Time Preferences for Life-Saving Programs: Evidence from Six Less

Environ. Sci. Technol. 2000, 34, 1445-1455

Time Preferences for Life-Saving Programs: Evidence from Six Less Developed Countries† C H R I S T I N E P O U L O S * ,‡ A N D DALE WHITTINGTON§ Center for Environmental and Resource Economics Policy, Department of Agricultural and Resource Economics, Box 8109, North Carolina State University, Raleigh, North Carolina 27695, and Department of Environmental Sciences and Engineering, Rosenau CB 7400, School of Public Health, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599

Individuals’ time preferences for saving lives are measured in six less developed countries in Africa, Eastern Europe, and Asia using a stated-preference method. The results indicate that individuals’ discount rates differ significantly by country, but they are much higher than those estimated for samples in the United States and Western Europe. Also, respondents’ time preferences for saving lives are characterized by a nonconstant exponential discount function. We conclude that the discounting practices currently used in standard economic analyses of development projects are poor representations of individuals’ actual time preferences.

Introduction A fundamental principle of welfare economics is that individuals’ preferences should count in the design of social and economic policy. Economists typically assume that the economic value to an individual of a public action that confers benefits over multiple time periods is the discounted sum of net benefits experienced by that person and that the net benefit of a policy to society is the algebraic sum of individuals’ willingness to pay (1). There is a voluminous literature and an active debate surrounding the selection of the social rate of time preference for aggregating benefits over time. Economists in the positivist tradition maintain that the only reasonable way to determine the social rate of time preference is to elicit time preferences at the individual level or to infer time preferences from market transactions (2). [A different school of economic thought asserts that there are several reasons why individual or market rates are inappropriate for social cost-benefit analysis (CBA) (3-6)]. In the United States, policy analysts typically use market interest rates to infer the social rate of time preference. [The U.S. Office of Management and Budget uses either the rate of return on private investment or the government borrowing rate as measured by the rate of return on U.S. Treasury securities. The National Oceanic and Atmospheric Administration, the Department of Interior, the Congressional Budget Office, and the General Accounting Office base their recommendations for selecting a social rate of time preference on the rate of return on U.S. Treasury securities.] The selection †

Part of the special issue on Economic Valuation. * Corresponding author e-mail: christy•[email protected]. North Carolina State University. § University of North Carolina at Chapel Hill. ‡

10.1021/es990730a CCC: $19.00 Published on Web 03/21/2000

 2000 American Chemical Society

of discount rates for CBA analyses in less developed countries (LDCs) is more challenging, in part because markets are not well-developed in LDCs and market imperfections can cause interest rates and time preferences to diverge widely (7, 8). There is little empirical research on individuals’ actual rates of time preference in LDCs. This lack of attention to the task of estimating individuals’ rates of time preference in LDCs is odd considering the popularity of demand-oriented development planning approaches. Analysts working on problems of developing countries often go to great lengths to obtain empirical information on individuals’ preferences for infrastructure services or environmental quality improvements only to make crude assumptions about individuals’ rates of time preference that can easily determine the results of a project or policy appraisal. For example, the primary objective of many development projects is to reduce mortality risks. This may be achieved through either curative or preventive health programs. In general, the benefits of preventive programs are more delayed than the benefits of curative programs, and thus the choice of a social rate of time preference may well determine which type of program is chosen. There is however no published literature on how residents of LDCs perceive the value of saving lives today versus saving lives in the future. Research on time preferences has implications beyond the choice of a social rate of time preference. Individuals’ time preferences are central to understanding households’ choices in such areas as education, savings, and preventive health activities. Time preferences may also have important effects at the macroeconomic level. Becker and Mulligan (9) postulate that heterogeneity in time preferences may partially explain different patterns of economic growth. This paper presents the first evidence on time preferences for lives saved by public programs in LDCs. A stated preference approach is employed, using a question developed by Cropper et al. (10). [We have slightly modified their question to make it more appropriate to a developing country context.] Household surveys carried out in Africa (Uganda, Mozambique, and Ethiopia), Asia (Indonesia), and the transition economies of Eastern Europe and the former Soviet Union (Bulgaria and Ukraine) collected respondents’ preferences for saving lives today versus saving lives in the future. Our analysis in this paper is based on these in-person interviews with almost 3000 respondents over the period of 1994-1997. There are three important findings from our research. First, individuals in all six countries in our study are much more present-oriented than the individuals in time preference studies conducted the United States and Western Europe. Second, the constant exponential discount function that is currently used in CBA is inadequate for describing respondents’ time preferences for saving lives. Although similar evidence of discount functions that are not constant exponential functions has been found in other settings, these multicountry results provide the first evidence that these findings are representative of populations in LDCs. Third, there are large differences in time preferences between different countries, and these are largely unexplained by income or other socioeconomic factors. The next section presents the concepts and definitions used throughout the paper and summarizes what is known about individuals’ time preferences in LDCs. The third section describes the research design and field procedures. The fourth section presents the modeling framework used for data analysis. The fifth section presents the results of the analysis VOL. 34, NO. 8, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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for all six countries. The final section offers some concluding remarks on the significance of our results.

