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Intertemporal choice Old results and new results

Intertemporal choice Old results and new results. Daniel Read. Thanks to: Robin Cubitt; Rebecca McDonald; Marc Scholten. Intertemporal choices. Choices between outcomes occurring at different times. Often between smaller-sooner ( SS ) and larger-later ( LL ) outcomes. YET LATER. NOW.

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Intertemporal choice Old results and new results

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  1. Intertemporal choiceOld results and new results Daniel Read Thanks to: Robin Cubitt; Rebecca McDonald; Marc Scholten

  2. Intertemporal choices • Choices between outcomes occurring at different times. • Often between smaller-sooner (SS) and larger-later (LL) outcomes. YET LATER NOW LATER

  3. Some more intertemporal choices • Children now or Children later • Dessert now or Slender later • Smoke now or Live longer • Work now or Education now and work later • Present research now or wait for definitive findings • Misery now orPurgatory later • £100 now or £150 in one year

  4. Smaller-Sooner: YLC 100 today is equivalent to Larger-Later: YLC ____ in one year. • Imagine a “Becker DeGrootMarschak” procedure will be carried out. • I randomly generate an amount YLC 100 or greater • If you demand no more than that amount you will receive what you specified • Otherwise you get SS. How much? Why?

  5. Economics of intertemporal choice Later t1 You are endowed with wealth (e0,e1) You can borrow or lend at rate r. These opportunities form a budget line When Marginal rate of intertemporal substitution = the interest rate Through borrowing or lending you will choose the optimal point on the budget line. e1 c1 U3 This person lends e0 – c0to achieve consumption (c0,c1). U2 U1 c0 e0 t0 Sooner

  6. Therefore what SHOULD you have chosen? One year Determine the best return you can get for YLC100. For most of you (lenders) it will be close to 0% £/$/€ For borrowers it could be as much as 40% Specify LL equivalent to that rate of return. YLC100 Now

  7. Excessive discounting • When making intertemporal choices for money, people typically exceed any plausible market rate of interest.

  8. The Magnitude Effect • People are typically more patient for larger amounts, holding rate of return constant. • 10K now 11K in two years but • 1K now 1.1K in two years (times two)

  9. Why is the magnitude effect an anomaly? The money pump argument • STEP 1: You exchange £1,000 this year for £1,100 in one year, and pay a fee. (Savings). • STEP 2: You exchange £110 next year for £100 now, and pay a fee. Repeat until all your money is available now. (Borrowing). • REPEAT STEP 1. • REPEAT STEP 2. • Etc … until you are pumped dry.

  10. Sign effect • People are more patient for losses than gains • 10K now 11K in two years but • -10K now -11K in four years

  11. Subadditivity • People are more patient over longer intervals, so that dividing an interval into subunits increases impatience. • 10K now 11K in two years But both • 10K now 10.5K in one year, AND • 10.5K in one year 11K in two years Note this is just an illustrative example – tests for subadditivity are a bit more complex.

  12. Framing effects • Degree of patience highly dependent on how options are described. • Violations of “descriptive invariance” – the rationality principle that preferences are over options and not their representation or descriptions.

  13. Some framing effects • Date/delay effect: Describing time in terms of dates increases patience. (Read, Frederick. Orsel; MS, 2005) • Age/delay effect: Describing time in terms of your age increases patience. (Frederick & Read, in progress) • Explicit zeroes: Making zero outcomes explicit increases patience. (Megan, Dweck & Gross, 2008; Read & Scholten, 2012; Read, Olivola & Hardisty, in progress) • Interest rates: People are generally more patient when returns are given as rates rather than amounts (Read, Frederick, Scholten, 2013).

  14. A framing effect in intertemporal choice Choice of LL Shows proportion of people choosing “Larger Later” options given 1, 3 and 10 year delays. “Hyperbolic” discounting for total returns (described as proportions) Anti-hyperbolic for rates of return. “Exponential” when both frames are combined. Read, Frederick & Scholten 2013 “Earn a total of 12% in 3 years” “Earn 4% a year for 3 years”

  15. New investigations: The puzzle • Are the motives of intertemporal choice properly characterized as “money now versus money later?” • Oreven as tradeoffs among qualitatively similar goods? Uni-modal choices • When they often involve tradeoffs among different kinds of goods. Cross-modal choices. • Does what we know about uni-modal choices apply to cross modal ones?

