Subjective Discount Rates and Household Behavior ... - CiteSeerX

Subjective Discount Rates and Household Behavior

Melvin Stephens Jr. H. John Heinz III School of Public Policy and Management Carnegie Mellon University and National Bureau of Economic Research 5000 Forbes Ave. Pittsburgh, PA 15213 e-mail: [email protected]

Erin L. Krupka Department of Social and Decision Sciences Carnegie Mellon University 5000 Forbes Ave. Pittsburgh, PA 15213 e-mail: [email protected]

August 2006

This research was supported, in part, by the Carnegie Mellon Berkman Faculty Development Fund.

Abstract While numerous papers use a variety of methods to elicit individual subjective discount rates, only a few studies directly explore the validity of this hypothetical choice format. Using a longitudinal dataset of over 4,800 households, we first examine the consistency of the implied subjective discount rates between the most commonly used hypothetical elicitation measures and find important differences in the implied discount rate within individuals across these measures. Next, we derive behavioral implications for the relationship between the discount rate and economic outcomes using a life-cycle model and find results that are consistent with the theoretical predictions for asset accumulation but not for hours worked. Finally, we exploit the longitudinal feature of the dataset to examine the stability of these measures over time and find, contrary to the assumption that these subjective discount rates are time invariant, that these measures both increase dramatically during an economy wide inflationary period and are sensitive to household level economic events.

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I. Introduction At the core of economic decisions involving the allocation of resources over time is the notion of a discount rate. A growing body of economic literature suggests that understanding variation in individual discount rates is critical to understanding variation across household economic outcomes.

Despite this recognized importance, few studies compare different

measures of the discount rate or how those measures relate to traditional economic behaviors. Previous work correlates implicit discount rates, derived from observed consumption choices, with behaviors of economic significance. However, the validity of the hypothetical choice format has not been well explored. In this paper, we compare three widely used subjective measures of the discount rate that are derived from hypothetical questions often used in laboratory studies, link these measures to economic outcomes at the household level, and the sensitivity of these measures to market conditions. Thus we provide an important, and widely missing, link between discount rates elicited using hypothetical question formats and economic outcomes. Empirical studies examining intertemporal relationships traditionally treat discount rates as a nuisance parameter. In the literature following Hall (1978) that estimates consumption Euler Equations, the discount rate is typically assumed to be constant across households and subsumed by the intercept. A comparable assumption is made in the voluminous literature spawned by MaCurdy (1981), which uses a similar empirical framework to estimate intertemporal labor supply elasticities, as well as in studies that directly estimate parameters of the objective function such as the discount rate and the coefficient of relative risk aversion. To the extent that the discount rate is allowed to vary at all, it is modeled as a function of a limited set of observable characteristics (Lawrance 1991; Gourinchas and Parker 2002).

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There is evidence, however, that understanding inter-individual variation in discount rates is a vital component to explaining heterogeneity in outcomes across individuals and, by extension, households (Lawrance 1991; Browning and Lusardi 1996). Lawrance (1991), Venti and Wise (1998) and Samwick (2006) present evidence that the distribution of financial assets observed in the US population can be attributed to heterogeneity in time preferences. Other research shows that heterogeneity in the discount rate (as well as alternative methods of discounting, e.g., hyperbolic discontinuity) can explain why households do not smooth consumption in anticipation of predictable changes in income (Thaler 1981; Angeletos et al. 2001; Bernheim et al. 2001; Hurst 2003; Laibson 2004).1 As more evidence points to the explanatory power of individual discount heterogeneity, a largely separate literature, in both economics and psychology, has emerged that elicits and estimates discount rates. “Field studies” typically infer discount rates from choices observed such as buying an air conditioner (Hausman 1979), purchasing a refrigerator (Gately 1980) and, more recently, taking either an annuity payment or a one-time lump sum payment (Warner and Pleeter 2001).2 Thus, field studies have the advantage of deriving implicit discount rates from actual consumer choices. However, they often collect limited socio-economic information let alone information on other economic behaviors of interest that are correlated with the measured time preference.

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Other research points to the importance of understanding inter-individual variation in discount rates for other types of choices besides savings and wealth acquisition. Kunreuther et al. (1998) discusses how inter-individual variation in discount rates can account for heterogeneity in the adoption of risk minimizing measures such as acquiring insurance, a smoke detector or deadbolt. Della Vigna and Malmendier (2004) show that hyperbolic discounting can account for contract choice and attendance at health clubs, Della Vigna and Passerman (2005) show the same to be true for job search intensity and duration and Fang and Silverman (2004) for the decision to take up welfare benefits. 2 Another literature, which can also be characterized as field studies, estimates discount rates from consumption bundles (such as aggregate wealth or savings) rather than from one observed or hypothetical choice. See for example, Carroll and Samwick (1997) or Gourinchas and Parker (2002). Helpful overviews of field studies that estimate discount rates are provided by Kunreuther et al. (1998) and Laibson et al. (2005).

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“Experimental studies”, which are far more prevalent, span a number of methodologies that elicit subjective discount rates across a variety of scenarios using hypothetical question formats.3 These studies consist of a pool of subjects who are presented with a set of hypothetical choices that vary across the size of the payoffs and the time span over which the choice is to be made. The majority of experimental studies are concerned with understanding the stability of discount rates across hypothetical situations to see which model of discounting (e.g., geometric or hyperbolic) is most consistent with subject responses and ignores establishing the validity of discount rate elicitation methods (Loewenstein 1988; Benzion et al. 1989; Loewenstein and Thaler 1989). As such, little information is collected concerning participants’ backgrounds or, if such information is available, samples are small and relatively homogeneous. Some studies use larger and more diverse samples to examine the link between subjective discount rates and individual or household behaviors such as educational attainment or health related behaviors such as smoking and obtaining a flu shot (Fuchs 1982; Chapman and Coups 1999).4 A second set of papers explores the relationship between subjective discount rates and financial decisions. Donkers and van Soest (1999) use a survey of Dutch households to obtain estimates of discount rates using hypothetical questions regarding tradeoffs between future and current payouts. They find that discount rates are negatively correlated with the decision to own a home and are positively related to holding risky assets.5 Collectively, these findings suggest

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For examples of different elicitation formats, see Thaler (1981), Loewenstein (1988), Benzion et al. (1989), Loewenstein and Prelec (1991), Kirby (1997), Kunreuther et al. (1998). 4 Chapman (1996) examines the relationship between hypothetical future health outcomes and money outcomes. She finds that implied discount rates within a domain (such as the domain of health or the domain of money) are fairly consistent while the correlation between discount rates measured in different domains is low. This finding suggests that there may be variation within individuals for different types of consumption as well as variation in discount rates across individuals. We focus on inter-individual discount rate variation in this paper. 5 Nielsen (2001) finds a positive correlation between experimentally elicited discount rates (controlling for riskiness) and the rate at which poor peasants in rural Madagascar are willing to deforest or cultivate crops.

