Quantitative Marketing Research

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Can a few words help us save? Method variance
in intertemporal choice

• Daniel Read
• Durham Business School

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What are intertemporal choices?

• Whether or not to have a flu shot
• The choice between fruit salad or tiramisu
• When to get down to work on a promised paper
• Whether to invest in a pension plan or buy a
  widescreen TV and
• (For a pigeon) one food pellet now, or two
  pellets in two seconds.
• 1100 in 3 months or 1300 in 3 years.

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Discounting Exhibit 1

• Life is not long enough human nature desires
  quick results, there is a peculiar zest in making
  money quickly, and remoter gains are discounted
  by the average man at a very high rate.
• Keynes, General Theory p. 157

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Discounting Exhibit 2

• When the journey from means to end is not too
  long, the means themselves are enjoyed if the end
  is ardently desired. A boy will toil uphill with
  a toboggan for the sake of the few brief moments
  of bliss during the descent no one has to urge
  him to be industrious, and however he may puff
  and pant he is still happy. But if instead of the
  immediate reward you promised him an old-age
  pension at seventy, his energy would very quickly
  flag.
• Bertrand Russell

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What characterises intertemporal choices?

• Choices between outcomes that occur at different
  times.
• Usually a trade off between waiting and earning
• Smaller-sooner (SS) versus Larger-later (LL)
  outcomes.
• The choice of LL, or a lower rate of tradeoff
  (discount rate) corresponds to saving.
• Waiting for more

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How should we make intertemporal choices?

• Three principles
• Maximise net present value based on our
  attainable borrowing rate and financial
  circumstances (Fisher)
• Maintain constant rate of discount with no
  dynamic inconsistency (Strotz)
• Discount rate should be independent of problem
  description or of how questions are asked
  (Everyone)

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How should we make intertemporal choices bottom
line

• Intertemporal choice will reflect a constant rate
  of discount with no dynamic inconsistency, and
  for money we will maximise NPV
• Discount rate will be independent of problem
  description or of how questions are asked
• Focus of my research is on how well these
  principals are adhered to, and the significance
  of any anomalies observed
• Preview The imputed discount rate depends on a
  host of normatively irrelevant variables.

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How discount rates are assessed The modal
experiment

• Provide indifference point between two outcomes,
  or choose between them
• Choice Choose between x1 at t1 or x2 at t2.
• Matching Fill in the blanks x1 at t1 or ____ at
  t2.
• x1 and x2 are amounts of money
• t1 and t2 are delays in units of time.

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Anomalies versus Method variance

• Anomalies Apparent violations of principles
• Readily rationalisable
• E.g., Overconfidence, hyperbolic discounting,
  magnitude effect.
• Method variance Violations of rationality
• More difficult to rationalise E.g, Framing
  effects, interval effects, date/delay effect,
  tradeoff currency effect

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Part 1 Interval effects(Read, 2002, Journal of
Risk and Uncertainty Read Roelofsma, 2004,
OBHDP)
Discount rate from t1 to t3 is (usually) less
than from t1 to t2 or t2 to t3.
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Subadditivity effect
Undivided
Divided
Undivided
Divided
Long intervals lead to more discounting than
short intervals
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Implications

• People willing to pay higher rates of interest
  the shorter the evaluation period.
• And, will want (proportionally) more in the
  future for short interval delays than for long
  ones.

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Part 2 Date/Delay effect(Read, Frederick
2005, Man Sci)

• The manner of discounting may depend on either
  or both of two things (1) the time distance of
  the future date from the present moment the
  delay, or (2) the calendar date of the future
  act of consumption. To the extent that
  time-distance is important, I may assign a
  different (and probably higher) weight to
  September 26 as it draws nigh if only the
  calendar date is important, the weight will not
  change as that date approaches. Strotz, 1955/56

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Experiment 1, choice
Date
Delay
Each respondent answers four questions Two delay
conditions Months and weeks Dependent measure
choosing Larger-Later (LL)
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Experiment 1, results (choice of LL)
Much more likely to make patient choice for dates
than delays
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Experiment 2, Matching (fill-in-the-blanks)
Matching can draw on different processes than
choice, so replication is not guaranteed