Background Individuals and public decision-makers are assumed to make intertemporal choices by comparing the time-weighted benefits of alternatives and selecting the alternative with the largest aggregate utility. More formally, the individual’s lifetime utility is a function of consumption over their lifetime:

U ) u(Ct) ) u(C0, C1, C2, ..., CT)

(1)

Assuming that (i) the lifetime utility is additively separable and (ii) the single-period utility function is the same for all periods, an individual’s lifetime utility is T

U)

∑ w u(C ) t

t

(2)

t)0

where U is the lifetime utility from the present (t ) 0) until the individual dies (t ) T); u(Ct) is the utility the individual receives in period t from consumption Ct; ∂u/∂Ct is positive and decreasing in Ct; wt are weights attached to utility in different time periods, called “discount factors” [we avoid an individual-specific index by assuming that all individuals have the same utility function]. The discount factor is a function of the individual’s patience or pure rate of time preference, r, and time:

wt ) f(r,t)

(3)

At the individual’s point of indifference between marginal changes in consumption in periods 0 and T

dU ) u′(C0) dC0 + f(r,T)u′(CT) dCT ) 0

(4)

or

( ) dC0 dCT

u′(CT) ) -f(r,T) ) wT u′(C0) U)constant

(5)

The discount factor, wT, is equal to the intertemporal marginal rate of substitution, which is a function of the individual’s time preferences (represented by r), the time horizon (T), and the marginal utility of consumption in periods 0 and T. The individual’s discount factor for T is thus equal to the rate at which they will tradeoff consumption today for consumption in T. This paper focuses on three main issues: (i) the magnitude of r and wt in LDCs, (ii) whether the discount function is constant exponential, and (iii) how time preferences are related to individual or household characteristics. A discount function relates a discount factor to time and other parameters. The most commonly used discount function is the constant exponential:

wt )

1 (1 + r)t

(6)

which is characterized by a rate of time preference, r, that is the same regardless of the time period, t. When Samuelson (11) introduced discounted utility theory, he acknowledged that the maintained assumption of a constant exponential discount function is arbitrary and that the discount rate may or may not be positive. Nevertheless, these assumptions are widely made in the practice of discounting and imply that individuals weight benefits conferred in the current time period more heavily than benefits conferred in future time periods. Equation 6 shows that the discount rate is inversely proportional to the discount factor. Therefore, patient 1446

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individuals have high discount factors and low discount rates, while impatient individuals have low discount factors and high discount rates. There is a growing body of empirical evidence that the discount functions of individuals in the United States and Western Europe are not best characterized as constant exponential functions (12-14). [Nonconstant exponential discounting has been found in stated-preference as well as revealed-preference studies, using not only monetary rewards (12, 15-22) but also nonmonetary rewards (4, 10, 23-25). Ainslie and Haslam (26) provide a review of much of this empirical research.] This evidence shows individuals’ discount rates decline monotonically as the time horizon increases. These results are inconsistent with the constant exponential discount function. Several alternative discount functions that can accommodate these empirical findings have been developed (e.g., refs 27 and 28). Within the class of nonconstant exponential functions is Loewenstein and Prelec’s (27) generalized hyperbolic discount function:

wt ) (1 + Rt)-F/R

(7)

where R, F > 0. [The constant exponential function is actually a special case of the generalized hyperbolic function.] Figure 1 compares the discount factors generated by the constant exponential function (r ) 0.10) and a generalized hyperbolic function (F ) 0.20; R ) 0.20). Given these parameter values, the hyperbolic discount function places less weight on the near future than the constant exponential discount function and greater weight on the more distant future. Although eq 7 is generally consistent with empirical evidence on individuals’ rates of time preference, there has been relatively little empirical work done on the value of the parameters in this generalized hyperbolic discount function or on whether this is the most appropriate functional form for a nonconstant exponential discount function. Discounted utility theory assumes that individuals’ time preferences are exogenous and thus offers no explanation for the relationship between individuals’ time preferences and their socioeconomic characteristics. A theory of individual choice that simply assumes time preferences are exogenous to the individual is not able to predict how time preferences in LDCs may be different from time preferences in the United States or Western Europe. Although the empirical evidence from the United States and Europe suggests that time preferences are correlated with observable variables, discounted utility theory in fact has limited explanatory power (29-33). Becker and Mulligan (9, 34) offer an alternative theory that provides a microeconomic basis for explaining how time preferences are related to economic variables. [In earlier work, Uzawa (35) supposes a correlation between time preferences and consumption but does not advance a theory of the relationship between economic variables and time preferences. On the other hand, Leshan (32) and Rogers (36) do hypothesize relationships between time preferences and economic variables, but neither proposes a comprehensive economic theory.] Their theory of endogenous time preferences provides theoretical grounds for hypothesizing that populations in LDCs are less patient than populations in developed countries. It proposes a mechanism through which time preferences are affected by individual characteristics, including those characteristics over which individuals make choices. To model endogenous time preferences, Becker and Mulligan (9, 34) introduce a concept called “future-oriented capital”, which is a choice variable from the individuals’ perspective. [Becker and Mulligan (9, 34) model the stock of F as a constant that does not depreciate over time.] Future-

FIGURE 1. Constant exponential and generalized hyperbolic discount functions. oriented capital is the intellectual or other resources that individuals dedicate to future time periods. Becker and Mulligan (34) suggest that F depends in part on the time and effort spent anticipating future benefits and costs (by forming images of the future and simulating future scenarios). It is also affected by spending on goods that distract one’s attention from the present to the future (e.g., disciplinary devices such as alarm clocks). Schooling is another activity that focuses individuals’ attention on the future. Futureoriented capital determines the weight the individual places on the future:

wt ) w(F)t

(8)

w(F) > 0, w′(F) g 0, w′′(F) e 0, for F g 0 where F is future-oriented capital. [Although Becker and Mulligan (9, 34) assume that the discount function is constant exponential, they also use discount factors rather than discount rates to describe time preferences.] According to Becker and Mulligan, the individual’s choice of F depends on individual and household characteristics. [Furthermore, F is not costless because the resources spent anticipating the future are not available for production, either at home or in the market. So F depends on individual or household characteristics that influence either the cost of F or the individual’s efficiency in producing F.] For ease of exposition, we limit the characteristics to consumption and mortality risk. The model predicts that future-oriented capital increases with current consumption and increases in life expectancy or decreases in mortality risk. [If the generation of F is time-intensive, then whether increases in consumption are due to increased assets or increased earnings becomes important (9).] Now eq 8 can be rewritten as