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that further examination of subjective discount rate measures is necessary to determine their usefulness in explaining the heterogeneity in outcomes across other domains. In this paper we use survey data to estimate the relationship between elicited discount rates and household economic outcomes such as work effort and accumulated assets. The Seattle and Denver Income Maintenance Experiments (SIME/DIME) began in the early 1970s as the last of four major evaluations of the proposed negative income tax (NIT).6 Over 4,800 households were experimentally assigned to different grant levels and tax rates on earned income. In addition to detailed demographic information, information on all sources of income and wealth, an experimental module elicited household discount rates using three different hypothetical measures (discussed below).7 Our analysis begins by examining the consistency of responses across the subjective discount rate. A small number of prior papers perform such comparisons (Tversky et al. 1988; Ahlbrecht and Weber 1997; Read and Roelofsma 2003).

We find that some methods for

inferring discount rates produce responses that appear to measure the same underlying trait while others do not. This finding is of note because these measures are often used interchangeably. We then examine the relationship between discount rate responses, household demographics, and economic outcomes that are theoretically linked to discount rates. We find that households with higher levels of current income and better education are more patient while Black and Latino

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The idea behind a negative income tax is to replace the myriad of programs supporting low-income families with a simple transparent program that has a grant amount and a not-too-substantial tax rate on earned income. The goal would be to both increase efficiency by reducing the number of programs and increase work effort by lowering the effective tax rate on earnings. For a review of the NIT see Moffitt (forthcoming). 7 To our knowledge, the only prior examination of the discount rate questions in the SIME/DIME are in unpublished working papers by Kurz, Spiegelman, and West (1973) and West (1978). Using data from the Denver site, the authors apply a factor analysis model to the multiple survey measures in order to estimate that latent factor corresponding to the discount rate. In their main analysis, the authors report the results of regressing this estimated factor on household demographic (e.g., age and education) and financial (e.g., earnings and assets) information.

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households are less patient. Using a two-period household life-cycle labor supply model we find that these discount rate measures produce mixed support for the model’s predictions. Finally, we address the issue surrounding how one should interpret responses to subjective discount rate questions. The rate of time preference traditionally is assumed to be a fixed parameter for each individual (across all choice contexts) that is used to discount utility over time. It is often computed by equating the net present value of two amounts at different points in time. However, if capital markets are perfect, the choice between values at different dates will depend upon the market rate of interest regardless of the individual’s discount rate. If this latter view is correct, then a discount rate elicited by equating the net present value of two amounts at different points in time will be correlated with time-varying factors that affect the market rate of interest.8 As “luck” would have it, the first wave of discount rate questions was asked in late 1972 while the second wave of questions occurred a year later. Over this period, the U.S. inflation rate nearly tripled. Contrary to the view that discount rates are time invariant, we find that the estimated discount rates also increased dramatically over this period. Moreover, if discount rates are fixed for each individual then an adverse labor market event should not be correlated with changes in the elicited discount rate. We find evidence to the contrary. These results cast doubt upon the notion that elicited discount rates using the hypothetical choice format measure the “pure” rate of time preference.

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Others have also suggested that discount rates estimated using a hypothetical-question format or from consumption choices (such as the decision to buy an energy efficient air conditioning unit) are in fact measuring intertemporal marginal rates of substitution (IMRS) rather than pure rates of time preference because they fail to separate heterogeneous tastes from differences in taxes, capital market imperfections and income uncertainty (see Lawrance 1991, footnote 2). Based on our findings here we would be inclined to agree with this concern. One of our goals in this paper is to give a sense of the extent to which these concerns should temper the use of these measurement methods.

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Frederick, Loewenstein, and O’Donoghue (2004), among others, point out that there is a high degree of variability in measured discount rates across studies and suggest that there may be a variety of confounding factors or a problem with the elicitation procedures themselves. The approach we take in this paper directly addresses these concerns. By examining the correlations of these responses across elicitation methods, we can assess the degree to which these questions provide a consistent measure of the intertemporal tradeoffs individuals are willing to make. By deriving the theoretical impact of discount rates in a simple model, we can test whether these measures are associated with economic outcomes in the direction predicted by the model. And by analyzing changes in an individual’s reported discount rate over time, we can examine whether these measures are systematically related to macroeconomic conditions or to household level labor force events. The paper is set out as follows. The next section describes the Seattle and Denver Income Maintenance Experiments data. Section three examines the consistency of responses to the subjective discount rate questions and is then followed by an analysis (in section four) of the relationship between these measures and demographic characteristics. In section five we present a theoretical model to understand the relationship between the subjective discount rate and household outcomes such as work effort and asset accumulation. The predictions from this model are then tested. The penultimate section examines whether the discount rate responses are stable when macroeconomic conditions are changing. Section seven concludes.

II. Data The Seattle and Denver Income Maintenance Experiments began in 1970 to examine the impact of a negative income tax (NIT) on a wide range of household outcomes for both dual and

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single-headed households.9 The SIME/DIME used three different grant levels ($3800, $4800, and $5600 annually)10 and four different marginal tax rates (50%, 70%, a declining 70%, and a declining 80%) to generate eleven experimental grant level-tax rate combinations. Households were randomly assigned an experimental period duration of either three or five years and a job training treatment status. More than 4,800 households were enrolled, beginning in 1970 in Seattle and in 1971 in Denver, and approximately 60 percent of households were assigned to an NIT treatment. Treatment and control observations in the three-year (five-year) program were interviewed approximately once every four to five months for four (six) years at which point they were disenrolled from the experiment.11 Assignment to experimental treatment used conditional random assignment (the Conlisk-Watts assignment model) and was run separately for each race, household status (single or dual headed), and program duration combination for each site (Conlisk 1973). Thus, the probability of assignment to treatment depended upon race, household status, normal income, and program duration; as a result, all of our empirical analysis controls for each of these factors. We use the Work Impact files contained in the Seattle and Denver Income Maintenance Experiment data. This file contains one observation for each of the original (i.e., present at enrollment) household heads from the single and dual-headed households. Labor supply data which are collected monthly, such as work effort and wages, are contained as six-month 9

For more information on the SIME/DIME see the United States’ Department of Health and Human Services’ Final Report (1983) and United States Department of Health and Human Services report (1985). 10 Median income in 1970 for a 4 person household was $11,176 ($56,160 in 2005 dollars). The SIME/DIME benefits correspond to about 95%, 120% and 140% (respectively) of poverty levels or alternatively, $19,000, $24,000 and $28,000 annually in 2005 dollars. The official poverty level was defined as the income necessary to provide a family with three times the necessary income to afford the nutritional goals for the lowest of four Dept. of Agriculture family food plans. $3,800, the lowest SIME/DIME benefit plan approximated existing welfare payments the family would have gotten from AFDC. However, there were some cases in Seattle (single headed households with 5 or more members) where the lowest SIME/DIME grant level did not dominate AFDC transfers. 11 Households were interviewed for one year following the end of their experimental period.

