Moving forward by looking back: comparing laboratory results with ex ante market data.

Chermak, Janie M. ; Krause, Kate ; Brookshire, David S. 等

I. INTRODUCTION

In this research, we address the central question of whether data obtained in an experiment with participants from the population of interest parallels market data from the same group. Utilizing information provided by our participants we construct salient payoffs, based on participants' revealed preferences to elicit the experimental responses. Combining these experimental data with naturally occurring market data for the identical set of consumers, we test for consistency between the two data sources. Unique to this research, the market data, unlike field experiment data, are not obtained through manipulation by the researchers. Instead these data are the actual expenditures and consumption choices of the participants reflected in billing records for the years preceding lab participation. Under these conditions, we find that experiment responses parallel ex ante market behavior.

Experiment data, if consistent with market data, could be used to fill data gaps. This is increasingly important as policy makers find themselves having to respond to situations for which data do not exist, making it difficult to assess the efficiency of proposed policies. Examples include consumer response to changes in depth and frequency of energy shortages, market responses to rapid technological advancements such as the Internet, and structural changes in markets where current and future conditions are fundamentally different from the historic record. This is the case of water in the arid western United States. Increases in demand associated with urbanization have stressed the limited supply of water, and the price of water--invariably set by a public utility and not the market--will surely rise. How can a policy maker design an effective, efficient policy, when the characteristics of the market and the potential range of data are outside anything seen before? The policy relevance of experiments depends on parallelism between the lab and the field (Smith 1982). This research provides evidence for that parallelism.

Because we focus on parallelism between the laboratory and the market we deviate from traditional economics experiments protocol. Traditional experiments that seek to test theory normally provide participants with explicit information concerning payoffs to induce preferences. In our case, as in any actual market, individual payoffs are endogenous and based on individual preferences. We could not directly link experiment payoffs to water consumption because no water was actually consumed as part of the experiment protocol. Instead, we linked experiment payoffs to estimated household water consumption based on information provided by participants prior to the experiment.

We offer an inquiry into residential water markets in Albuquerque, New Mexico, a midsize city in the desert southwestern United States. We compare participant response in an experiment to the actual water bill data generated by those same participants in the years preceding the experiment. The water bill data are unfettered by the experiment participation. It predates the experiments and the participants could not have predicted that their household consumption choice data would one day be used in an experimental investigation. Prior to the experiment participants completed a survey describing their household's water-using features (e.g., type of landscape), which we used to categorize their preferences and predict their water use. Participants' water bills and survey responses provide evidence of the underlying utility function for each participant, which were used to calculate payoffs as described in the following text.

For both the experiment data and the water bill data we econometrically estimate consumer water demand, using comparable explanatory variables. We find approximately 75% of the independent variables exhibit the same significance across the two data sets, over 90% of the statistically significant variables exhibit the same direction of impact, and for almost 70% of the participants, there is no statistical difference between the water demand elasticities estimated from the water bills and the experiment data. These results suggest well-designed experiments may be used as a tool to fill data gaps, extend data ranges, or test consumer response to other institutional changes--before those changes occur.

This paper is structured as follows. Section II presents the theoretical background, while Section III provides institutional background. Section IV discusses the experimental design, Section V presents the data and econometric results. Section VI presents the results of hypothesis tests and Section VII concludes.

II. THEORETICAL CONSIDERATIONS

Consider a residential water consumer's problem:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where w is the quantity of water consumed, x a composite of other goods consumed, [PHI] a vector of individual characteristics impacting tastes and preferences, p the price of water, the price of the composite good is normalized to one, and B the consumer's budget. The standard first order necessary conditions result in p = [U.sub.w]/[U.sub.x]. The consumer's demand for w is then estimated as w = f(p, B; [PHI]). We assume demand for water follows the standard conventions, thus [w.sub.B] > 0 and [W.sub.p] < 0. The final consideration is the effect of personal characteristics on demand. That is, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where n is a specific characteristic in the vector.

The historic prices paid by residential consumers in the United States have been extremely low and have resulted in estimated demands that are locally inelastic. At low prices, water use constitutes a minor component of a household's budget. Marginal rate increases provide little incentive to conserve. Given this we might expect to see the majority of all optimal consumption decisions fall within a small range. But consumers are heterogeneous with respect to tastes and preferences, budget constraints, and water uses. That is, [PHI] may be specific to the individual consumer or at least to a specific type of consumer. Thus, while we would expect consumer "types" to choose similar levels of water use, we would not expect, for example, a high-income, green grass-loving consumer to choose the same quantity of water as a high-income consumer with desert landscaping even if they faced exactly the same budget constraint. We consider these differences in actual use patterns as well as other observable differences in consumer types to construct a protocol that allows us to incorporate preferences revealed in actual water use into our experimental design. While many experimental studies induce the participants' preferences, this design is based on the consumers' revealed preferences in the years preceding the experiment. We incorporate this information about prior choices by using payoff functions that reflect participants' preferences.

III. BACKGROUND

This research compares experimental data with ex ante water bill data at the level of the individual household. Thus we contribute to three distinct literature areas. First the good in question is urban water demand at the level of the individual consumer household. This work contributes to the existing empirical estimates of water demand by demonstrating the potential for using lab-generated data to estimate elasticity of demand for water. Second, the experimental design is predicated on the fact that there are observable characteristics that can be used to categorize consumers into distinct groups. We investigate the heterogeneity of consumers with respect to demand for water. Finally, our comparison of water bill data to experimentally generated data draws on and contributes to the experimental literature that employs field experiments. We briefly discuss each of these below in what is intended to be an overview of the literature rather than an exhaustive review.