wt ) w(F)t ) w(C0, πt)t

(9)

where C0 is current consumption, πt is the probability of surviving until time period t, ∂w/∂C0 > 0, and ∂w/∂πt > 0. [Survival probability is equivalent to 1 minus the risk of dying by time period t.] Becker and Mulligan (9, 34) also suggest that education is likely to increase F because educated individuals should have greater skills for imagining the future and generating future-oriented capital. Future utilities and future-oriented capital are complements in Becker and Mulligan’s (34) model. For instance, when future utilities are enhanced by a public project generating health benefits, an incentive to invest in F is

created. When F is increased (the discount rate decreases and the discount factor increases), the discounted value of future utilities increases. Therefore, increases in F are reinforced by making the gains that motivate investment (increases in future utility) even more important. Current consumption also determines health status in general and survival probability in particular (37, 38). By including endogenous survival probability in the model of endogenous time preferences, the impact of current consumption on time preferences is reinforced by an indirect effect on F via its effect on πt. Gersovitz (38) models survival probability as a nonlinear function of consumption. Below a threshold level of consumption, c˜, current consumption increases survival probability. When current consumption is greater than or equal to c˜, additional consumption has no impact on survival probability:

πt ) π(C0)

(10)

where πc > 0 if C0 < c˜ and πc ) 0 if C0 g c˜. Combining eqs 2, 9, and 10, taking the total derivative, and solving for the individual’s point of indifference between consumption in periods 0 and T, the following expression for the discount factor is obtained:

( ) dC0 dCT

)

U)constant

u′(CT) ) wT (11) -w(F)T ∂w ∂w ∂π u′(C0) + u(Ct)Tw(F)T-1 + ∂π ∂C0 ∂C0

(

)

This discount factor incorporates endogenous time preferences and survival probabilities. Comparing eq 11 with eq 5 shows that, with endogenous time preferences and survival probabilities, the discount factor is smaller because there is an additional term in the denominator of eq 11. This additional term is greater than 0 and equal to the increment in discounted utility due to an increase in current consumption. It reflects the decreases in the discount rate or increases in the discount factor due to (i) the direct effects of current consumption on patience and (ii) the indirect effects of current consumption through survival probabilities. The indirect effect is likely to be more important in LDCs than in industrialized countries because consumption levels are low and more likely to be below threshold levels. VOL. 34, NO. 8, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Characteristics of Study Sites

country

study location

population of sampling frame

Ethiopia Mozambique Uganda Bulgaria Ukraine Indonesia United States

18 villages in Tigray Region Town of Marracuene Town of Lugazi City of Sofia City of Odessa City of Semarang nae

∼520 per village 66 000 10 000 ∼1 million ∼1 million 1.2 million 272 million

a

In 1995 $U.S.

b

In years, 1995. c Per 1000 births, 1995.

d

9

life expectacy at birthb

infant mortality ratec

sample sized

date of survey

96 77 305 1 518 694 1 019 26 037

48 46 41 72 69 63 76

119 118 122 18 16 58 9

889 284 384 514 737 319 na

January 1997 November 1994 June 1994 September 1995 June 1996 July 1995 na

Number of households. e na, not available.

This prediction that discount factors are lower in LDCs is borne out in the few studies of time preferences that have been conducted outside of the United States and Western Europe. Holden et al. (40) use stated-preference methods to measure rural households’ annual discount rates for money in Indonesia, Zambia, and Ethiopia. Assuming that time preferences are characterized by a constant exponential discount function, Holden et al. (40) estimate mean annual discount rates of 93% in Indonesia, 105% in Zambia, and 53% in Ethiopia (assuming a 1-year planning horizon). These discount rates are equivalent to first-year discount factors of 0.52 in Indonesia, 0.49 in Zambia, and 0.65 in Ethiopia. Holden et al. (40) find that poorer, liquidity-constrained households have higher discount rates; while larger households and more risk-averse households have lower discount rates. The sample sizes in these studies are small, however, ranging from 35 to 120 households. In a study of intertemporal consumption in LDCs, Khayum and Baffoe-Bonnie (41) find that individuals in LDCs have shorter planning horizons than individuals in The Netherlands. Households in four LDCs (Ghana, Jamaica, Kenya, and Philippines) were found to have planning horizons ranging from 4 to just over 10 months, while planning horizons in The Netherlands range from 9 to nearly 15 months. While there are few studies of time preferences in LDCs, there have been numerous studies of time preferences for health outcomes in the United States and Europe. Most of these measure time preferences for impacts to an individual’s own health, not saving the lives of others (23-25, 42-44). Nonconstant exponential discounting of health impacts has been found in several of these studies (23-25, 45). Cropper et al. (10), Horowitz and Carson (17), and Olsen (4) measure time preferences for lives saved by public programs. Cropper et al. (10) posed stated preference questions to several U.S. samples to measure time preferences for lives saved. They report three main findings from their research. [Their results are summarized in the first row of Table 3.] First, many people in their sample have very high discount rates for lives saved in the future. For time horizons of less than 25 years, the median discount rates are higher than most discount rates used in social CBA. Second, the median discount rates decline over time, indicating that the constant exponential discount function is inadequate for characterizing respondents’ time preferences for saving lives. Third, income and education are not statistically related to an individual’s rate of time preference. However, older respondents and African Americans have higher discount rates than other respondents do. Olsen (4) performed a similar study in Norway, and the results are nearly identical to those of Cropper et al.. The median discount rate for 5 years is 17% and falls to 9% for 20 years. The median discount factor for 5 years is 0.45, and it drops to 0.17 for 20 years. 1448

per capita GDPa


Horowitz and Carson (17) also used a stated-preference approach to measure time preferences for life-saving programs. They asked respondents to choose between two lifesaving programs. One saved fewer lives annually but was initiated earlier. The other saved more lives annually but was initiated after a delay. They found median annual discount rates for life-savings of 4.5% for a flight safety program, 4.7% for an occupational safety program, and 12.8% for traffic safety improvements. These correspond with median discount factors of 0.18, 0.18, and 0.07, respectively. Comparing the results from Holden et al. (40) with those from refs 10, 17, and 4, it appears that individuals in LDCs discount the future more heavily than individuals in the United States and Western Europe.