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aggregates on the Work Impact file which we further aggregate to annual measures. For each observation, the data span the year prior to enrollment as well as up to six years following enrollment.

The files also contain information on household demographics, assignment

variables, and treatment status, along with some wealth and asset information. The SIME/DIME discount rate module uses three methods to obtain subjective discount rate measures from subjects: choice, titration, and matching.12 Choice questions ask people to choose between a smaller immediate reward and a larger later reward or to state they are indifferent. For example, an individual may be asked to choose between receiving either $100 today or $120 in exactly one year. For a respondent who would prefer to take the $100 immediately, a discount rate of at least 20% is inferred. Titration questions allow the researcher to more precisely estimate individual discount rates by varying the amount of time or money in a series of questions.

In doing so, both an upper and lower bound can be placed on the

respondent’s discount rate. For example, if an individual responds that he prefers $100 today to $120 next year, he would then be asked whether he prefers $100 today to $130 next year and so on with choices presented with increasingly larger future values until the respondent elects to take the delayed amount (see Appendix, Table 2). Matching questions present the respondent with a matching task where he must choose the dollar amount at time t1 that he believes to be utility equivalent to some fixed amount at time t2. For example, an individual is asked to state what amount of money she would need to receive in exactly one year to make her indifferent between that amount and receiving $100 today. Questions eliciting household discount rates were initially asked in the third periodic interview (typically one year after enrollment) in Seattle and in the Post-Enrollment Interview 12

These are not the only methods used to elicit discount rates. As an example, see Barsky et al. (1995) and Kapteyn and Teppa (2003). They present respondents with a series of questions wherein each question asks the respondent to choose their most preferred consumption profile from among five potential consumption profiles.

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(typically 6 weeks after enrollment) in Denver.13

Thus, no pre-enrollment discount rate

information is available. However, as the analysis will show, responses to the discount rate question are not affected by treatment status (such as which tax rate individuals faced or the duration of the program). Discount rate responses were elicited from only one person in each household and each respondent answered all discount rate questions successively.

Interviewers were explicitly

instructed to interview male heads when there was more than one head present. Thus, we limit our sample to original male heads of dual-headed households (henceforth married males) and original female heads of single-headed households (hence forth single females) who were asked these questions. Although we will present results separately by gender, these results reflect differences due to both gender and household marital status. The first discount rate elicitation method is a matching question that reads: “Suppose you were given a bonus of $100 which you will definitely be paid exactly one year from now. You could get paid now but would have to accept less money. Given your present situation, what is the smallest amount you would take today rather than waiting a year?”

The second set of questions use the choice method of elicitation. Respondents are first prompted with the statement, “Now I would like to read you a list of choices. I would like you to tell me which is the better choice or if both choices are equally good.” Subjects provide responses to eight different choice questions which include monetary choices (consisting of both gains and losses) as well as questions involving a dinner now or later and a car now or later (see Appendix Table 1 questions a, b, g, and h). For our analysis, we focus on the choice between $100 today or $120, $135, and $150, respectively, a year from now.

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In Seattle, 84% of our female sample and 90% of our male sample have been in enrolled for at least 1 year. However, in Denver, 80% of our female sample and 87% of our male sample have been enrolled for less than a year.

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The third type of question elicits the discount rate using a titration method. Households are first asked “Suppose now that you have the choice between a cash bonus today and a different cash bonus next year. If you were given the choice of $100 today or $200 a year from now, which would you choose?” If a respondent says that they would choose $100 today, the response is noted and the next question is asked. However, if the individual says $200, they are then asked: “Suppose your choices were $100 today or $175 a year from now?” Again, a response of $100 will end the series of questions while a response of $175 will lead to another value being asked. The series continues until the respondent either says they would choose $100 instead of the listed dollar amount or they reach the final dollar amount (see Appendix Table 2). Discount rate questions are also asked in later interview periods. However, despite documentation suggesting otherwise, the only measure that is elicited with consistent wording across multiple interviews is the titration question which is asked during both the third (1971) and seventh (1973) periodic interviews in Seattle.14 We use these responses to explore how discount rates change over time. For our final sample, a small number of households are dropped because a) the household composition changed between the pre-enrollment information collection and the enrollment data, b) the family was subsequently entered into the twenty-year program, or c) there is missing data for the demographic variables used in the analysis. These restrictions affect about seven percent of the male observations and ten percent of the female observations. Because a respondent did not answer the discount rate questions (because the individual left the survey prior to being asked or because another person was asked the questions), 7% of females and 0.5% of males in Seattle

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The discount rate questions asked in the later periodic interviews use different time frames and different methods of eliciting responses than the initial questions.

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and 4.5% of females and 3% of males in Denver are dropped15 After these deletions are made, 2,175 married male respondents and 1,510 single female respondents are left in the sample. Table 1 contains summary statistics for the two sets of respondents.

III. Consistency Within and Across the Subjective Discount Rate Measures Before testing the relationship between the subjective discount rate measures and household choices, we first examine the consistency both within and between the discount rate responses as wide variation has been noted in these measures both across and within studies (Frederick, Loewenstein, and O’Donoghue (2004)).16 In light of these concerns, this section analyzes whether the information contained in the subjective discount rate measures is similar across elicitation procedures. IIIa. Consistency Within A Measure: Choice Panel A of Table 2 shows the distribution of the choice questions for married men. Over two-thirds of married men prefer to take $100 today over $110, which corresponds to having an annual discount rate that exceeds ten percent. The next row shows that 56 percent of married men would not wait a year for $120 and therefore have a discount rate that exceeds 20 percent. The final two rows indicate that 47 percent of married men have a discount rate that exceeds 35 percent and roughly 38 percent have discount rates in excess of 50 percent.

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Attrition prior to the discount rate questions being elicited occurs more frequently in Seattle than in Denver, most likely due to the questions being asked much earlier of the Denver respondents. Not being asked the discount rate questions because another household member was selected to answer the questions is far more common among the female respondents which is likely due to them either cohabiting or marrying at the time the questions were asked. 16 While they point to a number of factors that may be responsible for the spread of reported discount rates, Frederick et al. (2004) conclude that multiple psychological motives are likely at play when making intertemporal trade-offs. As such, no single discount rate is applicable across all scenarios. In the current paper, we focus only on subjective discount rates for monetary outcomes, an approach that should reduce the scope of this issue when comparing across responses.