• 370 in 4 months is equal to 450 in ___ months.
• 370 in ___months is equal to 450 in 12 months.
• 370 in 4 months is equal to ____ in 12 months
• ____ in 4 months is equal to 450 in 12 months

Date and delay versions of the questions Each
respondent gives one answer of each four
different questions
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Experiment 2,(implicit choice of LL)
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Hyperbolic discounting Experiment 3

• Hyperbolic discounting means ? increases with
  increasing delay.
• Widely held to be the best description of how
  people really discount
• Evidence for HD found sometimes when time is
  described as a delay but never when it is
  described as a date
• But no direct comparisons between date and delay
  descriptions

r gt
r gt
r gt
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Experiment 3, Materials
Four intervals defined by pairs of time points.
E.g., t1?t2 Choice titration method to find
indifference point
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Experiment 3 results(in discount FACTORS)
Date

• Date/delay effect
• No hyperbolic discounting for dates
• Strong hyperbolic discounting for delays

r
Delay
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Implications Competing loan descriptions

• Marketers You will get your money on Wednesday,
  March 18 you have 7 months to pay it back.
• Consumer advocates You will have to wait for 8
  days for your money you must pay it back by
  December 11, 2004.

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Part 3 The intertemporal tradeoff currency.
(Read, Airoldi, Loewe)

• Real world Choose Bank A because it offers 4,
  while other banks offer less.
• Experiment Choose between 100 today, or 120
  in one year.
• The tradeoff currency used in experiments is
  different than that used in the real world.
  (Coller Williams, 1999).

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The anomalies

• Excessive discounting -- Extremely high discount
  rates
• Interval effects discount rate is usually
  greater for longer intervals.

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The question

• Will anomalous phenomena persist if intertemporal
  tradeoffs made in terms of interest rates?
• I.e., If people stated their discount rate, or
  choose between rates?
• Perhaps not some evidence from Coller and
  Williams that discount rates are lower when
  interest rates are provided.

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Design

• 12 conditions
• Three descriptions Interest-rate
  InterestAmount Nominal-amount
• Four intervals 1?7 months 7?13 months 13?19
  months 1?19 months
• three short intervals and one long one
• 1460 members of internet panel in Spain

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Hypotheses

• H1 Lower discount rates for Interest-rate and
  InterestAmount conditions relative to (standard)
  Nominal-Amount condition.
• H2. InterestAmount rates between Interest-only
  and Money-only condition.
• H4 No (hyperbolic) interval effect for interest
  rate conditions.
• H3. Rates for same-length intervals unaffected
  by the delay to that interval.

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1 month
7 months
13 months
17 months
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The display
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Materials for tradeoff currency study
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True r between Min-r and Min-r2.5
Range of rational discount rates
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Results and conclusions

• Discounting highly dependent on problem
  representation.
• Trading off in terms of interest rates drives
  discount rates down.
• Brings people very close to correct discount
  rate
• Lower than loan rate for equivalent amount
• Also no dynamic inconsistency of any form in
  InterestAmount condition.

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Results and conclusions

• No delay (hyperbolic discounting) effect in any
  condition.
• Standard subadditive interval effect in
  Nominal-amount condition.
• Superadditive interval effect in Interest-only
  condition.

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Explanations

• Translation hypothesis people know about the
  money market, and want to obey it
• But have difficulty translating nominal amounts
  into interest rates (or may not even realise they
  should)

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Some lessons

• Studies that investigate impatience find
  extraordinarily high discount rates.
• Usually use one method
• Nominal amounts, delay descriptions
• Intervals often very short
• When method is changed in almost any way,
  impatience is reduced

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Can the results be reconciled with rational
choice?

• Transaction cost story
• It takes effort to transform questions into
  canonical form
• Incentives may be insufficient to warrant
  expending effort
• Use simplifying heuristics instead
• Charge fixed cost for delay
• Ignore dates, choose based on amount
• Do I have any use for money now?
• Problems
• Measurement of transaction costs
• Determination of rational expenditure of effort
• Is irrationality possible?

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