Research Design and Field Procedures We replicated Cropper et al.’s (10) experiment at sites in Ethiopia, Mozambique, Uganda, Bulgaria, Ukraine, and Indonesia. Table 1 shows the study and site characteristics for each country sample. The sample sizes vary from 284 households in Mozambique to 889 households in the Tigray region of Ethiopia. The study areas in Uganda, Ethiopia, and Mozambique are rural and much poorer than the urban sites in Bulgaria, Ukraine, and Indonesia. Wealth and income levels vary widely among the countries in which the surveys were conducted. Bulgaria has the highest annual per capita GDP at $U.S. 1500; Mozambique has the lowest at $U.S. 77 (46). When life expectancy and infant mortality rates are used as indicators of health status, the populations of Uganda, Mozambique, and Ethiopia have similarly poor health. Health conditions in Bulgaria and Ukraine are much better. Indonesia lies in the middle but is closer to Bulgaria and Ukraine in terms of life expectancy and infant mortality rates than to the three African countries. The following is an example of the stated-preference question that respondents were asked in our survey. “Suppose that the Lugazi (Uganda) Water and Sanitation Project was considering two hypothetical improved sanitation programs for Lugazi. Suppose that the two programs cost the same, but that there was only enough money for one of these programs to be implemented here. I want to ask you which one of these programs you would choose, or which one you would vote for. Program A would save 100 lives this year. Program B would save B [200, 500, 1000] lives in T [2, 5, 10] years. Which of the two programs would you choose?” The number of lives saved and the time horizon were randomly assigned to respondents, and each respondent faced only one combination. In-person interviews were conducted with either the household head or the spouse of the household head. [Mozambique has a slightly different research design because of the small sample size. There were only two different levels of lives saved and years rather than three levels.]

The primary purpose of the surveys was to estimate household demand for different environmental goods and services (improved water and sanitation, air quality improvements, and malaria prevention), not to estimate time preferences. Respondents always answered the question about saving lives after the main valuation question in the interview. It is possible that their responses to the question about saving lives was influenced by their answers to the previous valuation question.

Modeling Framework The discrete choice valuation question posed in our multicountry study requires each respondent to assess whether the utility obtained from saving A lives today (program A) is greater than, less than, or equal to the utility obtained from saving B lives in T years (program B). A respondent will choose program B instead of program A if the rate at which lives are traded off over time (A/B, i.e., lives saved today/lives saved in the future) is less than the respondent’s discount factor, wt. Assume that an individual’s lifetime utility (eq 1) is a function of lives that will be saved by environmental regulations in her lifetime. The utility function is

U ) u(L0,LT)

(12)

If the respondent chooses program B, this implies that

U(A,0) < U(0,B)

(13)

where A is the number of lives saved by program A, and B is the number of lives saved by program B in time period T:

U(A) < w(F)TU(B)

(14)

Totally differentiating eq 14, rearranging terms, and substituting from eq 11 yields

wt > A/B

(15)

The respondent’s choice of program B thus yields the information that the individual discount factor for time period T is greater than A/B, the implied discount factor. The individual discount factors, wt, are assumed to be randomly distributed in the population, and the cumulative distribution function (CDF) is F(wt). If the respondent is chosen randomly, the probability that the respondent chooses program B is the probability that the individual’s discount factor is greater than the implied discount factor, which is the value of the CDF at the implied discount factor:

Prob(W ) 1) ) Prob(wt > A/B) ) 1 - F(A/B)

(16)

Alternatively

Prob(W ) 0) ) Prob(wt < A/B) ) F(A/B) W describes whether a respondent chose program A or program B; it takes the value of 1 if program B is chosen and 0 if program A is chosen. We estimate the CDF with the discrete distribution function using sample proportions. The proportion of the sample choosing program A is an estimate of the value of the cumulative distribution of wT at the value of A/B. The median discount factors are taken from these CDFs by determining the value of A/B at which 50% of the sample chooses program A. The mean discount factor is also estimated from sample proportions using the Turnbull estimator of the lower bound mean. [The Turnbull estimator is one of a class of nonparametric estimators for referendum contingent valuation data, and it computes a mean that follows an asymptotic normal distribution (47). One of the advantages of the Turnbull estimator is that it restricts

estimates to be nonnegative, which is particularly useful for estimating discount factors. The disadvantages of the Turnbull estimator are that the estimate depends on the values in the bid vector, and it is not suitable for model testing (47).] The discount rate is then calculated assuming that the discount function is constant exponential. If the calculated discount rate is not, in fact, the same for all T, this is evidence that the constant exponential function is not the appropriate discount function. A probit model is used to explain the determinants of individuals’ program choices, W. The respondent’s discount factor, w/t , is unobserved:

w/t ) β′X +

(17)

X is an n × k matrix including a constant and other explanatory variables, β is a k × 1 vector of parameters; and is a n × 1 vector of random terms distributed N(0,σ2). The following is observed:

W ) 1 if w* > A/B

(18)

