Behavioural Economics Mark.Hurlstone @Uwa.Edu.Au Behavioural Economics Outline

Home , Hyperbolic discounting, Intertemporal choice

Behavioural Economics mark.hurlstone @uwa.edu.au Behavioural Economics Outline

Intertemporal Choice

Exponential PSYC3310: Specialist Topics In Psychology Discounting Discount Factor Utility Streams Mark Hurlstone Delta Model Univeristy of Western Australia Implications Indifference Discount Rates

Limitations Seminar 7: Intertemporal Choice

Hyperbolic Discounting Beta-delta model CSIRO-UWA Behavioural Present-Bias Strengths & Economics Limitations BEL Laboratory

[email protected] Behavioural Economics Today

Behavioural Economics • mark.hurlstone Examine preferences (4), time (2), and utility @uwa.edu.au maximisation (1) in standard model)

Outline (1) (2) (3) (4) Intertemporal Choice

Exponential Discounting Discount Factor Utility Streams Delta Model Implications Indifference Discount Rates • Intertemporal choice—the exponential discounting Limitations model Hyperbolic Discounting • anomalies in the standard Model Beta-delta model Present-Bias • behavioural economic alternative—quasi-hyperbolic Strengths & Limitations discounting

[email protected] Behavioural Economics Today

Behavioural Economics • mark.hurlstone Examine preferences (4), time (2), and utility @uwa.edu.au maximisation (1) in standard model)

Outline (1) (2) (3) (4) Intertemporal Choice

[email protected] Behavioural Economics Intertemporal choice

Behavioural Economics mark.hurlstone • Time is important in most decisions because the choices we @uwa.edu.au make will have future consequences Outline • Intertemporal choices relate to decisions involving Intertemporal Choice trade-offs between costs and beneﬁts occurring in different

Exponential time periods e.g., Discounting Discount Factor • when purchasing a 1-year warranty for a new tablet Utility Streams Delta Model computer, you are choosing between a certain loss now Implications Indifference and the possibility of suffering a loss later Discount Rates

Limitations • Some decisions have immediate beneﬁts and deferred costs

Hyperbolic (e.g., movie with friends vs. clean house) Discounting Beta-delta model • Others have immediate costs and deferred beneﬁts (e.g., Present-Bias Strengths & comfortable retirement vs. new car) Limitations

[email protected] Behavioural Economics Time discounting

Behavioural Economics mark.hurlstone @uwa.edu.au • People tend to be impatient—they prefer immediate rewards to delayed rewards Outline

Intertemporal • $100 today is preferred to $100 tomorrow; $1000 today Choice is preferred to $1000 next year Exponential Discounting • Discount Factor When things in the future do not give you as much Utility Streams utility—from the point of view of today—as things that Delta Model Implications happen today, we say you discount the future Indifference Discount Rates • the general term is time discounting Limitations Hyperbolic • The extent to which you discount the future is a matter Discounting Beta-delta model of preference—known as time preference Present-Bias Strengths & Limitations

[email protected] Behavioural Economics Exponential discounting: Discount factor

Behavioural Economics • The standard model explains the fact that people prefer their mark.hurlstone @uwa.edu.au money sooner rather than later in terms of exponential discounting Outline Intertemporal • Suppose that u > 0 is the utility you derive from receiving a Choice dollar today Exponential Discounting • Discount Factor From your current point of view (viz. today) the utility of Utility Streams receiving a dollar tomorrow is less than u Delta Model Implications Indifference • We capture this by multiplying the utility of receiving a dollar Discount Rates today by a parameter δ (0 < δ ≤ 1) known as the discount Limitations factor Hyperbolic Discounting • Thus, from your current point of view, a dollar tomorrow is Beta-delta model Present-Bias worth δ × u = δu; a dollar the day after tomorrow will be Strengths & 2 Limitations worth δ × δ × u = δ u