A. Empirical Water Demand Studies

Empirical water demand studies have been conducted at the aggregated level by, for example, Howe and Linaweaver (1967), Howe (1982), and Schefter and David (1986) and at disaggregated levels by Hewitt and Hanemann (1995) and by Dandy, Davies, and Nyugen (1997). Observable characteristics have been shown to affect the demand for water, including climate and season by Gibbs (1978), Danielson (1979), Nieswiadomy (1992), Lyman (1992), Renwick and Archibald (1998), and Renwick and Green (2000). Gibbs (1978), Foster and Beattie (1981), Jones and Morris (1984), Nieswiadomy and Molina (1989), Rizaiza (1991), Lyman (1992), Martin and Wilder (1992), Renwick and Archibald (1998), Renwick and Green (2000), and Kenney et al. (2008) find that income, lot size, or household size and/or other characteristics affect the demand for water. The vast majority of these studies found that demand for water is inelastic. Espey, Espey, and Shaw (1997) conducted a meta-analysis using the results from 24 previous journal articles and found the price elasticities in these studies ranged from -0.02 to -3.33, with an average of -0.51. Approximately 75% of the estimates were between -0.02 and -0.75. However, as Brookshire et al. (2002) suggest, this may be in large part because of the historically small range of prices over which the studies are conducted. But the combination of drought and rapid population increases suggest that those prices will not be the prices confronted in the future. Thus, there is a need for additional data over a wider range of prices.

B. Observable Characteristics and Heterogeneous Demand

Public utilities, not markets, supply and price water. Thus decisions about that provision and pricing must consider the preferences of all stakeholders. Given the potential heterogeneity among those stakeholders, we draw on the growing literature concerned with correlations between observable characteristics and behavior. That literature suggests that social, economic, and cultural variables, including age, religion, ethnicity, and gender may be correlated with demand. (1) We likewise test whether demand for water is a function of observable demographic and other variables, including ethnicity, political and religious affiliation, gender, and age. This information can help policy makers anticipate the concerns of the diverse population affected by their decisions.

C. Field Experiments

A growing literature uses field experiments and compares the outcomes of field experiments to either traditional laboratory experiments or other value elicitation methods to learn more about consumer behavior. List (2008) provides a short overview of the field methods and of the potential for gaining insight from field and lab experiments and econometric methods. For a more complete review of field experiments see, for example, Harrison and List (2004).

This innovation expands the pool of possible data sources available to researchers and policy makers. A number of studies have been conducted to cross-test stated preference, revealed preference, and experimental markets. For example, Battalio et al. (1979), Dickie, Fisher, and Gerking (1987), Brookshire, Coursey, Schulze (1987), Brookshire and Coursey (1987), Shogren et al. (1994), List and Lucking-Reiley (2000), and List (2001) compare field and laboratory experimental results, where the field results are either an application of experimental methods to participants in the field or a stated preference study. Poe et al. (2002) investigate consumer willingness to enroll in a green energy initiative, comparing an open-ended willingness to pay elicitation with a provision point elicitation. More recently Chang, Lusk, and Norwood (2009) compare hypothetical and incentivized consumer choice experiments with ex post real consumer purchases of dishwashing liquid, flour, and beef in a local grocery store. Their incentivized lab results more closely predict the market choices of residents of the same city, increasing confidence in the external validity of this approach. Owing to the nature of the products over which decisions are made, Chang et al. are able to actually deliver the product purchased in the experiment, a feature we are unable to replicate.

Research employing framed field experiments that seek to inform policy debates include Denton, Rassenti, and Smith (2001), Weiss (2000), and Rassenti, Smith, and Wilson (2001), all of which are specific to electricity markets. Murphy et al. (2000) bring a similar approach to water markets. These approaches have provided information on consumer behavior and preferences with respect to a wide variety of market structures and goods.

On the consumer side, Battalio et al. (1979) use field experiments to investigate demand elasticity for electricity. Chermak and Krause (2002) and Krause, Chermak, and Brookshire (2003) experimentally investigate water use from a common pool aquifer where current period use has implications for future water availability. Our current study borrows from the methods and insight gained in prior experimental research and adds the element of ex ante water bill data to investigate the degree to which contextualized lab experiments produce results that are similar to those observed in the market. Like Chang, Lusk, and Norwood (2009) we compare market data with experiment data. Our approach differs from that of Chang et al. in that our water bill data predate the experiment and are collected from the experiment participants.

IV. EXPERIMENTAL DESIGN

This research tests the statistical comparability of the lab responses of individual residential water consumers in Albuquerque, New Mexico (a city of approximately 600,000 located in the southwestern United States) to their actual market consumption of water. For saliency, the experimental design reflects the unique characteristics of the local market and water utility institutions. Albuquerque residential water consumers receive a monthly water bill that consists of a fixed charge (dependent on the size of the water main to their residence) and a commodity charge per unit of water (where a unit is 748 gallons, or 1,000 cubic feet of water). Partial units of water are not recognized--they are rounded up. In addition to the use and charge information, each monthly bill includes historical data showing the consumer's monthly usage over the past year and a comparison to the monthly usage of the "average" residential consumer in Albuquerque. Thus, participants are told each month how their use compares to average residential use. For the last several years the water utility has actively promoted water conservation with publicity campaigns, rebates for those who purchase low-water-use appliances and surcharges on "excessive" water use defined as a multiple of the average use, currently 300% of the consumer's winter use.

