to the time constraint, budget constraint, and production technologies yields a set of optimality conditions that are satisfied by the optimal combination of the choice variables. These optimality conditions provide testable relationships between variables of interest.

# Applications and Implications of the Grossman Model

## A Real-Life Example

Type 2 diabetes is an increasingly common disease characterized by a body that is unable to produce sufficient levels of insulin or one that produces insulin that cannot adequately regulate blood sugars. High levels of glucose in the blood damages body tissues and organs. Diabetes is the leading cause of adult blindness, kidney failure, and amputations. Diabetics have a higher risk for heart disease and stroke than nondiabetics. Currently, twenty million people in the United States have diabetes and over forty million people are prediabetic.

The clinical view with regard to diabetes treatment is to follow specific practice guidelines. Diabetes care guidelines recommend frequent (p.56) measurements of blood glucose levels, periodic feet and eye examinations, and regular physician checkups. Oral medications are often recommended to control blood sugar levels, and many diabetic patients require medications to control cholesterol and blood pressure levels. Exactly which drugs should be taken, how often patients should be examined, and what lifestyle changes should be made have been clearly spelled out by physicians. The guidelines do not allow for or specify trade-offs among these recommendations. In real life, however, people make trade-offs. One person with diabetes may exercise regularly, but not have eye exams at regular intervals. Another may attend all checkups, but continue to eat an improper diet and remain sedentary.

A policymaker may ask what the role of health insurance is in this scenario. That is, how would the behavior of an uninsured, employed person with diabetes change if health insurance were made available the person unconditionally (i.e., insurance coverage that was not dependent on employment or income and assets)? If the out-of-pocket price of medical care were to fall, then this person would consume more medical care. Based on economic theory, this response is accurate, but it is not complete.

## The Effect of a Reduced Price of Medical Care on Health Behaviors

To fully answer this question, I first set aside the dynamic effects of improved future health that may be associated with an increased consumption of medical care when the price falls. That is, medical care may improve, maintain, or at least prevent a further decline in health (i.e., medical care has a positive marginal impact on health). The improvement in health may lead to different medical and nonmedical input behaviors over time. First consider how behavior today might change, if the price of medical care falls considering only the effects of anticipated future health changes on current behavior.

As a person with diabetes, this individual may be fully aware of other behaviors, such as exercise and proper diet in addition to physician visits, that are important determinants of health. Depending on the relative effectiveness of exercising versus medical care in producing health as well as the happiness one receives from the consumption of other (nonmedical) goods, this individual may not alter medical care consumption behavior at all. In fact, the reduced out-of-pocket cost of medical care may allow this person to work less and exercise more (p.57) while still enjoying the same level of medical care consumption. Alternatively, if an individual with diabetes was substituting exercise for expensive medical care to begin with, the person may find that it has become worthwhile to work rather than to exercise, earning the income to purchase the now-cheaper medical care input.

## The Effect of Physician Advice on Health Behaviors

Next, consider the effect of physician advice (facilitated through a doctor’s visit due to increased insurance coverage) on health behaviors. Suppose the person diagnosed with diabetes was unaware of the relevance of those nonmedical treatments, which may be complements to or substitutes for medical care itself. The individual’s health knowledge may improve following a visit to a physician. The person with diabetes may be advised to increase the amount of exercise time. A change in exercise behavior, however, depends on one’s relative enjoyment of exercising today versus leisure, the opportunity cost of one’s time (i.e., one could be working and earning a wage with that time), and the relative effectiveness of an additional hour of exercising compared with the medical care one could buy with one more hour of wages. Similarly, one could improve one’s diet by purchasing appropriate foods for diabetics. Yet these foods may be more expensive than one’s previous dietary habits. But if the marginal effectiveness of a better diet in maintaining health is large enough, it might outweigh the effect of reduced consumption of other goods.

## The Effect of Improved Future Health on Health Behaviors

Now consider the effect of improved future health on health behaviors. Perhaps immediately or over time, changes in (health) input behavior (e.g., a greater consumption of inputs or a more efficient allocation of inputs) may cause health to improve or, at a minimum, reduce the probability of health complications. Improvements in health may magnify the happiness the individual receives from any of the goods that are consumed (i.e., the marginal utility of exercise, consumption, or leisure may depend on health). The improved health may make one more productive at work or result in less absenteeism (e.g., fewer lost days), leading to increased income. The potential future consumption and leisure changes induced by health gains may influence current behavior today because the forward-looking individual cares not just about the present but also about happiness in the future. The weight (p.58) an individual places on future happiness relative to current happiness (i.e., the person’s discount rate) reflects how much the person values the future.

## The Effect of Improved Health Knowledge on Health Behaviors

Additionally, this framework permits one to consider how improvements in health knowledge influence health behaviors. How informed is the individual prior to having health insurance (and increasing the number of his physician visits)? How knowledgeable is he of how his future health will evolve? Suppose he knows the technology of health production accurately; that is, suppose he knows the average marginal impact of different inputs although he may not know his particular health response exactly. In this case, expectations of one’s length of life will change since, if medical care is productive, he expects his health stock to improve given changes in his current behavior induced by the acquisition of insurance. But suppose he did not know the technology and thus inaccurately predicted his future health. Information acquired through a medical care visit about the health impacts of his choices may allow him to make more accurate forecasts of his future health. A person may not have known, for example, that a change in diet was so important. This more accurate understanding of the probabilities of future adverse health events may in and of itself change behavior today.7

# Policy Analysis

Grossman’s model can be used as a tool to answer a policymaker’s questions. How will people respond to changes in the health care market? How do we evaluate different public policy alternatives? It would be important to know if the increased medical care use induced by reducing the out-of-pocket cost of care leads to significant health improvement. It would be useful to know if exercise produces better results than medical treatment. Is the health knowledge that a medical care consumer gains from his provider more effective in changing behavior than a reduction in prices that induces more consumption of medical care? If so, is there a cheaper way to provide this information than extending health insurance benefits?