[email protected] Behavioural Economics Exponential discounting: Utility streams

Behavioural Economics mark.hurlstone @uwa.edu.au • In general, we want to be able to evaluate a whole sequence of utilities, that is a utility stream Outline Intertemporal • Letting t represent time, we will use t = 0 to represent Choice

Exponential today, t = 1 to represent tomorrow, t = 2 to represent the Discounting day after tomorrow, and so on Discount Factor Utility Streams Delta Model • We will let ut denote the utility you receive at time t Implications Indifference meaning that: Discount Rates • u represents the utility you receive today Limitations 0 • u1 represents the utility you receive tomorrow Hyperbolic Discounting • u2 represents the utility you receive the day after Beta-delta model Present-Bias tomorrow, and so on Strengths & Limitations

[email protected] Behavioural Economics Exponential discounting: Utility streams

Behavioural Economics mark.hurlstone @uwa.edu.au Utility streams for different choice options (viz. a, b, c, d)

Outline can be represented in table form:

Intertemporal Choice t = 0 t = 1 t = 2 Exponential Discounting a 1 0 0 Discount Factor Utility Streams b 0 3 0 Delta Model Implications c 0 0 4 Indifference Discount Rates d 1 3 4 Limitations Hyperbolic We can determine which option you should choose using Discounting Beta-delta model the delta model Present-Bias Strengths & Limitations

[email protected] Behavioural Economics Exponential discounting: The delta model

Behavioural Economics mark.hurlstone @uwa.edu.au According to the delta function, the utility U0(u) of utility Outline stream u = hu0, u1, u2, ...i from the point of view of time t = 0 Intertemporal Choice is:

Exponential Discounting ∞ Discount Factor 0 2 3 X t Utility Streams U (u) = u0 + δu1 + δ u2 + δ u3 + ... = σ ut (1) Delta Model t=1 Implications Indifference Discount Rates Where δ (0 < δ ≤ 1) is the discount factor which captures Limitations time preference (patience = values close to 1, whereas Hyperbolic impatience = values close to 0) Discounting Beta-delta model Present-Bias Strengths & Limitations

[email protected] Behavioural Economics Exponential discounting: The delta model

Behavioural Economics • Let’s apply the delta model to the utility streams in the mark.hurlstone @uwa.edu.au table on the earlier slide

Outline • Assume that δ = 0.9 and each utility stream is Intertemporal evaluated from t = 0 Choice • The expected utilities are: Exponential Discounting • 0 Discount Factor U (a) = u0 = 1 Utility Streams • U0(b) = δu = 0.9 × 3 = 2.7 Delta Model 1 0 2 2 Implications • U (c) = δ u2 = 0.9 × 4 = 3.24 Indifference 0 2 Discount Rates • U (d) = u0 + δu1 + δ u2 = 1 + 2.7 + 3.24 = 6.94 Limitations • Hyperbolic If given the choice between all four alternatives, you Discounting should choose option d Beta-delta model Present-Bias Strengths & • If given the choice between a, b, and c, you should Limitations choose c

[email protected] Behavioural Economics Exponential discounting: The delta model

Behavioural Economics mark.hurlstone @uwa.edu.au • What happens if we repeat this process, but this time assume that δ = 0.1? Outline • Intertemporal The expected utilities are: Choice 0 • U (a) = u0 = 1 Exponential 0 Discounting • U (b) = δu1 = 0.1 × 3 = 0.3 Discount Factor • U0 δ2u 2 × Utility Streams (c) = 2 = 0.1 4 = 0.04 0 2 Delta Model • U (d) = u0 + δu1 + δ u2 = 1 + 0.3 + 0.04 = 1.34 Implications Indifference Discount Rates • If given the choice between all four alternatives, you Limitations should still choose option d Hyperbolic Discounting • But now, if given the choice between a, b, and c, you Beta-delta model Present-Bias should choose a Strengths & Limitations

[email protected] Behavioural Economics Exponential discounting: Implications of discount factor

