The World Bank INU-46 Policy, Planning and Research Staff Infrastructure and Urban Develolpment Department Report INU 46 THE VALUE OF TIME SPENT ON COLLECTING VWATER: SOME ESTIMATES FOR IJKUNDA, KENYA by Dale Whittinciton Xinming Mu Robert Roches May 1989 CASE STUDlY This is a document published informally by the World Bank. The views and interpretations herein are those of the author and should not be aetributed to the World Bank, to its affiliated organizations, or to any individual acting on their behalf. - '. 7 This is a document published informally by the World Bank. In order that the information contained in it can be presented with the least possible delay, the typescript has not been prepared in accordance with the procedures appropriate to formal printed texts, and the World Bank accepts no responsibility for errors. The World Bank does not accept responsibility for the views expressed herein, which are those of the author and should not be attributed to the World Bank or to its affiliated organizations. The findings, interpretations, and conclusions are the results of research supported by the Bank; they do not necessarily represent official policy of the Bank. The designations employed, the presentation of material, and any maps used in this document are solely for the convenience of the reader and do not imply the expression of any opinion whatsoever on the part of the World Bank or its affiliates concerning the legal status of any country. territory, city, area, or of its authorities, or concerning the delimitations of its boundaries or national affiliation. The principal authors are Dale Whittington, Infrastructure and Urban Development Department of the World Bank; Xinming Mu, Asian Development Bank, Manila, Philippines; and Robert Roche, Abidjan, Cote d'lvoire, World Bank. ACKNOWLEDGEMENTS This research was supported by the United States Agency for International Development's Water and Sanitation for Health Project (WASH) and by the Infrastructure and Urban Development of the World Bank. We would like to thank David Nyamwaya, Stanislaus K. Mutinda, Samuel Momanyi, and David W. Makanda, African Medical Research Foundation, Nairobi, for their assistance with the field work. John Briscoe and David Guilkey provided many helpful suggestions during the course of the study. The World Bank THE VALUE OF TIME SPENT ON COLLECTING WiATER: SOME ESTIMATES FOR UKUNDA, KENYA CASE STUDY EXECUTIVE SUMMORY This paper presents two procedures for estimating the value that households assign to the time they spend collecting water. Both approaches are used to derive estimates of the value of time spent collecting water for a sample of households in Ukunda, Kenya. Each of the 69 households in the sample faced a choice between three water sources: a kiosk which sells water by the bucket, vendors who deliver water to the home, and an open well. The price of a bucket of water from a vendor was about 10 times the price of a bucket purchased from a kiosk. There was no charge for water obtained from an open well. The prices of water charged by kiosks and vendors were the same for all households, but the time required to collect water from the nearest kiosk and the nearest open well varied from household to household depending on the location of the house and the water sources in the area. The first approach described in the paper for estimating the value of time assumes that a household's water source choice decision is based on two factors: the price of water at the source ancL the time spent collecting water from the source. This "revealed preference" approach is used to calculate (i) lower and upper bounds on the value of time spent collecting water for all households in the sample which chose a kiosk, (ii) lower bounds on the value of time for households which chose vendors, and (iii) upper bounds for households which chose open wells. The results of the "revealed preference" analysis suggest that households which chose a kiosk assigned an average value of about US$0.38 per hour to the time they spent collecting water. This was about 50 percent higher than the market: wage for unskilled labor of US$0.25 per hour. The average value of time spent collecting water for those households which chose vendors was about US$0.57 per hour, or over -:wice the wage rate for unskilled labor. However, the average wage rate was estimated for the two groups of households, and in both cases the estimated value of time was very close to the each group's average wage rate. The second approach presented in the paper for estimating the value households assign to the time spent collecting water is based on a multivariate analysis of the determinants of households' water source choice decisions. The parameter estimates from a multinomial logit model are used to derive an estimate of the value of time spent collecting water. The results of this multivariate analysis indicate that households value the tLme they spend collecting water at about US$0.31 per hour. This estimate is abou: 20 percent higher than the market wage rate for unskilled labor, but 25 percent: lower than the estimated average wage rate for households in the sample. The results of both of these approaches yield surprisingly high values relative to the wage rate for unskilled labor. The results suggest that households in this sample consider the time spent collecting water as a significant economic cost. One of the most important policy implications of these findings is that the value of time savings from improved water supplies may be much higher than previously believed. Piped water distribution systems may thus be an economically attractive techno:Logy in many villages in developing countries. - ii - THE VALUE OF TIME S]?ENT ON COLLECTING WATER: SOME EST'IMATES FOR UKU1NDA, KENYA Table of Conterts Page No. EXECUTIVE SUMMARY . . .i.. . . . . . . . . . . . . . . . . . . I. OVERVIEW .1... . . . . . . . . . . . . . . . . . . . . . . . Introduction .1.. . . . . . . . . . . . . . . . . . . . . . Summary of Methodology ... . . . . . . . . . . . . . . . . 2 Summary of Results ... . . . . . . . . . . . . . . . . . . 3 II. THE APPLICATION OF DISCRETE CHOICE THEORY TO WATER SOURCE DECISIONS IN VILLAGES IN DEVELOPING COUNTRIES . . . . . . . . . 4 Case I - Household Chooses a Kiosk . . . . . . . . . . . . . 6 Case II - Household Chooses a Vendor . . . . . . . . . . . . 6 Case III - Household Chooses an Open Well . . . . . . . . . . 7 III. DESCRIPTION OF THE STUDY AREA . . . . . . . . . . . . . . . . . 