Next I describe how Grossman’s model can help us address these questions.

# (p.59) Testable Implications of Grossman’s Model

The Grossman model is much more elegant and comprehensive in its full mathematical presentation. Yet this simple description reveals that there are two fundamental concepts addressed by the model. First, healthy time, determined by one’s health capital, provides satisfaction; to maximize one’s satisfaction an individual allocates time to work, health, and home activities, and allocates income to medical care and other market inputs. Second, health capital is produced by an individual with market inputs (e.g., medical care) and nonmarket inputs (e.g., the person’s time). These two aspects of the model—demand behaviors and health production—yield many testable predictions about relationships among variables in the model. Here, I summarize some of the relationships that can be addressed using the Grossman framework. Later, I will discuss attempts to empirically test or provide evidence of these relationships.

The theoretical framework allows economists to understand relationships among a multitude of behaviors and individual or market characteristics. The first aspect mentioned above gives rise to three demand behaviors: individuals demand health; since medical care is an input to the production of health, the demand for medical care is a derived demand for this factor of production; and individuals value healthy time, but require income to purchase market goods, and hence must optimally allocate their healthy time to income production (i.e., work), health production, and home production. The model allows us to understand how individuals satisfy these needs.

A demand curve that is downward sloping, or negatively related to price, is a basic economic concept. The solution of Grossman’s optimization model yields a demand for health that is negatively related to its price. But health is not a good that can be traded in the market and thus does not have a market price. Theoretically, its price, or “shadow” price, depends on the price of medical care (which is used to augment the health stock) as well as many other things that directly or indirectly affect the cost of holding health capital, such as its depreciation rate and the opportunity cost.

Figures 3.1 and 3.2 reproduce this aspect of the mathematical model graphically. The marginal returns of health capital are represented by (p.60)

Figure 3.1 Optimal Health Capital and Changes in Age

Figure 3.2 Optimal Health Capital and Changes in Education or Wages

(p.61) a marginal efficiency of capital schedule (MEC). The shape and position of the curve reflects the marginal product of health capital in healthy time production, the marginal utility of health capital, and the marginal value of time (e.g., the wage rate), all expressed in monetary units. Changes in individual characteristics, or government or firm policies that alter one of these aspects of the individual’s optimization problem, shift the MEC curve. The cost of capital curve (COC) represents the supply price of capital or the cost of holding an additional unit of capital. Its position is determined by the depreciation rate of the health stock, the opportunity cost of holding health capital (e.g., the interest rate), and the rate of change in the marginal cost of investment. Changes in individual characteristics or policies that affect these cost components shift the COC curve.

How does the shadow price of health change as people age? An automobile’s parts typically perform worse with age. Similarly, our body’s ability to function declines as we grow older; it depreciates. If the shadow price of health increases with age (an assumption consistent with an increasing depreciation rate), the solution to the model suggests that people hold less health capital (i.e., have a lower health stock) as they age. The COC curve shifts upward with increases in the depreciation rate (fig. 3.1). Put differently, the model predicts that people will demand more health capital when it is less costly.

How is health affected by education? Grossman assumes that more educated individuals are more efficient producers of health (i.e., can produce the same amount of health with fewer inputs or can produce more health with the same inputs) than those with less education. Because a given amount of investment can be generated at less cost for a more educated person, that individual experiences a higher rate of return to a given stock of health. The MEC curve will shift outward with increases in education (fig. 3.2). This relationship suggests that more educated people have a higher health stock than less educated people.

Differences in wage rates also lead to differences in the demand for health capital. But differences in wage rates operate through different channels than education, which works through the production process in Grossman’s model. Higher wages increase the value of healthy time. Hence, at a higher wage, the individual wants to prevent more lost time on account of poor health. At the same time, time spent in healthproducing activities (e.g., visiting a physician) is more expensive; the value of one’s time is higher. One is therefore more likely to substitute (p.62) market goods for time spent in health-producing activities. Still, one must recall that healthy time is also used to produce the other home good. Depending on preferences for this good relative to healthy time, and depending on the marginal effectiveness of time relative to market goods in both health and home production, individuals may reduce or increase their demand for health as wages rise.

The relationships between these variables (age, education, and wages) and the demand for medical care do not necessarily parallel that of the demand for health. Under certain conditions regarding the elasticity of demand, an increase in the cost of holding health will lead to lower levels of health demanded, but higher levels of medical care demanded. For example, consider the medical expenditures of older individuals compared to that of younger ones. Theory suggests that the higher health depreciation rate of your grandparent would lead him to have a lower health stock than your parent. (A lower wage, however, may suggest the opposite.) But your grandparent is also likely to purchase larger amounts of medical care (i.e., health investment). It takes more medical care (and time in health-producing activities) to maintain a health stock that is depreciating faster. At some accelerated rate of health depreciation, though, Grossman’s model predicts that continued health investment is suboptimal and income should be used to purchase other consumption inputs that provide happiness.

The second area of Grossman’s model that leads to testable relationships is his conception of health production. He depicts health as being determined by market and nonmarket inputs and depreciation. While his model simplifies the market input to a single scalar (such as medical care) and the nonmarket input to individual time spent in health-producing activities (such as the time it takes to travel to, wait for, and see a physician), he admits that the health inputs could be expanded. Formal medical care could be categorized into preventive, diagnostic, and curative. Each of these inputs may have different impacts on future health levels. Similarly, health investment extends beyond formal medical care. Exercise and proper nutrition are considered beneficial lifestyle practices that maintain or improve health. Housing and sanitation have been shown to improve health levels more than medical care in some developing countries. Analogously, some inputs, such as (p.63) smoking, may be detrimental to health. Activities like skydiving or motorcycle riding without a helmet can also increase the risk of a sudden decrease in health stock.8 The marginal impacts of these inputs influence the evolution of one’s health stock. They also affect an individual’s demand for these inputs. With multiple inputs, it may not be simply the level of each input, but the combination of inputs, that matters.