It is this market that provides the setting for our experiments. We design a context-specific, experimental market for water, consistent with the summer months' market in Albuquerque where residents have both indoor and outdoor water use components. Summer use was chosen because, on the margin, demand is more elastic during the summer and so more amenable to conservation policies, including premium pricing for high use.

We obtained the data used in this research from several different sources. An initial survey instrument (the "presurvey") collected information about participants' family size, house and lot size, and investments in water-saving or water-using landscape features and household appliances. Participants returned their presurveys and a copy of their current water bills (which include the most recent 12 months of use) 2 weeks prior to the experiment sessions. This information was used to categorize participants as having high water use, average water use, and low water use.

At the experiment sessions, each participant recorded 20 water-use choices, with five decisions being made in each of four sets. These provided data on choices made under varying water price, wealth, and rainfall conditions. Specifically, the experiments were designed to examine choices made when prices fell outside the current water bill ranges. Finally, at the end of the experiment, each participant completed a post-survey, which asked for basic demographic and socioeconomic information as well as attitudes about water conservation and scarcity. (2)

Smith (1982) cautions researchers that participants arrive in the lab with unobservable preferences, but that experimentalists must exert some control over preferences by designing salient rewards. Unlike many experiments where utility is induced by uniform payoffs, the design of our research allows us to provide this required control by constructing a payoff structure that reflects our participants' own revealed preferences and constraints. Preexperiment survey responses and current water bills were used to differentiate the participants' consumption patterns. We assume participants' water use, landscape, and water-using appliances resulted from the participants' implicit solutions to their constrained optimization problems and that the preferences that drove those choices are relatively stable. Thus choices consistent with those revealed preferences should yield the highest utility. In our experiments those choices yielded the highest payoff.

In the experiment instructions, we remind participants that we have information regarding their household's use and inform them that their payment for participation will be highest if "the decisions you make tonight are consistent with the pattern of water use shown in your water bills and on your survey..." We provide additional guidance in the instructions with the goal of encouraging participants to respond realistically while avoiding inducing decisions that were driven solely by the payoff structure. The specific instructions state, in part:

 Some participants' water bills show that their summer
 water use is higher than average. For some,
 it is because they are maintaining a lawn. These
 participants will earn money in this part of the study
 by making sure that they put enough tokens into their
 Water Accounts to maintain their lawns.

 People whose information shows that they use less
 water than average will make less money if they put
 too many tokens into their water accounts, and will
 earn more money if they put more tokens in their
 balance accounts. But those participants should put
 enough tokens into their water accounts to support
 the water uses that they reported on their surveys. If
 they do not they will earn less money.

 Most people reported several different kinds of
 water uses. They will earn more money tonight by
 making sure that they "buy" enough water for those
 uses.

 Here is one way to think about this. The way to earn
 the most money in this study is to make the same kinds
 of decisions here that you make in your own home.
 If you invest a large number of tokens in your water
 account, but your survey and water bill show that you
 do not use a lot of water at home, your earnings will
 be low. lf you use a lot of water at home, but do not
 invest very much in your water account here, your
 earnings will also be low.

While participants were told that their payoffs were calibrated to their type, they were not told their type. Because the water bill data for each participant were from 10 months to 7 years old, it would be difficult for a participant to remember how he or she acted in years gone by and try to strategically mimic that behavior in the experiment.

Postexperiment, individual participant data were matched (via the water bill information) to the City of Albuquerque's Water-Wise Data Set (January 1994-December 2000), which provided up to 84 months of water usage, rates, and charges at the individual account level. The linking was done postexperiment in order to alleviate the potential for design bias. Ten participants in the experiment could not be linked to their water bill data and so were dropped from the data set.

A. Participants

Participants were recruited by placing an advertisement in the Albuquerque Journal, the largest circulation daily newspaper in the Albuquerque metropolitan area. Participants were required to be 21 years of age or older and to have lived in Albuquerque for a minimum of 5 years. A total of 43 Albuquerque residents participated in the experiment portion of this research and had the historical data necessary for the field portion of the research. The sample is fairly representative of the metropolitan area. The city is divided into four quadrants; northeast (NE), northwest (NW), southwest (SW), and southeast (SE). Of the 43 participants, 45% are from the NE (the most heavily populated quadrant of the city), 33% from the SE, 13% are from the NW, and the remaining 9% are from the SW. The NE and SW quadrants representation is consistent with single-family residential water accounts (47% and 9% of accounts, respectively), while it slightly overrepresents the SE quadrant and underrepresents the NW quadrant (19% and 25%, respectively). (3)

The geographic dispersion of the participant pool has implications for our results for at least two reasons. While the entire city of Albuquerque is arid, rainfall varies across the four quadrants of the city. In addition, as is the case in many metropolitan areas, different areas of the city are associated with different wealth levels. It is plausible that these climate and economic factors might affect water consumption. Participant characteristics are discussed in more detail in the following section.