8 IV. RESULTS OF THE ANALYSIS ... . . . . . . . . . . . . . . . . . 10 Estimates of the Value of Time Based on the Revealed Preference Approach ... . . . . . . . . . . . . . . . . . 10 An Estimate of the Value of Time Based on a Random Utility Theory Approach . . . . . . . . . . . . . . . . . . 14 V. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 19 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . 20 - iii - Page No. TABLES Table 1: Estimates of the Value of Time Obtained from the Revealed Preference Inequalities . . . . . . . . . . . . 7 Table 2: Estimates of the Value of Time Spent Hauling Water for Households Choosing Kiosks . . . . . . . . . . . . . . . 11 Table 3: Estimates of the Value of Time Spent Hauling Water for Households Choosing Vendors . . . . . . . . . . . . . 13 Table 4: Estimates of the Value of Time Spent Hauling Water for Households Choosing Open Wells . . . . . . . . . . . 14 Table 5: Mean Values of Independent Variables Used in the Conditional Multinomial Logit Model of Water Source Choice . . . . . 17 Table 6: Results of the Conditional Multinomial Logit Model of Households' Water Source Choice . . . . . . . . . . . . . 19 FIGURES Figure 1: Frequency Distribution of the Estimates of the Value of Time for Households Choosings Kiosks . . . . . 12 Figure 2: Frequency Distribution of the Estimates of the Value of Time for Households Choosing Vendors . . . . . . . . 12 THE VALUE OF TIME SPENT ON COLLECTING WATER: SOME ESTIMATES FOR UKIrNDA. KENYA I. OVERVIEIT Introduction 1.01 Many women in developing countries spend a significant portion of their day hauling water from sources' to their home, One of the principal benefits of improved water delivery systems such as yard taps, handpumps, and standposts is that the time women spend carrying water is reduced (Churchill et.al., 1987). The time saved by not having to haul water from more distant sources may be put to many other productive uses, such as child care, wage employment, agricultural labor, or food preparation (Curtis, 1986, Cairncross and Cliff, 1987). 1.02 Because different water system improvements result in different time savings, the choice of water service level involves a tradeoff between increased costs and the benefits from reduced time spent hauling water by members of the community (typically women). For example, yard taps or house connections reduce the time spent collecting water the most, but they are also the most expensive service option. Handpumps and public fountains are often cheap in terms of capital and operating and mainitenance costs, but water must still be carried from the source to the home. More handpumps or public fountains in a village can reduce the average travel times from houses to sources, but this also increases total capital costs. The choice of which technology is most appropriate for a given community may thus be heavily influenced by the value of time which households assign to the time savings. 1.03 There is, however, little empirical evidence concerning the value people actually place on the time they spend collecting water. In its water project appraisal methodology the InterAmerican Development Bank assumes that time savings should be valued at '50 percent of the market wage rate for unskilled labor in the local economy, but there is no empirical justification for this assumption. Estimates of the value of time obtained from studies of people's travel mode choices in developed countries indicate that people typically value travel time savings at less than their market: wage rate (Bruzelius, 1979; Yucel, 1975), but whether these kindl of findings have any relevance for time savings resulting from improved water service in villages in developing countries is not known.11 1.04 The purpose of this paper is to present two approaches for estimating the value of time spent collecting water and to illustrate their application in a specific location, Ukunda, Kenya. The remainder of this first chapter summarizes the two methodologies and the results of the analyses. The second 1/ See Becker (1977) and Evans (1972) for an introduction to some of the theoretical work on the valuation of time. - 2 - chapter of the paper summarizes the application of discrete choice theory to the problem of a household choosing among different water sources, and develops a methodology for estimating a household's value of time spent hauling water. In the third chapter we briefly describe the study area where the case study was conducted and the field procedures which were utilized to collect the data for the analysis. The fourth chapter presents the results of this first approach to calculating the value of time spent collecting water, and then presents an estimate of the value of time based on a conditional multinomial logit model estimated with the same data set. In the fifth and final section we discuss the implications of the analysis. Summary of Methodology 1.05 In this paper two approaches are used to derive estimates of the value households assign to the time they spend collecting water. Both approaches utilize data on the actual water source choice decisions of 69 households in Ukunda, Kenya. Each household in the sample faced a choice between three water sources: a kiosk which sells water by the bucket, vendors who deliver water to the home, and an open well. The price of a bucket of water from a vendor was about 10 times the price of a bucket purchased from a kiosk. There was no charge for water obtained from an open well. The prices of water charged by kiosks and vendors were the same for all households, but the time required to collect water from the nearest kiosk and the nearest open well varied from household to household depending on the location of the house and the water sources in the area. 1.06 The first, "revealed preference" approach assumes that a household's water source choice decision is based on two factors: the price of water at the source and the time spent collecting water from the source. Consider a single household that collects its water from a kiosk. This household could have purchased water from a vendor at a higher price, but chose not to do so. The household thus preferred to spend time collecting water rather than pay a premium to have a vendor deliver water to its door. Since we have data on the time each household must spend to collect water from the nearest kiosk, we can calculate an upper bound on the value of time each household assigns to collecting water. In other words, if the household's value of time spent collecting water were higher, it would make sense for it to purchase water from a vendor rather than collect it from a kiosk. 