Apart from input decisions that maintain or repair our health stock, this stock deteriorates with age. But is the rate of depreciation dictated by heredity, health behaviors, or environmental factors? Does health decline at the same rate for different genders and people of different races or ethnicities? Do health behaviors simply replenish the health stock or might they also reduce the rate of health stock decline? In addition to the influence of different variables of interest on demand behaviors, health production as a technological and biological process suggests many testable relationships.

As mentioned earlier, Grossman also assumes that education increases the efficiency with which we convert input behaviors into health. Yet he admits that the relationship between education and health is not fully developed in his theoretical model. A decade after his seminal work, he issued a plea for more research that addresses the joint determination of education and health, since they are likely influenced by the same observables and unobservables.9 But twenty years after his suggestion, an estimable model of educational attainment and health capital formulation has not materialized.10 I will return to this issue in the discussion of empirical work based on the Grossman framework.

Although Grossman did not fully develop the relationship between health and work in his basic model, he suggested its obvious connectedness. Labor economists are increasingly finding that health plays a key role in employment participation, earnings, performance, absenteeism, job mobility, and retirement.11 Grossman’s model has implications for employment and hours of work behavior. The onset of poor health clearly results in changes in time allocation as individuals experience more ill (i.e., lost) time. As the health stock falls, the amount of lost time increases, thereby reducing the amount of available time for health, home, and income production. Depending on the (p.64) relative happiness one receives from healthy time and consumption, and the marginal effectiveness of time spent producing the consumption good and investing in health, an individual whose health declines may work (for wages) more or less than he worked prior to his health decline.

The model could easily be extended to further elucidate the relationship between health and employment. One could allow preferences for income (or the marginal utility of consumption) to vary by health levels. One could also allow health levels to affect productivity or earnings. Health could influence one’s ability to perform job requirements. It could affect both presenteeism (i.e., the quality of work on the job) as well as absenteeism.

While Grossman’s model contains prices for medical care inputs and can be used to predict how changes in these prices influence behavior, it does not explicitly introduce health insurance as a mechanism for reducing the out-of-pocket price that a consumer faces. In the United States, nearly two-thirds of individuals with health insurance have it through employment. Herein lies another avenue through which health and employment behavior are connected.

# Extensions of Grossman’s Model

The sophistication of Grossman’s model of individual demand for health is evidenced in its widespread use among health economists. In fact, as of late 2006, the Web of Science recorded that nearly four hundred articles had cited Grossman’s seminal 1972 paper. Over 40 percent of those citations were from scholarly articles published between 2001 and 2006. Despite being a model that stands the test of time, there have been several extensions of Grossman’s original framework.

## Uncertainty

The most obvious aspect of health demand and formation that is missing from Grossman’s original model is that of uncertainty. M. L. Cropper brings realism to the model by introducing different illness states that occur randomly.12 She also allows the satisfaction one receives from consumption to depend on the illness state. As a source of illness, Cropper considers the case where employment may influence health. Some jobs that offer higher wages are associated with (p.65) health hazards such as industrial pollutants or safety concerns. This aspect introduces an additional trade-off between income and health. Valentino Dardanoni and Adan Wagstaff further extend the introduction of uncertainty to the Grossman framework and the Cropper extension by allowing the effectiveness of medical care to be random.13 The addition of uncertainty to the Grossman model permits economists to evaluate the role of risk aversion and expectations on individual behavior.

## Role of Education

Jaana-Marja Muurinen also seeks to generalize Grossman’s model and focuses on the role of education.14 She considers education to be a human capital stock, much like health. Her analysis examines not only education’s role in providing production efficiency but also its allocative effects. That is, education plays a role in the selection of different types of health inputs as well as the productivity of different inputs. Additionally, she allows education to directly influence the rate of depreciation of the health stock. From the outset, Grossman was deeply curious about the relationship between education and health. He proposed one causal avenue through which a positive correlation between the two would occur. Muurinen introduced two different avenues. Other economists have suggested that health knowledge, as opposed to general education, is a key determinant of the demand for health.15 Still others suggest that the extent to which an individual is forwardlooking, or the rate at which one discounts future happiness, varies across people and can determine optimal health stock.16 Another argument claims that more educated individuals have higher-paying jobs that allow them to afford more medical care.17 Alternatively, unobserved individual characteristics may drive a person to demand more health and more education (or less health and less education). It is this avenue of unobserved heterogeneity that requires the modeling of education and health accumulation jointly.

## Mathematical Refinements

Some refinements of the mathematical assumptions of the health capital model make it more realistic. Nevertheless, as Grossman points out, many of those extensions obscure the simplicity of the model, making (p.66) derivations and hence understanding more difficult.18 For example, Isaac Ehrlich and Hiroyuki Chuma contend that the marginal cost of investment in health is not constant, as Grossman assumes.19 Their technical extension affects the determination of the optimal investment in health. Among other technical improvements, Walter Ried suggests that the determination of an optimal length of life must be arrived at through an iterative process of resolution if the health stock level has not fallen below a life-sustaining level at the end of the optimization period.20 Grossman discusses the merits of both considerations in detail.21

# Child and Family Health

Many researchers, including Grossman himself, recognize that his original model applies to individual demand and production only, and adult health only. One cannot understand the health behavior of children within the original framework, since parents, who make many of the input decisions for their children, may have preferences, discount rates, or incorrect expectations that may not lead to optimal health input decisions for the child. For example, a single working parent may not have the time (or money or education) to acquire preventive care for her children. It is also interesting to understand the family dynamics of medical care consumption and the distribution of family resources to all household members. Of further interest is the effect of family members’ health (and their medical care consumption) on the health of each other. Although her model assumes complete certainty, Lena Jacobson analyzes health from a family perspective.22

# Role of the Physician

Other researchers assert that the individual is not the decision maker with regard to the use of medical care but rather the physician is.23 Peter Zweifel and Friedrich Breyer maintain that the individual may initiate treatment, but the provider determines the amount and type.24 They also suggest that much of the basis of Grossman’s model is contradicted by empirical evidence. Zweifel and Breyer report that health and medical care are negatively rather than positively related, as Grossman’s theory assumes. They propose that medical care is not a productive input to health.