From the information provided by the participants in their presurvey and on their current water bill, we characterize each participant as being one of three consumer types. The division is based on the sample usage mean and the natural break points that occur above and below this mean for summer water use (high water use time in Albuquerque). Type 1 (T1) participants' summer water usage is below the city average as well as the sample average and falls below the observed break point. Their responses to the presurvey questions suggest either conservation tendencies or lifestyles that are consistent with low water usage. For example, many of these participants indicated they had converted their lawns to native plants.

Type 2 (T2) participants are those whose use is consistent with average use patterns. Type 3 (T3) participants' summer water usage is above the natural break point we found in the data. Their responses to the presurvey questions suggest that they have little interest in conservation or have lifestyles inconsistent with low water use. Approximately 38% of the participants are classified as T1, 26% as T2, and 36% as T3. Figure 1 presents water usage for the month of July 2001 for the three participant types. July was chosen as it is the peak summer month for water use in Albuquerque.

As can be seen from the graph, there is an increasing water use pattern across the types. The average usage for T1 participants is 6.9 units, for T2 participants it is 15.8 units, and for T3 participants it is 26.5 units. This equates to average daily household use levels of 170 gallons, 389 gallons, and 652 gallons, respectively for the T1, T2, and T3 categories. Differences in mean water use among the three groups are statistically significant at 5%.4

[FIGURE 1 OMITTED]

B. Experimental Protocol

Three experiment sessions were conducted on three separate evenings. Each session took place in the Economics Department conference room on the campus of the University of New Mexico. Each participant participated in four sets of five rounds each. The basic task in each round was to allocate a budget of tokens between a "water account" and a "balance account." Participants were told that we had determined a water use pattern based on information they had provided to us, and that their payment for participation would be highest if their consumption decisions were similar to those they would make in their own homes. To avoid inducing extreme behavior (i.e., corner solutions) participants were not informed as to the type to which they had been assigned. However, Albuquerque water utility bills include a bar chart that compares the billing address water use to the city average. Thus, we would expect most users to be aware of their relative use.

At the start of each round, participants were told their total token budget and the price of water. Prior to making any decisions, the rainfall for that round was determined by a public draw from a bingo cage containing 20 balls. The probability distribution of rainfall was skewed toward less than average rainfall because years of low rainfall present the most pressing policy challenges. Participants were told to consider each round to be a summer month with the rainfall level as given by the draw. However, because even in an average year there may be no rainfall in a single month, participants were told to consider the rainfall as determined by the random draw to be the rainfall for the entire summer in which that month fell. Participants were given copies of Table 1.

At the start of each round of the first set, each participant was endowed with their budget: 25 tokens. A unit of water cost one token, so the relative price was constant at one. Recall that high water users used, on average, 26.5 units of water. Participants were given copies of Table 2 to guide their decisions about water use. Given these amounts and the scaling of the endowment, high water users would have been expected to use all of their tokens to purchase water while other users would be expected to allocate tokens between water and cash. Only the rainfall varied. Each round was a separate event. Participants were not allowed to carry tokens forward, and the results of each round had no effect on participants' options in subsequent rounds. Therefore, we provided no feedback between rounds. Experiment administrators merely collected response sheets and delivered them to assistants in a nearby office who entered the data. As soon as all response sheets had been collected, new sheets were distributed, a bingo ball was drawn indicating rainfall, and participants entered their decisions.

Subsequent sets of the experiment were like the first set, except that economic factors expected to influence water use varied. In the second set, the price of a unit of water varied, but the endowment remained fixed at 25 tokens. In the third set, the endowment varied, but the price remained fixed at one unit per token. In the fourth set, both the price and the endowment varied. In all five rounds of each of the four sets, rainfall was determined by a random draw. The four sets took approximately an hour-and-a-half to complete.

Participation payments were calculated by subtracting the absolute deviation from the predicted use for each type from the endowment in each round. For example, a T2 participant who starts with an endowment of 25 would be expected to use 13 units of water in a normal summer month. If the participant used exactly 13 units, then the payoff would be 25 - [absolute value of 13(actual) - 13(expected)] = 25. As actual water allocation diverged from the predicted water use (in either direction), the payoff declined. Payoffs for each round were totaled and then scaled to increase payment amounts to the promised range of $75-$100. The average payment to participants was approximately $95, which included a bonus for those who returned their presurveys and water bills within 1 week of our sending them out.

V. DATA AND ECONOMETRIC RESULTS

The data set used in the analysis combines data from the experiments, the pre-and postsurveys, the results of a risk task each participant completed that allows us to ascertain participant risk preferences, and up to 84 months of actual water use and pricing information from the City of Albuquerque for each participant.

Tables 3 through 5 present statistics for the participants. Our final data set consists of complete observations for 43 participants (resulting in a total of 3,477 market observations and 860 experimental observations across the 43 participants). Table 3 presents the price, quantity, and budget statistics for both the water bill (market) and the experimental data. The market budget data in the table are based on estimates provided by the participants for their monthly household budget for 2001 and for 1997 and our modifications to those estimates. The time horizon, however, covers the period from January 1994 to December 2000. We assume monthly budgets between 1994 and 1996 to be equal to 1997, while we assume equal incremental changes between 1997 and 2001 (e.g., for a participant who has a $1,000 increase in budget between 1997 and 2001, their budget was increased by $250 per year [$1,000/4] for 1998, 1999, and 2000). The experimental budget is the number of tokens the participant is given at the beginning of each round. Note that this represents a difference between the two data sets.