W ) 0 if w* e A/B The estimation function is

Pr(W ) 1) ) Pr(w* > A/B) ) Pr(β′X + > A/B) ) Pr( > A/B - β′X) ) F(β′X - A/B) (19) Table 2 defines the independent variables, and Table 3 presents their samples means. On the basis of annual household income collected in the surveys, Bulgaria is the wealthiest country and Ethiopia is the poorest. [Annual household incomes for our samples do not follow the income rankings in Table 1. This difference may due to the fact that we have locally rather than nationally representative samples. Annual household income in Uganda is measured by annualizing average weekly expenditures.] We do not have annual household income data for Mozambique, although we do have information on asset holdings that allow us to create a qualitative indicator of wealth. On average, respondents in Bulgaria and Ukraine have completed at least some post-secondary education, respondents in Uganda and Indonesia have completed at least some secondary school, and respondents in Ethiopia and Mozambique have not completed primary school. In general, the respondents in the wealthier countries (Bulgaria and Ukraine) tend to be older and have fewer children than respondents in the poorer countries (Ethiopia and Mozambique). We test several hypotheses. First, we expect that the respondent is less likely to choose program B as T increases and more likely to choose program B as the number of lives saved increases. Furthermore, we hypothesize wealthier respondents to be more likely to choose program B, and this effect should be exhibited both within samples and between countries. Following Becker and Mulligan (9, 34), we expect that more educated respondents and younger respondents will be more likely to choose program B. The direction of influence of the respondent’s gender and marital status are unknown. We also test whether the constant exponential discount function is an adequate representation of time preferences.

Results of the Analysis The raw results for the program choice question are shown in Table 4. The χ2 statistics show that responses vary systematically with variations in both the number of lives saved (B) and/or the time horizon (T), suggesting that responses are not random. Figure 2 shows the CDFs of VOL. 34, NO. 8, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Variables Used in Data Analysis variable name

expected influence on dependent variable

type of variable

variable definition

CHOOSEB RATIO YEARS GENDER EDUC

dichotomous continuous continuous dichotomous categorical

MARRIED NONCHRIS INCGROUP LINCD INCSQRD NUMCHILD AGE MOZAM BULGARIA INDONESIA UKRAINE UGANDA

dichotomous dichotomous categorical continuous continuous continuous continuous dichotomous dichotomous dichotomous dichotomous dichotomous

0 if respondent chose program A; 1 if respondent chose program B ratio of lives saved by program A to lives saved by program B no. of years from present in which lives are saved by program B 0 if male; 1 if female 0 if no schooling completed; 1 if some or all of primary school completed; 2 if some or all of secondary school completed; 3 if some or all of college/university completed 0 if not married; 1 if married 0 if Christian; 1 if non-Christian 1, first quartile; 2, second quartile; 3, third quartile; 4, fourth quartile log of annual household income square of log of annual household income no. of children in household age of respondent in years 1 if observation is from Mozambique; 0 otherwise 1 if observation is from Bulgaria; 0 otherwise 1 if observation is from Indonesia; 0 otherwise 1 if observation is from Ukraine; 0 otherwise 1 if observation is from Uganda; 0 otherwise

na ? +

? ? + + ? + ? ? ? ? ?

TABLE 3. Sample Means

a

independent variables

18 villages in Ethiopia

Marracuene, Mozambique

Lugazi, Uganda

Sofia, Bulgaria

Odessa, Ukraine

Semarang, Indonesia

sample size INCGROUP EDUC AGE FEMALE NONCHRIS NUMCHILD MARRIED

889 2.49 0.24 42 0.58 0 2 0.83

284 2.21 0.84 40 0.41 0.61 2 0.81

384 2.88 1.49 33 0.48 0.24 2 0.84

514 2.4 2.2 46 0.56 0.21 1 naa

737 2.58 3.24 46 0.59 n.a. 1 0.67

319 2.37 1.72 49 0.39 0.79 1 0.88

na, not available.

discount factors estimated using raw data from Ethiopia. [The CDFs from the other study sites are available as Supporting Information.] Two of the results in Figure 2 suggest that respondents took the stated-preference question seriously. First, the percentage of respondents choosing program A (on the y-axis) increases as the ratio (on the x-axis) increases. Thus, as expected, the percentage of respondents choosing program A increases as the number of lives saved by program B decreases. Second, we observe that the CDF for T ) 10 years is above the one for T ) 5 years, which is above the one for T ) 2 years. As the time horizon increases, the percentage of respondents choosing program A increases because they have to wait longer for the benefits of program B. The median and mean discount rates and discount factors for different values of T are shown in Table 5. Median and mean discount rates are calculated by assuming that the discount function is constant exponential. In general, mean and median discount rates (and mean and median discount factors) are similar, implying that the distributions of discount rates and discount factors in the population are not skewed. The countries for which more than one median discount rate can be calculated (Ethiopia, Mozambique, Bulgaria, and Indonesia) exhibit a consistent pattern: discount rates decline over time. The median discount rate for Ethiopia falls from 49% for the 2-year time horizon, to 39% for the 5-year time horizon, to 28% for the 10-year time horizon. Uganda and Ukraine have extremely high discount rates for the 2-year horizon. The median discount factors for these two countries essentially fall to 0 by the 5-year planning horizon, implying infinitely high discount rates. These results provide strong evidence against the constant exponential discount function. 1450