# (p.67) Empirical Applications

With numerous citations of Grossman’s original work in over a hundred different academic journals and numerous extensions to the theory of health capital by other authors, it is quite difficult to effectively summarize research that weds empirical observation and analysis with the theoretical framework in an effort to quantify or test predictions of the economic model. Additionally, in seeking to apply Grossman’s unified framework of health behavior, several authors have extended it to encompass their specific areas of research. Many of these considerations have led to similar applications with different specifications of the health inputs or the included individual characteristics. But the basic model and its implications are unchanged. I sort the empirical work to date into three broad categories that describe what part of the theoretical framework the empirical findings address.

First, much health economic empirical research seeks to understand determinants of the demand for medical and nonmedical care inputs. The theoretical framework yields demand functions relating explanatory variables such as prices, demographic characteristics, and income to health behaviors such as medical care consumption, smoking, and exercise.

Second, the theoretical framework indicates that health is produced with various health inputs. Hence, quantifying the role of various inputs in producing health by estimating a health production function has been the goal of many researchers.

Finally, the economist’s model of health capital seeks to fuse both elements of consumption and production in a dynamic framework with uncertainty. It is possible to specify estimable parameters of the functions in the model (i.e., utility, health production, constraint, and expectation parameters) and solve for the optimal combination of behaviors that are at the individual’s discretion. The solution and estimation of the theoretical model itself would yield the most comprehensive empirical understanding of health behavior, and would allow for the evaluation of alternative policies that influence these individual decisions

## Estimating the Demand for Medical Care and Nonmedical Inputs

The demand function for medical care is derived by solving the individual’s optimization problem (not shown here). Particular (p.68) assumptions about the curvature of the utility function (i.e., which indicates the degree of risk aversion) and the relationship between its arguments yield a linear demand function that depends on prices, income (i.e., wages), and individual characteristics. The estimation of this linear demand function has been a long-researched topic among health economists. They have sought to understand the marginal effects of a whole host of characteristics that influence medical care consumption; these include health insurance, age, education, race, chronic health problems, and the distance to treatment, to name a few.

This interest has led to debate about the appropriate econometric specification since the dependent variable (the quantity of medical care demanded) has a particular distribution regardless of how the variable is defined. That is, medical care expenditures, the number of physician visits, the number of hospital nights, and the length of prescription drug use tend to be characterized by a mass at zero and a remaining distribution that is skewed right (i.e., a long thin tail at higher levels of the outcome). The estimation results are available in this vast literature from an array of different models: ordinary least squares, tobit, two-part, Heckman selection, count data, and generalized linear models as well as conditional density estimation techniques.25

The long list of specific issues that academicians have researched regarding the demand for medical care ranges from the effects of cost-sharing insurance characteristics (published in health economics journals), to nonmonetary factors such as travel time (published in leading economic journals), to particular concerns about the effect of chronic conditions such as asthma and allergy (published in medical journals).26 The next chapter provides a detailed summary of work assessing the effects of health insurance on the demand for medical care.

Nonmedical care inputs also influence health outcomes. Those that have received a great deal of empirical attention include behaviors such as smoking, drinking, drug use, exercise, and nutrition. Grossman’s model even lends itself to understanding the effects of toilet ownership in developing countries.27 Jonathan Gruber as well as Anthony Culyer and Joseph Newhouse summarize many of these findings.28 From a public policy perspective, the role of prices and taxes as a means of curbing behaviors detrimental to health has evoked great interest among economists.

Understanding the role of individual demographic and socioeconomic characteristics on these health behaviors continues to interest health economists and policymakers, but other factors such as (p.69) neighborhood and peer effects have also been analyzed. More recently, economists have been interested in understanding the role of expected utility maximization, uncertainty, and the future in models of individual decision-making behavior. In particular, reformulations of optimization models have been used to examine unhealthy input behaviors with habitual characteristics, such as smoking, drinking, taking drugs, engaging in risky sex, and eating excessively.29

## Estimating Health Production Functions

Unlike the health or medical care demand functions that must be derived from solution to an individual’s health optimization problem, the health production function is an explicit part of the model of health capital determination as it represents the technology an individual encounters. Medical and nonmedical inputs serve as factors of production that improve or maintain a depreciating health stock over time. Theoretically, various individual characteristics may improve the efficiency with which health is produced. Higher levels of education, for example, may increase the marginal effectiveness of medical care inputs and health behaviors. There is an abundance of research that seeks to verify these two basic assumptions posited in Grossman’s work: How effective is medical care in producing health, and are more educated individuals better producers of health?

There is a voluminous literature on the role of health inputs in health production. In fact, complete summaries of this literature do not exist because the scope is so broad.30 A snapshot of the many input and output relationships include measurement of the effects of stressful inputs—such as irregular work schedules, late-night entertainment, or the rapid crossing of several time zones—that produce insomnia; food stamp participation, to proxy for the quality of food consumption, on obesity; airborne particulate matter on bronchial health; and grab bars on elderly (bathing) functionality, each of which cites the Grossman model as the framework behind the empirical investigation.31 One should, however, be cautious in interpreting empirical reports on the marginal effectiveness of particular health inputs. Failure to control for unobserved individual characteristics that might lead different individuals to allocate resources to different inputs will result in inaccurate measurement of the effects of those inputs.

