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 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 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 1 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