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The responses to the choice questions for single women are presented in Panel B of Table 2. The implied discount rates for single women are slightly higher than those found for married men, a finding that is not too surprising given the differences across these households shown in Table 1. (Single women have lower total pre-experimental income, more than double the preexperimental transfers and have slightly less than half the assets and net worth than married men have). Sixty-nine percent of single women have discount rates over 10%, 61 percent have discount rates in excess of 20%, 52 percent have discount rates that exceed 35% and 46 percent have discount rates that top 50%. While these discount rates are high relative to the numbers typically used in macroeconomic calibration exercises, they are within the range of estimates summarized by Frederick et al. (2004, Table 1) and Kunreuther et al. (1998). The consistency within all of the choice questions is shown in Table 3 for married men. We define consistency as giving choice responses such that it is possible that the respondent has a single discount rate that falls within the bounds implied by his choices. Panel A of Table 3 compares responses for the choice of $100 today against $110 in a year (in the rows) with the choice of $100 today against $120 in a year (in the columns). The discount rate implied by the indifference row is 10 percent. Therefore, respondents falling in the top row have discount rates that exceed 10 percent (69.4% of the sample), those in the bottom row have discount rates less than 10 percent (20.4%), and those in the middle row have discount rates of exactly 10 percent (10.3%). Similarly, the discount rate implied by the indifferent ‘column’ is 20 percent. The inconsistency is directly observed in Panel A of Table 3. Roughly 2% of the sample have a discount rate that exceeds 20 percent (the first column) but give responses to the ‘$110 question’ that correspond to having a discount rate of 10 percent or less (in the bottom rows). Working our way through the table in this manner suggests that approximately 10 percent of

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responses fall into these inconsistent cells – the four cells in the bottom left of Panel A. The amount of inconsistency observed for married men in Panels B and C of Table 3 is roughly the same as in Panel A: about ten percent. Throughout Table 3, the modal form of inconsistency is due to individuals stating that they are indifferent to both choices. We repeat the analysis shown in Table 3 for single women and, although not shown here, the degree of inconsistency for single women across the choice responses is similar to that of married men. As with married men, the majority of the inconsistency is due to individuals stating that they are indifferent between both choices.

IIIb. Consistency Across Measures: Choice, Matching and Titration While the responses appear to be fairly consistent within the choice questions, the consistency of responses across elicitation methods is also of interest. Figures 1 and 2 show the distribution of the matching responses conditional upon the respondent’s answer to the choice question. The vertical line in each of the three distributions is at $83.33 -- the dollar value response to the matching question that would be consistent with having a discount rate of 20 percent (an indifferent response to the ‘$100 vs $120’ choice question). Figure 1 presents the results of this comparison for married men. Higher values for the matching response correspond to having a lower subjective discount rate. Thus, those whose choice response indicates a discount rate exceeding 20% (top left of Figure 1) should state a dollar value less than $83.33 when responding to the matching question. In contrast, only 50% of married men report an answer to the matching question that is consistent with their response to the choice question. For those reporting a discount rate below 20% (top right, Figure 1), we expect responses to be greater than $83.33. We find that nearly 80% of their matching responses

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indeed fall below 20% (lie to the right of $83.33).

For the nearly 10% of married male

respondents who reported being indifferent to the choice question (bottom left of Figure 1), the distribution is spread almost evenly above and below the corresponding 20% level for the matching question.17 Almost 80 percent of married male respondents who exhibit the highest level of patience when presented with the choice question give a response to the matching question that implies a consistent discount rate. Thus, married men who are either indifferent or impatient according to the choice question show a much more disperse distribution in their matching responses. Figure 2 tells a similar story for single women. Unlike the results for married men, however, the distribution for the indifferent single women is not evenly split: nearly 55% give a response that corresponds to a discount rate lower than 20%. In figures not shown here, these patterns remain fairly similar across the other choice categories. Figures 3 and 4 show a comparison of the titration responses to the “$100 today vs. $120 a year from now” choice question. Because the titration question allows households to give answers within a range we can learn that an individual would be willing to wait a year to get $200, but unwilling to wait a year to take $175.18 Therefore, the actual value needed a year from now that would make the individual indifferent to taking $100 today falls somewhere between $175 and $200. Here, we will assign households to the mid-point of these ranges and, rather than make an arbitrary choice, we assign households that are unwilling to wait a year to take $200 a value of $200 even though the value that would make them indifferent must exceed $200. As can be seen in Figure 3, nearly 93% of the married men who give an impatient response to the choice question (top left corner of the Figure) also give a titration response that 17

Similar patterns emerge when responses to the other choice questions are examined (not shown here) When we use this titration method we now expect that individuals with a higher discount rate will give very large numbers to the titration question.

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implies a discount rate above 20%.19 For those categorized as patient responders to the choice question (top right of the Figure), the fraction giving a titration response that is consistent with a discount rate of less than 20% is roughly 64%. Among the married men who are indifferent in the choice version of the question (bottom left of the Figure), about 24% give a low discount rate response to the titration question. Unlike the nearly identical distributions of the matching responses in Figure 1, the titration responses indicate a higher degree of patience among the indifferent choice group than the impatient choice group. The distributions presented in Figure 4 for women give a similar picture.20 To summarize the degree of consistency across the subjective discount rate measures, correlations of the responses are presented in Table 4. Results for married men are presented in Panel A while the findings for single women appear in Panel B. In order to include the choice questions in the table, the variables have been recoded. Individuals who choose $100 today are assigned a value of –1. Those who choose the future dollar amount are assigned a value of +1. Indifferent individuals are assigned a value of 0. Thus, higher values of the modified choice variables correspond to more patient individuals. Many of the patterns discussed above, assessing the consistency of responses across the elicitation procedures, are apparent when examining the correlations in Table 4. As the first two columns of Table 4 show, the correlations between the choice answers and the titration response are much stronger than those between the choice answers and the matching response. The lower right portions of each Panel in Table 4 also reveal that the correlations for “adjacent” choice

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Comparable to Figures 1 and 2, the vertical line in Figures 3 and 4 represents the titration response that would yield a discount rate which equals the discount rate for the indifferent response to the choice question. 20 In addition, the amount of consistent responses increases when examining the titration responses with the answers given to the “$100 today vs. $135 in a year” and the “$100 today vs. $150 in a year” choices (not shown here).

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questions (i.e., those where the future amounts are closest together) are much stronger than for choice questions that are further apart. Table 4 also includes the discount rate that can be computed from the matching question in the third column and provides an interesting finding.21

The top two off-diagonal elements of

each Panel in the table indicate that the titration response is much more strongly correlated with the dollar value stated for the matching response than with the implied discount rate from the matching response (-0.293 vs 0.093 for males). In addition, a comparison of columns 1 and 3 of Table 4 shows that the implied discount rate from the matching question has a much lower correlation with the choice responses than is found when simply using the direct (dollar value) responses to the matching question. Thus, using the non-linear transformation of the matching response rather than the response itself leads to a much lower implied degree of consistency between the matching response and other time preference elicitation procedures. Overall, the results of this section present mixed evidence for the consistency of the subjective discount rate measures. The choice questions are highly consistent when compared to each other (correlations are 0.613 or higher).22 Furthermore, comparisons between the choice questions and the titration questions in column 2 show a consistent set of responses (aside from the small fraction of households reporting that they are indifferent in the choice question). However, the matching question and the choice questions show a much weaker correlation (the highest correlation for either males or females is 0.252). Also, the correlation of the titration and

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Since the matching response is the amount needed today to make the individual indifferent to waiting one year for $100, this discount rate is computed as (100/X) – 1, where X is the individual’s response to the matching question. Since this computed discount rate is an inverse function of the individual’s matching response, the computed and actual response will have different linear relationships with the other discount rate measures. 22 For both males and females Cronbach’s Alpha is greater than 0.8 among the choice questions but less than 0.8 for matching and titration questions. Cronbach’s Alpha is commonly used as an index of internal consistency. We can interpret a Cronbach’s Alpha of 0.80 as indicating that at least 80% of the variance in responses to the choice questions can be explained by common factors which underlie responses to those questions. For more on this measure see Crocker and Algina (1986).