There are several articles summarizing the evidence to date on education’s role in health production.32 Using a number of different (p.70) measures of health and education, and different statistical models, the null hypothesis of no relationship between health and education is strongly refuted in this literature. A central theme in these studies, though, is that we still don’t know exactly why education matters.

To fully understand what mechanisms are at play, researchers should model all the avenues through which educational attainment may affect health capital accumulation. The solution and estimation of a fully parameterized optimization model is necessary to quantify the interrelated effects of risk aversion, discounting, demand, production efficiency, and employment—all of which are affected by education—that leads to the positive correlation between education and health observed empirically.

# Estimating the Theoretical Model of Behavior

The goals of econometric policy evaluation are often to determine the causal relevance of observed variables, consider the impact of policy interventions on the economy, compute their consequences for economic welfare, and forecast the effects of new policies. In the area of health economics and applied microeconomics in general, two approaches to accomplishing these goals stand out.

## The Structural Approach

The structural approach involves specifying a formal economic model of individual optimization in which variation in preferences, constraints, technologies, and expectations of future events are defined explicitly. The stochastic and often dynamic optimization problems incorporate rational expectations and forward-looking behavior that is influenced by past and current decisions. This approach emphasizes the clarity with which identifying assumptions are postulated, and advocates an approach to estimation that tests, and consequently accepts or rejects, well-posed models. The estimated parameters of such models are the underlying primitives of decision making: the parameters that define preferences, constraints, technologies, and expectations processes.33 One of the advantages of applying the structural estimation approach is the ability to impose and evaluate policy, and forecast the effects of new policies never previously experienced.34

## (p.71) The Natural and Social Experiment Approach

Another approach to causal analysis is the natural experiment. In an effort to measure causal parameters, researchers using this approach search for credible sources of identifying information (such as natural or social experiments), with truly random experiments being the ideal data to analyze. That is, a researcher can use information that is not correlated with individual unobservables to identify and measure the empirical effects of interest. The economic theory used to interpret data is often discussed intuitively and, in the case of health behavior, usually cites Grossman’s model for a formal framework. The natural experiment approach provides estimates obtained from simple econometric methods, frequently reduced forms, whose transparency and simplicity have promoted their widespread use.35 Much of the health literature uses this approach.

## Evaluation of New Policies and Incentives

As James Heckman argues, “If a policy has previously been in place, and it is possible to adjust outcome variables for changes in external circumstances unrelated to the policy that also affect outcomes, then econometric policy evaluation is just a table look-up exercise. Structural parameters are not required to forecast the effect of a policy on outcomes although causal effects may still be desired for interpretive purposes.”36 If the policy to be evaluated is the same basic one with levels of the policy parameters that differ from what is observed in the data, then the interpolation or extrapolation of estimated relationships is all that is required. A disciplined way to do this is to impose functions forms on simple estimation equations.

Put differently, nonstructural estimation, or statistical models, can be used to evaluate new policies when the policy directly varies itself (e.g., in the case of extrapolating the effect of health insurance copayment rates on medical care consumption) or when there is policyrelevant variation (e.g., in the case of extrapolating the effect of universal health insurance that pays the full cost of medical care using existing variation in medical care prices and health insurance coverage). The case for knowing structural parameters comes in when one wants to predict the effects of a new policy that has never been implemented.37

# (p.72) Structural Estimation of Models of Health Behavior

In the thirty-five years since Grossman’s formalization of health behavior, health economists have extended his model to incorporate uncertainty, health insurance, preventive care, and retirement policies, among other things. Nevertheless, few economists have attempted to parameterize and estimate the optimization behavior of individuals with regard to their health and health care consumption. Models that make explicit the dynamic behavior and the uncertainty do exist.38 Yet few empirical studies have numerically solved these optimization problems and used iterative estimation techniques to fit the behavior generated by the solution of the model to the observed data. In fact, only five papers, to my knowledge, explain medical care and nonmedical input decisions and their influence on health outcomes in a manner suggested in health economics’ infancy by Grossman: Gilleskie (1998), Crawford and Shum (2005), Davis and Foster (2005), and Khwaja (2001, 2006). Rather than simply measuring correlations in linearized demand functions or stand-alone production functions, these authors estimate the preferences, constraints, technologies, and expectations of forward-looking individuals, thereby allowing for the evaluation of interesting health policy alternatives.

The estimation of a comprehensive model of health outcomes, medical care use, and time allocation over an individual’s lifetime would require data that simply do not exist. Among the available data sets that detail health and health behavior of a nationally representative sample, few are longitudinal (i.e., data from surveys that track individuals and their behavior over time), and the time frame is generally short. Moreover, often the detail necessary to estimate a Grossman-like model is missing. Perhaps information is available about medical care inputs, but the data lack information about other health-related inputs such as smoking and exercise behavior. Annual measures of health may be available, but detailed measures of health that led to medical care use during the survey periods may be missing. Hence, attempts to estimate the underlying theoretical model of health demand and production have been limited to what is doable with the available data.

## (p.73) Example 1: Medical Care Use and Work Absenteeism during an Acute Illness Episode

In a 1998 work, I model daily medical care and absence decisions over an episode of acute infectious, parasitic, or respiratory illness.39 I estimate the preference parameters that determine the happiness (i.e., utility) that an ill individual receives from work (or not missing work) and general consumption. Also, I allow medical care itself to affect current utility as it may be palliative today in addition to productive for future health. A daily budget constraint reflects the income loss associated with the consumption of medical care and absences from work. Included in the dynamic optimization problem is a health production function that measures the effectiveness of medical care and recuperation (work absences) as well as time on recovery probabilities. The model provides predictions of how health insurance and sick leave policies affect medical care consumption and absenteeism.

