Time Inconsistency or Inconsistency?

Transcription

1 Time Inconsistency or Inconsistency? Syngjoo Choi (UCL) Wieland Müller (Tilburg and Vienna) Shachar Kariv (UC Berkeley) Dan Silverman (ASU) May 6, 2014 ECARES

2 Introduction Intertemporal choices are important and ubiquitous. One major debate on intertemporal choices is about time inconsistency. It suggests that when preferences are well-defined and time-separable, the discount factor changes over time. It is thus natural that researchers in economics and psychology have focused on testing the presence of time-varying discount factor. One widely documented anomaly is declining discount factor, i.e., hyperbolic discounting.

3 In This Paper We present a novel experimental design on time preferences. The design enables us to collect rich, individual-level data in the domain of intertemporal choices. A richness of data allows us to conduct nonparametric analysis of consistency with utility maximization and time consistency. We report experimental evidence from both a traditional lab environment (with university students) and a field environment (an existing household panel survey)

4 In This Paper Our data suggests a different view on the controversy surrounding intertemporal choices. There is a high level of individual heterogeneity in intertemporal choices (in both demand behavior and level of consistency). We find experimental evidence that lack of consistency per se is quantitatively important, probably more important than time inconsistency. We relate measures of compliance to consistency and time consistency to socioeconomic information.

5 Lab and Field Environments The experiments were conducted at Xlab at UC Berkeley; the CentERpanel in the Netherlands. The CentERpanel, an online household panel survey, consists of over 2,000 households (5,000 individuals). 1,636 subjects participated in the experiment: 211 subjects from Xlab and 1,425 subjects from the CentERpanel.

6 Decision in the Experiment Subjects are presented with a sequence of standard intertemporal choice problems of allocating an endowment over two payment dates, and. Choose any non-negative allocation x = (x t, x t+k ) satisfying the budget constraint, for some, ௧ ௧ Each subject faces two time frames near-term and distant by varying the sooner payment date, ᇱ. Time horizon are held constant.

7 Decision in the Experiment Near-term time frame Distant time frame ௧ ௧ ᇲ ௧ ௧ ᇲ

8 Further Detail of the Experiment In each frame, subjects were randomly presented with many such problems in sequence: 50 choices in a frame at the Xlab 20 choices in a frame at the CentERpanel. The order of time frame was randomized across subjects. The same set of budgets were shown in the two time frames. At the end of the experiment, one decision problem was randomly chosen for payment.

9 Sample Screen

10 Decision in Conventional Design Near-term time frame Distant time frame ௧ ௧ ᇲ ௧ ௧ ᇲ

11 Advantages Compared to decisions in conventional designs such as the multiple price list design, our design has several distinct advantages: Continuous vs. discrete (binary) choices (c.f., Andreoni and Sprenger, 2013) Rich variation in budget sets ( and ) to have many crossing budget lines. The design allows us to conduct nonparametric analysis for Consistency with utility maxization; Time consistency.

12 Further Details of the Experiment 1. Xlab In total, 211 subjects (university students) in September 2011 The sooner payment date in the near-term (distant) frame is a next business day (about a month later) and 28 days as time horizon between two payment dates. 2. CentERpanel In total, 1425 CentERpanel members in June (wave 1) and September (wave 2) 2011 The sooner date in the near-term (distant) frame is about one week later (13 weeks later) and 12 weeks as time horizon between two payment dates.

13 Description of Sampling: CentERpanel

14 Sociodemographic Information: CentERpanel

15 Order Treatment of Time Frames In each experiment, approximately equal number of subjects was allocated to two order treatments. Near-term frame first Distant frame first Total Xlab 104 (49%) 107 (51%) 211 CentERpanel 699 (49%) 726 (51%) 1,425

16 Roadmap 1. Revealed Preference Analysis Consistency with time frame Consistency between time frames 2. Nonparametric Demand Analysis Stationarity of demand behavior between two time frames Aggregate & individual patterns of short-term impatience 3. Parametric Demand Analysis (ongoing) Time-separable versus time-nonseparable preferences

17 Revealed Preferences within Time Frame Let, for, denote observed individual data within time frame. Generalized Axiom of Revealed Preferences (GARP) ଵ ଵ ଵ ଶ ଶ ଶ ଶ ଷ ଵ ଵ ଵ ଵ Afriat s Theorem If the data satifies GARP, then there exists a utility function that rationlizes the observed choices. GARP offers an exact test: either the data satisfy GARP or not.