Quantity refers to the units of water consumed during a month. The price is the average total price per unit, which incorporates both the variable charge per unit, plus a portion of the fixed charge. Average price, rather than marginal was used in this preliminary analysis to be consistent with the experimental design. As a result, a customer using few units faces a higher average price than a customer who consumes more units of water. The quantity measure in the experimental data is participant responses in the experiments. A unit of water was not defined in terms of an actual quantity. The price and budget data are determined by the structure of the experiments.

In addition to the price and quantity data we incorporate other individual, household, water use and conservation characteristics, climate, and timing factors into the analyses. These data are described in Tables 4 and 5. Table 4 presents the descriptive statistics for those variables that are quantitative, whereas Table 5 presents the descriptive statistics for those variables that are qualitative in nature. These variables were chosen, in most cases, for their consistency with the existing literature and availability in our data. One of our objectives is to test for consistency across two data generating processes. However, for some variables we did not have data from both data sources. In those cases, we have matched the variables as closely as the existing data allowed.

The participants are 54 years old on average with a range from just over 29 years of age to 79 years of age. The high average age may be due in part to our requirement that each participant have had a minimum of 5 years of water billing in the Albuquerque area.

The average education level attained by the participants was almost 15 years, but ranged from 12 to 21. The monthly budget reported by participants is $1,923, ranging from $250 to $5,000.

As indicated in Table 5, our sample consisted of approximately 47% women. Most of the participants are Caucasian or Hispanic, reflecting the ethnic composition of the city as a whole. The participants are diverse in their political and religious affiliations. In addition, 79% of participants reported that they attended religious services. Of specific interest to this study a full 72% reported that they consider supply issues when thinking about their water use, while only 12% indicated that they considered price when considering their use levels.

The final information necessary for the econometric analysis is weather data for Albuquerque and the simulated weather data from the experimental games. While the ideal real weather data would include temperature and precipitation for all the measurement locations in Albuquerque, which could then be matched to the zip codes, such detailed data are not available. The best data available were from the reporting station at the Albuquerque International Sunport. Because precipitation varies substantially over the metropolitan area, using a single precipitation measure was not viable. Instead, we opted to use the monthly mean temperature recorded at the Sunport. We chose the temperature data over Sunport rainfall data because, in Albuquerque, temperature varies less among the four quadrants of the city than does rainfall. For the experimental data, the weather data are the draws at the beginning of each round. Of the 60 rounds, 9 were very low rainfall, 17 were low rainfall, 28 were average, and 6 were high rainfall. These data are incorporated into the econometric analysis, discussed in the following section.

VI. ECONOMETRIC ANALYSIS

These data are employed to estimate disaggregated demand functions for both the experimental and the market-generated water bill data. In order to compare results we employed a fixed effects model with a linear specification, which allows for changes in responsiveness across price. This allows us to estimate disaggregated demand functions for both experimental and market-generated water bill data and to statistically test the effects of individual characteristics on demand. That is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [[beta].sub.0] is the intercept term, N refers to the total number of intercept shifters in each estimation. In the market data this would include the qualitative individual and household characteristics, as well as the water use, conservation characteristics, and city quadrant location shifters. The experiment estimation includes these variables as well as the experiment, set, and round estimates. In both estimations, the [p.sub.i] refers to the average per-unit price for water for participant i and [B.sub.it] refers to the individual's budget. (5) [X.sub.ij] denotes the j-length vector of quantitative variables for participant i in each of the two estimations. These are similar across the two estimates with some exceptions. Both include age, level of educational attainment in years, years lived in house, and household size. The market data estimation also includes the climate variable temperature and a monthly categorical variable. The last variable, t, is the time trend included in the market data estimation in order to account for any exogenous changes in the market. The experimental estimates do not include monthly or time trends. In both cases, we assume a random error term, e, with a zero mean.

The results of the two estimations are presented in Table 6. Variable and coding detail are provided in Appendix S1 (Supporting Information) and additional results are shown in Appendix S2. Columns two through four present the water bill and market data results and columns five through seven present the experiment data results for variables of interest. In each case, the parameter estimate, the standard error, and the p value are presented. (6) The last two columns present the mean for water bill and market data and experimental data, respectively.

We find price, budget, and education to be significant in both regression results. In addition, we find religious, political, and some water use or attitude factors significant. In the case of the function estimated from water bill data, several of the estimates for months are statistically significant and the signs and magnitudes are consistent with what we would expect. That is, water use in the summer months is high, while February, historically the month with the lowest water consumption, has low water use. These results are consistent with other disaggregated demand studies in the literature.