1.07 Similarly, the household had the choice of collecting water free from an open well, but chose not to do so. Typically the time required to collect water from an open well is longer than from a kiosk because water from a well is obtained by dropping a small metal container tied to a rope into the well, and it takes longer to fill a container than at a kiosk. If the collection time for an open well is longer than for a kiosk, and the household still chooses the kiosk, then it is possible to derive a lower bound on the value the household assigns to time spent collecting water. If the household's value of time were less than this lower bound, it would make sense for the household to choose the open well rather than pay to purchase water from a kiosk. The "revealed preference" approach was used to calculate (i) lower and upper bounds on the value of time spent collecting water for all households in the sample which - 3 - chose\kiosk, (ii) lower bounds on the value of time for households which chose vendors, and (iii) upper bounds for households which chose open wells. 1.08 Of course, households' water source choice decisions may well depend on other factors than simply the price of water and the collection time. For example, more educated households may better understand the health risks of using water from open wells, and thus be more likely to choose kiosks or vendors. Households with more women may be less likely to purchase water from vendors because they have more labor available for collecting water. The second approach to estimating households' value of time spent collecting water takes account of such additional factors which may influence households' water source choice decisions. A multivariate statistical analysis of the data set was carried out in order to determine the factors which influence households' water source choice decisions. The parameter estimates from this multinomial logit model are then used to derive an estimate of the value of time spent collecting water. Summary of Results 1.09 The first, "revealed preference" approach yielded interesting results for households which chose vendors and kiosks. Unfortunately, there were too few households in the sample which chose open wells to derive meaningful results for this group. For each household which chose; a kiosk, an upper and lower bound on the value of time was calculated, as well as the mid-point of the range defined by the upper and lower bounds. The mean of the values of the mid-points was US$0.38 per hour, about 50 percent higher -han the market wage for unskilled labor of US$0.25 per hour. The mean of the lower bounds was US$0.12, about 50 percent of the market wage rate for unskilled labor. 1.10 For those households wlhich chose vendors, the mean of the lower bound estimates of their value of time spent collecting water was US$0.57 per hour, over twice the wage rate for unskilled labo:. The lower bound estimate for households which chose vendors is thus 50 percent higher than the mid-point for households which chose kiosks. This is consistent with the fact that households which chose vendors had 60 percent higher incomes than households which chose kiosks. 1.11 The results of the multivariate analysis, which takes into account other factors which affect households' water source choice decisions, yield an average value of time for households in the sample of US$0.31 per hour. This estimate is about 20 percent higher than the market wage rate for unskilled labor, but 25 percent lower than the estimated average wage rate for households in the sample. 1.12 The results of both of these approaches to calculating the value of time spent collecting water yield surprisingly highn values relative to the wage rate for unskilled labor. The results suggest that households in this sample consider the time spent collecting water as a significant economic cost. One of the most important policy implications of these findings is that the value of time savings from improved water supplies may be much higher than previously believed. Piped water distribution systems may thus be an economically attractive technology in many villages in developing countries. - 4 - II. THE APPLICATION OF DISCRETE CHOICE THEORY TO WATER SOURCE DECISIONS IN VILLAGES IN DEVELOPING COUNTRIESZ' 2.01 Traditional microeconomic theory postulates that a consumer chooses quantities of goods and services in order to maximize his utility, subject to a budget constraint. The solution of this maximization problem yields first- order conditions which can be solved for demand functions which describe the individual's decision regarding the quantity of a good to consume as a function of given prices and his income. The quantity of the good demanded is typically assumed to be continuous. 2.02 This framework for understanding consumer behavior needs to be modified when a consumer faces choices that are discrete rather than continuous. For example, a household in a village typically chooses from among a limited number of water sources. In rural areas households typically do not use more than one source for the same purpose. After a source is chosen, the quantity of water used is a continuous variable, but the initial choice of the water source is discrete.3/ 2.03 Discrete choice theory offers an alternative theoretical framework which is still based on the concept that utility maximization is the household's criterion for determining the set of preferred consequences. However, instead of deriving a demand function from the first-order conditions of the consumer's utility maximization problem, analysts using discrete choice theory work directly with the utility function. The conceptual framework suggested by discrete choice theory is as follows ... Among J exclusive alternatives (e.g., water sources), household h will choose alternative j if and only if Ujh > Uih for j,i e J and i / j (1) where Ujh and UTih are indirect utility functions conditioned on the choice decision. 2.04 The utility derived from using a water source may be expressed as a function of the attributes of the source--such as quality, reliability, and price--and households' tastes, which are usually measured by socioeconomic characteristics of the household such as income, education, demographic structure, and religion (Lancaster, 1966). Conceptually these indirect utility functions transform the attractiveness of alternative i (including its cash 2/ For a more formal treatment of the theoretical framework presented in this section, see Ben-Akiva and Lerman, 1985, pp. 43-48. 