18 Quantifying GARP violations: CCEI Afriat s critical cost efficiency index (CCEI) The amount by which each budget constraint must be relaxed in order to remove all violations of GARP. CCEI is the largest number such that ଵ ଵ ଵ ଶ ଶ ଶ ଶ ଷ ଵ ଵ ଵ ଵ CCEI measures the extent of GARP violations in terms of monetary costs.

19 Distribution of CCEI within Time Frame The majority of subjects have virtually no violations. Nonetheless, there is substantial heterogeneity of CCEI with time frame. Average CCEI is higher in the first time frame than in the second one.

20 Who Is (More) Rational? We use the minimum of CCEIs of the near-term and distant time frames as an overall summary of consistency with utility maximization (within time frame). We correlate heterogeneity in CCEI and sociodemographic information of subjects in the CentERpanel experiment. Findings in the domain of intertemporal decision making corroborate those in an earlier work in the domain of decision making under uncertainty, Choi et al. (2013).

21 Minimum of CCEI Scores of Two Time Frames (sample means and 95% CIs)

22 The correlation between min CCEI scores and subjects' individual characteristics (OLS) Female (0.006) (0.006) Age *** *** *** *** *** *** (0.008) (0.008) (0.014) (0.008) (0.008) (0.014) Education Medium High 0.015** 0.028*** *** (0.007) (0.007) (0.007) (0.007) Income ** 0.029*** * 0.023*** (0.009) (0.008) (0.009) (0.009) (0.008) (0.009) Occupation Paid work House work Others (0.012) (0.015) (0.015) (0.012) (0.015) (0.015) Household composition Partner # of kids ** ** (0.008) (0.003) (0.008) (0.003) Treatment Wave Axis Order 0.012** ** (0.006) (0.005) (0.005) (0.005) (0.005) (0.005) Cognitive abilities Financial literacy CRT Raven's matrices Constant (0.003) 0.014*** (0.003) 0.008*** (0.003) 0.919*** 0.925*** (0.023) (0.023) R-squared # of obs. 1,422 1,413

23 Consistency between Time Frames In order to examine patterns of consistency between time frames, we first compute the CCEI of the combined data of the two time frames. We relate this with the minimum of CCEIs of the near-term and distant time frames. By definition, the CCEI of the combined data cannot be higher than the minimum of CCEIs. Different models of time preferences predict different relationships between these two variables.

24 Two Canonical Models ௧ ௧ ௧ ௧ ఛ ఛ Exponential discounting model (Samuelson, 1937; Koopmans, 1960) ఛ Quasi-hyperbolic discounting model (Phelps and Pollak, 1968; Laibson, 1997) ఛ

25 Predicted Relation between min CCEI and CCEI of the combined data Quasi-hyperbolic discounting model Exponential discounting model

26 Relation between min CCEI and CCEI of the combined data: Xlab data 52% of subjects: (CCEI for the combined data) % of them: (CCEI for the cobmined data) = (min CCEIs) Only around 6% of them: (min CCEIs) 1

27 Relation between min CCEI and CCEI of the combined data: CentERpanel data 57% of subjects: (CCEI for the combined data) % of them: (CCEI for the combined data) = (min CCEIs) Only around 5% of them: min CCEIs 1

28 Summary The majority of subjects show high level of compliance with utility maximization within and between time frames. Nevertheless, there is a high level of heterogeneity in (within-frame) consistency, which is strongly correlated with socioeconomic information. Inconsistency between time frames is largely driven by within-frame inconsistency. So far there is little evidence on (time-separable) quasi-hyperbolic discounting.

29 Demand Behavior: Nonparametric Analysis First, we overview the aggregate features of demand behavior from the data. Relate average demand share for sooner payment with sociodemographic information. We then show some prototypical individual behaviors from the data. Compare with simulation of quasi-hyperbolic discounting model. We present nonparametric test for the equivalence of demand shares between two time frames. Choice problems between two time frames are matched. We use Wilcoxon matched-pairs signed-ranks test.