My model mimics the Grossman one of health behaviors and health production on a smaller scale. While my model is limited to behavior during an episode of illness, it allows for the estimation of utility function parameters and parameters of the health production function. These so-called structural parameters, or primitives, of the model are policy invariant. That is, they reflect preferences, beliefs, or technologies that are not likely to change as policy changes. This estimation procedure differs from nonstructural or statistical techniques that produce quantifiable relationships between two variables, but that often do not reflect the direction of causality. Furthermore, if the statistical model is misspecified, a seemingly significant relationship may not really exist; the estimated parameters of interest may be biased. Finally, the estimated marginal impact, using such statistical models, reflects the policies that exist at the time of data collection since the estimated parameters are actually functions of the underlying primitive parameters of the theoretical model.40

Alternatively, the estimation of the structural parameters of individual optimization problems (i.e., the economist’s theoretical model of human behavior) allows for the evaluation of different public policies of interest. After model parameters have been estimated (i.e., after the values of the parameters that yield behavior similar to that observed in the data have been found), my model can be solved under different scenarios. My model, for example, simulates the effect of increasing (p.74) insurance coverage and eliminating sick leave policies.41 Admittedly, extremes of insurance, and sick leave coverage exist in my data, and hence simulated effects of variation in this coverage might be similarly captured by nonstructural estimation methods. Yet I also simulate the behavior of individuals under policies that do not exist in the data. How would a person behave if medical care (for these relatively minor illnesses) were prohibited during the first three days of illness in an effort to reduce the consumption of (or reliance on) medical care inputs? That is, perhaps a day of rest, as opposed to the consumption of medical care, may be sufficient and more effective to return the individual to full health. Of course, such a policy does not exist in the United States, but it is useful for understanding the effect of waiting times or queues that might exist for medical care services.

## Example 2: Prescription Drug Use during an Episode of Illness

Gregory Crawford and Matthew Shum focus on prescription drug decisions during an episode of gastrointestinal illness.42 Tat Chan and Barton Hamilton model the use of AIDS drugs to improve immune system response among HIV-infected individuals.43 Their models specifically address the uncertainty and learning about health production that takes place when a person consumes (or does not consume) a particular medical care input. Their models are examples of optimal behavior when the marginal product of a particular health input for a particular individual is not known with certainty in advance of using it and must be updated over time through experimentation.

Crawford and Shum’s dynamic model of demand for antiulcer drugs allows for current period effects of individual decisions (i.e., the relief of symptoms or side effects) as well as productive effects that reduce the (uncertain) duration of the episode. Both of these effects, however, are uncertain prior to the use of a particular drug by the individual. Hence, the individual learns over time which drugs make one feel best while taking them, and which drugs reduce the length of one’s spell (and dependence on the drug). Having solved the model and estimated the preference and belief parameters, the authors can solve the model under the case of certainty, where experimentation to discover health effects is not necessary. Despite extensive heterogeneity in drug efficacy across patients, the ability to learn which drug is best appears to minimize the welfare losses associated with initial bad decisions. Their (p.75) research has implications for policy regarding information diffusion, such as direct-to-consumer advertising, in drug markets.

Chan and Hamilton’s model of drug use to improve immune response focuses on the attrition that plagues many randomized experiments designed to evaluate treatment effects. The researchers find that participant failure to continue a medication can be explained by side effects and the declining efficacy of the treatment. Rather than simply calculate the treatment effect by examining the outcomes of randomly treated individuals, they model the utility of the patients as a function of both the observed health outcome (e.g., indicators of immune response) and side effects. They find that AZT—an older, traditional treatment for AIDS—yields the highest level of utility despite having the lowest impact on the immune system. This finding stems from the mild side effects associated with this treatment alone compared to being additionally treated with more recently introduced HIV drugs. The framework allows the authors to distinguish between learning, side effects, and the direct effects of treatment when explaining participant behavior over the course of the experiment.

## Example 3: Mental Health Care Decisions during Childhood

Morris Davis and E. Michael Foster model semiannual mental health care decisions during childhood.44 This research provides an example of the trade-off between completeness with regard to the types of medical care inputs considered with the duration in which health production can be modeled. The authors are able to model decisions over a long period of time (ages five to seventeen), but choose to focus specifically on mental health care services and mental health outcomes. This study provides an example of how children’s demand for health may need to be modeled differently since the decision makers are parents; parents care about household consumption and the mental health of their child. While mental health care may improve mental health (i.e., through the mental health production function), the consumption of such services reduces household consumption and may cause disutility directly. Davis and Foster find a significant but small effect of mental health care services on the long-term mental health of a small subset of the children in their sample. They also find that intermediate care services could replace inpatient stay services with little differential consequences for mental health outcomes. The estimation of preference parameters indicates that the stigma associated with (p.76) mental health care use is large, and is an important determinant of parental decisions regarding its use. Given these estimates, policies that attempt to promote the use of such services (i.e., parity in health insurance coverage) can be evaluated.

## Example 4: Health Input Demand and Health Production during an Adult Lifetime

Finally, the work of Ahmed Khwaja models health behaviors and health production over a long period of time, most closely aligning with Grossman’s model of health capital formulation.45 Khwaja models annual smoking, exercise, drinking, and medical care decisions over an adult lifetime. Unlike Grossman, he allows for joint production where these behaviors provide current period utility while also impacting future health. Another departure from Grossman’s model is that he excludes the employment decision from the complicated set of decisions that he does model. The author focuses on the role of insurance in affecting the medical and nonmedical health input behaviors both before and after eligibility for Medicare.46 In addition to offering a model that can quantify many responses to dynamic life cycle changes over time, the research contributes to our understanding of the incentive structure of elderly health insurance and provides a vehicle for evaluating changes in the age of Medicare eligibility and coverage.

