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