3/ See Whittington, Briscoe, and Mu, 1987, for a presentation of a discrete- continuous model of household water demand. - 5 - price) to household h to a sca]Lar which the decision maker attempts to maximize through his or her choice. 2.05 To illustrate, let us assume a village has three kinds of water sources: kiosks4/, open wells, and vendors which deliver water to the house. Since each source is different in terms of price, collection time, and taste, the utility that a household derives from using one source will be different from the utility derived from using the others. We define the indirect utility function in terms of the following attributes of- the water sources: (i) price of water, P; (ii) collection time per liter--travel time for the household to the source and return, plus queue and fill time at the source, COL; and (iii) taste, T.51 Each of the three water source alternatives has different values of these attributes so that the utility of each of the three water sources (assuming it is chosen) is given by: U, = U(P,, COLV, T,) -- [Utility of using a vendor] (2) Uk = U(Pk, COLk, Tk) -- [Utility of using a kiosk] (3) UW = U(Pw,, CL0,,,, Tw) -- [Utility of using an open well] (4) The utility Ui, (i=v,k,w), is clearly condit:ional on source i being chosen (Hanemann, 1984). For simplicity, we assume an additive form of the indirect utility function so that ... U, = B1P,+ B2COLI+ B3T, -- [Utility of using a vendor] (5) Uk = BlPk+ B2COLk+ B3Tk -- [Utility of using a kiosk] (6) U. = B1Pw+ B2COIk+ B3T. -- [Utility of using an open well] (7) The B's are parameter values of the indirect utility functions representing the household's preferences. We expect B1 and B2 to be negative because higher prices and higher collection times reduce the utility a household derives from a source, and for B3 to be positive because better taste improves the utility derived from a source. 2.06 However, for purposes of the calculations presented in this section of the paper, we ignore the influence of taste, and assume that the household's choice of source is based solely on collection time and cash price. Dividing the indirect utility functions by B1, we obtaLn the household's utility per unit of water ... iy A water "kiosk" is generally a small structure which sells water to customers on a volumetric basis. The source of water may be privately or publicly owned. 5/ We use the term "taste" here to refer not only to the "flavour" of the water (as experienced by taste buds on the tongue), but to all dimensions of a consumer's preferences for a particular water source except money, price, and collection time--including, for example, the consumer's perception of the health effects of water from various sources. -6- U,/Bl = P, + (B2/Bl)COLv (8) Uk/Bl = Pk + (B2/Bl)COLk (9) U,/Bl = Pw + (B2/Bl)COL,, (10) The coefficient (B2/B1) is simply the value of time spent carrying water. 2.07 We now assume that the alternative with the highest utility will be chosen, which here means selecting the source with the lowest total price per liter (including collection costs). Assume that there is no charge for water from the open wells so that Pw = 0, and the collection time per liter associated with using a vendor (COL) is zero.6/ Case I - Household Chooses a Kiosk 2.08 If household h chooses a kiosk instead of water vendors or an open well, this implies that ... Uk > Uv or Pk + (B2/Bl)hC°Lkh < P, (11) and Uk > UW or Pk + (B2/Bl)hCOLkh < (B2/Bl)hCOLwh.2' (12) These two inequalities provide an upper and lower bound on the value of time (B2/Bl)h for household h as long as COLI*Jh > COLkh. The upper bound on the value of time for a household h choosing a kiosk is ... (B2/Bl)h < (P, - Pk)/ C0Lkh (13) and the lower bound is ... (B2/Bl)h > Pk/(COL.,h - C0Lkh) (14) If the term (COLWh - COLIh) is negative, this implies that the collection time per liter of the kiosk is greater than for the open well. In this case the open well is clearly the dominant solution because of the assumption that taste does not affect source choice. In the context of this framework it would be irrational for the household to choose the kiosk. Case II - Household Chooses a Vendor 2.09 If household h selects a vendor, this revealed preference approach yields two lower bounds on the value of time spent hauling water: P, < Pk + (B2/Bl)hCOLkh or (B2/Bl)h > (P, - Pk)/COLkh (15) and P, < (B2/Bl)hCOLWh or (B2/Bl)h > PV/C°LJh (16) §/ Both of these assumptions are true for the case study described in this paper. 7/ Note that B1 and B2 are negative, so that U,/Bl and Uk/Bl are negative. - 7 - If the household's value of time is less than the higher of these two lower bounds, it would make sense to switch to either the kiosk or open well. Vended water would be too expensive in terms of the time saved. Case III - Household Chooses an Open Well 2.10 If household h selects the open well, the procedure yields two upper bounds on the value of time: (B2/Bj)hC`OLWh < P, (17) (B2/Bl)h < P,/ COL., (18) and (B2/Bj)hCOL,,h < Pk + (B2//Bl)hCQLkh (19) (B2/Bl)h < P'k/(C0OL,Jh - CoLkh) (20) If the household's value of time is greater than the lower of these two upper bounds, it would make sense to switch to either the kiosk or the vendor.81 2.11 Table 1 summarizes the formulas for estimating the value of time obtained from these inequalities. -Table: i: -ESTIMATES. OFO'E VALU, OP 'TI OBTAINID FROM THE: 1tSVEAED: PR FIRENCE INEQUALITIES rce Chosen Value of Time. ' by Household . Loveir Bound U..per -Bound ,'(a>'-Kiosk. Pk(COL-COLk) - Pv-Pk) COLk b)-endor (1- (-Pk) CoLk Op(M)en V.e1 I 1) PV1 COLw4 -. . :.....:. . . -(2) -k,(CL .:COLk whre 'v '.-ricCe-of water from ' a vendor Pk = priLe of watet: from a klosk COLk' = co'ledtio4 t ire .per lite for water obtained from a kLosk- -.