9


Figure 3 shows that the median discount functions for the six LDCs are clearly lower than those from the U.S. sample in Cropper et al. (10). One striking aspect of these results is the variation between countries. T-tests of the equality of mean discount factors by time horizon show that, with one exception, no two countries’ mean discount factors for a given time period are equal. The only exception is that the 5-year mean discount factors for Bulgaria and Ethiopia are not statistically different. Although discount factors differ by country, the similarity in the discount functions among groups of dissimilar countries is remarkable. The median discount factors for Bulgaria and Indonesia are similar and do not drop to 0 until about 10 years in the future. On the other hand, respondents from both Uganda and Ukraine place essentially no weight on lives saved more than 5 years in the future. While the respondents in the LDCs are much more present-oriented than those for the U.S. sample, the expected effects of income and life expectancies on time preferences are not evident between countries. Ukraine has the second highest income (in terms of annual household income) and life expectancy among the LDCs countries in our sample, but it has the highest median discount rate (lowest discount factor). On the other hand, Mozambique has the lowest income and the second lowest life expectancy, but it has the lowest median discount rates (highest discount factors). Table 5 shows that all of the mean and median discount rates from LDCs for all time horizons are far above the 10% discount rate that is commonly used by donors and planning agencies. Figure 3 shows that the median discount factors for LDCs are far below the discount factors implied by a constant exponential discount function with a 10% discount

TABLE 4. Percent of Respondents Choosing Program Aa T (years)

χ2 (p-value)b

no. of lives saved in T (years) by program B

2 5 10 χ2 (p-value)c

200 65 83 89 19.25 (0.00)

18 Villages in Ethiopia 500 29 56 85 58.55 (0.00)

1000 19 46 60 31.17 (0.00)

44.04 (0.00) 28.52 (0.00) 26.52 (0.00)


200 78 84 97 7.33 (0.03)

Lugazi, Uganda 500 59 79 91 13.30 (0.00)

1000 53 73 82 7.49 (0.02)

6.64 (0.04) 1.60 (0.45) 5.28 (0.07)

2 10 χ2 (p-value)c

100 57 66 0.99 (0.32)

Marracuene, Mozambiqued 500 29 43 2.14 (0.14)


200 63 83 87 10.63 (0.01)

Sofia, Bulgaria 500 23 59 67 26.44 (0.00)

1000 25 43 77 26.83 (0.00)

24.05 (0.00) 18.55 (0.00) 5.93 (0.05)


200 75 94 95 15.75 (0.00)

Odessa, Ukraine 500 58 78 71 13.95 (0.00)

1000 54 71 95 29.44 (0.00)

6.96 (0.03) 12.97 (0.00) 4.13 (0.13)


2000 79 69 95 8.43 (0.02)

Semarang, Indonesiae 5000 30 87 81 28.29 (0.00)

10 000 26 49 77 16.08 (0.00)

22.82 (0.00) 11.19 (0.00) 4.70 (0.09)

9.39 (0.00) 6.01 (0.01)

a Program A saves 100 lives in the current year unless otherwise noted. b This column reports the results of the Pearson χ2 test of whether program choice is independent of the number of lives saved for a given time horizon. c This row reports the results of the Pearson χ2 test of whether program choice is independent of time horizon given the number of lives saved. d Program A saves 50 lives in the current year. e Program A saves 1000 lives in the current year.

FIGURE 2. Percent of respondents choosing program A versus ratio of lives saved today to lives saved in T years (18 villages in Ethiopia). rate. For a planning horizon of up to 5 years, the constant exponential discount factor associated with a 10% discount rate is from 2-8 times larger than individuals’ median discount factors in the six LDCs. This suggests a wide difference in planning perspective between policy analysts and the individuals in developing countries who are affected by projects.

Tables 6 and 7 present the results of the multivariate probit regression analyses of the determinants of individuals’ responses to the stated preference question. Table 6 shows the results of these analyses by country. The country-specific multivariate models have little explanatory power either in terms of statistically significant socioeconomic variables or goodness-of-fit measures [R level of 5% is used to indicate VOL. 34, NO. 8, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 5. Median Discount Factors and Median Discount Rates T ) 2 years

United Statesd Ethiopia Mozambique Uganda Bulgaria Ukraine Indonesia

T ) 5 years

T ) 10 years

median discount factora

median discount rateb

median no. of lives savedc







nae 0.38 0.40 0.04 0.40 0.02 0.32

na 49 46 158 45 206 57

na 3 3 25 3 50 3

0.46 0.14 na 0.00 0.15 0.00 0.10

17 39 na

2 7

0.35 0.06 0.22 0.00 0.00 0.00 0.00

11 28 15

3 17 5

38 45

∞ 7 ∞ 10

a

The median discount factor is obtained from the raw data. It is the discount factor at which 50% of respondents choose program A. b A constant exponential function is used to calculate the median discount rate from the median discount factor, where r ) wt-(1/t) - 1. c In T equivalent to one life saved today. d These results are from ref 10. e na, not applicable.

FIGURE 3. Median discount factors versus years in the future. statistical significance; these model specifications were chosen because they provided the greatest explanatory power among alternative specifications, and they facilitate comparison between countries]. Nevertheless, the number of years in the future that program B would save lives (T) and the ratio of lives saved in program A and program B (A/B) are statistically significant and have the expected direction of influence in all models. Table 7 shows that the multivariate results for the pooled data set have greater explanatory power than the countryspecific regression models, in terms of both statistically significant explanatory variables and goodness-of-fit measures. [We test whether these data may be pooled using Wald tests of whether the parameters estimated for a given country are equivalent to the parameters estimated using the remaining five countries. For parameters that are significantly different, we control for these slope differences using the interaction terms toward the bottom of Table 7. Intercept differences by country are controlled for in the pooled model using country-specific dummy variables. The reference country is Ethiopia. We suspect greater variation in the independent variables within the pooled data set is responsible for improving the explanatory power of this model (48).] T and A/B are statistically significant and have the expected direction of influence in all of the models in Table 7. All of the country dummy variables are significant except for Mozambique’s, confirming the differences observed in Figure 3. [By changing the omitted country, we find that (i) the intercepts for Bulgaria and Uganda are not different from one another and (ii) the intercepts for Indonesia and Ukraine are not different from one another.] Moreover, the magnitude 1452