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the matching question (the two “continuous” measures of the discount rate) never exceeds 0.3. 23 Given these findings, the following analysis examines the relationship between discount rates and household outcomes using all three types of elicitation methods.

IV. The Relationship Between Subjective Discount Rates and Household Demographics Tables 5a and 5b present the correlations of the subjective discount rate responses with pre-experimental household demographics for married men controlling for the variables used in the assignment to treatment model as well as indicators for treatment status. These specifications include indicators for the pre-experimental normal income categories, indicators for the racial groups, an indicator for the location, a dummy variable for being a control that fills out an income reporting form (IRF), and an indicator(s) for assignment to the negative income tax treatment. In addition, all of the regressions include an indicator for being enrolled in either the three- or five-year program as well as interactions between this indicator and the job training experiment indicators.

IVa. Comparing Dollar-Value and Computed Discount Rates From The Matching Response The first three columns of Table 5a present the results using dollar amount given by the respondent to the matching question as the dependent variable.

The base specification is

presented in the first column while the second column adds the respondent’s age, education, family size, and the number of children under 5 as regressors.24 The third column splits the

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Donkers and van Soest (1999) examine measures of discount rates available at two points in time, 1993 and 1995. Across the three measures they present that are asked in both survey waves, the highest correlation among the estimated discount rates for the same question over time is 0.23. 24 This specification is similar to the one used to estimate the labor supply response to the NIT in the Final Report of the SIME/DIME (1983). That specification also includes hours of work in the pre-experimental year and total amount of AFDC in the pre-experimental year as regressors although it does not include education.

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treatment variable into three- and five-year groups. All three columns show that increases in preexperimental income are correlated with a lower subjective discount rate. However, only the dummy variable for being in the next-to-highest income group is significant. The results indicate that Blacks and Latinos have significantly higher subjective discount rates, although the results for Latinos becomes insignificant once age and education are included in the model. Lower discount rates are associated with better-educated households and, as found in previous studies, older households (Donkers and Van Soest 1999; Read and Read 2004). The results in the first three columns of Table 5a also indicate that the results are not related to the experimental assignment variables.25 These results are re-assuring since the subjective measures are asked shortly after the experiment began in Denver and roughly a year after enrollment in Seattle. Columns (4) and (5) of Table 5a show the results using the discount rate computed from the matching response (recall that this measure had the lowest correlation to the other discount rate measures). The results differ somewhat from those found in the first three columns. There is no longer a positive relationship between the discount rate and normal income, although the standard errors are relatively large, and while it is negatively correlated with education, the discount rate is uncorrelated with age. Consistent with columns 1-3, Blacks on average have a discount rate that is significantly higher than that of Whites by 36% percentage points but the discount rate for Latinos is estimated to be lower than that of Whites.26 Most of the variables corresponding to program assignment are again insignificant. Comparing columns 1 through 5 of Table 5a suggest that transforming the matching response into a discount rate obscures some of the relationships between these responses and

25

Indicators for being an IRF control and being a control in the five-year experiment are all statistically insignificant. In addition, the indicators for being in an NIT treatment, whether pooled or split by program duration, or in a job training experiment are statistically insignificant. 26 When both age and education are excluded, the discount rate for Latinos is the same as it is for Whites.

19

demographic characteristics. Part of the issue is that over six percent of men (and over nine percent of women) give matching responses below 50, an amount that corresponds to a discount rate above 100 percent. Further, most of these responses are either 25 or less, which represents a discount rate of 300 percent or more. This skewness in the distribution of implied discount rates is apparent when comparing the median and means of the discount rates. The median discount rate is 11% for both men and women while the mean discount rates are 69% for men and 102% for women (not shown here). Thus, to avoid having the results driven by these few outliers, the remainder of the analysis uses the dollar response to the matching question, which we refer to as the dollar-value matching response, rather than the corresponding computed discount rate.27

IVb. Titration and Choice Discount Rates and Household Demographics Columns (6) and (7) of Table 5b present the results using the titration response as the dependent variable (where lower titration responses indicate higher discount rates). As with the matching responses (columns (1)-(3) of Table 5a), higher levels of income are correlated with falling discount rates although the estimates are insignificant. Black and Latino households have significantly higher discount rates of 21 percent and 6 percent, respectively, relative to Whites. The program parameters are again insignificant with two exceptions. First, the indicators for being in a five-year program (both overall and as an NIT treatment) are significant in column (7). Combining these two coefficients indicates that five-year controls have significantly lower discount rates while there is no difference for five-year treatments (when adding together the two

27

Roughly a third of respondents also gave a matching amount of $100 which corresponds to a zero discount rate. In comparison, four percent of respondents gave the lowest titration responses; this would lie roughly around a zero percent discount rate. Only twenty percent of respondents stated that they would take $110 in a year rather than $100 in the current year, a choice which corresponds to having a discount rate of less than 10 percent.

20

corresponding estimates). Second, being assigned to a job training treatment that includes a work subsidy (not shown in the Table) is now correlated with a slightly higher discount rate. The final two columns (columns (8) and (9)) of Table 5b present the results using the “$100 today vs. $120 in a year” choice response that is coded in the same manner as it is in Table 4. The results indicate that there is a strong gradient between pre-experimental income and the choice response with higher income families being more patient. Significant effects are also found for race, education, and age. Of the program parameters, only location is close to being significant. When the other choice variables are used as the dependent variable (not shown here), similar patterns emerge. However, the strong income gradient does not appear for the other choice responses.28 Tables 6a and 6b present the results for women when regressing the subjective discount rate measures on the same specifications used in Tables 5a and 5b. The general patterns found for men are generally true for women as well. The main difference between the male and female regressions is that no relationship between discount rates and pre-experimental income is found for women across any of the specifications. In summary, we find that the choice, dollar-value matching, and titration responses all have correlations in the expected directions with education and income, but that across specifications these relationships are not terribly robust. Further, using the computed discount rate from the dollar-value response to the matching question yields results that differ in important ways from the specifications using the choice, dollar-value matching, and titration responses. Computing the implied discount rate from the matching response obscures some of the correlations that we find using the other three measures. However, choice, matching, and 28

The interpretation of columns (8) and (9) does not substantially change when we use a probit model with identical independent variables and a dependent variable which takes the value 1 if the person selects the smaller sooner reward and 0 if he is indifferent or selects the larger later reward.