---COLw- .cel1weion tie per 1itet fo- water obtaie d f om axOpen o eiL.: 8/ Recall that (CO01h - COLh) is assumed to be positive; see discussion of Case I. - 8 - III. DESCRIPTION OF THE STUDY AREA21 3.01 Ukunda is a large village or small town of about 5000 people located 40 kilometers south of Mombasa, Kenya. The economy of Ukunda is heavily influenced by its proximity to the luxury hotels on Kenya's South Coast. Most people either work in agriculture or tourist-related activities. Over 90 percent of the Kenyans living along the South Coast are Moslem, although the percentage in Ukunda is somewhat less due to substantial in-migration by individuals from many parts of Kenya in search of employment in the tourist industry.l11 In 1986 per capita income was approximately US$350 per year. 3.02 Residents of Ukunda have numerous water sources available in the village. A pipeline built to serve the beach hotels runs through Ukunda. There are only about 15 private connections in Ukunda; the vast majority of people obtain water by purchasing it from water kiosks which are connected to the pipeline serving the hotels and are run by licensed operators, or from water vendors who buy water from the kiosks and deliver it to the household. The vendors carry water in 20- liter plastic jerricans which they transport by large carts or by bicycles. Most of the carts carry 10 jerricans; a full load weighs 200 kilograms. Almost anywhere in Ukunda a person can simply step out of his house and hail a vendor. 3.03 In addition to the kiosks and vendors, there are six open wells and five handpumps scattered around the village. The depth of the wells ranges from quite shallow to as much as 30 meters, and most provide water year around. Wells are typically private and paid for by wealthier members of the village, but anyone in the community is free to use them. The handpumps in the village were provided by various donors. 3.04 In the summer of 1986 staff of the African Medical Research Foundation (AMREF) carried out interviews with 69 randomly selected households in a part of southeastern Ukunda where households have access to several nearby water sources. This area of Ukunda was selected because households have several alternative water sources and the decision as to which one to choose is not at all obvious. Numerous vendors work in this area. There are two kiosks and two open wells, but no handpumps in the study area. Each household is assumed to have three basic choices for its water source: (i) a vendor, who would charge 1.5 Kenyan shillings (ks) per 20 liters (US$0.10); (ii) the nearest kiosk, which would charge 0.15 ks per 20 liters; and (iii) the nearest open well, at no 9/ For a more detailed description of the Ukunda field study, see Whittington, Lauria, Okun, and Mu, 1989. I1/ In strict Islamic cultures women may be discouraged from queuing at wells or kiosks in full view of the general populace. This was not, however, a significant factor in Ukunda in preventing women from using these water sources. - 9 - charge.L11 In our sample, 43 households chose a kiosk (62 percent), 17 chose vendors (25 percent), and 9 chose open wells (13 percent). 3.05 At the time of the field work, the market wage for unskilled labof in Ukunda was about US$0.25 per hour. Wage rates are somewhat higher in the peak tourist season (December-February). Agricultural activities were underway at the time of the survey, but it was not a period of peak demand for agricultural labor. 3.06 The household questionnaire consisted of three parts. The first dealt with basic demographic, occupational, and educational data for the family members. The second part consisted of quest:ions on perceptions of the water quality of different sources, the average nunber of times family members went to the chosen source each day, and the amount of water collected.121 The third part of the interview dealt with questions about family income, such as livestock and agricultural production and wage employmEnt. In addition, the enumerators collected data on the distance and travel time to each alternative source from each household in the sample by walking from the house to each source. Data were also collected on queue times through observations of each kiosk and open well. 3.07 All of the data required for the calculation of the inequalities presented in the Chapter 2 are thus available: price of water charged by the vendor, price charged by the kiosks, collection time per liter for each household for each alternative water source, and each household's source choice decision. Moreover, households in the study area generally obtained their water from only one source, and thus this important assumption of the methodology is valid for this village. In other settings individuals may bath or do their laundry at a different source than they obtain drinking and cooking water, but in Ukunda surface supplies for bathing and laundry were not readily available. 11/ In 1986 US$1 - 16 ks. 12/ Although households were asked about their perception of the quality of water from different sources, no bacteriolcgical or chemical tests of water samples from different sources were carried out. - 10 - IV. RESULTS OF THE ANALYSIS Estimates of the Value of Time Based on the Revealed Preference Approach 4.01 Tables 2-4 present the results of the revealed preference calculations outlined in second section for each of the three groups of households: (i) those households that chose kiosks, (ii) those households that chose vendors, and (iii) those households that chose open wells. The first and second columns indicate the collection times per trip for each household for the well and kiosk, respectively (in minutes). The third and fourth columns in Tables 2 and 3 present the bounds on the value of time spent carrying water (in US$ per hour) based on the calculation of the inequalities developed in the presentation of this revealed preference approach. The estimates of the collection time per liter for the well and kiosk assume 20 liters are collected by each household each trip.131 4.02 Consider first the results for households which chose kiosks (Table 2). The calculations for 4 of the 43 households in this group yield inconsistent answers with respect to the upper and lower bounds, and these households were eliminated from Table 2.14 The upper bounds on the value of time for the other 39 households are presented in the third column. All are greater than the market wage rate of US$0.25, and all but two are less than US$1.00 per hour (mean = US$0.64). The lower bounds on the value of time presented in the fourth column are much less than the values for the upper bounds, and thus do not create a "tight" range for the value of time. Column 5 in Table 2 presents the mid-point of the range between the lower and upper bounds on the value of time for each household. The mean value of these mid-points is US$0.38 per hour (median = US$0.33). Figure 1 presents a frequency distribution of these mid-point estimates of the value of time of households using kiosks. As shown, the estimated values of time do not vary widely (standard deviation = US$0.11). The vast majority fall between US$0.20 and US$0.50 per hour). 