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CHAPTER I Introduction
1 Motivating background
Wellbeing has two very clear attributes: wealth and health. Without a question they are interrelated and they both have a high economic importance. For most people in Western Europe, at least some part of wealth and health is insured by a social security system. Hence, even small changes in the social security system can e¤ect a vast number of people and the accumulated consequences can be extensive. Recently, the social security systems have been under pressure due to the ageing populations of Western Europe, and it is commonly made clear in the public debate that some reforms to provide a cushion against the pressure must take place to maintain long-term budgets in balance. On the focal points there have been two parts of the social security systems: pension and health care. The reason is very clear, ageing puts more pressure on the publicly …nanced retirement systems and health care.
To facilitate the burden of the social security system, more responsibility about retirement
…nancing as well as …nancing of health care has been transferred from public …nances to individuals.
It is suggested that individuals save for their pension by themselves through retirement savings programs and accounts since an adequate replacement rate by means of a public pension can not any longer be guaranteed in the distant future. In the same manner, driven by an overuse of the health care system and also on …scal grounds, the out-of-pocket payments in public health care
systems have been increased and in this way …nancial responsibility is also transferred within health care from public …nances to private individuals.
So far, most of the reasoning behind the planned and implemented reforms in social security have been based on conventional economics theories. It is exactly there where a potential danger lurks. Namely, along several recent empirical and experimental studies (see the next subsection) there are plenty of choice situations in reality where individuals do not behave as the conventional theory predicts but rather they procrastinate, preproperate, and have time-inconsistent preferences.
Moreover, there are di¤erent kinds of time-inconsistencies: those who seem to know that they are not able to stick to their intertemporal plans, those who seem to be aware of that but fail to know the magnitude of their self-control problem, and those who do not know (or care) if they plan to complete a task tomorrow but then end up postponing it again ad in…nitum. Thus, implementing a reform through an analysis that is based on the conventional economics might lead individuals and an economy on a completely undesirable trajectory. As an example, delaying the opening of a retirement savings account can lead to too little pension savings, meanwhile procrastination in seeking medical help within an appropriate time after observing symptoms causes unnecessary large expenses for the public health care system and lower quality of health-related wellbeing for the individual, resulting in lower quality-adjusted life expectancy and less wealth in retirement for the individual and possibly higher tax payments for everyone.
While conventional economics has been mostly incapable of explaining the observed irrational and unpredicted behaviour of individuals, a fairly new branch, behavioural economics, has been able to o¤er a helping hand by building up frameworks and models that explain and predict the behaviour far better.1 Since we now have the tools to explain some behaviour more accurately than previously, it is very interesting and important to contemplate and be aware of how the predicted e¤ects of some reforms in social security depart from conventional predictions when applying the frameworks and models from behavioural economics. It is immediately obvious that the di¤erences in results can be large, implying in the most extreme cases completely contrary policy suggestions on reforms.
1For a very recent and thorough overview about behavioural economics, its frameworks and applicability to solve problems that have been mostly puzzles for conventional economics see Diamond and Vartinainen eds. (2007).
1.1 Literature and thoughts behind the study objectives
In this subsection I give an overview of how the literature connects to the ideas and thoughts that are developed further in the Essays. It is natural that I concentrate here only on the most relevant literature behind the study objectives, and hence I strongly encourage the reader to explore the additional references found in the Essays. I will …rst give an overview of the development of economics around time-discounting and how it relates to time-inconsistent decision-making. The research related to the ideas behind Essays I and II is then presented in more detail, and …nally the interrelation between health and wealth is discussed and the connection to Essay III is presented.
1.1.1 Time-inconsistency, hyperbolic discounting, and procrastination
The discounted-utility model entered into economic analyses through the work of Samuelson (1937).
Paul Samuelson seemingly anticipated some potentially undesirable e¤ects of his work since he o¤ered very clear reservations on the exponential-discounting model that he used. He emphasised among other things that "...for simplicity, we assume in the …rst instance that [the] rate of discount of [the] future is constant" and continued "...unlike [the] previous two [assumptions], [it] is in [the] nature of [the] hypothesis, subject to refutation by the observable facts...". Regardless of Samuelson’s reservations, exponential discounting quickly established its place in neoclassical (or conventional) economics as a standard way to discount the future, no matter what was discounted.
Strotz (1955–56), for his part, pointed out that if an individual uses any other method to discount the future than exponentially when making an intertemporal consumption plan and if there does not exist a commitment device, he or she is will be unable to stick to his original intertemporal consumption plan when revising the plan later, and hence his or her intertemporal choices will imply time-inconsistent preferences. I.e. he or she su¤ers from a self-control problem.2 Formal work on time-inconsistency has not inspired, though, a large group of researchers until recently.