Behavioural Economics mark.hurlstone @uwa.edu.au

Outline • As this example shows, your discount factor can have a Intertemporal dramatic impact on your choices Choice Exponential • If your discount factor is high—viz. close to one—you Discounting Discount Factor exhibit patience and do not discount the future much Utility Streams Delta Model • Implications If your discount factor is low—viz. close to zero—you Indifference Discount Rates exhibit impatience and discount the future heavily Limitations • You can see how δ captures time preferences Hyperbolic Discounting Beta-delta model Present-Bias Strengths & Limitations

[email protected] Behavioural Economics Exponential discounting: Implications of discount factor

Behavioural Economics mark.hurlstone @uwa.edu.au • Economists believe that discount factors can be used to Outline

Intertemporal explain a great deal of human behaviour Choice • Exponential If your discount factor is low, you are are more likely to Discounting spend money, procrastinate, do drugs, and have unsafe Discount Factor Utility Streams sex Delta Model Implications Indifference • If your discount factor is high, you are more likely to Discount Rates

Limitations save money, plan for the future, say no to drugs and

Hyperbolic use protection Discounting Beta-delta model Present-Bias Strengths & Limitations

[email protected] Behavioural Economics Exponential discounting: Indifference

Behavioural Economics • So far, we have used our knowledge of δ to determine a mark.hurlstone @uwa.edu.au person’s preferences over utility streams

Outline • Sometimes we want to go the other way—viz. use a person’s Intertemporal preferences to calculate their discount factor Choice

Exponential • Discounting is measured by getting participants to choose Discounting between an immediate and delayed reward: Discount Factor Utility Streams Delta Model • would you prefer $100 today or $110 1-year from now? Implications Indifference • would you prefer $100 today or $130 1-year from now? Discount Rates • would you prefer $100 today or $160 1-year from now? Limitations • and so on ... Hyperbolic Discounting Beta-delta model • As soon as the participant is indifferent between an Present-Bias Strengths & immediate and delayed reward we can calculate his or her Limitations discount factor

[email protected] Behavioural Economics Exponential discounting: Indifference

Behavioural Economics mark.hurlstone @uwa.edu.au • Suppose that you are indifferent between a = $100 now, and b = $160 in 1-year Outline

Intertemporal • Let’s convert the monetary amounts into utilities ﬁrst: a Choice = 1000.5 = 10; b = 1600.5 = 12.65 Exponential Discounting • Given you are indifferent between a and b at time zero, Discount Factor Utility Streams we know that: Delta Model 0 0 Implications • U (a) = U (b) Indifference Discount Rates • which implies that 10 = 12.65δ Limitations • which is to say that δ = 10/12.65 = 0.79 Hyperbolic Discounting • The calculated discount factor indicates that you are Beta-delta model Present-Bias relatively patient Strengths & Limitations

[email protected] Behavioural Economics Exponential discounting: Indifference

Behavioural Economics mark.hurlstone @uwa.edu.au • Now, let’s suppose that you are indifferent between a = $100 now, and b = $1000 in 1-year Outline

Intertemporal • Lets again convert the monetary amounts into utilities Choice ﬁrst: a = 1000.5 = 10; b = 10000.5 = 31.62 Exponential Discounting • Given you are indifferent between a and b at time zero, Discount Factor Utility Streams we know that: Delta Model 0 0 Implications • U (a) = U (b) Indifference Discount Rates • which implies that 10 = 31.62δ Limitations • which is to say that δ = 10/31.62 = 0.32 Hyperbolic Discounting • The calculated discount factor indicates that you are Beta-delta model Present-Bias relatively impatient Strengths & Limitations