In comparing these results, we note that the experimental results are based on 860 observations for the 43 participants, compared to the market-based water bill results that have 3,477 observations for the same 43 participants. There are some caveats, which need to be made concerning the results. First, given that the demographic variables do not change over time or rounds, this potentially reduces the variation across distinct observations (i.e., someone who is a Native New Mexican in a given round or year will still be a Native New Mexican in a subsequent round or year). Given this, we would expect the parameter estimates for the non-demographic variables to be relatively robust. Second, given the larger sample for the market-based results, we expect these results to be more robust than those for the experimental results. For example, while the parameter estimates on price are statistically significant and negative for both results, there is a difference in the magnitude. There are a number of factors that could contribute to this result. However, disentangling these is beyond the scope of this paper and is an interesting topic for future research. Nonetheless, the quality of the experimental results in echoing the market-based results is good, as supported by our hypotheses tests in the next section. (7)

VII. HYPOTHESES TESTS

Employing the econometric results, we test a series of three interrelated hypotheses. These hypotheses are structured such that the higher numbered hypotheses are tested conditional on non-rejection of lower-numbered hypotheses.

H1 : The same characteristics that are related to water use in the water bill and market data are related to water use in the experiment data.

H2 : The characteristics that are negatively correlated with water use in the water bill data are negatively correlated in the experiment data, and those that are positively correlated in the water bill data are positively correlated in the experiment data.

H3: The magnitudes of the estimated elasticities are consistent across the experimental and water bill results.

Our first hypothesis is that variables that are statistically significantly associated with water demand in the market data are also statistically significantly associated with water demand in the lab. Our null hypothesis is therefore

[H.sub.0]: [beta]'.sub.i] and [[beta]".sub.i] are both statistically significant.

where [[beta]'.sub.i] refers to the parameter estimate on the ith variable from the market data function and [[beta]".sub.i] refers to the parameter estimate on the same ith variable from the experiment data function. This hypothesis addresses a central concern of this paper. Are the determinants of behavior in the laboratory comparable to those in the market? Of 33 comparable variables used in both regressions, 20 were significant in both and five were insignificant in both. Thus, almost 76% of the comparable independent variables exhibit consistent statistical significance for both the laboratory and water bill data results comparisons.

Table 7 lists the 20 variables for which the null from Hypothesis 1 is not rejected. Note that while actual temperature and the climate variables from the experimental data are not directly comparable, we consider them to be proxies for each other, and find that they are positively correlated with water use.

Focusing solely on the factors in Table 7, we consider whether these variables influence the demand for water in the same direction. Thus the null hypothesis for Hypothesis 2 is

H0: The signs on significant [[beta]'.sub.i] and [[beta]".sub.i] are the same.

The parameter estimates in Table 7 include a "plus" or "minus" sign after them. If there is a single sign, this indicates the same direction of impact for both the water bill and the experimental data. In the two cases for which there are two signs, the first sign refers to the water bill results and the second refers to the experimental results. Those two cases are having a drip irrigation system and owning a swimming pool. In the water bill data, households with drip systems and pools tend to use less water, all else equal. Only one participant in our sample had a pool and so little inference can be drawn from the result. In the case of drip irrigation systems, the negative sign in the water bill results is as expected. Drip irrigation systems use water more efficiently than do other irrigation systems. The positive sign in the experiment data is inexplicable.

Of the 20 statistically significant variables, we find 17 for which the second null hypothesis cannot be rejected. In addition, the results for temperature and the climate variables are consistent in their direction of impact. In Albuquerque, high summer temperatures are associated with dry weather, while lower temperatures are observed during the monsoon, or rainy season. Thus higher temperatures in the market data are hypothesized to have the same direction of influence as lower precipitation in the experiment data. Ninety percent of the statistically significant variables have the same direction of impact.

This leads to the third hypothesis, which is that the influence of variables in the lab are similar in magnitude to the influence of those same variables in the market. Thus the null hypothesis is that

H0: The magnitude of the elasticities estimated using water bill data are consistent with the magnitude of the elasticities estimated using laboratory data.

We test this by first estimating each participant's elasticity of demand for each water bill and each laboratory observation. The average individual experimental elasticity was -0.60, while the market average was -0.75. These means are statistically indistinguishable and are consistent with estimates from the literature (Brookshire et al. 2002 for a review). Using the data for each participant, we perform a t-test across their water bill and their experimental results. We find no statistical difference in elasticities for 30 of the 43 participants. That is, for approximately 70% of participants their estimated experimental elasticity is statistically indistinguishable, at the 90% confidence level, from their estimated market elasticity. Thus, there is no significant difference in their response to price changes. The water bill data were generated by households over a multiple-year period, while the lab data were generated in a single evening by an individual participant imagining his or her household's water use under different economic and weather conditions. Despite these differences, we find remarkable similarities in estimates of water demand.

VIII. IMPLICATIONS AND CONCLUSIONS

This study compares individual consumer water demand estimates generated experimentally with water demand estimates using observed market data. We test the consistency between ex ante water bill data and data generated in an artificial laboratory environment. The water bill data are unaffected by experiment participation. When the participants made their household consumption choices they could not have anticipated that their data would one day be used in this investigation.

We test response correspondence through the results of three related hypothesis tests: independent variable significance, direction of impact, and magnitude of impact. Twenty-five or 75% of the independent variables exhibited consistent statistical significance across the data sets, and in all but two of those the direction of impact was the same. Finally, for approximately 70% of the participants, the elasticity of demand is statistically equivalent across the market and experiment data. Thus, the observed market data provides support for the experimental approach to data generation.