Strotz’s (1955-56) ideas were developed by Phelps and Pollak (1968) in their intergenerational non-overlapping model, by Pollak (1968) in his critical comment on Strotz’s (1955-56) …ndings, by Peleg and Yaari (1973) in their work on changing tastes and consistent planning, questioning the
2An individual has a self-control problem if he or she seeks immediate grati…cation in ways he or she earlier would not have approved of. See e.g. O’Donoghue and Rabin (1999a, 1999b). According to the theory of self-control proposed in Thaler and Shefrin (1981) a self-control problem occurs because the agent is myopic in the sense that he underestimates his future willingness to consume.
generality of an existence of Strotz’s (1955-56) and Pollak’s (1968) equilibrium concept, and by Goldman (1979, 1980) in his studies on Pareto e¢ ciency and Strotz’s (1955-56) and Pollak’s (1968) equilibrium concept.3
It is enough to contrast Strotz (1955-56) results with Samuelson (1937) to make it apparent that if people did not use exponential discounting when making intertemporal planning, some conventional models would be in need of revision.4 Naturally, exponential discounting had its ease of use, strengths and suitability for certain intertemporal considerations but not for all, as empirical and experimental studies have re‡ected. Several studies demonstrate people to have self-control problems and hence possibly time-inconsistent preferences.5 It is thus reasonable to question models of certain types of intertemporal decision-making that utilise originally exponential discounting.6
In the recent literature, exponential discounting has been replaced by and large by hyperbolic discounting when modeling myopic choice behaviour.7 Hyperbolic discounting as a modeling device follows from Ainslie (1991). He notes that in parametric studies on decision–making, graphs of discount functions have been more bowed than graphs of exponential discount functions, i.e. the graphs are found to be hyperbolic. This implies such preferences that when considering trade-o¤s between two future moments, an individual gives stronger relative weight to the earlier moment as it gets closer. In other words, discounting is hyperbolic when an individual has a declining time preference. The discount function (t)is then a generalised hyperbola (t) = (1 + t) = ; ; >
3Pollak (1968) critizes quite heavily Strotz’s proof and the result concerning the strategy of consistent planning.
His argument is that the optimal strategy for consistent planning is falsely derived and the result itself incorrect.
Pollak then gives a counter-example to the Strotz’s result. Finally, a characterisation of the best attainable consump- tion path that is obtained in the counter-example is shown to be inconsistent with the Strotz’s result. However, the Strotz’s paper has been cited and used as base material in most of papers that handle time-inconsistency problems, mostly because the part that is shown to be incorrect has only a minor e¤ect on an otherwise great contribution provided by to the work to the literature on intertemporal allocation.
4Peleg and Yaari (1973) make an important point in emphasising the fact that preferences are something that are usually de…ned ex-post and hence discussing today about tomorrow’s preferences can be tricky and problematic.
5For a very thorough and critical literature review about time discounting and time preference see Frederick et al. (2002). For empirical and experimental evidence about time-inconsistency and for discussion about the topic see e.g. Thaler (1981), Ainslie (1992), and Kirby and Herrnstein (1995), and O’Donoghue and Rabin (2001a) and further references therein.
6Of course, selection of the models that utilise non-exponential discounting must be adequately reasoned but basically in several cases where individual decision-making is the study ob jective, empirical evidence re‡ects non- exponential discounting. For attempts to model time-inconsistent choices with conventional models see e.g. Gul and Pesendorfer (2001, 2004) where preferences are time-consistent but choices are a¤ected by temptation, and Dasgupta and Maskin (2005) where uncertainty causes the choices to be such that those look like caused by preferences that are time-inconsistent.
7For critics of hyperbolic discounting as a standard way to model time-inconsistency, see Rubinstein (2001a, 2001b). In that work, he notes that decisions that can look like a consequence of hyperbolic discounting can be caused also by several other reasons and hence plain observation of such choices does not justify hyperbolic discounting to be the reason.
0; where t is time and and constants.8;9 Quite often and due to its convenience, a quasi- hyperbolic discounting is used instead of the pure hyperbolic discounting. Discounting is called quasi-hyperbolic when discounting is exponential for all periods from t+ 1 onwards, given that a current period is t; and captures only the key qualitative property of the hyperbolic discount function, i.e. a faster rate of decline in the short run than in the long run, between periods t and t+ 1: In a discrete set up, the quasi-hyperbolic discount function takes the following form:
f1; ; 2; :::g, where <1 is a short run discount factor and the standard long run discount factor.10;11
In the simulations of Angletos et al. (2001), the level of labour income and the size of the shocks are calibrated to match empirical data and the message of their study is very clear: "... a model of consumption based on a hyperbolic discount function consistently better approximates the data than does a model based on a exponential discount function." Leaning on their results, they are able to show hyperbolic function to be useful in explaining households’(i) low levels of liquid assets, (ii) irrational credit-card borrowing, (iii) why households are less able to smooth their consumption, and (iv) why consumption drops so much around retirement.12 As Rader (1981) and Lengwiler (2004) consider that there is no reason to believe that the discount rate would be constant across consumers, Gollier and Zeckhauser (2005) make use of their statements and show the hyperbolic discounting to be very reasonable for presenting the discounting for representative individual models. They show that when a constant discount factor varies in a population where individuals have decreasing absolute risk aversion, the aggregate discount function for a representative individual is hyperbolic.