[email protected] Behavioural Economics Exponential discounting: Discount rates

Behavioural Economics Sometimes discounting is expressed in terms of a discount mark.hurlstone rate r rather than a discount factor δ. The conversion is as @uwa.edu.au follows: Outline 1 − δ Intertemporal r = (2) Choice δ Exponential Discounting If your discount factor is 0.79 then your discount rate is 0.27. Discount Factor Utility Streams This means you would require an interest rate of 27% to Delta Model Implications delay receiving the $100 (the interest rate would be 212% if Indifference Discount Rates your discount factor is 0.32). Limitations Hyperbolic Knowing r, you can calculate δ as follows: Discounting Beta-delta model Present-Bias 1 Strengths & δ = (3) Limitations 1 + r

[email protected] Behavioural Economics Exponential discounting: Limitations

Behavioural Economics • mark.hurlstone A major shortcoming of this model is that it assumes @uwa.edu.au that people have time consistent preferences:

Outline • implies that your preferences over two options should Intertemporal not change simply because times passes Choice • if you feel (today) that a is better than b, then you felt Exponential Discounting the same way about a and b yesterday, and will feel the Discount Factor Utility Streams same way tomorrow Delta Model Implications • Indifference The bad news is that people violate this assumption all Discount Rates the time: Limitations • saying you will give up alcohol ... Hyperbolic Discounting • promising to stop smoking ... Beta-delta model • Present-Bias purchasing that gym membership ... Strengths & • Limitations planning to do your homework ...

[email protected] Behavioural Economics Exponential Discounting: Limitations

Behavioural Economics mark.hurlstone @uwa.edu.au

Outline • Further shortcomings of the model of exponential Intertemporal discounting: Choice • Exponential speaker 1: sign effect, magnitude effect, & temporal Discounting loss aversion Discount Factor Utility Streams • speaker 2: delay speed-up asymmetry & preference for Delta Model Implications improving sequences Indifference Discount Rates • speaker 3: date-delay effect & violations of Limitations independence Hyperbolic Discounting Beta-delta model Present-Bias Strengths & Limitations

[email protected] Behavioural Economics Quasi-hyperbolic discounting

Behavioural Economics • mark.hurlstone The evidence we have covered suggests that people do not @uwa.edu.au have time consistent preferences Outline • People tend to be patient for long-term gains, but impatient Intertemporal for short-term gains: Choice Exponential • on Friday you might plan to do your homework on Discounting Discount Factor Saturday, but when Saturday comes you prefer to do it Utility Streams Delta Model on Monday Implications • today you might prefer to reject $100 tomorrow in favour Indifference Discount Rates of $110 the day after, but tomorrow you change your Limitations mind Hyperbolic Discounting • We say that there is time inconsistency if someone plans to Beta-delta model Present-Bias do something in the future, but subsequently changes their Strengths & Limitations mind

[email protected] Behavioural Economics Quasi-hyperbolic discounting: Beta-delta model

Behavioural Economics mark.hurlstone @uwa.edu.au 0 Outline According to the beta-delta function, the utility U (u) of Intertemporal utility stream u = hu0, u1, u2, ...i from the point of view of time Choice t = 0 is: Exponential Discounting Discount Factor ∞ Utility Streams 0 2 3 X t Delta Model U (u) = u0 + βδu1 + βδ u2 + βδ u3 + ... = u1 + β σ ut (4) Implications Indifference t=1 Discount Rates Limitations Where δ is as before, and β is the present bias Hyperbolic Discounting Beta-delta model Present-Bias Strengths & Limitations

[email protected] Behavioural Economics Quasi-hyperbolic discounting: Beta-delta model

Behavioural Economics mark.hurlstone @uwa.edu.au • The beta-delta model is the same as the delta model, except for the inclusion of the parameter β Outline

Intertemporal • When β = 1, the model reduces down to the delta model Choice • Exponential However, when β < 1, all outcomes beyond the present time Discounting get discounted more than under exponential discounting Discount Factor Utility Streams Delta Model • Hence, when β < 1 more weight is given to today than the Implications Indifference future and we say there are present-biased preferences Discount Rates • If you exhibit such preferences, then given the choice Limitations between a small earlier reward and a bigger, later reward Hyperbolic Discounting you will end up choosing the smaller immediate reward (but Beta-delta model Present-Bias regret it afterwards) Strengths & Limitations