It follows that experiments may provide information where little or no market data or behavioral understanding exists. In the case of water, the good in question cannot be literally delivered (or denied) in the experiment and so participant responses are, on some level, hypothetical. Yet understanding consumer response is critical to policy makers. Residential water is not bought or sold in competitive markets; municipalities or their agents typically set the price of water often in a politically charged setting. These features of the commodity and the institutions surrounding its provision limit the availability of market data and the ability of researchers to reproduce the market experimentally.

As is true of all experiments, our participants arrived at the lab with unobservable preferences. We did, however, have some information about market choices they had made previously, both in investments that would tend to increase or reduce their water use and in the amount of water they had used in the past. This information allowed us to design salient payoffs even though we could not deliver (or constrain the use of) actual water in the lab. Under those conditions, we find that experiment responses parallel ex ante market behavior. Experiments that look backward at prior market behavior may provide valuable insight looking forward--to consumer response to prices, situations, or policies that do not yet exist.

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SUPPORTING INFORMATION

Additional Supporting Information may he found in the online version of this article:

Appendix S1. Variable definitions.

Appendix S2. Remaining econometric results.

ABBREVIATIONS

LM: Lagrange Multiplier

NE: Northeast

NW: Northwest

SE: Southeast

SW: Southwest

VIF: Variance Inflation Factor

doi: 10.1111/j.1465-7295.2011.00419.x

(1.) See, for example, Rogers (1994), Iannaccone (1998), Stark Iannaccone, and Finke (1996), Roth et al. (1991), Eckel and Grossman (1996), Andreoni and Vesterlund (2001), Chermak and Krause (2002), and Krause, Chermak, and Brookshire (2003).

(2.) Copies of the survey instruments and the experimental protocol are available upon request from the authors.

(3.) Personal communication with K. Yuhas, Water Conservation Officer, City of Albuquerque (06/03/08).

(4.) The t-statistic for the T1 versus T2 test is -3.61; for the TI versus T3 test the t-statistic is -5.21, and for the T2 versus T3 it is -2.48, with critical t values of 2.20, 2.10, and 2.06, respectively.

(5.) The experimental budget for each participant i is specific to the round and the set, so the complete representation for the experimental estimation would be [[beta].sub.sri] where s refers to the set and r refers to the round in the set. We suppress this notation in the text.

(6.) Standard tests were employed. Durbin Watson statistics indicated first-order autocorrelation in both models and so feasible generalized least squares was employed. An iterative Prais-Winsten algorithm was used in the corrections.

(7.) To determine if the demographic variables that are individually insignificant are also jointly insignificant, we conduct a test restricting the parameters estimates to be jointly zero ([beta](i)= 0, where i = 1, ..., n are the statistically insignificant parameter estimates). The distributed Lagrange multiplier (LM) statistic for each regression leads us to reject the null. Estimated variance inflation factor (VIF) statistics for individual variables range from about 1 to slightly less than 10 in either regression. The LM and VIF results indicate correlation between groups of variables. Therefore, we have opted to include individually insignificant variables rather than to remove some, which could introduce contemporaneous correlation bias via omitted variables.

JANIE M. CHERMAK, KATE KRAUSE, DAVID S. BROOKSHIRE and H. STU BURNESS *

* This material is based upon work supported by SAHRA (Sustainability of semi-Arid Hydrology and Riparian Areas) under the STC Program of the National Science Foundation, Agreement No. EAR-9876800. Opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of SAHRA or of the National Science Foundation. I. Abibova, J. Little, A. Kaminsky, J. Clark, and G. Kervin assisted with experiment administration. We'd also like to thank M. Ewers for research assistance, J. Witherspoon for providing background on the Albuquerque Water Utility, and the City of Albuquerque for providing the market data.

Chermak: Professor, Department of Economics, University of New Mexico, Albuquerque, NM 87131. Phone 505277-4906, Fax 505-277-9445, E-mail [email protected]

Krause: Professor, Department of Economics, University of New Mexico, Albuquerque, NM 87131. Phone 505-2773429, Fax 505-277-9445, E-mail [email protected]

Brookshire: Professor, Department of Economics, University of New Mexico, Albuquerque, NM 87131. Phone 505-277-1964, Fax 505-277-9445, E-mail [email protected]

Burness: Professor Emeritus, Department of Economics, University of New Mexico, Albuquerque, NM 87131. Phone 505-277-5304, Fax 505-277-9445, E-mail [email protected]

TABLE 1
Determination of Rainfall

If the Number Rainfall This
Drawn Is Round Is

1, 2, or 3 Very low
4, 5, 6, 7, or 8 Below average
9, 10, 11, 12, 13, 14, 15, 16, or 17 Average
18, 19, or 20 Above average

TABLE 2
Water Use Ranges per Round

 Ranges of Water
Water Use Use per Round

Maintaining a lush lawn during a 14-18 units
 very dry season
Maintaining a lush lawn during an 8-12 units
 average season
One car-washing 1-2 units
Average monthly laundry, 3-5 units
 dishwashing requirements
Average household personal use 2-4 units
 (e.g., showers, cooking, drinking)

TABLE 3
Price, Quantity, and Budget Descriptive Statistics

 Market Data Statistics

 Standard
Variable Mean Minimum Maximum Deviation N

Quantity 15.2 0.0 378.0 15.7 3,477
Price 1.95 0.0 16.81 1.24 3,277
Budget 1821 100 5000 1,135 3,277