It is, thus, not surprising that the use of hyperbolic discounting is getting more and more attention in relation to consumption-saving analyses.
Strotz (1995-56) and Pollak (1968) use two di¤erent types of individual in their studies. The
8It is easy to see that the discount function of given form has the declining discount rater(t) = (t)0(t) =(1+ t), and hence it has an increasing discount factor in time, whereas for exponential discounting both the discount rate and factor are constants and do not depend on time interval.
9Loewenstein and Prelec (1992) provide an axiomatic derivation of the generalised hyperbolic discount function.
1 0The form of the quasi-hyperbolic discount function was …rst developed by Phelps and Pollak (1968) and then in- troduced in the consumption-saving context by Laibson (1994,1996,1997). For theoretical foundations and a thorough analysis about hyperbolic discounting in a consumption-saving framework see Harris and Laibson (2001).
1 1There are several names given for the time-inconsistent preferences. E.g. O’Donoghue and Rabin (1999a) consider that the term present-biased preferences would be more meaningful than hyperbolic preferences and hence they use it from thereon, while Krusell and Smith (2003), for their part, use quasi-geometric discounting to describe the same phenomena.
1 2See also Laibson (1996), Laibson et al. (1998), and Laibson et al. (2003) for the simulation literature on the
…eld.
types are de…ned in the terms of individual’s awareness of his or her future preferences. A naive is one who does not know his future preference reversals while a sophisticate is completely aware of this. O’Donoghue and Rabin (2001b) and O’Donoghue and Rabin (forthcoming) top up the original type-classi…cation by incorporating a partially naive into the analysis as one more type. A partially naive is aware of future preference reversals but underestimates the magnitude of the reversal.
Finally, having the di¤erent types is not enough to model decision-making where an individual has possibilities to revise intertemporal plans. To facilitate a neat framework, an approach with multiple selves, a.k.a. a multiselves model, has been utilised. In the multiselves model, an individual’s identity usually has as many selves as there are decision periods in the model. Then, a present self plays an extensive form game with his future selves with a strategy that depends on the individual’s type.
Now, in all set ups the naive, the partially naive, and the sophisticate stick to their type with the passage of time. In particular, for the naive and the partially naive there would also seem to be a possibility for backwards-looking behaviour. However, all the analyses so far are lacking in possibilities for learning, which is not considered and almost never mentioned. In Essay I, I contribute to this important and mainly unexplored new topic by trying to …ll the gap to some extent.
Procrastination and retirement saving One very interesting implication of the time-inconsistent preferences is delaying the completion of a task, i.e. procrastination. O’Donoghue and Rabin (1999a, 1999b) develop micro-theoretical foundations and models on a procrastinator’s behaviour in the context of the hyperbolic discounting. They show that the naives are eager to procrastinate tasks where costs are immediate and rewards are delayed while the sophisticates preproperate (hasten) the tasks where rewards are immediate and costs delayed. The result follows from a non-monetary utility cost that leads the naive to consider that he will su¤er from the utility cost proportionally less if he completes the task tomorrow while the sophisticates are trying to avoid procrastination and discover that if the task is not completed immediately it will be procrastinated for as long as possible, and hence it is utility maximising to complete the task immediately. In O’Donoghue and Rabin (1999c), it has been shown with a calibrational exercise how a hyperbolic individual can loose, due to a very small utility cost, fairly large amounts of money by procrastinating the transfer of money from a lower-interest paying account to a higher interest-paying account. Nowhere in
their work, however, do they discuss the cases where either or both costs and rewards would be realised in part immediately or later for both. In Essays I and II, I contemplate this kind of new problem setting.
O’Donoghue and Rabin’s (1999c) ideas are supported by empirical evidence on procrastination in the retirement savings context. Choi et al. (2004a, 2004b), for example, show that people are passive-decision makers when it comes to the 401(k) retirement savings accounts. When an employee is not automatically enrolled in the savings program, it takes a very long time before the enrollment takes place, when an employee is automatically enrolled with a default savings rate, it takes a very long time for him or her to make any changes to the default, even if the default rate were set to 0. However, in O’Donoghue and Rabin’s (1999c) paper the individual does not have any other task than transferring the money, and hence they are missing in their analysis a very interesting topic, namely the individual’s possibility to consume a part from his initial amount of money. Revising and connecting the theoretical work of Laibson (1996) and O’Donoghue and Rabin’s (1999a, 1999b, 1999c) ideas and model of procrastination with the empirical …ndings of Choi et al. (2004a, 2004b) leads to an intriguing speculation on what kind of e¤ects the existence of retirement savings programs can have on individual behaviour. In Essay I, I analyse these considerations and problems.