# Problems Encountered in Empirical Research on Health

Despite the large empirical literature on demand for medical and nonmedical inputs and health production, a definitive understanding of behavior in these realms of health economics does not exist. The sources of the remaining questions lie largely in the difficulties associated with estimating these economic and largely biological processes. I end this chapter with a brief discussion of some of the obstacles encountered by economists doing empirical work on these subjects.

## Measurement of Health

The economist’s model of health behavior revolves around the central concept of health capital, or an individual’s stock of health. But how does one measure health empirically? Survey questionnaires often ask respondents to self report their health as excellent, very good, good, (p.77) fair, or poor. While the response provides a general measure of health, it is not objective; nor is it assessed by a physician, thereby making it difficult to compare responses across people. Alternatively, more objective measures such as the number or presence of chronic conditions, or the number of activities of daily living that are limited, provide comparability.

A related difficulty is the measurement of the flow of health from a given stock. This flow can be thought of as sickness or morbidity. In data collection, though, reports of sickness are frequently tied to work or school absences, and hence require an endogenous action (e.g., being absent or visiting a physician) in order to be recorded. Health shocks, such as the onset of a chronic condition, are sometimes used to capture health flow. Estimation of the determinants of the health stock or its flow requires a measure of health in which different inputs or input levels have the opportunity to matter. If the measure is too general, it may not vary with changes in individual behavior. If it is too specific, it might not capture changes (or stability) in other areas of health.

# Health Production Is a Dynamic Process That Requires Data over Time

While the theory of health input demand and health production assumes that medical care has a positive marginal impact on health, the data do not always validate this assumption. In fact, a statistical regression of health on a medical care input, whether measured as expenditures or the number of visits, is likely to reveal a negative relationship. This result logically stems from the observation that individuals who need the most care (i.e., those in the poorest health) consume the most medical care. Yet theoretically, Grossman’s model, and human behavior in general, suggests that rational individuals compare where they would be if they do not consume the medical care with where they would be consuming it (and weigh that against the monetary cost of consuming care). In many cases, health would deteriorate or not improve in the absence of care. Thus, the appropriate measurement of medical care’s productivity requires observations on individuals over time. That is, health production is dynamic by nature. Many data sets are cross-sectional and do not follow individuals over time, however.47 Econometrically teasing out the effect of unobserved individual characteristics from that of particular individually chosen (p.78) inputs can only be achieved with longitudinal observations on both input behaviors and health outcomes.

## Omission of Relevant Health Inputs

The evaluation of medical care as a productive input to health requires more than simply good measurement of the output and observations on individuals over time. It necessitates modeling the many inputs that might affect health. Grossman’s model specifies medical care (and time spent consuming medical care) as the input. Yet other inputs affect health: preventive care, different types of medical care (e.g., hospital care, physician visits, and prescription drugs), exercise, nutrition, smoking, drinking, and risky behaviors (e.g., skydiving, motorcycle riding, etc.), to name a few. Estimation with omitted inputs that are correlated with the input of interest will lead to incorrect estimates of the marginal effect (and its variance) of included inputs. Similarly, the determination of which inputs are substitutes for or complements of one another is important for evaluating insurance policies that may provide differential reimbursement for particular services.48

# Health Input Behaviors Are Choices

We know that the inputs that affect health are endogenous; that is, they are optimally chosen by an individual as part of attempt to achieve happiness over time. People choose whether to exercise or not. It is likely that unobserved individual characteristics affecting some input decisions will also influence the health outcomes of interest. For example, it has already been suggested that exact measures of health capital are difficult to obtain. It is quite likely that variations in unobserved health may influence health input decisions as well as the available measure of health that is being explained by the econometric model. Other examples of individual unobservables, both time varying and time invariant, include the degree of risk aversion, discounting of future happiness, self-esteem, unobserved health shocks, and unobserved determinants of both health and input behavior such as the presence of children. Proper treatment of unobserved individual heterogeneity is a must if one is to obtain reliable and useful measures of input effectiveness.

Despite these econometric concerns, modeling all the aspects of health demand and production that are captured by the economist’s health (p.79) capital framework is difficult empirically. For instance, we typically think that a person consumes curative care because it improves health. Such care increases the stock of health capital and hence its consumption today provides future benefits. Curative care consumption is also costly today; it reduces both the amount of money available for other consumption and the amount of time available for other activities. Only if the future benefits outweigh the current costs will an individual consume the curative care. Theory would predict, then, that a myopic individual would not seek care. Nevertheless, it is likely that curative care affects current levels of happiness also. Such care, for example, may offer immediate relief from pain. From a policy perspective, it may be important to know the extent to which demand is based on the current relief of symptoms or expectations of the future health outcome. These effects cannot be estimated without fully parameterizing and solving a model that makes these incentives (and potential policy instruments) explicit. Similarly, if one theorizes that aversion to risk or discounting of future events plays a role in health capital demand, then evaluation of the relevance of these behavioral concepts must involve an estimation procedure that explicitly accounts for or measures them.

# Conclusion

A question was posed at the beginning of the chapter: How would an employed person with diabetes behave if acquired health insurance? Grossman’s model and its extensions allow us to consider the different ways in which this person may respond and the variables that explain that behavior. Policymakers have a tool with which they can evaluate or interpret the effects of policies that alter the constraints faced by an individual.

For example, health behaviors and health outcomes are the focus of the Asheville Project and similar experiments being repeated in the Ten City Challenge.49 Since 1997, the city of Asheville, North Carolina, a self-insured employer, has provided free medicine and medical devices, free counseling and education by pharmacists, and regular checkups to employees with chronic health problems such as diabetes, asthma, hypertension, and high cholesterol who take their medicine regularly and change their unhealthy lifestyles. As expected (and as indicated by my initial answer to the hypothetical scenario posed at the start of this chapter), pharmaceutical costs have gone up. But hospital costs are down. And even more surprisingly to the program administrators, (p.80) absenteeism has been reduced considerably. The model of health behavior and health production presented in this chapter provides an explanation for these observed experiences.

