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 rsc

• 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

Vary treatment and use responses to infer parameters.

Research Strategy

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 SurveyWave 2 (Fall 2004)

• 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

Use graphics on internet to test other measures:

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

• Encourage active choices

• Increase informative responses

• Isolate framing effects

Purpose of Innovations

Response Statistics

% N % NAny Responders 100.0 366 100.0 930 Complete Sequence 82.2 301 88.2 820

Complete Responders 100.0 301 100.0 820 Second Choice Pairs 77.1 232 90.6 743 All Extreme Pairs 2.0 6 17.2 141

Internet Mail

• Internet lower completion rate• Internet fewer second choices• Internet fewer non-informative responses

Consumption Growth at 0% Interest Rate

0

5

10

15

20

25

30

35

40

45

-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

Consumption Growth at 0% Interest Rate

Pe

rce

nt

Internet Mail

• Constant consumption is modal choice

Change in Consumption Growth as Interest Rate to 13.8% from 0%

0

10

20

30

40

50

60-2

3.1

-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

Growth at r = 13.8% Minus Growth at r = 0%

Pe

rce

nt

Internet Mail

• Interest rates change consumption more on internet

Internet Mail% Increase Growth 48.5 26.5% Decrease Growth 25.9 17.2

Change in Consumption Growth as Interest Rate Increases - Internet

• Decrease in growth is a sign of survey response error

0

5

10

15

20

25

30

35

40

45-2

3.1

-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

Consumption Growth - Growth at 0% Interest Rate

Pe

rce

nt

r = 4.6% r = 13.8%

4.9% 13.8%% Increase Growth 34.2 48.5% Decrease Growth 22.9 25.9

Estimates of Parameters

Average in Sample Internet Mailsρ: Growth at r = 0% 0.13% 1.3%

s: IES by Interest Rate 0% to 4.6% 0.13 0.004 4.6% to 9.2% 0.14 0.01 9.2% to 13.8% 0.05 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

• Graphics require more programming– More programming → more bugs– Coordinate programmer and analyst

• Internet captures more data: number of clicks and interim responses

Internet expands preference measures, but

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