ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued) Simon Grant 27 September – 1 October, 2021. Last Time • Talked about two key features of time preferences and intertemporal choice. 1. People discount heavily tradeoffs between the present and near future, but don’t seem to discount so heavily tradeoffs between nearby periods in the future. 2. People seem to have internal conflicts regarding their choices through time. • Beforehand, we seem to disapprove of our tendency to seek immediate gratification. – Ulysses ties himself to the mast because he disapproves of his urge to join the nymphs. – Shoppers disapprove of impulse spending before heading to mall. – We think we should exercise more than we actually do. • But EDU preferences generate dynamically consistent choices. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 1 / 52 (Quasi-)Hyperbolic discounting and the β − δ model • Today we will study a model that aims to capture the phenomena cited above: – impatience when it comes to short-run tradeoffs; – greater patience when it comes to tradeoffs in the future; – the conflict generated by these changing tradeoffs. • A (Quasi)-Hyperbolic Discounter is a person whose preferences %T at time T > 0 over consumption streams cT = (cT , cT+1 , cT+2 , . . .) can be represented by a function of the form: HDU(cT ) = u(cT ) + βδu(cT+1) + βδ2u(cT+2) + βδ3u(cT+3) + . . . = u(cT ) + β [ ∞∑ t=1 δtu(cT+t) ] , where 0 < β 6 1 is the short-term discount factor. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 2 / 52 A Student’s Predicament • A student has to do a problem set in exactly one of three periods t = 0, t = 1 or t = 2. • Without loss of generality, can describe this as an IHDP B = {c0 , c1 , c2}, where: c0 = (γ0 , 0 , 0 , 0 , . . . ) , c1 = (0 , γ1 , 0 , 0 , . . . ), c2 = (0 , 0 , γ2 , 0 , . . . ). • Suppose the student’s preferences can be represented by a β − δ model with β = 12 , δ = 1, u(0) = 0, u(γ0) = −1, u(γ1) = −32 and u(γ2) = −52 . So her HDU from different perspectives is: Period 0 Period 1 Period 2 u0 + 1 2u1 + 1 2u2 u1 + 1 2u2 u2 Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 3 / 52 A Student’s Predicament Q. When does the student do the problem set? • Suppose the student can commit in period 0 to doing the problem set on any of the three possible dates. That is, formally, she solves the problem maxc∈B HDU(c). • From perspective of period 0: – If problem set is done in period 0, HDU(c0) = u(γ0) = −1. – If problem set is done in period 1, HDU(c1) = 12u(γ1) = − 34 . – If problem set is done in period 2, HDU(c2) = 12u(γ2) = − 54 . • Hence, “self 0” plans to do the problem set in period 1. – Because of her taste for immediate gratification, she prefers to delay, but she realises she should not delay too much. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 4 / 52 Commitment Issues • Now suppose the student can’t commit herself. She decides whether to do the problem set period by period. Q. Would she actually do it in period 1? • From perspective of period 1: – If problem set is done in period 1, HDU(c11) = u(γ1) = − 32 . – If problem set is done in period 2, HDU(c12) = 1 2u(γ2) = − 54 . • “Self 1” prefers to do the problem set in period 2! • The student’s preferences are dynamically inconsistent. Q. Given this conflict, when does she actually do the problem set? Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 5 / 52 Naivete versus Sophistication • Answer depends on whether student is aware of her time inconsistent preferences. • Two polar assumptions, student is either 1. a Naif, who does not realize she will change her mind, so assumes her future selves will follow through on her most preferred plan; or, 2. a Sophisticate, who understands her mind will change, so does the best given her correct prediction of the behavior of her future selves. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 6 / 52 Behavior of a Naif • We’ve calculated that self 0 prefers to do problem set in period 1. – Since she’s naive, she believes she will do it in period 1. – So she doesn’t do it in period 0. • Also calculated that self 1 prefers to do problem set in period 2 – So she doesn’t do it in period 1. • Hence naive student does the problem set in period 2. • Since a naive student believes she will do the problem set before the cost becomes too high, she believes she doesn’t lose too much by delaying. But when the next period comes around, she again perceives the cost of delay to be relatively small, so she delays again! • This is a kind of irrational procrastination. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 7 / 52 Behavior of a Sophisticate • We’ve shown that if the student doesn’t do the problem set in period 0, her period 1 self will choose not to do it in period 1, hence it will be done in period 2. • A sophisticated self 0 understands this, so she realizes her choice is effectively between doing the problem set now or in period 2. • Recall, from perspective of period 0: – If problem set is done in period 0, HDU(c0) = u(γ0) = −1. – If problem set is done in period 2, HDU(c2) = 12u(γ2) = − 54 . • So she does the problem set in period 0. • A sophisticated student understands that if she delays “today”, her future self will delay “tomorrow”, so the problem set won’t get done until the “day after tomorrow.” As this is too costly, she (reluctantly?) does the problem set “today”. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 8 / 52 Welfare? Table of (Hyperbolic) Discounted Utilities Perspective t = 0 t = 1 t = 2 Preference Instantaneous −1 −3/2 −5/2 n/a from t = 0 −1 −3/4 −5/4 c1 c0 c2 from t = 1 – −3/2 −5/4 c12 1 c11 • Most behavioral economists would say the sophisticated student does better than the naive student. • Moreover, they would argue this may not seem surprising, since the sophisticated student understands herself (“herselves”) better than the naive student. • But why is this so self-evident? Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 9 / 52 Comparative well-beings Q. How should we compare “welfare” of sophisticate versus naif? – From period 0 perspective, • the sophisticate has to do the problem set now to avoid incurring a much higher cost in two periods time. • naif blissfully avoids incurring cost in period 0, secure in the (as it turns out) incorrect belief that her period 1 self will shoulder the burden. – From period 1 perspective, • the sophisticate can relax since the problem set was done in the previous period. • the naif avoids incurring the cost of doing the problem set in period 1 (i.e. today) knowing her future period 2 self will incur the (higher) cost. – From period 2 perspective, • again, the sophisticate can relax since problem set is already done. • naif stuck “holding the (proverbial) baby”. Q How can (should?) we connect these HDU numbers to DM’s welfare? Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 10 / 52 Comparative well-beings Table of (Hyperbolic) Discounted Utilities Perspective t = 0 t = 1 t = 2 Preference Instantaneous −1 −3/2 −5/2 n/a from t = 0 −1 −3/4 −5/4 c1 c0 c2 from t = 1 – −3/2 −5/4 c12 1 c11 Perspective Naif Sophisticate from t = 0 HDU (c1) = −3/4 HDU (c0) = −1 from t = 1 HDU ( c12 ) = −3/4 HDU (c10) = 0 from t = 2 HDU ( c22 ) = −5/4 HDU (c20) = 0 Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 11 / 52 What about Going to a Movie • Let’s consider now the timing of a pleasant task where the student can go to a movie in exactly one of four periods: t = 0 , 1 , 2 , 3 . • Again wlog, describe this as an IHDP B = {c0 , c1 , c2 , c3}, where: c0 = (γ0 , 0 , 0 , 0 , 0 , . . . ) , c1 = (0 , γ1 , 0 , 0 , 0 , . . . ), c2 = (0 , 0 , γ2 , 0 , 0 , . . . ), c3 = (0 , 0 , 0 , γ3 , 0 , . . . ). • As before, suppose the student’s preferences can be represented by a β − δ model with β = 12 , δ = 1, u(0) = 0, u(γ0) = 1, u(γ1) = 32 , u(γ2) = 9 4 and u(γ3) = 27 8 . Q. When does she go to the movie? Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 12 / 52 Table of (Hyperbolic) Discounted Utilities Perspective t = 0 t = 1 t = 2 t = 3 Preferences Instantaneous 1 3/2 9/4 27/8 n/a from t = 0 1 3/4 9/8 27/16 c3 c2 c0 c1 from t = 1 – 3/2 9/8 27/16 c13 1 c11 1 c12 from t = 2 – – 9/4 27/16 c22 2 c23 Naive student • Period 0: plans to go in period 3, so doesn’t go. • Period 1: plans to go in period 3 so doesn’t go. • Period 2: prefers to go now than in period 3, so goes. Sophisticated student • Period 2: Goes if she hasn’t already • Period 1: realising she won’t wait until period 3 she goes now. • Period 0: realising she won’t wait until period 2 or period 3, she goes now. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 13 / 52 Table of (Hyperbolic) Discounted Utilities Perspective t = 0 t = 1 t = 2 t = 3 Preferences Instantaneous 1 3/2 9/4 27/8 n/a from t = 0 1 3/4 9/8 27/16 c3 c2 c0 c1 from t = 1 – 3/2 9/8 27/16 c13 1 c11 1 c12 from t = 2 – – 9/4 27/16 c22 2 c23 Perspective Naif Sophisticate from t = 0 HDU (c3) = 27/16 HDU (c0) = 1 from t = 1 HDU ( c13 ) = 27/16 HDU ( c10 ) = 0 from t = 2 HDU ( c22 ) = 9/4 HDU ( c20 ) = 0 from t = 3 HDU ( c32 ) = 0 HDU ( c30 ) = 0 Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 14 / 52 The General “Lesson” • The sophisticate’s problem is her pessimism about her future behavior. – She knows she doesn’t have the patience to wait until the movie is really enjoyable. – But given her taste for immediate gratification, the only reason she would wait is to go to go to a much better movie later. – So she goes immediately. • Same pessimism that leads her to do worse with movies leads her to do better with problem sets. • Principle: • If future misbehavior raises the cost of current misbehavior, then sophistication helps in overcoming short-run impatience. • But if future misbehavior lowers the costs of current misbehavior, then sophistication hurts in overcoming short-run impatience. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 15 / 52 Solving Problems with Hyperbolic Discounting • Naive decisionmakers: 1. Start at the beginning. 2. Solve for the optimal plan, assuming future selves will follow this plan. 3. The DM’s choice in this period is the first step in the plan. 4. Goes to the next period, and keep doing the same. • Sophisticated decisionmakers: 1. Start at the end. 2. Solve for the optimal action. 3. go back to the previous period. 4. solve for the optimal action, taking into account what happens in the next period. 5. go back to the previous period, and keep doing the same. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 16 / 52 Is it Really Not Beneficial to be Sophisticated? • Theoretically speaking it’s unclear. – Instance of general result in “strategic interaction”, ‘equilibrium’ need not be ‘efficient’. • But perhaps there are more important tasks of the “problem set” structure than the “movie” structure: 1. Finishing reports/papers/presentations. 2. Finding good investments for retirement. 3. Quitting bad habits. 4. Finding a job • Alternatively, perhaps we are missing some key features of the nature of the intertemporal trade-offs the DM faces. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 17 / 52 Sophisticated Hyperbolic Discounters: Are we missing something? • Resolved time inconsistency by supposing that the decision-maker is sophisticated enough to anticipate her future selves’ preferences and so chooses today taking into account how her future selves will choose tomorrow. – Counter-intuitively, sometimes the sophisticated DM does worse than the naive DM. Q But does this really model a DM subject to temptation who may at some cost exercise self-control? Q Does it really capture the benefit of commitment in situations like the one that Ulysses faced with the Sirens? Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 18 / 52 Temptation and Self-control • Consider a DM deciding in the morning what to eat for lunch: vegetarian dish or hamburger. • In the morning, when she feels no hunger, she prefers the vegetarian dish to the hamburger but at lunchtime, she experiences a craving (an urge) for the hamburger. • So were she able to commit in the morning, she would try to restrict her options at lunch – perhaps by arranging to meet friends at a vegetarian restaurant. • To model this, Gul and Pesendorfer (hereafter GP) propose a framework where DM’s preferences % are defined over menus (that is, sets of alternatives). Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 19 / 52 Temptation and Self-control • GP’s insight is that when an individual resists selecting the most tempting option available, she can only do so at a cost (a self-control cost). – That is, she can only avoid incurring any self-control cost by choosing the most tempting option. • In the situation described above, should she go to a restaurant where both the vegetarian dish and the hamburger are available, either she resists the tempting option at a cost or she succumbs to temptation. • In a more complicated setting (like an infinite horizon decision problem (IHDP)) we would expect the DM’s choice in each period to be affected by a trade-off between her “commitment” preference and her cost of self-control. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 20 / 52 Useful Notation • Let B denote an infinite-horizon decision problem (IHDP). • Recall from slides for week 7’s lectures, for each consumption stream c¯ ∈ B and each period T > 0, we let BT (c¯) denote the set of consumption streams that commence in period T and are still available for the DM to choose from given her consumption choices for the past T periods have been c¯T−1 = (c¯0 , c¯1 , . . . , c¯T−1). More formally, BT (c¯) = { cT : c ∈ B and cT−1 = c¯T−1 } . Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 21 / 52 Dynamically Consistent Self-Control Preferences • Suppose a DM’s preferences % are defined over IHDPs, that is, defined over menus of consumption streams. • First, let V (c| B), where c ∈ B , denote the utility of choosing consumption stream c from the IHDP B . V (c|B) = u (c0) + v (c0)−max cˆ∈B v (cˆ0) + ∞∑ t=1 δt [ u (ct) + v (ct)− max cˆt∈Bt(c) v (cˆt) ] . • GP(2004) characterize the class of Dynamically Consistent Self-Control Preferences as ones for which the preferences % defined over IHDPs can be represented by a function of the form: SCU(B) = max c∈B V (c|B) . Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 22 / 52 Instantaneous Utility with Costly Self-Control • Notice for a singleton IHDP B = {c}, we have SCU({c}) = V (c|{c}) = u(c0) + ∞∑ t=1 δtu(ct) . • More generally, when a DM chooses the consumption stream c = (c0 , c1 , . . . ) from the IHDP B , we may view her “instantaneous utility” in period t as comprising: u (ct)︸ ︷︷ ︸ commitment utility + v (ct)︸ ︷︷ ︸ temptation utility − max cˆt∈Bt(c) v (cˆt)︸ ︷︷ ︸ utility of most tempting consumption available in period t = u (ct)︸ ︷︷ ︸ commitment utility − [ max cˆt∈Bt(c) v (cˆt)− v (ct) ] ︸ ︷︷ ︸ self-control cost . Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 23 / 52 Dynamically Consistent Choice Suppose for each IHDP B , each consumption stream c¯ ∈ B , and each period T > 0, the DM’s choice at time T in the (continuation) IHDP BT (c¯) is a solution to: max cT∈BT (c¯) V ( cT |BT (c¯) ) where V ( cT |BT (c¯)) = u (cT )︸ ︷︷ ︸ period T commitment utility − ( max cˆT∈BT (c¯) v (cˆT )− v (cT ) ) ︸ ︷︷ ︸ period T self-control cost + ∞∑ t=1 δt  u (cT+t)︸ ︷︷ ︸ period T+t commit. utility − ( max cˆT+t∈BT+t(c) v (cˆT+t)− v (cT+t) ) ︸ ︷︷ ︸ period T+t s-c cost  . Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 24 / 52 Dynamically Consistent Choice Thus her choice in any IHDP B will be dynamically consistent since SCU(B) can be re-expressed in a recursive form: SCU(B) = max c∈B u (c0)︸ ︷︷ ︸ period 0 commitment utility − ( max cˆ∈B v (cˆ0)− v(c0) ) ︸ ︷︷ ︸ period 0 self-control cost + δ × SCU(B1(c)). Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 25 / 52 Commitment and Self-Control • The preferences % exhibit a preference for commitment at the IHDP B if there is a B ′ ⊂ B such that B ′ B . • The preferences % exhibit self-control at the IHDP B if there are subsets B ′ ⊂ B and B ′′ ⊂ B with B ′ ∪ B ′′ = B and B ′ B B ′′. • Key Axiom allows both a preference for commitment and the ability for the DM to exert self-control. Set Betweenness B ′ % B ′′ implies B ′ % B ′ ∪ B ′′ % B ′′. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 26 / 52 A Student’s Predicament • Recall the student from last lecture who has to do a problem set in exactly one of three periods t = 0, t = 1 or t = 2. • Without loss of generality, can describe this as an IHDP B = {c0 , c1 , c2}, where: c0 = (γ0 , 0 , 0 , 0 , . . . ) , c1 = (0 , γ1 , 0 , 0 , . . . ), c2 = (0 , 0 , γ2 , 0 , . . . ). • Suppose the student’s preferences can be represented by a dynamically consistent self-control preference model with δ = 1, u(0) = 0, u(γ0) = −1, u(γ1) = −3, u(γ2) = −4, v(0) = 0 and v(γ0) = v(γ1) = v(γ2) = −3. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 27 / 52 A Student’s Predicament Q. When does the student do the problem set? V (c0|B) = u (γ0)︸ ︷︷ ︸ period 0 commit. utility − ( max cˆ∈B v (cˆ0)− v(γ0) ) ︸ ︷︷ ︸ period 0 self-control cost = −4 V (c1|B) = u (γ1)︸ ︷︷ ︸ period 1 commit. utility − ( max cˆ1∈B1(c1) v (cˆ1)− v(γ1) ) ︸ ︷︷ ︸ period 1 self-control cost = −6 V (c2|B) = u (γ2)︸ ︷︷ ︸ period 2 commit. utility − ( max cˆ2∈B2(c2) v (cˆ2)− v (γ2) ) ︸ ︷︷ ︸ period 2 self-control cost = −5 Hence SCU(B) = maxc∈B V (c|B) = −4. Moreover, SCU ({c0}) = −1 > −3 = SCU ({c1}) > −4 = SCU (B) > −5 = SCU ({c2}) . And so we have {c0} {c1} B {c2} . Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 28 / 52 What about Going to a Movie • Let’s consider now the timing of a pleasant task where the student can go to a movie in exactly one of four periods: t = 0 , 1 , 2 , 3 . • Again wlog, describe this as an IHDP B = {c0 , c1 , c2 , c3}, where: c0 = (γ0 , 0 , 0 , 0 , 0 , . . . ) , c1 = (0 , γ1 , 0 , 0 , 0 , . . . ), c2 = (0 , 0 , γ2 , 0 , 0 , . . . ), c3 = (0 , 0 , 0 , γ3 , 0 , . . . ). • Suppose again the student’s preferences can be represented by a dynamically consistent self-control preference model with δ = 1, u(0) = 0, u(γ0) = 1, u(γ1) = 32 , u(γ2) = 9 4 , u(γ3) = 27 8 and v(c) = u(c). Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 29 / 52 When does she go to the movie? V (c0|B) = u (γ0)︸ ︷︷ ︸ period 0 commit. utility − ( max cˆ∈B v (cˆ0)− v(γ0) ) ︸ ︷︷ ︸ period 0 self-control cost = 1 V (c1|B) = −1 + 32 = 1 2 V (c2|B) = −1− 32 + 9 4 =− 1 4 V (c3|B) = −1− 32 − 9 4 + 27 8 =− 11 8 So we have SCU ({c3}) = 278 > SCU ({c2}) = 9 4 > SCU ({c1}) = 32 > SCU ({c0}) = 1 = SCU (B) that is, {c3} {c2} {c1} {c0} ∼ B . Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 30 / 52 Preference Changes • Three categories of ways that preferences change over time: 1. Temporary fluctuations (e.g. hunger). 2. Adaptation, both big (e.g., standard of living, parenthood) and small (e.g., mug ownership). 3. Addiction and other long-term changes (e.g. aging). • An additional stylized fact: we are bad at predicting these changes. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 31 / 52 Projection Bias [DEF] Projection Bias People underappreciate changes in their preferences, projecting current preferences over consumption onto future preferences. • So projection bias isn’t just a random misprediction, but a misprediction with a systematic direction. • We’ll first look at evidence on projection bias, and then think about its consequences for economics. • The evidence is best for short-term changes (because experimentation is easier), so we’ll focus on that. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 32 / 52 Hunger • Underappreciation of effects of hunger is not so important economically, but two reasons to consider the evidence on it: – Perhaps the clearest evidence of projection bias. – People have had lots of experience with changes in their level of hunger, so misperception not due to a lack of opportunity to learn. • It’s folk wisdom that shopping on an empty stomach leads people to buy more. This has been confirmed using variants of a simple experimental design: – Give random sample entering a supermarket a candy bar. – Monitor how much food every one buys. – Interpret finding: “people buy more on an empty stomach” as “people who are hungry act as if their future taste for food will reflect such hunger”. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 33 / 52 Hunger • But these studies are not completely unambiguous evidence of projection bias: it could be that shoppers are buying food for later that evening, so that it’s reasonable for them to buy less if they’ve had a candy bar. • Read and van Leeuwen (1998) provide a cleaner experiment. – Office workers asked to choose now between a healthy snack or an unhealthy snack, to be received either late in the afternoon (in hungry state), or immediately after lunch (in satiated state), in one week. – Their current choice was made (now), either in a hungry state or in a satiated state. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 34 / 52 Read and van Leeuwen (1998) • Proportion choosing the unhealthy snack: Will be hungry Will be satiated Now Hungry 78% 56% Now Satiated 42% 26% • Workers who expected to be hungry the following week were more likely to opt for unhealthy snacks. – Reflects increased taste for unhealthy snacks in the hungry state. • Workers who were hungry when they made the choice were more likely to opt for unhealthy snacks. – They project their current preferences onto their future selves. • Overall, they seem to understand the direction of the preference change, but not the magnitude. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 35 / 52 Altered States • Badger et al (2007) conducted a similar study on addiction using actual drug addicts. • All addicts were to receive a dose of the heroin substitute Buprenorphine (BUP) on Day 5. • The authors elicited addicts’ monetary valuations for an extra dose of BUP on Day 5 in four conditions. • Elicitation done on Day 1 or Day 5. • Elicitation done either before a dose of BUP, elicitation done or after a dose of BUP. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 36 / 52 Immediate craving’s impact on current & future valuations • Median valuations: Day 5 (immediate) Day 1 (delayed) Satiated $50 $35 Deprived $75 $60 • Addicts valued the extra dose significantly more if they were deprived of BUP at the moment of elicitation than if they were satiated at the moment of elicitation. – When satiated, addicts don’t seem to appreciate how powerfully cravings will influence their desire for BUP. • The results also consistent with hyperbolic discounting. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 37 / 52 Additional evidence • Male sexual behavior: when not aroused, men can’t predict how they’d feel when aroused. • Fluctuations in hunger, arousal and (for addicts) cravings are things for which we have lots of experience. • That we mispredict changes in preferences even for these things suggests projection bias is hard to unlearn. • But consider major decisions such as starting a family or deciding on a career: confronted by the brutal fact – – we can only know very little about our subjective futures. – with fewer opportunities to learn such changes resulting from long-term decisions suggests projection bias is even stronger! Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 38 / 52 Transformative Experience • Serious implications for our major decisions. • If we try to make choice by considering what we care about (now), and what our future selves will be like if we choose to have the experience, potential for projection bias is huge! • Essentially only learn what we need to know after we have already committed ourselves! BUT! If we try to escape the dilemma by avoiding an experience, then we have still made a choice! • The philosopher, L.A. Paul, suggests choosing “rationally” may require us to regard big life decisions as choices to make discoveries, small and large, about the instrinsic nature of experience, and to recognize that part of the value of living authentically is to experience one’s life and preferences in whatever way they evolve in the wake of the choices one makes. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 39 / 52 Projection Bias in Adaptation • People underestimate adaptation to changes. • Gilbert (author of Stumbling on Happiness) in various papers gives many examples of such underestimation, which he and his coauthors call “immune neglect”. • For example: – Assistant professors at U Texas forecasted their well-being at various points in time following their positive and negative tenure decision. – Former U Texas assistant professors reported well-being at various times after their tenure decision. • Professors were relatively accurate in predicting the immediate impact of the tenure decision, but overestimated the long-term impact. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 40 / 52 Naive Hyperbolic Discounting v. Projection Bias • Naivete in hyperbolic discounting is also a kind of misprediction: you think you’ll have more self-control in the future than you actually will. • Projection bias is a state-dependent misprediction. – You’re more likely to predict future temptation to over-eat when hungry. – You’re more likely to predict future smoking when you haven’t had a cigarette for a while. • But sometimes hard to distinguish. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 41 / 52 Child-birth example • Consider a woman looking forward to childbirth who thinks she should and will give birth without anaesthetic. But! when time comes, she wants anaesthetic. • Could be naive hyperbolic discounting: – thought she’d be patient and bear the immediate pain, but she isn’t patient. • Could be projection bias: – when not in pain, she fails to appreciate how hard it is to bear the pain. • Important distinction: – if it’s hyperbolic discounting then administering anaesthetic might be the wrong thing for her. – if it’s projection bias then administering anaesthetic is right for her. • Challenge for you: how can we tell which one it is? Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 42 / 52 A Model of Projection Bias • ‘True utility’ at time t depends on both consumption ct at time t and the state st at time t: u(ct , st). – The state can be anything that affects utility from consumption: level of hunger or addiction, past consumption, and so on. • The person’s prediction at time t about utility from consuming cτ at time τ > t is αu(cτ , st) + (1− α)u(cτ , sτ ) . i.e., perception of future preferences lies between current preferences and what they will actually be in the future. α is degree of perception bias. • α = 0 is correct understanding of future utility. • α = 1 is full projection bias. • The person maximizes according to her perceived preferences. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 43 / 52 An Example with Hunger Willingness to pay for a burger • Two states, hungry (H) and not hungry (N). • Let utility be defined over burgers and money, with u (ct ,H) = 5× (# of burgers) + $ u (ct ,N) = (# of burgers) + $ • This means the person is willing to pay $5 for a burger when hungry, and $1 when not hungry. • Suppose now (at time t): α = 3/4 and the person isn’t hungry. Q. What’s the most expensive burger she’s willing to order now for tonight (at time τ > t) when she’ll be hungry? A. She thinks her utility function tonight will be: 3 4 u(cτ ,N) + 1 4 u(cτ ,H) = 2× (# of burgers) + $ so now (at time t) she’s willing to pay at most $2. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 44 / 52 Endowment Effect • Consider 2 groups of people, owners & non-owners of mugs. Recall: – In this situation, the selling price is higher than the buying price. – The natural explanation for this endowment effect is loss aversion. • Since a mug is a durable good, we now add a time element and projection bias. – Buyers and sellers take into account their utility in future periods. – State: whether you owned a mug in the previous period. Let α = 1. Utility is a function of whether you have a mug now (y or n) and whether you had a mug in the previous period (y or n): u(y , y) = 1 + 0 ; u(n, y) = 0− λk ; u(y , n) = 1 + k ; u(n, n) = 0 + 0 . Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 45 / 52 Projection Bias and Endowment Effect • Seller: – Feels bad about losing a mug (utility u(n, y) = −λk). This’ll last for one period (after that, it’s u(n, n) = 0). – But she thinks that it’ll last forever (that is, her per period utility will always be −λk). – She correctly predicts what it’s like to have a mug (per period utility u(y , y) = 1). ⇒ values having the mug more than a seller with no projection bias. • Buyer: – Feels good about getting a mug (utility u(y , n) = 1 + k . This’ll last for one period (after that, it’s u(y , y) = 1). – But he thinks it’ll last forever (that his per period utility will always be 1 + k). – He correctly predicts what it’s like not to have a mug (per period utility u(n, n) = 0). ⇒ values having the mug more than a buyer with no projection bias. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 46 / 52 Projection Bias and Endowment Effect So: projection bias leads to overvaluation of reference-dependent durable goods relative to non-reference-dependent/non-durable goods. • The selling price is likely exaggerated more than the buying price. – Since the intial sensation is stronger for sellers, sellers’ projection bias has a greater effect than buyers’. • Projection bias qualifies earlier interpretation of endowment effect. – Earlier we viewed endowment effect as manifestation of loss aversion – a preference to avoid losses. • But projection bias exaggerates endowment effect. – So endowment effect is most likely an exaggerated response to real preferences. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 47 / 52 Similar Logic Applies to Other Settings • A reinterpretation of the model: – “having a mug” → “having higher income” – “money” → “working hard to increase income” – “buying price for mug” → “willingness to work hard to increase income” – “selling price for mug” → “willingness to work hard to avoid decreases in income” • So the model implies a person is willing to work too hard to increase income, and especially to avoid decreases in income. – Thinks she’ll enjoy higher living standards forever, so she works really hard to get richer. – After a while, she’s surprised that she doesn’t enjoy it . . . but she thinks going back would be terrible, so works hard to avoid that. – Due to diminishing sensitivity, she might value now further increases in living standards more than originally, so works even harder!! • Hyperbolic discounting acts against all these predictions. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 48 / 52 Projection Bias: Connections to other Biases • In an endowment-effect experiment, sellers were asked to estimate how much buyers would pay and buyers were asked to estimate how much sellers would charge, with all subjects rewarded for accurate predictions. • Sellers overestimated buying prices, buyers underestimated selling prices. • Consistent with interpersonal projection bias: people project their preferences onto others. • Actually, people project many types of information onto situations where this not appropriate. – Hindsight bias: if learn something, believe always known it. – Curse of knowledge: if know something, can’t appreciate what it’s like not to know it. – False consensus effect: people overestimate the extent to which others agree with them. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 49 / 52 Concept Recap • (Quasi-)Hyperbolic discounting • The β − δ HDU model • Commitment solution • Naive decisionmaker • Sophisticated decisionmaker • Temptation and self-control • Dynamically consistent self-control preferences • commitment utility and temptation utility • Dynamically consistent choice • preference for commitment and the ability to exhibit self-control • Set Betweenness Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 50 / 52 Concept Recap (continued) • Projection bias • Transformative experience • Projection bias in adaptation • Projection bias and endowment effect • Reference-dependent durable goods • Hindsight bias • Curse of knowledge • False consensus Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 51 / 52 References Badger, G.J., W.K. Bickel, L.A. Giordano, E.A. Jacobs, G. Loewenstein, L. Marsch (2007), “Altered states: The impact of immediate craving on the valuation of current and future opiods,” Journal of Health Economics 26, 865–876. Gul, F. and W. Pesendorfer (2001), “Temptation and Self-Control,” Econometrica 69, 1403–1435. Gul, F. and W. Pesendorfer (2004), “Self-Control and the Theory of Consumption,” Econometrica 72, 119–158. Paul, L.A. (2014). Transformative Experience, Oxford University Press, Oxford, England. Read, D. and B. van Leeuwen (1998), “Predicting Hunger: The Effects of Appetite and Delay on Choice,” Organizational Behavior and Human Decision Processes 76, 189–205. Grant (ANU) ECON2013 Behavioral Economics Week 8: Intertemporal Choice (continued)27/09 – 01/10 52 / 52