Grossman’s model of the demand for and production of health capital remains the basic framework on which most economists have based subsequent investigations of health behavior. But the nature of health itself has led to a continuous and continuing stream of research. Researchers provide policymakers with more and more information regarding the marginal impact of various incentives or mechanisms through which improved health can be achieved on an ongoing basis. There is abundant literature attempting to quantify the value of this improved health. Recent work shows that improvements in health have a substantial value and that economic theory can explain why there is value in extending life.50

The theoretical and empirical work to date has shed light on three important considerations for future work in this area of economics. First, empirical analyses would benefit from the use of longitudinal observations on individuals in order to provide relevant information for policy consideration. Hence, supporting the acquisition of these types of data is necessary at the data collection level. Second, researchers seeking to measure quantitative relationships must address the existence of unobserved heterogeneity that is likely to create spurious correlation or bias the measured effect unless proper steps are taken to model it. Finally, estimation of a model of individual optimization behavior that allows a researcher to recover the primitives of the model—the fundamental preference, constraint, and expectation parameters that are invariant to policy—will allow the evaluation of alternative public policies. Despite theoretical and empirical achievements, exploration of health capital behavior will continue.

# Acknowledgments

I thank Frank Solan and Ahmed Khwaja for their suggestions on the organization of this chapter, and Luis Fernandez for useful comments during his discussion of this summary at the conference at Oberlin.

## Notes:

(1.) For recent surveys of this literature, see Grossman (2000); Cutler and Lleras-Muney (2006).

(p.81) (2.) Becker (1965); Grossman (1972a, 1972b).

(3.) In Grossman’s original model, only two inputs are considered in health production: medical care and the time spent in health-producing activities. An important component in this health production process, Grossman theorized, is education. He assumed (and tested empirically) that education improves the efficiency with which an individual converts a health input into the output health.

(4.) Economists refer to these goods as “home goods” or home production. Technically, health production can also be home production because there are many activities (e.g., a nutritious meal or a bike ride) that affect one’s health. For expositional purposes, however, health and home production are treated here as distinct goods, as in the original Grossman model.

(5.) Grossman assumes no joint production. That is, an individual cannot produce a home good while also traveling to the doctor’s office. Similarly, exercise cannot produce health while also producing recreational pleasure. Nor can an individual do anything productive with one’s days lost due to illness.

(6.) Grossman’s original model did not include uncertainty about future health shocks, health deterioration rates, wage rates, interest rates, or commodity prices. These rates are assumed to be known with perfect foresight.

(7.) It is difficult to say how behavior might change in this case without further assumptions.

(8.) Grossman’s model assumes no joint production so exercise (smoking), for example, cannot be both a positive (negative) input to health and provide negative (positive) utility.

(9.) Grossman (1982).

(10.) Grossman (2000).

(11.) For a comprehensive summary of research that addresses the relationship between health and labor, see Currie and Madrian (1999).

(12.) Cropper (1977).

(13.) Dardanoni and Wagstaff (1990).

(14.) Muurinen (1982)

(15.) Kenkel (1991).

(16.) Fuchs (1982).

(17.) This argument as an explanation for the positive correlation between health and education, however, requires that medical care improve health.

(18.) Grossman (2004).

(19.) Ehrlich and Hiroyuki (1990).

(20.) Ried (1996).

(21.) Grossman (2004).

(22.) Jacobson (2000).

(p.82) (23.) See the discussion of this issue in chapter 10 of this book.

(24.) Zweifel and Breyer (1997).

(25.) See, for example, Maddala (1983); Cameron and Trivedi (1998); Manning and Mullahy (2001); Gilleskie and Mroz (2004).

(26.) On cost sharing, see, for example, de Meza (1983); on nonmonetary factors, see, for example, Acton (1975); on chronic conditions, see, for example, Bolin and Lindgren (2002).

(27.) See, for example, Kirigia and Kainyu (2000).

(28.) Gruber (2000); Culyer and Newhouse (2000).

(29.) See chapter 5 of this book.

(30.) For summaries of work focusing on particular topics, see Culyer and Newhouse (2000).

(31.) Yaniv (2004); Gibson (2003); Phelan (2000); Kutty (1998).

(32.) See, for example, Grossman (2000, 2004); Cutler and Lleras-Muney (2006).

(33.) More specifically preferences are the parameters of the utility function u(ht, zt) that define the relationship between arguments of the utility function and the level of satisfaction or happiness. Constraint and technology parameters include those that define the relationship between health stock and healthy days, ht = f(Ht); between inputs and health investment, g(mt, THt); and between inputs and the home good, z(xt, TZt). Expectations parameters include, for example, parameters that define the relationship between individual characteristics and the distribution of future wages.

(34.) Todd and Wolpin (2003).

(35.) Heckman (2000).

(37.) Marschak (1953). Such an evaluation, however, requires the assumption that the new policy will not alter preferences.

(38.) Keeler et al. (1977); Cameron et al. (1988).

(39.) Gilleskie (1998).

(40.) Lucas (1976).

(41.) Gilleskie (1998).

(42.) Crawford and Shum (2005).

(43.) Chan and Hamilton (2006).

(44.) Davis and Foster (2005).

(45.) Khwaja (2001).

(46.) Khwaja (2006).

(p.83) (47.) Data collection surveys that follow individuals over time and inquire about health behaviors as well as outcomes are increasingly available. These include the Health and Retirement Survey, the Medicare Current Beneficiary Survey, the National Long-Term Care Survey, the Longitudinal Survey of Adolescent Health, and the Panel Study of Income Dynamics.

(48.) Yang et al. (2006).

(49.) Employer groups in ten different communities nationwide have established a voluntary health benefit for employees similar to that of the Asheville Project.

(50.) Murphy and Topel (2006); Hall and Jones (2007).