30 Aggregate Demand Share for Sooner Payments (local polynomial kernel regression) CentERpanel Xlab log price ratio TS_near-term 2 TS_dist log price ratio TS_near-term TS_dist Aggregate demand behavior is responsive to price changes. No difference of aggregate demand behavior between the near-term and distant frames. Thus, no evidence on present bias or short-term impatience.

31 Aggregate Demand Share for Sooner Payments (Near-term time frame) Demand behavior varies significantly across sociodemographic characteristics. Younger (more educated) people are more patient than older (less educated).

32 The correlation between average demand share for sooner payments and subjects' individual characteristics (OLS) Early Late (Early - Late) Female (0.011) (0.011) (0.007) Age ** 0.073*** 0.062*** 0.032* 0.072*** 0.046** (0.016) (0.017) (0.023) (0.017) (0.017) (0.023) (0.010) (0.011) (0.017) Education Medium High *** ** (0.013) (0.013) (0.013) (0.013) (0.010) (0.009) Income (0.015) (0.014) (0.016) (0.015) (0.014) (0.016) (0.011) (0.009) (0.011) Occupation Paid work House work Others (0.019) (0.021) (0.022) (0.019) (0.021) (0.022) (0.014) (0.015) (0.018) Household composition Partner # of kids (0.014) (0.005) (0.014) (0.005) (0.009) (0.003) Treatment Wave Axis Order ** ** ** ** (0.010) (0.010) (0.010) (0.010) (0.010) (0.010) (0.007) (0.007) (0.007) Cognitive abilities Financial literacy CRT Raven's matrices Constant *** ** 0.220*** *** *** 0.174*** * (0.005) (0.005) (0.004) (0.039) (0.005) (0.005) (0.004) (0.038) (0.003) (0.003) (0.004) (0.028) R-squared # of obs. 1,413 1,413 1,413

33 Individual Behavior There is a high level of heterogeneity in individual demand behavior. We look at the relationship between demand share for sooner payment and log price ratio (interest rates). To give a glimpse of individual heterogeneity, we present a selective set of individual scatterplots. To put them into perspective, we first look at the simulated demand behavior of quasi-hyperbolic discounting model, the model. Per-period utility function: ௫ ௫

34 Simulated Demand of Quasi-hyperbolic Discounting Model

35 Simulated Demand of Quasi-hyperbolic Discounting Model

36 Simulated Demand of Quasi-hyperbolic Discounting Model

37 Individual Behavior 1 The relation of log price ratios and token shares for ID 101 The relation of log price ratios and token shares for ID Part E Part L Token share for early date Token share for early date Part E Part L log(pearly / plate) The relation of log price ratios and token shares for ID Part E Part L 0.9 Part E Part L Token share for early date Token share for early date log(pearly / plate) The relation of log price ratios and token shares for ID log(pearly / plate) log(pearly / plate) 2 2.5

38 Individual Behavior 2 The relation of log price ratios and token shares for ID 223 The relation of log price ratios and token shares for ID Part E Part L 0.9 Token share for early date log(pearly / plate) log(pearly / plate) The relation of log price ratios and token shares for ID Part E Part L Token share for early date Token share for early date Part E Part L log(pearly / plate)

39 Individual Behavior 3 The relation of log price ratios and token shares for ID 635 The relation of log price ratios and token shares for ID Part E Part L Token share for early date Token share for early date Part E Part L log(pearly / plate) log(pearly / plate) 2 2.5

40 Nonparametric Demand Analysis Choice problems are matched between near-term and distant time frames. We exploit this feature and test the equivalence of demand behavior in matched pairs of choice problems between the two time frames. Two-sided Wilcoxon sign test ଵ ௧ ௧ One-sided Wilcoxon sign tests ௦௧ ௧ ௦௧ ௧

41 Wilcoxon Sign-Rank Tests: Rejection of the Null (5% significance level) The majority of subjects exhibit similar demand behavior between the two time frames. A small proportion of subjects exhibit significant short-term impatience: 27% of Xlab subjects and 14% of CentERpanel subjects.

42 Summary At the aggregate level of demand behavior, there is no evidence on present bias. There is a high level of heterogeneity in individual demand behavior. Nonparametric analysis reveals that the majority of subjects exhibit similar demand behavior between two time frames. Only a small proportion of subjects exhibit significant patterns of shortterm impatience.