4.03 Table 3 presents two lower bounds on the value of time for the 17 households which chose vendors (columns 3 and 4). Column 5 presents the maximum of the two lower bounds. Figure 2 presents the frequency distribution of these lower bound estimates on the value of time of households using vendors. The 13/ This estimate of the quantity of water collected per trip is based on source observation data. There is little variance among households; the vast majority of adults use standard 20-liter containers to carry water. ii/ Two of these five households chose kiosks even though the total collection time for the open well was less. Such decisions could be due to poor taste or other water quality characteristics of the open wells. ~Table Z. ESTIM4ATES OF: THE: VALUE OV T1IM8 SPENT HAULING WATER FOR BOUJSEHOLDS CHOCHING ICTOSXS 2 ~ ~ ~ ~ ~~~~~3 45 Upper bounid`: Lower: bound Time required: to coll:ect. water f tom.:.. Astimiate: oni estimate on mIdpolnt Wells (in mm) Rioska Cm mm) value of ~~~~tilme valuei of time. of: initerval 22,98 ~~~~~~5.50 0.92. 0,03- 22.56 7.40 0.:68: 0:.04:03 21.10 .008 0.04 04 20.98 6.60 0:O. 76 .0.04: 0.68: 20.80 ~~~~~~~330: 1.33. 0.0 0.6 19.86 ~~~~~~12.30 '0. 4.1 0.07 0.:24 18. 87 14.5,0 0.5 .1 .24: 18.80: 14.00 .6 0.12O 0. D24 18.80 7.0DO 0. 72: 0. 05. 0a .18.44 1I.30 0.45,, 0,08 :0.27 17. E88 6.00 0.84 0.0:5 0.45 ~17. 80 :8.10: 0.62 -0.06 0.34 17.58 ~ 10. 80 0.70.08 -0.27 16.71 ~~~~~~13,40,:0.36 0.:17 0.27 16.70 10.20 0.49 0..09: 0.29 .:I6.68 12.30 040.30.27 16.68 ~ 12.30 ~ 0.41 0.13 0:.27 1:5.81 10:.70 0.47 0.11 50.2 15.:59 ::7,40 0.68 0.76.38 '15. 03. 9.7 05 0.11 0.32 14.65 ~~~~~~6.00 0.84 0..06 0.45 14.20 1 7.70- 0.50.109 0.37 ~.14.~14. 7.00- 0.72: 0.08 0.40. 13.83 3.30 1.49 0.05: 0.77 13.8 7.60 06 .903 .13. 56: :9.30 0.401303 13.53 ~~~~9. 70 0.20.0.34 13.51 10.20 0.9 .17: 0.33 ~13.49: -10, 70: 0.47- 0.20 0:.34 :13.06-71 0.71 0.09 0.40 12.93 ~~~~~~7.60 0..66 0.11 :0.39 :12,79: 6.8 S 0..74 0:.:09 0.42 12.72 6.10 0.83 .0.08 0.45 12.20 9.30o 0.54 0.19 0. 37. 12.04 9:.7 0 :0.52 0.24. 0.38 12..02 10,.20 0.49 0.31 0.40 11.56 8. 90, 0.57 0.21 03 11.43 6.00 0.4 .10 0:.4.7: 11.39 10.20 040.47 04 ::Average value ~tie 0.640.2.8 Standard:.deviatLon: 0O.:24 0:.:08:01 ~~4edian ya1u~~~: 0.52 0.~09 :0.33 - 12 - mean of the lower bounds on the value of time presented in Column 5 is US$0.57 per hour, more than twice the market wage for Figure 1: FREQUENCY DISTRIBUTION OF THE unskilled labor. ESTIMATES OF THE VALUE OF TIME FOR HOUSEtHOLDS CHOOSING KIOSKS 4.04 These data suggest that families Percent of Household in Ukunda which purchase water from vendors implicitly place a surprisingly high value on the time spent collecting water. Households which purchased water 30 from vendors were spending about 8 percent of their income on water, which is consistent with findings from other 20 - countries regarding the percentage of income which people will pay water vendors (Fass, 1988; Linn, 1983; Whittington, Lauria, and Mu, 1989). 10 V 4.05 The results of the inequality calculations for the 9 households which chose open wells are presented in Table 0 , _ .- _____ O 4. In 5 of the 9 cases, the collection Maximum2 o Lower Bound 9 *60-69 Oer 60 time per liter for the kiosk is greater than for the open well, and thus the open well is clearly the preferred alternative, assuming water quality does not affect source choice. The remaining Figure 2: FREQUENCY DISTRIBUTION OF THE four cases are not a large enough sample ESTIMATES OF THE VALUE OF TIME fou FOR HlOUSEHOLDS CHOOSING VENDORS upon which to base any conclusions. The fact that these 9 households did not choose a vendor does provide upper bounds PercentofHousehold on their value of time (Table 4, Column 3), but these values are quite high (mean of US$0.53) and do not provide much 40 _ lnsight into the value of time for households choosing open wells. , 30_ 4.06 The results from these revealed preference calculations for households choosing vendors and kiosks appear 20 - consistent with respect to the average incomes of households using vendors and kiosks. For example, the estimated 10 average annual income of households in the sample using vendors was US$2000. Assuming an average of 1.5 working adults o -- per household and an average work week of .0-.20 .20-.2S .30-.3% .40-.49 .60-.69 Ovr.60 50 hours per adult, the household' s Midpoint ot Lower Bound Estimate-US$/Hr annual labor supply would be about 3600 hours. This would imply an average - 13 - imputed wage rate of US$0.56 per hour. Given the rough nature of these approximations, this is surprisingly close to US$0.57 per hour, the lower bound estimate of the value of time spent collecting water derived from the revealed preference calculations. 4.07 The average annual income of households using kiosks was US$1250. Again assuming an average annual household labor supply of 3600 hours, the average imputed wage rate for households using kiosks, would be US$0.35 per hour. The estimate of the value of time spent collecting water based on the mean of the mid-points of the upper and lower bounds--US$0.38--is again very close to the average imputed wage rate. 4.08 Similarly, these estimates of the value of time are consistent with the data on the average number of women in different groups of households. Because women collect about 75 percent of the water fetched by households in Ukunda, one would expect that households with more adult women would have a greater labor supply for hauling water, and would thus be less likely to purchase water from vendors. This is, in fact, the case. Households using vendors average only 0.88 women, while households using kiosks average 1.45 women, and households using open wells average 1.78 women. Table 3: ESTIMATES OF THE VALIIE OF TIME SPENT.RAULING WATER FOR SOUSEHOLDS CHOOSTNG VENDORS- (us$): 1 2 ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~3 :45 - -ower bound L Lower bound Time re quired to collect water from'.. estimate on~ estimate,on: Maximum of Wells (in min) Kiosks (in mm) value of time value of time columns 3 E 4 (Pv-Pk IcrOLk Pv/COLw 29.72 11.33 0.45 0.19- 0.45 21.12 13.95 0.36 - 0.27 0.36 16.81 7.52 ,0.67 0.33 0.67 15.73 9.64 0.52 0.36 0.52 15.73 ' 11.75 '43 0.36 0i43 14.40 3.50 1-.45 0.39 1.45 -13.58 10.15 0.50 0.41 0.50 13.58 13.86 0.37, 0.41 0.41 12.50 14.11 0.36 0.45 0.45 12.50 6.47 0.76:- 0.45 -0.76 12.50 7.61 0.,66 0.45 0.66 12.50 24,42 0.21 0.45 0,45 11.64 13.86 0.37 0,45 0.45 11.43 28.64 0.18 - 0.49 0.49 11.00 20.20 0.25 0.51 0.51 10.57 10.27 0.49 0.53 0:5s 20.35 9.64 0.52 00.54 054 Average value of time: 0,50 0.41 0.57 Standard deviation: 0.28 -0.09 0.24 Median value ,0.47 0.;45 0.47 - 14 - Tble 4: ESTIMATES OF: THE ALEO TIME: SPENT -A-LING- WATER FOR A HOUSEOLDS CHOOSING OPEN: WELSt (US$) esim t ate: ~on:: x ...... -::Time required to collect vater from ... Minimum of. Wells:: (ln,mm) iosks;0 t (in ml Pi p CO!w o Pk[( (OCOL 0Lk) 12.50 8.15 0.45 4 i ;:f:;0:ii::: E:12.i20- : 10.;12Wig;; :: : S.fg:E;g :d gi0.46i-g ti:i:::R ::::::t:::::ttEi::::C:103.80:::- :::: : :: 12.53 : i:::: :::i0 :52 ~10:.30 3.00.54 9. 