Procrastination and health It is not only individuals’preparation for retirement that is poor and subject to delays, but neither does health seem to be any more important for individuals.
According to several studies, there are severe and very long delays in seeking medical help after observing initial symptoms, even when a public health care system would carry all or almost all the costs.13 Köszezi (2003) explains the feature by using the ideas of Caplin and Leahy (2001) and constructs a model in which delays are a consequence of anticipatory feelings and anxiety. That is, in the model, procrastination follows from information aversion as people who are observing bad symptoms can be assumed to be reluctant to seek medical help since they anticipate the e¤ect of possible bad news on their utility. On the other hand, Becker and Mulligan (1997) builds up a consumption-savings model where an individual with better future expectations appreciate the future more than an individual with less bright future predictions, and thus discounting across individuals may di¤er.
1 3See e.g. Faccione (1993), Caplan (1995), and Meechan et al. (2002), Mohammed et al. (2005).
Adapting ideas from Becker and Mulligan (1997) with some minor changes in the health eco- nomics framework and connecting those with Köszegi’s (2003) ideas gives the possibility to speculate as to whether observing symptoms causes a need for immediate grati…cation, and hence could im- ply hyperbolic preferences. In Essay II, I give attention to these novel considerations and analyse this kind of problem setting. These ideas are supported at least by …ndings of Wu (2003) and Picone et al. (1998, 2004). Their empirical studies reveal that a third of their study objects are quite myopic, and that those who are myopic, uninsured, or both are less eager to demand medical tests. In contrast, those who have longer life expectancy are engaged in preventive actions more frequently. While still incorporating the …ndings about treatment-cost formation from Butler et al.
(1995)— where treatment costs are shown to be rather exponentially rather than linearly increasing in time— and the …ndings on the noteworthy value of an early detection of a disease from Howard (2005), the economic relevance of procrastination in seeking medical help becomes even stronger.
1.1.2 Health overrides wealth
Wealth and health are interrelated and they both certainly a¤ect quality of life. However, one very important matter distinguishes between them: wealth does not guarantee health. In his seminal work on the special features of health care sector markets, Arrow (1963) notes one important feature as being that one is not able to assure perfect health to him or herself even with an in…nite amount of wealth. In addition and as an extreme example, quality of life that springs from wealth becomes meaningless if one is dead. Hence, quality of life that springs from health has its special meaning and attention when considering quality of life. Moreover, when people are not doing well in health they do not usually do well in wealth-related activity, e.g. at work. Thus the state, development and expectation for the development of health related quality of life throughout the expected life span of the population is the focal point of economically relevant policy and decision making. In the same vein as Grossman’s (1972) seminal work on the demand for health, the same question asks how the health capital is changing and developing in population.
The quality-adjusted life year (QALY) has been widely used to measure the e¤ectiveness of medical treatments and interventions.14 It is a measure that combines a quality and quantity of
1 4Together with analysing the costs of the treatments and interventions one has been able to conduct cost- e¤ectiveness analysis and make comparisons between the interventions. For a systematic review of empirical studies that use QALYs see Räsänen et al. (2006).
life. For the very same reason longevity has been seen as an incomplete measure for the development of health in a population as it lacks a quality component. In particular, the quality component refers to the health-related quality of life (HRQoL). In QALYs a year in perfect health usually receives a value of 1, while 0 signi…es death, and all other health states are values in between. QALYs is then the sum of expected HRQoLs over the lifetime.
Not surprisingly, a QALY has its roots in the operational research of the mid 1970s, when cost- bene…t analysis was being replaced by a cost-e¤ectiveness analysis to avoid the unpleasant task of placing dollar values for health e¤ects, such as death.15 To accomplish the task, QALYs were proposed, developed and chosen to be a measure which would capture the health-related e¤ects in a way that it represents the preference of an individual for his or her own health. It is not the quantity part that causes problems in measuring QALYs but de…ning and measuring HRQoL weights. In fact, HRQoL weights themselves are usually constructed as a weighted sum of di¤erent dimensions or attributes that are considered important to health-related wellbeing.16 Di¤erent ways to measure and elicit the preferences over health states have been developed. The three most often used ways to de…ne weights for di¤erent health states fall into the class of direct methods that incorporate a standard-gamble method, a time trade-o¤ method, and a rating-scale method.
The standard-gamble method asks people to choose between certain health states and a lottery of immediate death and perfect health. The time trade-o¤ method asks people to de…ne how much time spent in some health state is worth in terms of time of perfect health. In the rating-scale method people are asked to value health states on a line scale from 0 to 100.17;18 An indirect method incorporates a two-step procedure where respondents are asked to indicate the level of a particular health state with regard to several attributes, such as vision, hearing, speech, mobility
1 5For an analysis and review of how cost-e¤ectiveness analysis, cost-bene…t analysis and cost utility analysis relate to each other in a health economics context see Torrance (1986). See also Garber (2000) for the welfare economic foundations of cost-e¤ectiveness analysis. For a thorough review and analysis of the history of QALYs and its counterparts (health-adjusted life years (HALYs), disease-adjusted life years (DALYs), health-adjusted life expectancy (HALEs)) see Gold et al. (1996, 2002) and further references therein.
