Measuring Time Preference and
the Elasticity of Intertemporal
Substitution with Web Surveys
Miles S. Kimball, Claudia R. Sahm
and Matthew D. Shapiro
October 31, 2007
Motivation
• Wide range of estimates for these
key parameters
• Limitations to existing survey data
• Web surveys enable new formats for
intertemporal choice
Behavioral Model of
Intertemporal Consumption
 log c  s(r   )
• c : consumption,
• r : real interest rate,
• s : elasticity of intertemporal substitution
• ρ : subjective discount rate
Research Design
Vary Treatment : r
Observe Response : c1, c2
Estimate Parameters : s, ρ
Previous Implementation
Discrete choice: spending before and after retirement in
Health and Retirement Study
• 1992 HRS Module
– Barsky, Kimball, Juster, and Shapiro (QJE 1997)
– Estimates: s = 0.18, -s ρ = 0.78%
• 1999 HRS Mailout
– Compares to a version in Internet survey
– Anchoring in discrete choice
Mail Survey
• Question with 0% interest rate
• Consumption growth choices: -2.2%, 0%,
2.2%, 4.6%, and 7.3%
Internet Implementation
• Web Graphics to Visualize Intertemporal
Trade-offs
• New Continuous Choice and Improved
Discrete Choice Versions
• Two Waves of Responses in American
Life Panel began in 11/2004 and 8/2006
Outline of Talk
1. Internet Versions
2. Summary Statistics
3. Preference Parameter Estimates
4. Ongoing Analysis
Hypothetical Scenario
Web Versions
• Moveable Bars
– Vary Spending Trade-off
• Wide Bars
– Vary Length of Periods
• Discrete Choice
– Vary Spending Trade-off
Moveable Bars: r = 0%
• Spending tradeoff implies 0% interest rate
• 4 questions with different interest rates of
r = {0%, 4.6%, 9.2%, 13.9%}
Moveable Bars: r = 0%
• Initial value randomized
• Click buttons or drag bars
Moveable Bars: r = 0%
• $200 more early, $200 less later
• Tradeoff visualized
Moveable Bars: r = 13.9%
• Spending tradeoff implies 13.9% interest rate
Moveable Bars: r = 13.9%
• Same saving  more spending later
Moveable Bars: r = 13.9%
• $200 more early, $1600 less later
Wide Bars: r = 13.5%
• Length of periods implies 13.5% interest rate
• 5 questions with different interest rates of
r = {-13.5%, -4.8%, 0%, 4.8%, 13.5%}
Wide Bars: r = 13.5%
• $100 less for 5 years, $100 more 25 years
Discrete Choice: Situation 1
• Spending tradeoff implies 0% interest rate
• 4 questions with different interest rates of
r = {0%, 4.6%, 9.2%, 13.9%}
Discrete Choice: r = 0%
• Choose A or E, see 3 more options
• Randomize discrete choice set
Respondent Characteristics
Mean Age
(Std. Dev.)
Internet
Survey
52.9
(11.1)
Mail Survey
All
Use Web
56.0
55.2
(5.4)
(5.5)
College Degree
51%
29%
45%
Male
46%
39%
37%
$70,000
$55,800
$72,604
842
386
203
Median Income
Respondents
NOTE: Tabulations include individuals with at least
one active response to a valid survey instrument.
• Large differences in education and income by
Internet use
Technical Issues with Web
Respondents Assigned
% Technical Difficulties
Moveable
Bars
431
49%
Wide
Bars
397
54%
Discrete
Choice
928
6%
NOTE: Tabulations of moveable bars pool ALP w aves 2 and 6.
• Moveable and wide bars need Java
• Rounding and other coding issues
Active Responses
Web Survey
Moveable
Wide
Discrete
Bars
Bars
Choice
Respondents
% No Active
% Most Active
% All Active
220
2%
93%
71%
214
0%
84%
56%
876
3%
93%
86%
Mail Survey
Use
All
Web
476
17%
77%
75%
224
8%
88%
86%
• Active response: move bars, check box
• Web survey prompts after inactive response
Slope of Desired Consumption
Path at 0% Interest Rate
Mail
60
60
45
45
Percent
Percent
Web
30
30
15
15
0
0
Down
Flat
Consumption Path r=0%
Up
Down
Flat
Up
Consumption Path r=0%
• Mail respondents strongly favor upward slope
• Web respondents favor downward slope
Why Is Mail Survey So Different?