21

titration all show a strong gradient between pre-experimental income and responses even though the standard errors are too large to obtain significance in most instances. We also find that older and more educated households have lower estimated values of time preference. And perhaps most striking of all, Blacks and Latinos are significantly more impatient than Whites according to these measures.

V. The Relationship Between Subjective Discount Rates and Economic Behaviors We next examine the relationship between the discount rate and household choices such as work effort and the accumulation of assets. To understand the theoretical relationships, we use a two-period life-cycle model where the period-specific utility function includes both consumption and leisure. Thus, households maximize Ut = v(c(0), l (0)) + F (1)v(c(1), l (1))

subject to c(0) +

c(1) w(1) = A(0) + w(0)(1 − l (0)) + (1 − l (1)) 1+ r 1+ r

where c(t ) , l (t ) , and w(t ) are consumption, leisure, and the wage rate, respectively, in period t=0,1, A(0) is wealth at the beginning of life, and r is the interest rate. Leisure is normalized to range between zero and one. As above, F (1) is the discount function for utility in the second period of life. The period-specific utility function v(⋅,⋅) is assumed, as is standard, to be strictly concave and twice differentiable. Our interest is to understand the impact that changing the discount function has on the optimal levels of consumption and leisure in each period.29 With the added assumption that both

29

Proofs of these results are available upon request from the authors.

22

consumption and leisure are normal goods, the following comparative static results hold for the first period d [c(0)] d [l (0)] < 0 and < 0, dF (1) dF (1) while in the second period d [c(1)] d [l (1)] > 0 and > 0. dF (1) dF (1) Thus, an increase in the discount function leads to a decrease in both consumption and leisure in the first period and an increase in both goods in the second period. Intuitively, households that care more about the future will allocate more of total lifetime resources to the second period. An increase in the discount function tilts the life-time profile of consumption and leisure in favor of the later period. Notice that a change in the discount function does not change relative prices within either period. Rather, changes in the discount function only affect the optimal allocation of lifetime resources to each period.

Va. The Relationship Between Discount Rates and Asset Accumulation As highlighted by the theoretical model presented above, an individual’s discount rate should be correlated with a number of household outcomes such as work effort and wealth accumulation. The above model predicts that younger households with higher discount functions (i.e., lower discount rates) will consume less. While we do not have consumption data, we do have information on the stock of assets. The above prediction for consumption implies that the stock of assets accumulated should increase with the discount function (decrease with the discount rate) for younger households. In addition, since these assets are carried over into later years, older households with lower discount rates should also accumulate more assets. The

23

model also has interesting predictions for work effort. Younger households with higher discount functions (lower discount rates) should be observed exerting higher levels of work effort. For older households, this prediction is reversed.

Among older households, higher discount

functions (lower discount rates) lead to lower levels of work effort. Table 7 presents the relationship between each of the three discount measures and household assets and work effort by the respondent in the year prior to the experiment for single men. The specifications presented in the Table are the same as the one used in column 2 of Table 5. However, to focus the discussion, only the coefficient on the relevant discount rate measure is shown in Table 7. Panels A and B of Table 7 present the results using asset holdings as the dependent variable. Assets in the SIME/DIME are computed as liquid assets (cash on hand, the value of savings and checking accounts, and stocks and bonds) and the equity in owned property including the household’s own home. To interpolate household assets, information on household net worth (collected four to five months post-enrollment) and property information (collected four to five months post-enrollment in Seattle and eight to ten months post-enrollment in Denver) is used. The SIME/DIME Work Impact data include estimates of household assets in the pre-experimental period that were created using an algorithm to interpolate between interviews as well as extrapolate into the pre-experimental period (including adjustments based on the date items were purchased or disposed). The relatively short duration between the enrollment date and the initial periodic interviews most likely results in only a small amount of error between the imputed and actual pre-experimental measures. When pooling across single men of all ages, all three subjective discount rate measures indicate that more patient households accumulate more assets (Panel A).

The estimated

24

coefficient of 15.7 for the matching response indicates that the difference in assets between the most impatient (response=$0) and the most patient (response=$100) individuals is 15.7*(100-0) = $1570. The comparable difference using the titration response is -14.1*(100-200) = $1410. From the choice question, this difference is 227*(1 - (-1)) = $454. However, as we have seen above, the choice questions pool individuals across a wide range of discount rates and therefore conceal the range of the correlation between these measures and accumulated assets. Relative to average household assets of $3200, the amount of variation in assets due to differences in discount rates is fairly substantial. The model presented above indicates that that the relationship between assets and the discount rate should be of the same sign for both young and older households. To test this prediction, the specification presented in Panel B allows the relationship between asset accumulation and the discount rate to vary by age. Households are split into two groups around the sample average age which is 32.30

For the matching and the titration responses, the

relationship between assets and the discount rate is statistically significant and of the hypothesized sign for both younger and older households.

The results also indicate the

relationship is somewhat stronger for the older households although the differences are not statistically significant. For the choice response, the estimates are again of the correct sign although only the estimate for the older households is significant. Table 8 presents the results for married women. When pooling across all married women (Panel A), the titration and matching responses are not significantly related to asset accumulation. The choice measure, however, is significantly related to asset accumulation. The estimates using this last measure imply that moving from the most impatient respondents to the 30

This sample average may not accurately reflect the “correct” age to split between younger and older households. Gourinchas and Parker (2002) estimate the early 40s is when households switch from being precautionary to lifecycle savers. Results splitting the sample at age 41 yield qualitatively similar results to those presented here.

25

most patient respondents increases asset accumulation by over $600 or one-third of the sample average level of assets. Splitting the sample at the average age (Panel B) indicates a stronger relationship for the older households relative to the younger households across all three measures although these differences are far from being significant. Oddly, the choice estimate for the younger households is wrong-signed and statistically significant.

