Measuring Time Preference and the
Elasticity of Intertemporal Substitution
Miles S. Kimball, Claudia R. Sahm
and Matthew D. Shapiro
September 6, 2006
Internet Project Meeting
Behavioral Model
 log c  s(r   )
• c is consumption,
• r is the real interest rate,
• s is the elasticity of intertemporal
substitution, and
• ρ is the subjective discount rate
Research Design
• s, ρ : Preference parameters
• r : Treatment
• c : Behavioral response
Research Strategy
Vary treatment and use responses to
infer parameters.
Implementation
• Vary Interest Rate
– Vary cost of current consumption
– Vary length of time periods
• Measure Consumption Choice
– Choose among small set of paths
– Actively form a desired path
• Infer Preferences
– Summary statistics of responses
– Statistical model with response error
Previous Survey Measures
• HRS 1992 Module K, N = 198
– Analyzed by Barsky, Kimball, Juster, and
Shapiro (QJE 1997)
• HRS 1999 Mailout, N = 1,210
– Similar content to part of Internet Survey
Questions explicitly vary the cost of current
consumption and offer a discrete choice over a
small set of consumption paths
MS Internet Survey
Wave 2 (Fall 2004)
Use graphics on internet to test other measures:
• Version 1, N = 350
– Vary cost of consumption
– Choose from set of pairs
• Version 2, N = 155
– Vary cost of consumption
– Move bars to create pair
• Version 3, N = 183
– Vary length of period
– Move bars to create pair
Series Introduction
- Version 1 -
• Series includes four questions with varying interest rates
Introduction – 0% Interest Rate
• Sequence r = {0%, 4.6%, 9.2%, 13.8%} is random
• Introduction repeated for each interest rate
Patterns – 0% Interest Rate
• Asked to choose two patterns
• Above screen (1 of 6) is identical to HRS Mail Out
Expansion Screen
• Follow-up if first choice
on boundary (A or E)
• New feature on Internet
Randomize Pair C
• Choice of ($3000, $3000)
moves from B to C to D
• 3 values to the parameter
• New feature on internet
• Top screen on mail out
Randomize Left-to-Right
• Screens mirror image
• New feature on internet
• Top screen on mail out
Randomize Shifts with Interest Rate
• Example with r = 9.2%
• Choice of ($2750, $3900)
moves from E to C to A
• 3 values to the parameter
• New feature on internet
• Middle screen on mail out
Summary of Innovations in
Internet Question Series
• 18 different screen groups
• 6 different sequences of interest rates
• 11 discrete choices per question
Purpose of Innovations
• Encourage active choices
• Increase informative responses
• Isolate framing effects
Response Statistics
Internet
Mail
Any Responders
Complete Sequence
%
100.0
82.2
N
366
301
%
100.0
88.2
N
930
820
Complete Responders
Second Choice Pairs
All Extreme Pairs
100.0
77.1
2.0
301
232
6
100.0
90.6
17.2
820
743
141
• Internet lower completion rate
• Internet fewer second choices
• Internet fewer non-informative responses
Consumption Growth at 0%
Interest Rate
45
40
35
Percent
30
25
20
15
10
5
Consumption Growth at 0% Interest Rate
Internet
Mail
• Constant consumption is modal choice
13.9
11.6
9.2
6.9
4.6
2.3
0.0
-2.3
-4.6
-6.9
-9.2
-11.6
-13.9
0
Change in Consumption Growth as
Interest Rate to 13.8% from 0%
60
50
Internet
% Increase Growth
48.5
% Decrease Growth
25.9
Percent
40
Mail
26.5
17.2
30
20
10
23.1
20.8
18.5
16.2
13.9
11.6
9.2
6.9
4.6
2.3
0.0
-2.3
-4.6
-6.9
-9.2
-11.6
-13.9
-16.2
-18.5
-20.8
-23.1
0
Growth at r = 13.8% Minus Growth at r = 0%
Internet
Mail
• Interest rates change consumption more on internet
Change in Consumption Growth as
Interest Rate Increases - Internet
45
40
35
% Increase Growth
% Decrease Growth
Percent
30
4.9%
34.2
22.9
13.8%
48.5
25.9
25
20
15
10
5
23.1
20.8
18.5
16.2
13.9
11.6
9.2
6.9
4.6
2.3
0.0
-2.3
-4.6
-6.9
-9.2
-11.6
-13.9
-16.2
-18.5
-20.8
-23.1
0
Consumption Growth - Growth at 0% Interest Rate
r = 4.6%
r = 13.8%
• Decrease in growth is a sign of survey response error
Estimates of Parameters
Average in Sample
sρ: Growth at r = 0%
s: IES by Interest Rate
0% to 4.6%
4.6% to 9.2%
9.2% to 13.8%
Internet
0.13%
Mail
1.3%
0.13
0.14
0.05
0.004
0.01
0.04
• Responses reveal low time preference and IES
• Median and modal values in both surveys equal 0
More Graphical Questions
- Version 2 -
• Move bars to select a consumption path
More Graphical Questions
- Version 3 -
• Vary length of current and future periods
Implementation Issues
Internet expands preference measures, but
• Graphics require more programming
– More programming → more bugs
– Coordinate programmer and analyst
• Internet captures more data: number of
clicks and interim responses
Extensions / Renewal
• Refine and analyze data on IES, time
preference, and risk tolerance
– Improve instrument and output delivery
– Estimate statistical model
• Measure complementary parameters
– Diminishing marginal utility
– Labor supply elasticities
– Retirement elasticity