1 6For example, EuroQoL has 5 dimensions and three levels for each dimension, while a measure that has been shown (see e.g. Stavem 1999) to be very accurate, consistent and sensitive, namely the 15D developed by Sintonen (1994, 1995), has 15 dimensions and 5 levels for each dimension.
1 7There is a vast theoretical and empirical literature about which one of the methods should be exercised but no consensus has been reached yet. See e.g. Torrance and Feeny (1989) for a defence of the standard gamble method, Broome (1993) for a defence of the rating scale method, and Richardson (1994) for a defence of the time trade-o¤
method. For an empirical comparison of the ability of the di¤erent methods to predict preferences over health states in an experimental setting see Bleichrodt and Johannesson (1997).
1 8According to the review of Tengs and Wallace (2000), approximately 51% of studies used the direct methods to elicit preferences over health states.
etc. Attribute levels are then mapped into an interval[0;1]by using weights for di¤erent attributes that have already previously been elicited by some method.
As QALYs do well in expressing the e¤ectiveness of medical treatments, there is no reason why it would not do well in measuring the development of health at a population level. Dolan (1998) notes that people can be interested in knowing how QALYs are distributed in the population. The reason for this kind of interest is very clear and well reasoned in the context of a publicly …nanced health care system. People want to know how their tax money is used and what do they gain in the form of QALYs. Of particular interest are the changes in QALYs between the genders and across age groups since from the distributional viewpoint these are very important groupings when an allocation of scarce health care resources is considered. The capability to use QALYs for a national-level analysis has been mostly absent, however. This has mainly been so due to the lack of proper and accurate data about health state of the population at a national level. Cutler and Richardson (1997,1998) make use of Grossman’s (1972) health capital model and estimates the development of QALYs in the USA between 1950 and 1990 from self-reported health status data and the prevalence of certain diseases. Their …ndings of changes in QALYs across age groups reveals something that has not received attention in the literature; namely, they …nd that depending on the discount factor used, younger habitants have gained or lost QALYs more than older inhabitants. A similar implication is apparent from the study of Burström et al. (2003). For policy judgements and welfare analysis these kind of inconsistent results are problematic, as the discount factor plays a leading role in the decision about allocating resources.19 It is thus important to study and develop a measure that gives the same results independently of discounting for the expected QALY gains across the age groups and which will thereby improve the possibilities to conduct e.g. a welfare analysis. Hence, Essay III is built on these important and certainly neglected observations.
2 Summaries of the essays
In this section I provide short summaries of the essays and their main …ndings and implications.
The order here corresponds to their order in the dissertation.
1 9For an axiomatic approach to resource allocation in the QALY context see Østerdal (2005).
2.1 Essay I: Existence e¤ects of retirement savings program
Among others Börsch-Supan and Brugiavini (2001) state that one of the most important interactions between savings and policy is the pension. On the other hand, the …ndings of Choi et al. (2004a, 2004b) imply that people are passive in making decisions about their retirement savings while recent
…ndings by e.g. Loewenstein and Prelec (1992) show people to also be professionals in intertemporal misplanning. When these …ndings are connected with a growing tendency to put more pressure on the individuals to take care of their own pension, the set up for Essay I is complete. What happens when people are responsible for saving for their retirement in the presence and in the absence of a lucrative retirement savings program? This is the question addressed by Essay I.
To model individual consumption-saving behaviour we depart from conventional models and use instead a stripped down version of Laibson (1996) hyperbolic multiple-selves consumption model that has its origins in the work of Strotz (1955-56), Phelps and Pollak (1968) and Pollak (1968).
In Laibson’s (1996) model an individual with di¤erent kinds of consumption-saving possibilities is subject to the hyperbolic discount function instead of the exponential. Using the hyperbolic discount function enables intertemporal plans to be time-inconsistent as Strotz (1955-56) pointed out. Laibson (1996) uses only one agent type, the sophisticate, while we make use of O’Donoghue and Rabin (1999a, 1999c) richer type-classi…cation by having also a naive agent. Furthermore, to study the e¤ect of backwards-looking behaviour on misplanning, we replace the O’Donoghue and Rabin’s (1999c, 2001b, forthcoming) partially naive agent-type with a learning naive agent. The learning naive agent is initially naive but realises through backwards-looking behaviour that he is having time-inconsistent preferences, learns from their magnitude with the passage of time, and takes the future preference reversals into account when making consumption-saving plans. While we loosely follow the set up of O’Donoghue and Rabin (1999c), where a transfer of a capital stock from one account to a better paid account is studied, we depart from their model by making it possible for the agent to consume and save along the passage of time.