Vb. The Relationship Between Discount Rates and Work Effort The bottom two panels of Table 7 show the estimated relationship between the discount rate measures and annual hours worked in the pre-experimental year for married men. For the full sample, the estimates in Panel C of Table 7 indicate that more patient individuals exert more work effort. The coefficient on the matching response is marginally significant. However, the coefficients on the titration response and the choice response (again using the “$100 today vs. $120 in a year” question) are highly significant. In addition, the estimated impact on hours worked is roughly the same across all three measures. Going from the most impatient to the most patient allowable matching response increases annual hours worked by 1.22*(100-0) = 122 hours. The range for the titration response is –1.38*(100-200) = 138 hours, while the differences between the most impatient and patient individuals according to the coefficient on the choice response is 64*(1 - (-1)) = 128. Relative to average annual hours worked of 1,727 hours, this range corresponds to a seven to eight percent increase in work effort due to differences in discount rates. Panel D of Table 7 tests the prediction of the model that work effort is positively associated with the discount rate for younger households and is negatively associated with the discount rate among older households. However, the findings across all three columns in Panel

26

D show virtually no difference in the estimated relationship by age of the respondent.31 Moreover, the estimates are still positive for both sets of households. In addition, the results indicate that the titration response is actually larger for the older households. The bottom two panels of Table 8 presents the relationship between hours of work and the discount rate for single women. Hours of work are negatively related to all three discount rate measures when pooling across all single women (Panel C). However, the estimates for the matching and titration responses are marginally significant while the choice estimate is significant at the conventional level. The implied increase in hours worked moving from the most impatient to patient respondent is about 10 percent (100 hours relative to an average of 1028 annual hours worked) across all three of these measures. The estimates in Panel D of Table 8, which report the relationship between work effort and impatience, do not support the hypothesized differences across ages. Similar to estimates found for married men, the differences between the younger and older groups are small and insignificant for the matching and titration responses. The estimates using the choice response are statistically different for the two groups but the findings are nearly opposite those predicted by the model. The estimated relationships are positive for both the younger and older married women and the estimate for older single women is larger than that found for the younger single women. As with married men, the theoretical differences expected in hours-worked are not found in the data. Overall, the results in this section indicate mixed support for the theoretical model. The prediction for assets is consistent with the empirical findings. Across all groups, more patient individuals are found to have accumulated more asset heterogeneity. The results also indicate

31

In results not shown here that split the sample at age 41, the estimates for the matching and choice responses are somewhat larger (although not significantly) for the younger households than for the older households.

27

that more patient individuals provide higher levels of work effort. However, the prediction that the relationship between patience and work effort differs between the younger and older households is not supported. Of course, one potential problem with our analysis is that patience also influences other factors involved in labor force decisions (e.g., the wage rate through schooling decisions) for which we do not control. Secondly, we assume that our measures of time preferences capture a pure rate of time preference. However, our previous analysis of correlations between these measures indicates that they are imperfectly correlated with one another and are not always significantly correlated with socio-economic variables where we expect they would be.

VI. Are These Measures of Discount Rates or Market Interest Rates?

One of the most important issues concerning subjective discount rates is attempting to understand exactly what these measures represent. Thus far, we have taken the approach that dominates the literature which is to assume that these measures represent an individual’s true rate of time preference. However, as we discussed above, if individuals try to equate cash values at two points in time then these measures are really indicative of the (nominal) interest rate faced by individuals in the market. Whereas an individual’s rate of time preference is assumed to be time invariant, the interest rate one faces in the market can vary with a number of factors such as inflation and a lack of access to credit markets. Given the information we have on the market conditions in which these individuals live, we can examine how these relate to the elicited discount rate measures. A feature of the SIME/DIME data that is not true of nearly every other dataset that has elicited discount rates is that these measures are asked at multiple points in time. Unfortunately,

28

some of the methods used to gather discount rates differed over time. However, the titration question was asked during the third and sixth periodic interviews for the Seattle sample allowing us to examine the stability of these questions over time.

VIa. Rising Inflation The timing of the third and sixth periodic interviews in Seattle coincided with large increases in the inflation rate that took place in the early 1970s. Among those individuals responding to both of these interviews, the third periodic was fielded for nearly 98% of the men between August and November of 1972 and for over 94% of the women between August and October of 1972. The sixth interviews fell between September 1973 and March 1974 for almost every man and between September and December 1973 for 88 percent of the women. Over the time frame spanned by these responses (September 1972 to March 1974), the national inflation rate rose from 3.2 percent to 10.4 percent.32 Figures available from the University of Michigan’s Survey of Consumers indicate that inflation expectations took a similar path, rising from 3.9 percent in the third quarter of 1972 to 10.1 percent in the first quarter of 1974.33

The

unemployment rate actually fell slightly over this period from 5.5 percent to 5.1 percent before rising dramatically between late 1974 and early 1975. If these subjective discount rates are invariant to the inflation rate, as one would expect if they are eliciting pure rates of time preference, then we would not expect to see changes in the measured responses over this period. Figures 5a and 5b show changes in the mean discount rates elicited from the titration questions over this period.

Both Figures also include the national inflation rates and

unemployment rates. The average discount rates range between 43% and 49% percent for 32

The CPI-U figures for the Seattle area show an even sharper increase, rising from 1.8 percent in August 1972 to 10.1 percent in February 1974. 33 Data from the Survey of Consumers is available at http://www.sca.isr.umich.edu.

29

married men and between 56% and 63% for single women in the Fall of 1972. However, in late 1973 and early 1974, these ranges were between 71% and 80% for married men and 72% and 85% for single women. Thus, while the rate of inflation rose by over 6% (roughly tripling over this period), the average discount rate responses rose by 27 percent for married men and 22 percent for single women.

Furthermore, these increases in the discount rates were likely

suppressed since the titration question limited the highest reported discount rate to be 100%. While a quarter of men gave the maximum discount rate in late 1972, nearly 60% did so in late 1973 and early 1974. For women, two-thirds gave the maximum response to the later survey while only 36% did so in the earlier survey. Thus, the strong correlation between the interest rate and the inflation rate found here likely understates the true strength of this relationship.

VIa. Work Effort Another approach for examining whether these measures are time invariant is to test whether changes in reported discount rates over time are correlated with changes that occur at the household level. In particular, we regress the change in the response to the titration question on changes in the respondent’s work effort. These results are reported in Table 9. Panel A of the Table includes, in addition to the controls from the specifications used above (e.g., Table 5), the change in the respondent’s hours worked. As can be seen in the Table, the coefficient on this regressor is negative for both married men and single women. However, the result is only marginally significant for women and it is insignificant for men. Panel B of the Table shows the results when using the change in the share of time spent unemployed as the regressor.34 These estimates are marginally significant for both men and women. These results provide suggestive 34

The share of time spent unemployed on the Work History file is the fraction of days during the year the individual reports being either voluntarily or involuntarily unemployed. The number of days spent unemployed is constructed from information on the start and end dates of unemployment spells

30

evidence that changes over time in the subjective discount rates elicited from respondents are sensitive to changes in the economic conditions facing the household. Overall, the results in this section suggest that a relationship exists between the prevailing inflation rate and adverse household outcomes and the estimated subjective discount rate. This is in direct contrast to the typical ‘time-invariant’ assumption made by studies using these experimental measures.

VII. Conclusion

Individual discount rates are an integral part of decisions to allocate resources over time. Subjective discount rates, which are typically elicited through responses to hypothetical choices, have been the focus of a large literature in behavioral economics and psychology. However, the validity of the hypothetical choice format has not been well explored. Using data from the Seattle and Denver Income Maintenance Experiments, we examine a number of issues regarding subjective discount rates. First, we explore the consistency of the discount rates elicited by three commonly used methods and find that these measures are not perfectly correlated with one another despite often being treated as substitutes. However, we do find that when we examine responses within the choice question, correlations are stronger suggesting that subjects can be consistent within a response mode but have difficulty across response modes.