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of the effects of the country dummy variables are large, suggesting that country differences that are not controlled for by the socioeconomic variables in our data set may account for differences in time preferences. All three models in Table 7 show that richer respondents are more patient, and these results are statistically significant in all three cases. Furthermore, the results for models 1 and 2 show that individuals’ time preferences are nonlinear in income (indicated by the variable income squared, INCSQRD). Although we failed to find the expected positive correlation between income and patience between countries, the multivariate results show that the anticipated relationship holds within countries when the data are pooled, and we control for study site. Education increases patience in Bulgaria, Indonesia, and Ukraine as expected, although the effect is not statistically significant in Bulgaria. The education variable (EDUC) has the opposite sign for Mozambique, Ethiopia, and Uganda, although it is only statistically significant for Mozambique. Older respondents are generally less patient, and there is some evidence that respondents with children are more patient. Marriage decreases patience everywhere except Mozambique. This effect is not due to an income effect as incomes are similar for married and unmarried respondents. It is not clear why married respondents might be less patient than unmarried respondents. Time preferences do not vary by gender and religious affiliation; the variable (NONCHRIS) was insigificant in all models. In summary, the multivariate analyses provide strong support for our hypotheses regarding the effects of program characteristics (T and A/B). We failed to find the expected

TABLE 6. Multivariate Probit Model by Country (Dependent Variable ) CHOOSEB) independent variables YEARS RATIO

Bulgaria -0.1369 0.000a -2.3209 0.000a

INCGROUP INCOME INCSQRD GENDER EDUC

-0.1390 0.000a -2.3712 0.000a -0.0030 0.963

0.0001 0.337 0.0000 0.530 -0.0635 0.603 0.0278 0.642

-0.0687 0.580 0.0190 0.757

-0.0045 0.338 0.0475 0.524 1.1631 0.002a 506 70

NUMCHILD CONSTANT

N % of responses correctly predicted χ2 Prob > χ2 log likelihood pseudo-R 2

88.86 0.0000 -295.95 0.1305

-0.1563 0.000a -2.7926 0.000a

-0.1560 0.000a -2.8164 0.000a 0.0716 0.129

-0.0044 0.357 0.0795 0.303 1.2904 0.001a 488 70

0.0003 0.735 0.0000 0.817 -0.1638 0.139 -0.0470 0.595 -0.6927 0.000a -0.0042 0.275 0.0671 0.090c 2.0094 0.000a 807 72

-0.1480 0.179 -0.0383 0.662 -0.7100 0.000a -0.0037 0.332 0.0683 0.082c 1.8913 0.000a 807 72

85.30 0.0000 -285.29 0.1301

206.85 0.0000 -443.57 0.1891

207.00 0.0000 -443.49 0.1892

MARRIED AGE

Ethiopia

Mozambique -0.0422 0.063c -1.8723 0.000a 0.1758 0.029b

Indonesia -0.1641 0.000a -1.9754 0.000a

-0.0362 0.856 -0.4171 0.033b -0.0552 0.824 -0.0087 0.269 -0.0193 0.669 1.3895 0.011a 212 63

0.0000 0.998 0.0000 0.966 0.0052 0.978 0.2283 0.117 -0.4629 0.096c 0.0100 0.197 0.0236 0.697 0.5048 0.425 292 73

27.23 0.0006 -133.10 0.0928

61.20 0.0000 -157.06 0.1631

-0.1686 0.000a -2.2422 0.000a 0.0774 0.345

Uganda -0.1211 0.000a -1.6005 0.001a

0.1313 0.516 0.2296 0.163 -0.2932 0.337 0.0053 0.536 -0.0258 0.709 0.4901 0.484 251 66

0.0002 0.398 0.0000 0.434 0.1596 0.327 -0.0893 0.456 -0.1451 0.510 -0.0100 0.244 -0.0011 0.980 0.6683 0.156 376 77

56.07 0.0000 -135.18 0.1718

39.82 0.0000 -176.01 0.1016

-0.1194 0.000a -1.6559 0.001a 0.0121 0.848

Ukraine -0.1480 0.000a -1.5694 0.000a

-0.1453 0.000a -1.5636 0.000a -0.0040 0.950

0.1748 0.277 -0.0738 0.548 -0.1309 0.550 -0.0093 0.276 0.0034 0.939 0.6666 0.151 376 78

0.0001 0.012a 0.0000 0.077c 0.1182 0.382 0.2049 0.008a -0.1138 0.433 -0.0055 0.180 0.1096 0.211 -0.1796 0.636 580 78

0.0974 0.468 0.2267 0.004a -0.1060 0.472 -0.0066 0.115 0.1106 0.203 -0.1482 0.710 580 78

38.92 0.0000 -176.46 0.0993

94.45 0.0000 -247.12 0.1604

85.35 0.0000 -251.67 0.1450

a The hypothesis that this parameter is equal to 0 is rejected at an R level of 0.01. b The hypothesis that this parameter is equal to 0 is rejected at an R level of 0.05. c The hypothesis that this parameter is equal to 0 is rejected at an R level of 0.10.

income effect between countries, but the multivariate results show that the effect is present within countries. The distributions of discount factors and discount rates are quite different between countries, and these differences are not explained by differences in income or life expectancies. The hypothesis that more educated respondents will be more patient is rejected in some countries but not others. Finally, we reject the hypothesis that discount rates are constant over time.

Discussion There are three main findings from our research. First, households in LDCs attach much less value to lives saved in the future than to lives saved today. Very few individuals in our multicountry study attach any value to saving lives 10 years in the future. In Cropper et al.’s (10) study, the median respondent in the United States considers saving one life today equivalent to saving two lives in 5 years (assuming constant exponential discounting, this implies a discount rate of 17%). In Tigray, Ethiopia, and in Sofia, Bulgaria, the median respondent considers saving one life today equivalent to saving seven lives in 5 years. In Semarang, Indonesia, the median respondent considers saving one life today equivalent to saving 10 lives in 5 years. These results are consistent with our expectation, based on eq 11, that individuals’ discount rates will be higher in LDCs than in the United States and Western Europe (and discount factors will be lower) and will vary with individuals’ socioeconomic characteristics. Second, constant exponential discounting, commonly used on social CBA, appears to be an inadequate framework for representing respondents’ time preferences in LDCs. Third, there are substantial differences in time preferences between countries that do not appear to be related to income.