Web - More Up Options
Priming Effects
60
Percent
45
Mail - More Up Options
60
30
15
0
45
Down
Flat
Up
Percent
Consum ption Path Slope
30
Web - Equal Options
60
15
Percent
45
0
Down
Flat
Up
30
15
Consum ption Path Slope
0
Down
Flat
Up
Consum ption Path Slope
Web - More Down Options
60
45
Percent
• Compare discrete choice
• Mail survey 3 of 5 “Up” options
• Internet randomizes
30
15
0
Down
Flat
Consum ption Path Slope
Up
Change in Consumption Ratio as
Interest Rate to 14% from 0%
Mail
60
60
45
45
Percent
Percent
Web
30
15
30
15
0
0
Decreases
Same
Increases
Consumption in Late to Early Period
Decreases
Same
Increases
Consumption in Late to Early Period
• Internet react more to interest rate change
• But more also move in the “wrong” direction
Again, Why Is Mail So Different?
Internet - Higher Options
Anchoring Effects
75
Percent
60
Mail - Same Options
45
30
15
75
0
Decreases
Same
Increases
Consumption in Late to Early Period
45
Internet - Same Options
75
30
60
Percent
Percent
60
15
0
45
30
15
Decreases
Same
Increases
0
Decreases
Consumption in Late to Early Period
Same
Increases
Consumption in Late to Early Period
Internet - Lower Options
75
60
Percent
• Compare discrete choice
• Mail survey 5 ratios static
• Internet randomizes ratios
45
30
15
0
Decreases
Same
Increases
Consumption in Late to Early Period
Estimates: Annual Consumption
Growth at Zero Interest Rate
Consumption Growth
at r = 0%: -s ρ
Web
Survey
Mail
Survey
-0.10
1.90
(0.11)
(0.15)
Observations
1137
355
Respondents
845
355
Mean (Std. Error)
NOTE: Estimates in percent per year. Average
parameter value from regression of individuals'
parameters on a constant. ALP w aves are pooled.
Standard errors are clustered.
• Web: flat path
• Mailout: upward slope
Estimates: Average Elasticity of
Intertemporal Substitution
Elasticity of Intertemporal
Substution: s
Mean (Std. Error)
Web
Survey
0.09
(0.01)
Mail
Survey
0.01
(0.01)
Standard Deviation
Overall
Between
Within
0.76
0.34
0.70
0.41
0.19
0.36
Observations
Respondents
3587
844
1065
355
NOTE: Regression pools the elasticity estimates across
respondents, w aves, and versions. Standard errors are clustered.
• Internet: higher elasticities, well below log utility
Upper Bound on Elasticity?
Web
Survey
Average EIS (Std. Error)
Positive EIS
Non-Negative EIS
0.57
(0.02)
0.40
(0.01)
Average Growth at r = 0%
Positive EIS
-0.64
(0.18)
Non-Negative EIS
-0.39
(0.13)
NOTE: Regressions pool all versions.
• Average of positive elasticities well below 1.0
• Similar consumption path at zero rate
Heterogeneity I
Consumption Growth
at r = 0%: -sρ
Age 50-64
Age 65-79
Ages 80+
Web
Survey
0.03
(0.24)
0.22
(0.45)
0.79
(0.59)
Male
College Degree
Log Income
-0.15
(0.23)
0.06
(0.24)
-0.05
(0.17)
Note: Regression controls for version
and w ave. Standard errors clustered.
• Consumption path steeper for older respondents
• No effect statistically different from zero
Heterogeneity II
Elasticity of Intertemporal
Substution: s
Age 50-64
Age 65-79
Ages 80+
Web
Survey
-0.01
(0.02)
-0.07
(0.03)
-0.11
(0.09)
Male
College Degree
Log Income
-0.003
(0.02)
0.01
(0.02)
-0.03
(0.01)
Note: Regression controls for version and
w ave. Standard errors clustered.
• Older respondents, less elastic
• Higher income, less elastic
Ongoing Work
• Improve the Moveable Bar Version
– In 2008 Cognition Survey
• Estimate Statistical Model
– Repeat observations address response errors
• External Check on Responses
– “Reverse” question: vary spending growth and
elicit desired interest rate