The model allows us to study and compare intertemporal planning and consumption-saving behaviour of the di¤erent agent-types in two separate cases. In the …rst case, retirement savings programs are absent, and the agent’s only task is to make an intertemporal consumption-saving plan and choose the current consumption. This analysis provides us with some key properties about misplanning and the tools to contemplate the agent’s behaviour in the second case, where a lucrative,
…xed contribution retirement savings program is present. The lucrativeness of the retirement savings
program is guaranteed by giving greater interest in the retirement savings program than what is paid on savings in a regular checking account. However, enrolling on the retirement savings program requires an e¤ort that causes a non-monetary utility cost similarly to that assumed in the study of O’Donoghue and Rabin (1999c), which is supported by the empirical …ndings of for example Madrian and Shea (2001). The agent’s task in the second case is then to plan simultaneously intertemporal consumption and when to enrol (if ever) on the retirement savings program, in addition to choosing the current consumption. Finally, to make comparisons across the agent types and between the two cases interesting, and to ease numerical analyses, we consider instantaneous utility to be logarithmic, since then— in accordance with Strotz’s (1955-56) …ndings— the naives and the sophisticates will make the same current consumption-savings choices in the …rst case. We show that this holds also for the learning naive agent. To enable a wider and more rigorous grasp of the results from the formal analysis, we solve and interpret some results numerically.
The main results establish that for the same range of e¤ort-cost and in terms of retirement savings, the naive su¤ers, the sophisticate never su¤ers and always gains from, and the learning naive can su¤er or gain from the existence of retirement savings program. If the e¤ort-cost is at a low or intermediate level the learning naive gains from the existence of the savings program but starts to su¤er from it when the e¤ort-cost level increases to relatively high or very high. These interesting and novel results spring mainly from two sources and their interaction: a non-binding budget constraint and the agent’s awareness about his future preferences. Flexibility in intertemporal budget constraint enables the agent to borrow against future incomes. When borrowing is possible the agent is able to make such a consumption plan where he anticipates to start the retirement savings program in the future and thus takes this extra income from the program into account when choosing the current consumption. If the savings program is not started in the future at the planned period, it follows directly that less will be saved than previously planned. When this type of behaviour can continue throughout several periods, the savings for retirement can be substantially lower than what they would have been if the retirement savings program was completely absent.
Moreover, it is the plain existence of the retirement savings program that causes this undesirable behaviour. The results show that the naives are in the worst situation, as they always plan to start the retirement savings program in the future but never immediately, except if the e¤ort-cost is so low that one period of procrastination is too costly even for the …rst self. If the latter is not the case for naives, they then make their current consumption choice always by using anticipated wealth from
the retirement savings program until they abandon it for good due to the fact the e¤ort-cost has become too high relative to the remaining utility increments from the program. The sophisticates do not su¤er from the program’s existence since they take the future preference reversals into account in their planning and hence start the program immediately whenever they observe that their future selves would procrastinate the starting too far ahead from his current viewpoint. Some mild procrastination can, however, emerge. The learning naives can have— depending on the level of e¤ort-cost and learning ability— su¢ cient time to learn enough about their preference reversals, and thus start the retirement savings program before they abandon it because e¤ort-cost has become too high relative to the remaining utility increments from the program. When there is not enough time to learn, the learning naives are in the same boat with the naives and their retirement savings fall short of the original plans.
The results emphasise that fairly low levels of e¤ort-cost as well as capabilities to learn about one’s own behaviour can make relatively big di¤erences in retirement wealth. In light of a possible reform of a pension system where the burden of public pensions is considered to have been eased by private saving, these …ndings imply that special attention to the level of e¤ort-costs and learning ca- pabilities is needed. If we consider all the agents to be the learning naives with di¤erent capabilities to learn, then if lowering the e¤ort-cost is expensive relative to improving the learning capability, possibilities to learn about self-control problems should be improved. If they are both expensive, then heterogeneity between di¤erent saving options should be avoided or the e¤ort-cost should be allowed to rise so that only fast learners or self-assertive individuals start the retirement savings program while slow learners and less self-assertive individuals abandon it fairly quickly. By leaving some room for speculation, as a …nal intuitive implication we can say that if the publicly …nanced retirement system initially provided more than the savings program yields for the sophisticates, the publicly …nanced system could be maintained by decreasing the replacement rate at the respective level that the sophisticates are able to save along the savings program, and all the types should accept it.
2.2 Essay II: A public health care puzzle
The resources of a public health care system are scarce and they are subject to increasing pressure due to considerations of budget cuts. Kenkel (2000) points out the importance of people’s preventive actions to the medical expenditures formation of a health care system. In the public debate an
overuse of the public health care system is the subject of criticism due to the unnecessary costs the overuse can cause to taxpayers. On the other hand, according to for example the empirical
…ndings of Faccione (1993), Caplan (1995), and Meechan et al. (2002), Mohammed et al. (2005), people do delay visits to a doctor. This can be very costly to the public health care system, since the study of for example Butler et al. (1995) implies treatment costs can increase very quickly if seeking medical help has been delayed beyond a certain threshold. It is thus not only preventive actions that a¤ect the cost formation when considering peoples’health-related behaviour but also, and maybe even more importantly, on how long after …rst observing some symptoms people decide to wait before seeking medical help. Less attention is given to an underuse of the public health care system and to the reasons for the behaviour behind the underuse. Essay II gives attention to this very important and unexplored topic.