90 04 0.57 ~9.90 9.14 0.57 9.60 10.320:: (Y.:58 9.20 . 11.00 06 :AVerage:valu o;f t:ime: i0.53] :Standard deviation :i006 ~Media value:0.5 4 An Estimate of the Value of Time Based on a Random Utility Theory Approach 4.09 In the second chapter we derived upper and lower bounds for the value of time spent hauling water based on the assumption that the households' source choice decisions depend only on the time spent collecting water and the cash price paid for water. In this section of Chapter 4 we relax this assumption and take into account other factors which may affect source choice decisions, such as the quality of water at the different sources. 4.10 As discussed in Chapter 2, a more complete model of households' source choice decisions would posit that the utility a household derives from a water source would depend upon at least two sets of explanatory variables: (i) source attributes which affect the household's utility, and (ii) household characteristics which reflect differences in tastes and preferences among households. Let X be a vector of source characteristics, and Z be a vector of household characteristics. The conditional indirect utility function of household h may be written as ... Uih = Uih(Xih, Zh) (21) where again i indicates the water source and h denotes households. Since the utility Uih is not directly measurable, researchers attempt to estimate the utility Uih from the observed independent variables Xih and Zh. Such an - 15 - approximation of ULh will be subject to error, and, as a result, some inconsistencies in observed behavior are generally inevitable (as indeed was the case in the data analysis presented in the last section). 4.11 According to random utility theory, such unobservable or unmeasurable influences are assumed to be captured in a random term, which for operational purposes is usually assumed to be added to the systematic (or observed) term in the household's random utility function (Manski, 1973; Ben-Akiva and Lerman, 1985). Thus, in our example the random utility function is ... Uih = Vih + eLh i e J (22) where V is the systematic term and e is the random term. Let the variable Yjh indicate household h's choice decision on source j such that ... 1 if Vjh + ejh > Vih + eih Yjh = i,j 1, .. . J (23) 0 otherwise i j The expected value of Yjh is thus ... E(Yjh) = P(yjh = 1) (24) = P(Ujh > Uih) (25) = P(Vjh + ejh > ijih + eLh) (26) In other words, the probability that household h chooses alternative source j equals the probability that the utility derived from using source j is greater than the utility derived from any other alternative (Amamiya, 1981; McFadden, 1973, 1982). 4.12 Based on this random utility framework, we postulate the following utility function for household h choosing water source i ... Uih = Vih(TIME, CASH, TASTE, INCOM, WOMEN, EDUCT) (27) where TIME = total time spent collecting water per day, including travel time, queue time, and fill time (minutes per day); CASH = total amount of money paid for collecting the water per day, i.e., the cash price times the amount of water consumed per day (US$ x 10-2 per day)1'51; TASTE = household's perception of the taste of water from the open wells--equal to one if the taste is poor, zero otherwise; 15/ Note that this variable is defined as price times quantity of water rather than simply the price of water. This is necessary in order to derive an estimate of the value of time (see Bruzelius, 1979, and DeSerpa, 1981). - 16 - INCOM = total annual household income (in thousands of Kenyan shillings) WOMEN = number of adult women in the household; EDUCT = number of years of formal education of family members. The means of the independent variables are presented in Table 5 for households in IJkunda which chose each of the three types of water source. 4.13 The three source characteristic variables--TIME, CASH, and TASTE--are all expected to have a negative effect on the probability of a household choosing a particular source because people prefer to spend less money and less time collecting water, and they prefer better tasting water. The household characteristic variables INCOM and EDUCT are expected to have a positive influence on the probability that a-household chooses a vendor or a kiosk. The household characteristic variable WOMEN is expected to increase the probability that a household chooses a kiosk or an open well because the more women in a household, the more labor is available for carrying water to the home. 4.14 Since the distribution of Uih depends on the distribution of eih, different assumptions about the distribution of eih will lead to different discrete choice models. Here we assume that eih has a Gumbel distribution so that the probability of choosing a source will have a logit-type function (Ben- Akiva and Lerman, 1985). Note that the independent variables in the random utility function which describe the source attributes vary across sources; the independent variables which describe the household's socioeconomic characteristics do not vary across sources (the latter group of variables are included to explain variations in tastes across households). The standard statistical method for dealing with the first group of independent variables is a logit model; the standard approach for the second group of independent variables is a polychotomous model. McFadden (1973, 1976, 1982) and Maddala (1983) have developed the following conditional logit model to deal with a data structure which includes both groups of independent variables: J Ph(j) = exp(BXjh + ajZh) / Z exp(BXLh + 0iZh) (28) i=l where it is assumed the household's utility function is additive: (29) Vih = BXih + a!iZh *-/ 16/ The estimation procedure for this conditional logit model is essentially the same as for a standard logit model because the household-specific vector Zh can be easily transformed into a choice-specific vector. Therefore, the maximum likelihood method will give a consistent estimate of the parameter vector B. - 17 - Table5:- MEAN VALUES OF INDEPENDENT VARIABLES USED IN THE CONDITIONAL MUJLTINOMIAL LOGIT MODEL OF WATER SOURCE CHOICE- Independent .Households Using... Total for Variable - iosks Vendors::. .Open Wells All Households CASH -2 4.25 42.46 0.00 18.37 :(US$ x 10o - .:per. day) TIME .4.39 0.00 ..57.90 34 .68 (Minutes per- day) .TASTE .1o9 0.14 0.91 0.42 (l=poor; : O-tOtheizs se)- :-- INNCM 0.174 32.46 19.05 2324 (10 Kenyan . shlilin8s - -- - ..