Second, we test whether these measures are correlated with economic

outcomes such as work effort and asset accumulation as implied by the life-cycle model and find the empirical results match the predictions for accumulated assets. However, the results for hours worked are not consistent with the theoretical predictions. Finally, we examine whether these measures are stable over time as should be the case if they capture pure rates of time

31

preference. We find that the elicited discount rates increase dramatically when the rate of inflation increases and changes in these measures are related to changes in individual labor force events. Our results stand in strong contrast to common assumptions (and usage) that the discount rate is measuring a pure rate of time preference and implies that a degree of caution should be used when utilizing discount rates elicited with these methods. In summary, our analysis provides an important, and widely missing, link between discount rates elicited using hypothetical question formats and economic outcomes. It also raises questions about how interchangeable these elicitation methods are and implies that these measures are not capturing pure rates of time preference. However, the correlation between these measures and important economic decisions (such as work effort) and household characteristics (such as asset accumulation) substantiates that there is important variation in the discount rate (however imperfectly measured) and that this variation can explain differences in economic behavior across individuals and households.

32

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Appendix Table 1 – Discount Rate Elicitations Using Choice in the SIME/DIME

2. Now I would like to read you a list of choices. I would like you to tell me which is the better choice or if both choices are equally good.

a.

A lump sum bonus of $100 today A lump sum cash bonus of $120 a year from now Both equally good

b.

A $100 gift today A $110 gift a year from now Both equally good

c.

Paying off a $100 debt today Postponing a $100 debt due today for $105 payable next year Both equally good

d.

A free new car today A free new car a year from now Both equally good

e.

Paying off a $100 debt today Postponing a $100 debt due today for $115 payable next year Both equally good

f.

A free first class dinner this month A free first class dinner next year Both equally good

g.

A lump sum cash bonus of $100 today A lump sum cash bonus of $135 a year from now Both equally good

h.

A $100 gift today A $150 gift one year from now Both equally good

36

Appendix Table 2 – Discount Rate Elicitations Using Titration in the SIME/DIME

4. Suppose now that you have the choice between a cash bonus today and a different cash bonus next year. If you were given the choice of $100 today or $200 a year from now, which would you choice? Suppose your choices were $100 today or (READ NEXT AMOUNT FROM TOP OF COLUMN 2) a year from now?

Column 1

Column 2

Bonus Today

Bonus A Year From Now

a.

$100

$200

b.

$100

$175

c.

$100

$150

d.

$100

$140

e.

$100

$135

f.

$100

$130

g.

$100

$127

h.

$100

$124

i.

$100

$121

j.

$100

$118

k.

$100

$115

l.

$100

$112

m.

$100

$109

n.

$100

$106

o.

$100

$103

p.

$100

$100

37

Table 1 - Summary Statistics Men in Dual-Headed Households

Women in Single-Headed Households

Years of Education

11.1

11.2

Age

33.8

34.5

Household Size

4.4

3.5

HH Members Under 16

2.1

2.0

HH Members Under 5

0.8

0.5

Black

0.33

0.47

Latino

0.20

0.15

Denver

0.57

0.56

Five-year Program

0.34

0.32

Treatment Group

0.56

0.61

Pre-Experimental Total Income

7,842

4,814

Pre-Experimental Earned Income

7,007

2,797

Pre-Experimental Transfer Income

835

2,014

Pre-Experimental Assets

3,260

1,799

Pre-Experimental Net Worth

4,079

2,318

81

78

Matching Response Discount Rate

0.69

1.02

Titration Response

148

156

2,175

1,510

Matching Response

N

Table 2 - Distribution of Choice Responses

N

Prefer $100 Today

Indifferent

Prefer Future Value

$100 Today or $110 in a year

2,175

69.4

10.3

20.3


2,175

56.3

10.4

33.3


2,175

46.7

5.8

47.5


2,172

37.9

5.8

56.4


1,510

68.9

11.2

19.9


1,510

60.9

10.3

28.8


1,509

52.4

7.3

40.4


1,510

46.2

7.4

46.4

A. Men Choice:

B. Women Choice:

Table 3 - Consistency of Choice Questions for Men A. $100 vs. $110 choice and $100 vs. $120 choice $100 Now (%)

Indifferent (%)

$120 Next Year (%)

Total (%)

$100 Now

1172 (53.9)

77 (3.5)

260 (12.0)

1509 (69.4)

Indifferent

27 (1.2)

141 (6.5)

56 (2.6)

224 (10.3)

$110 Next Year

25 (1.2)

9 (0.4)

408 (18.8)

442 (20.4)

Total

1224 (56.3)

227 (10.4)

724 (33.3)

2175 (100.0)

B. $100 vs. $120 choice and $100 vs. $135 choice $100 Now (%)

Indifferent (%)

$135 Next Year (%)

Total (%)

$100 Now

901 (41.4)

31 (1.4)

292 (13.4)

1224 (56.2)

Indifferent

45 (2.1)

86 (4.0)

96 (4.4)

227 (10.5)

$120 Next Year

70 (3.2)

9 (0.4)

645 (29.7)

724 (33.3)

Total

1016 (46.7)

126 (5.8)

1033 (47.5)

2175 (100.0)

C. $100 vs. $135 choice and $100 vs. $150 choice $100 Now (%)

Indifferent (%)

$150 Next Year (%)

Total (%)

$100

774 (35.6)

31 (1.4)

210 (9.7)

1015 (46.7)

Indifferent

10 (0.5)

79 (3.6)

37 (1.7)

126 (5.8)

$135 Next Year

38 (1.8)

15 (0.7)

978 (45.0)

1031 (47.5)

Total

822 (37.8)

125 (5.8)

1225 (56.3)

2172 (99.9)

Table 4 - Correlations Between Subjective Discount Rate Measures

Matching Response

$100 today $100 today $100 today $100 today Titration Matching or or or or Response Discount Rate $110/year $120/year $135/year $150/year

A. Men Matching Response

1

Titration Response

-0.293

1

Matching Discount Rate

-0.442

0.093

1

$100 today v. $110/a year

0.176

-0.431

-0.041

1


0.242

-0.534

-0.069

0.649

1


0.252

-0.639

-0.086

0.453

0.613

1


0.245

-0.683

-0.078

0.400

0.501

0.747

1

B. Women Matching Response

1

Titration Response

-0.238

1

Matching Discount Rate

-0.320

0.068

1


0.173

-0.440

0.019

1


0.180

-0.493

0.018

0.691

1


0.197

-0.615

0.018

0.536

0.633

1


0.178

-0.664

0.010

0.470

0.544

0.781

1

Table 5a - Correlations of Discount Rates and Household Demographics for Men

Independent Variable

Dependent Variable = Matching Response (1) (2) (3)

Dependent Variable = Discount Rate from Matching Response (4) (5)

$1000