Individuals health-related behaviour is something of a puzzle: a number of patients that should seek medical care stay inactive while the system is utilised mainly by those who are not in need of medical care. Caplin and Leahy (2001) and Köszegi (2003) …ndings provide some answers to this behaviour as they explain delayed visits as a kind of information aversion. It would then be reasonable to …nd those who do not anticipate a bad diagnoses from medical centre visits while those who stay at home are possibly anticipating bad news and are hence reluctant to …nd out the diagnoses. Becker and Mulligan (1997) show that delayed visits can occur even without anticipatory feelings if the time discounting is a¤ected by for example uncertainty, mortality, and addictions.
We instead consider the e¤ects of hyperbolic discounting on patient behaviour and approach the puzzle through the interaction between patient behaviour and government actions, and explain the patient behaviour with the direct e¤ects of out-of-pocket payments and the indirect e¤ects of time-inconsistent preferences.
We model the time-inconsistent preferences with the hyperbolic discounting which has its origins in the seminal work of Strotz (1955-56) and Phelps and Pollak (1968), and hence we use quasi- hyperbolic discounting. In addition, an exponentially discounting patient provides a benchmark.
We consider the behaviour of two di¤erent patient types for the hyperbolic patients: a naive and a sophisticate with the standard de…nitions for naivety and sophistication à la O’Donoghue and Rabin (1999a). That is, the naive is completely unaware about future preference reversals while the sophisticate knows that perfectly. Patient’s task is to decide when to seek medical help if he observes symptoms. For a solution concept that the patient uses, we revise a piece of the O’Donoghue and
Rabin (1999a) seminal work. We assume that symptoms persist or then afternperiods, they vanish, but the patient does not know this fact about the persistence of the symptoms. Instead, the patient is equipped with a subjective probability with respect to the symptoms’ persistence and it is an increasing function of time. The treatment-cost function that we use captures the key qualitative properties presented in Butler et al. (1995) while the consultation costs are proportional to the size of the treatment costs. The government’s available actions are reduced to possibilities to set a consultation fee, a deductible for such and a budget-balancing tax rate. The redemption is accepted for those patients whose diagnoses reveal persisting symptoms, i.e. a disease that must be treated with some non-self-medication method, while all treatments are considered to be free of charge.
Among other contributions we make to the recent research, one contribution that is notable is that we assume that instead of only one patient type at a time in the economy that there is a partition of all the types in the economy at the same time. We use numerical analyses to gain more insight, illustrate the results and even to enable the solving of some results.
The main results establish that fairly small increases (decreases) in the consultation fee (the deductible) can cause substantial changes in patient behaviour. The naives are a¤ected the most and actually their delays can become so long that a decrease (increase) instead of an increase (decrease) in the fee (the deductible) would decrease the total costs for the public health care system, and hence also the tax rate, yielding a higher expected welfare from the social planner’s point of view. It is more important to use a high enough fee and a low enough deductible to make the sophisticates and the time-consistents wait long enough than to ensure they visit a doctor. On the contrary, it is more important to use a low enough fee and a high enough deductible to make the naives visit a doctor soon enough rather than to ensure they wait long enough. Finally, when all the patient types exist, assuming the existence of the naives is more important than assuming the existence of some other patient types, as assuming their absence can hurt the sophisticates, the time-consistents and all individuals with unnecessary high tax rates. This is even while assuming the absence of the time-consistents or the sophisticates does not hurt the naives in a similar way and the tax rates stay comparably low, resulting in comparably higher expected welfare.
One implication of the study is that since it is plausible to assume that there are all the patient types in the real word, we should always develop policy for the public health care system so that the naives play the leading role. We should thus consider the possible behavioural e¤ects of using
…scal instruments in health care much more than currently, since an assumption of the conventional
partition for the individuals in the economy can actually lead to more expensive and a worse situation than that where the unconventional partition is assumed.
2.3 Essay III: Changes in QALYs in Finland 1995/96-2004
To optimally distribute the scarce public health care resources, it is necessary and important to know the development and the incidence of health-related wellbeing. The ease of obtaining life expectancy data has meant it is quite often used in the analysis of national level wellbeing, as for example in Cutler and Richardson (2006). However, plain longevity does not reveal anything about quality of the life. It would thus be possible that people lived longer but with lower quality than before. This could lead to a fallacious conclusion about the development of population wellbeing and hence result in a suboptimal allocation of resources. To get more accurate information about the outcomes of the public health care system and population health and its development, life expectancy must be weighted against health-related quality of life. One then has a measure for the quality adjusted life years (QALYs). Essay III looks at how QALYs have developed and how this development is distributed across genders and age groups in Finland between 1995/96 and 2004, and also introduces a measure that provides consistent information about the distribution across the age groups that would otherwise be di¢ cult to give.