Respondents in Lugazi, Uganda, and Odessa, Ukraine, placed much less value on saving lives in the future than respondents in Ethiopia, Mozambique, Bulgaria, or Indonesia. We cannot explain these intercountry differences, but we speculate that there are other factors, perhaps perceived mortality risk, political stability, or culture, that account for them. For instance, time preferences in Ukraine may be strongly influenced by widespread doubt and pessimism about the future of macroeconomic and political reform efforts. Time preferences in Uganda may reflect the high prevalence of AIDS. What do these results imply for planning? Respondents in all six LDCs prefer that life-saving programs provide nearterm benefits rather than delayed benefits. Incorporating these time preferences from LDCs into social CBA of economic development projects will clearly preclude most projects with delayed benefits. The use of such low discount factors and nonconstant exponential discount functions would certainly be debated. Some economists claim that nonconstant exponential discounting may be rational (4951, 13), and others argue that it is irrational (52-54). Even if the social rate of time preference is judged to be a political decision, empirical evidence on individuals’ rates of time preference, such as presented in this paper, would certainly appear to us to be important information for policymakers to consider before coming to such a judgment. Moreover, if planners and policy-makers choose to override individuals’ time preferences when selecting a social rate of time preference for use in project appraisal and policy analysis, empirical data on time preferences is still needed to inform project design and guide implementation. Finally, our findings raise questions about the relevance of theories of economic growth that implicitly assume that individuals’ time preferences are constant across countries VOL. 34, NO. 8, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 7. Multivariate Probit Model: Parameter Estimates for the Pooled Data Set (Dependent Variable ) CHOOSEB) independent variables YEARS RATIO

parameter estimates (p-values) model 1 model 2 model 3 -0.1314 0.000a -2.1646 0.000a

-0.1317 0.000a -2.1243 0.000a

0.0001 0.009a 0.0000 0.013a 0.0007 0.990 -0.0470 0.569 -0.4770 0.000a -0.0050 0.019b 0.0347 0.148 -0.5526 0.004a 0.1131 0.722 -1.2254 0.018b -0.7445 0.006a -1.5991 0.000a 0.0854 0.402 0.5007 0.073c 0.3486 0.041b 0.0123 0.116 0.3229 0.180 -0.0414 0.387 0.2490 0.024b 0.3832 0.038b -0.4198 0.043b -0.0435 0.757 0.1737 0.033b 1.6016 0.000a 2714 72

0.0000 0.022b 0.0000 0.027b -0.0167 0.767 -0.0444 0.590 -0.5054 0.000a -0.0051 0.017b 0.0419 0.075c -0.5234 0.005a 0.3525 0.226 -1.2634 0.008a -0.7547 0.005a -1.6223 0.000a 0.0735 0.467 0.5959 0.031b 0.2922 0.065c 0.0142 0.050b 0.3459 0.149 -0.0456 0.338 0.2515 0.022b 0.4081 0.026b -0.3595 0.077c -0.0419 0.765

0.0056 0.922 -0.0431 0.601 -0.5111 0.000a -0.0050 0.020b 0.0351 0.144 -0.4380 0.018b 0.3869 0.185 -1.1421 0.028b -0.7189 0.008a -1.5865 0.000a 0.0712 0.483 0.5866 0.035b 0.3171 0.065c 0.0116 0.137 0.3623 0.134 -0.0437 0.363 0.2406 0.029b 0.3916 0.033b -0.3757 0.065c -0.0635 0.654

1.6174 0.000a 2773 73

1.5100 0.000a 2714 72

601.04 0.0000 -1442.05 0.1725

604.05 0.0000 -1477.67 0.1697

592.00 0.0000 -1446.57 0.1699

INCGROUP INCOME INCSQRD GENDER EDUC MARRIED AGE NUMCHILD BULGARIA MOZAM INDO UGANDA UKRAINE BULGARIA* EDUC MOZAM* MARRIED INDO* EDUC INDO* AGE UGANDA* MARRIED UGANDA* NUMCHILD UKRAINE* EDUC UKRAINE* MARRIED MOZAM* EDUC UGANDA* EDUC MOZ* INCGROUP CONSTANT

N % of responses correctly predicted χ2 Prob > χ2 log likelihood pseudo-R 2

-0.1309 0.000a -2.1582 0.000a 0.0489 0.052b

(55, 56). These results highlight the importance of further research on Becker and Mulligan’s (9) suggestion that variations in time preferences drive and explain differences in economic growth patterns across countries. 9

We would like to thank Paul Portney, David Pearce, Maureen Cropper, Julian Lampietti, and Jennifer Davis for their comments and suggestions on previous drafts of this paper.

Supporting Information Available Cumulative distribution functions (CDFs) of the discount factors in samples from six different countries (1 page). This material is available free of charge via the Internet at http:// pubs.acs.org.

Literature Cited

a The hypothesis that this parameter is equal to 0 is rejected at an R level of 0.01. b The hypothesis that this parameter is equal to 0 is rejected at an R level of 0.05. The hypothesis that this parameter is equal to 0 is rejected at an R level of 0.10 (indicated by an asterisk).

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Acknowledgments


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Received for review June 30, 1999. Revised manuscript received February 1, 2000. Accepted February 1, 2000. ES990730A

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Time Preferences for Life-Saving Programs: Evidence from Six Less

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