- - - -- - . : :- per-year) ..E- WOMEN 1.45 0.88 1.78 1.36 (Niumber of) .-EDUCT 12.75 12.45 . .8.13 11.81 (Years) 4.15 The results of the model estimation are presented in Table 6. The overall model is highly significant; the adjusted likelihood ratio is 0.51. The signs of all of the explanatory variables are as expected. The two variables TIME and CASH, which are used to calculate the value of time, are both significant at the 1 percent level. 4.16 The purpose of presenting this discrete choice model in this paper is to derive an estimate of the value of time spent hauling water. 17 If the value of time is defined as the marginal rate of substitution between the time spent collecting water and the money paid for the water, it can be calculated from two of the estimated parameters of this conditional multinomial model. The value of time is simply given by the ratio of the coefficients B, and B2) D The value of time spent hauling water may thus be calculated as ... 17/ For a more detailed presentation of the results of the discrete choice model of households' water source selection decisions, see Whittington, Lauria, Okun, and Mu, 1988. 18/ See Ben-Aki and LermaLn, 1985, pp. 75-80 and 174-177, and Stopher and Meyburg, 1976 for detailed discussions of the derivation of the value of time based on this random utility framework. - 18 - Value of time = (Bl/B2) (30) = (-0.053/-0.101) = US$0.0052 per minute = US$0.31 per hour This result is almost 25 percent more than the market wage rate for unskilled labor in Ukunda in 1986 of US$0.25 per hour. This estimate of the value of time spent hauling water should be interpreted as an average for the households in the sample, in contrast to the estimates of the value of time derived using the "revealed preference" inequalities, which were household specific. able 6: RESIULTS~: ~OF THE, CONDITION ALULTINGMIAL :LOC1T ::MODEL FHOUS EHOLDS' WATERC SOURCE CHOICE StAnidad Sgnificanc e V a r i:abl e Coefficient' Errr -Ra.oLevel: TIME......... 0 ~CASH 0 1 003i 00. TASTE- 0 305652: ~~V-INCOMtl 0 09 0050 VWOMEN.' 1 0 00.607 009 ~V-EDUCT .0 0.07. T 25 K-INCOM 0,04. 0,0: 4 33 1<1-W~OMIEN . 034.0 7 :: .3 K- EDUCT. 0.010.61 Log-Likelihood' Ratio: ~-46.0~ Restric:ted ~Log-~Likel~ihood: Ration: -75.8 Chi - Squarted: 05 ~l No. iofbservations: ..... *The coeffidients ~6f the.~iindependent variables rpcdb. n K, ilndicate the change i:n the log-odds o:~f choosingt~: tat particul ar~source:~ (i.e., V = vendor andK=.kiosk) relati~~~~~1ve: tote mttdsource a open, well)...... ...... - 19 - V. CONCLUSIONIS 5.01 We feel that both procedures outlined in this paper have significant potential for yielding insights into the value households place on the time spent collecting water. Although the upper and lower bounds on the value of time for those households which chose kiosks were farther apart than we might have wished a priori, we interpret the evidence to indicate that the value of time spent collecting water for most households which chose kiosks is likely to be near--or even above--the market wage rate for unskilled labor. The lower bounds on the value of time for households which chose kiosks suggest that the value of time spent collecting water is at least 50 percent of the market wage rate (Table 2). Households using vendors appear to have a significantly higher value of time than households using kiosks, and in absolute terms, the lower bounds on the value of time fcor households choosing vendors (Table 3) are much higher than we would have anticipated (more 1than twice the market wage). 5.02 Our estimate of the average value of time derived from the parameters of the conditional multinomial logit model is surprisingly close to the current market wage for unskilled labor. If additional research shows that the value of time spent hauling water in other villages in developing countries is close to the market wage rate for unskilled labor, this result will have important policy implications for choice of service level. If the value of time spent hauling water is as much as US$0.25 per hour, piped distribution systems are an economically attractive technology in many villages in developing countries (Churchill et.al., 1987). 5.03 In closing, it is important to emphasi'ze that the estimates of the value of time spent collecting water which are presented in this paper should be considered preliminary. Additional research should be carried out in other locations to determine whet'her these results are generalizable to other communities in Kenya, and to different countries and cultures. Future research efforts on this subject should also improve upon the study presented here in three important respects. First, the sample size should be increased so that one can place more confidence in the magnitucLe of the estimates of the value of time. Second, an indepth anthropological investigation should be carried out to determine whether sociaL, cultural, and political factors influence households' water source choice decisions. Third, future research efforts should examine whether households' value of time varies significantly by hour of the day, day of the week, or season of the year. - 20 - REFERENCES Amamiya, T. "Qualitative Response Models: A Survey." Journal of Economic Literature, 19, pp. 1483-1536, 1981. Becker, G.S. "A Theory of the Production and Allocation of Effort." NBER Working Paper No. 184. 47 pages, July, 1977. Ben-Akiva, M. and S. Lerman. Discrete Choice Analysis: Theory and Application to Travel Demand. Cambridge, Mass.: MIT Press, 1985. Bruzelius, N. The Value of Travel Time. London: Croom Helm Ltd., 1979. Cairncross, S. and J.L. Cliff. "Water Use and Health in Mueda, Mozambique. Transactions of the Royal Societv of Tropical Medicine and Hygiene, 81, pp. 51-54, 1987. Churchill, A. et. al. 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