[email protected] Behavioural Economics Quasi-hyperbolic discounting: Present-bias

Behavioural Economics mark.hurlstone @uwa.edu.au • Suppose you are on a diet but have to decide between Outline having a piece of cake at a party on Saturday Intertemporal Choice • Eating the cake gives you a utility of 4 Exponential Discounting • However, if you eat it, you will have to exercise for four hours Discount Factor Utility Streams on Sunday, giving you a utility of 0 (assuming you are like Delta Model Implications most people) Indifference Discount Rates • Alternatively, you could skip the cake, giving you a lowly Limitations utility of 1, but obtain a utility of 6 on Sunday by watching Hyperbolic Discounting back-to-back episodes of The Batchelor Beta-delta model Present-Bias Strengths & Limitations

[email protected] Behavioural Economics Quasi-hyperbolic discounting: Present-bias

Behavioural Economics mark.hurlstone @uwa.edu.au

Outline

Intertemporal Choice Friday (t = 0) Saturday (t = 1) Sunday (t = 2) Exponential Discounting a 0 4 0 Discount Factor Utility Streams b 0 1 6 Delta Model Implications Indifference Discount Rates

Limitations

Hyperbolic Discounting Beta-delta model Present-Bias Strengths & Limitations

[email protected] Behavioural Economics Quasi-hyperbolic discounting: Present-bias

Behavioural Economics • Let’s apply the beta-delta model to this example, with β = 0.5 mark.hurlstone @uwa.edu.au and δ = 0.67

Outline • On Friday, the utility of eating the cake a and skipping it b is:

Intertemporal 0 2 Choice • U (a) = 0 + 0.5 × 0.67 × 4 + 0.5 × 0.67 × 0 = 1.33 0 2 Exponential • U (b) = 0 + 0.5 × 0.67 × 1 + 0.5 × 0.67 × 6 = 1.67 Discounting Discount Factor Utility Streams • On Saturday, the utility of eating the cake a and skipping it b Delta Model Implications is: Indifference Discount Rates • U1(a) = 4 + 0.5 × 0.67 × 0 = 4 Limitations • U1(b) = 1 + 0.5 × 0.67 × 6 = 3 Hyperbolic Discounting • Beta-delta model On Friday, you would prefer to skip the cake, but come Present-Bias Saturday impulsivity causes you to change your Strengths & Limitations mind—time inconsistency at work

[email protected] Behavioural Economics Quasi-hyperbolic discounting: Strengths & limitations

Behavioural Economics mark.hurlstone @uwa.edu.au • Quasi-hyperbolic discounting can explain time

Outline inconsistent preferences Intertemporal • Choice It can account for the fact that people emphasise their

Exponential present over their future well-being Discounting Discount Factor • It can also account for the fact that people change their Utility Streams Delta Model minds about how to balance the present versus the Implications Indifference future Discount Rates Limitations • Thus, it can explain why people intend to diet, stop Hyperbolic Discounting smoking, do homework, and quit drugs, and then fail to Beta-delta model Present-Bias do so Strengths & Limitations

[email protected] Behavioural Economics Quasi-hyperbolic discounting: Strengths & limitations

Behavioural Economics mark.hurlstone • @uwa.edu.au The model can therefore explain a number of phenomena that are inconsistent with the model of exponential Outline discounting Intertemporal Choice • Yet, there are other aspects of the data reviewed by our Exponential Discounting speakers that the model cannot explain, such as the sign Discount Factor effect, preferences for improving sequences, and the Utility Streams Delta Model peak-end rule Implications Indifference Discount Rates • The book chapters in the general reading section describe Limitations more elaborate behavioural models that are capable of Hyperbolic providing a more complete account of the data—the chapter Discounting Beta-delta model by Cartwright (2011) provides a nice overview of these Present-Bias models Strengths & Limitations

[email protected] Behavioural Economics