QALY is a measure that combines a quantity and a health-related quality of life (HRQoL), where HRQoL should re‡ect individual preferences over health states. The problem is that national level data on HRQoL are rarely available and in those studies where QALYs have been measured on a national level, the HRQoL measures have been mappings from some health-related data to HRQoL measures. For example, in Cutler and Richardson (1997, 1998) self-reported health-state information and disease information together with the prevalence of certain data on diseases are used to estimate HRQoLs. Burström et al. (2003), for their part, estimate HRQoLs by using …rst a mapping from the responses to selected survey questions in the Swedish Survey of Living Conditions to EQ-5D and then to the UK EQ-5D index tari¤. We are however able to use cross-sectional data that covers the adult Finnish population in 1995/96, 2000 and 2004 and includes, among other information, 15 health-related attributes, enabling us to compute a direct HRQoL measure, namely a 15-dimensional measure (15D). The 15D was developed by Sintonen (1994, 1995) and has been shown to be a very accurate, consistent and sensitive HRQoL measure (see e.g. Stavem 1999).
Hence, we are not only able to analyse how HRQoLs have been developing in time, but also how
the di¤erent dimensions have been developing in Finland for the period 1996/96-2004. Finally, to conduct undiscounted and discounted expected QALYs we develop and use a recursive method where for HRQoL we use 15D data, as already mentioned, and for the quantity of life we use data on mortality and survival probabilities from the life tables provided by Statistics Finland.
In addition to being able to give more precise results about QALYs and their development than most other studies, the results from Cutler and Richardson (1997,1998) and Burström et al. (2003) inspire us also to contemplate the e¤ect of discounting on the incidence of QALY changes across age groups, a matter that has received little attention thus far in health economics research. Cutler and Richardson (1997,1998) and Burström et al. (2003) do not pay any attention to the inconsistency of the incidence of QALY changes across age groups that their results show for the undiscounted and the discounted cases. They report only the …ndings about QALY changes across the age groups and do not consider why those are almost contrary between younger and older inhabitants depending on whether discounting is used or not. Neither do they consider the implication of this kind of inconsistency between the results. From the social planner’s perspective this kind of inconsistency can be very problematic as the selection for distributional and allocative policy could be completely di¤erent after using the undiscounted results than if the discounted results were used.20 To get rid of this problem of inconsistency, we develop, study and use a measure that we call the relative change out of attainable (RCOA). It is a measure that compares the realised change in QALYs to the maximum possible— that is, attainable— change in QALYs given the development of life expectancy.
The main results establish that QALYs for 18-79 years old females and males have increased in Finland during 1995/96-2004. Approximately and throughout the age groups, 20% of QALY changes for the males and more than 50% of the QALY changes for the females are due to the positive development in 15D, while the rest is due to the increased quantity of life. Males are nearing females in terms of life expectancy but the development of the 15D values has been more favourable for females than for males. Use of RCOA to measure the change in the discounted and the undiscounted QALYs shows consistently that the incidence of greatest improvements in QALYs is for older inhabitants.
2 0There is a vast literature whether discounting for health e¤ects should be used or not, and if yes, then what size of discount factor should be used and should this discount factor be the same for QALYs and costs. For very thorough overview for the literature see Gold et al (1996).
The results imply that QALYs in Finland are still increasing in time and more for older than for younger inhabitants. The latter …nding especially is very challenging for the publicly funded health care and pension systems as the pressure for a tighter …scal policy with budget cuts is increasing.
On the other hand, since the positive development is throughout the age groups, it should re‡ect a decreasing pressure on the health care system in the future instead of the formerly anticipated increasing pressure.
For the moment, there exists an intractable dilemma. What has actually caused the increase in QALYs? If it has been the increasing volume of taxpayers money put into the system, we might face the di¢ culty of maintaining the current QALYs in a situation where health care funding is subject to cuts. On the other hand, if the increase is due to better treatment, we could reallocate ine¤ective money from the health care system to some other important part of social security without QALYs falling from the levels already attained. The results indicate that if the investments in health care lag behind QALY development then it would be, from the health-related quality perspective, more detrimental to females than to males to cut the health care budget. From the life expectancy perspective, the case is naturally reversed between the genders. The observed development of QALYs implies also that older inhabitants are healthier than previously. This leads to pressure on the publicly funded pension system. When older people are getting healthier it probably means that they will also live longer, and as a consequence, the demand for a private pension system will increase along with the decreasing tax base. Hence, to be able to maintain the status of the welfare state and the already achieved positive developments, we have to be acutely aware of what is cause and what is e¤ect in this matter, before making any radical changes to the current health care system and its funding.
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