  16. Uni-modal versus cross-modal choices Sooner Later Uni modal Cross modal

  17. t1 t2 Basis for our method $XAA A1 A2 $XAB $XBA B2 B1 $XBB A1~ A2+ $XAAB2 + $XAB B1~ B2 + $XBB A2+ $XBA A2+ B2 + $XAA + $XBB B2 + A2+ $XAB + $XBA $XAA + $XBB = $XAB + $XBA

  18. t1 t2 Basis for our method (example) $6 A1 A2 $12 -$2 B2 B1 $4 A1~ A2+ $6 B2 + 12 B1~ B2 + $4A2+ -$2 $6+ $4= $12+ -$2 It follows that if four groups make one choice each, the average uni-modal and cross-modal exchange rate will be equal.

  19. Experiment 1 • 442 participants on MTURK • Hypothetical choices between options plus a payment. • Multiple price list • (Vertical) order of questions counterbalanced • Dependent measure: Payment required to switch from right option to left • For intertemporal choice questions the right option is delayed • Higher payment = more discounting

  20. Symmetric price list Payments in 90 days for both options. Payment varied from $48 to $1. … … …

  21. Willingness to pay to speed up receipt Cross-modal Uni-modal The standard hypothesis is that the average of the red bars will equal the average of the blue bars.

  22. Discounting: Cross-modal < uni-modal But it was greatly reduced or eliminated when choices were cross-modal There was discounting Further analysis with demographics showed nothing more. The effect of cross-modal discounting is stable across models.

  23. Did time matter at all in cross-modal choice? Focus on cross-modal choices only. Includes atemporal and intertemporal. No significant effect of delay: All that matters is which option is preferred.

  24. Experiment 2 • 602 participants on MTURK made hypothetical choices • First choose preferred option; Then answer price list questions with values up to $100. • Two option pairs: Chocolates and pen; Camera and headphones • Standard time-preference questions : Do they predict uni-modal and cross-modal choices?

  25. Willingness to pay to speed up receipt:Red and blue bars “should” have same average height Uni-modal Uni-modal Cross-modal Cross-modal

  26. Strong (negative) effect of cross-modality But it was greatly reduced when choices were cross-modal There was discounting In HeadCam discounting completely wiped out, in ChocPen two thirds of effect eliminated.

  27. Standard time preference measures • Kirby items: Subset of items tested by Kirby, Petry & Bickel (1999); A widely used choice measure. • VandenBergh items: Two items used by Van den Bergh et al. (2008). Index is area under the curve. Widely used test of matching.

  28. Standard time preference measures and uni/cross modal discounting • No significant correlation (or borderline) for cross-modal • Highly significant for uni-modal • All differences highly significant • Correlation for “VDB” items lowest

  29. Moving to explanation: Alternative versus attribute-based model • Alternative-based: Options independently assigned a value before choosing. • E.g., discounted utility/hyperbolic discounting • Predicts uni-modal and cross-modal choices identical • OR with concave utility uni-modal < cross-modal • Attribute-based: Valuation is by making attribute by attribute comparisons and summing the results • Winner is option whose advantages outweigh disadvantages • Time is one attribute among many

  30. Attribute-based model Options are a vector of three attributes [Choc, Pen, Later] Choc = 1; Pen = r; Later = -dd 0 if attribute absent

  31. The Difference Vector Within attribute comparisons are made between Options, and the differences between attributes form a difference vector

  32. WTA d d WTA is the sum of the elements of the Difference Vector Average cross-modal WTA is the same as uni-modal

  33. What role do unique and shared features play? Many studies suggest that attribute-wise evaluations systematically underweight shared features. More attention on unique features which become overweighted. Or, less attention on additional unique features so they are underweighted. ** Thanks to Sudeep Bhatia for the heads up.

  34. WTA with boost given to unique features d+w d

  35. WTA with boost given to unique features d+w d

  36. Incorporating loss aversion into an attribute based model also reduces cross modal discounting d d- (λ-1)(1+r)

  37. What about choices like these • Preference reversals are common when choosing between current pleasure and future health. • These are also cross modal choices … 95 kCal per 100 g 530 kCal per 100 g

  38. t1 t2 $XAA A1 A2 $XAB $XBA B2 B1 $XBB

  39. Cross modal conclusions • Discounting over time has been studied primarily when trading off goods identical except for quantity and time. • Time plays a much smaller and non-significant role in cross-modal choices, than in uni-modal ones. • An attribute-based model with plausible psychological assumptions can capture this effect (and many more). • Standard time preference measures are uncorrelated with cross-modal choices, but highly correlated with uni-modal choices.

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