 Experimental Data Statistics

 Standard
Variable Mean Minimum Maximum Deviation N

Quantity 13.3 0.5 40.0 5.8 860
Price 1.80 0.5 5.0 1.39 860
Budget 35.25 20 90 20.35 860

TABLE 4
Quantitative Descriptive Statistics from Surveys

 Standard
Variable Mean Minimum Maximum Deviation N

Age (years) 54.3 29.8 79.0 12.5 43
Education (years) 15.0 12.0 21.0 2.3 43
Household size (people) 2.25 1.0 6.0 1.2 43
Years lived in current 12.2 0.0 50.0 12.8 43
 home (if owned)

TABLE 5
Qualitative Descriptive Statistics

 Percentage of
Variable Participants

Personal and household characteristics
 Male 53
 Native Albuquerquean 26
 Own your home? 81
Ethnicity
 Anglo 69
 Hispanic 26
 Native American 5
Religious affiliation
 Catholic 30
 Protestant 53
 Non-denominational Christian 2
 Other religious affiliation 7
 Did not report religious 7
 affiliation
 Attend religious services 79
 regularly
Political affiliation
 Democrat 44
 Republican 37
 Independent 7
 Other political affiliation 7
Risk preferences as determined by lottery
 task
 Risk averse 26
 Risk neutral 39
 Risk seeking 35
Water use and conservation considerations
 Received low flow toilet 7
 rebate
 Received landscape rebate 2
 Low flow showers in house 43
 Low flow toilets in house 56
 Automatic sprinklers in yard 30
 Drip irrigation system in yard 23
 Have pool 2
 Consider supply of water 72
 when making use decisions
 Consider price of water when 12
 making use decisions
 Cannot cut back water use 16
 NE quadrant 45
 NW quadrant 13
 SW quadrant 7.5
 SE quadrant 32

TABLE 6
Econometric Results

 Market Data Results
 (N = 3,477)

 Standard p[[absolute
Variable Coefficient Error value of Z] > z]

Price -2.037 * 0.181 0.000
Budget 0.004 * 0.001 0.000
Age 0.050 0.059 0.399
Education -1.210 * 0.418 0.004
Gender (Male = 1) 3.102 ** 1.568 0.048
Household Size 6.276 * 1.076 0.000
Native Albuquerquean 6.447 * 1.904 0.001
Own home -12.992 * 2.527 0.000
Years there -0.069 0.045 0.127
Hispanic -1.918 1.931 0.321
Native American -6.159 * 2.409 0.011
Protestant 11.096 * 2.216 0.000
Non-denominational 10.998 ** 4.285 0.010
Other religion 0.520 2.876 0.856
DNR religion 5.357 ** 2.557 0.036
Attend services? -0.271 1.687 0.872
Republican -12.545 * 2.130 0.000
Independent -0.238 3.535 0.946
Other political -20.683 * 5.921 0.001
 affiliation
DNR political affiliation -10.346 * 2.234 0.000
Risk averse 0.477 1.737 0.784
Risk seeking 7.386 * 1.667 0.000
Low flow toilet rebate -1.329 1.803 0.461
Landscape rebate -7.553 5.032 0.133
Low flow shower 2.679 1.645 0.104
Low flow toilet rebate -1.185 *** 0.654 0.070
Automatic sprinklers 16.102 * 1.452 0.000
Drip irrigation -3.350 ** 1.686 0.047
Pool -8.627 *** 4.860 0.076
Consider supply 5.597 ** 2.219 0.012
Consider price 20.587 * 3.222 0.000
Temperature 0.166 * 0.048 0.001
Very low n.a n.a. n.a.
Low n.a n.a. n.a.
Average n.a n.a. n.a.
Northwest -2.786 2.383 0.243
Southwest -22.514 * 4.456 0.000
Southeast 1.629 2.417 0.500
Constant 1.778 6.692 0.790
Rho 0.550 0.014 0.000

 Experimental Data Results
 (N = 860)

 Standard P[[absolute
Variable Coefficient Error value of Z] > z]

Price -2.811 * 0.170 0.000
Budget 0.143 * 0.015 0.000
Age 0.029 0.035 0.404
Education -0.288 *** 0.177 0.101
Gender (Male = 1) 3.869 * 0.698 0.000
Household Size 0.117 0.476 0.806
Native Albuquerquean 2.363 ** 0.952 0.013
Own home -4.675 * 1.236 0.000
Years there -0.057 ** 0.024 0.015
Hispanic 1.169 1.210 0.334
Native American -1.147 1.213 0.345
Protestant 6.243 * 1.145 0.000
Non-denominational 3.501 ** 2.161 0.105
Other religion 2.518 *** 1.430 0.078
DNR religion 6.994 * 1.357 0.000
Attend services? 2.537 ** 1.024 0.013
Republican -2.977 * 0.890 0.001
Independent -9.976 * 1.737 0.000
Other political -4.372 *** 2.521 0.083
 affiliation
DNR political affiliation -5.363 * 1.007 0.000
Risk averse 3.084 * 0.809 0.000
Risk seeking 2.737 * 0.826 0.001
Low flow toilet rebate n.a n.a. n.a.
Landscape rebate n.a n.a. n.a.
Low flow shower -0.041 0.792 0.958
Low flow toilet rebate -0.511 0.322 0.113
Automatic sprinklers 1.434 ** 0.717 0.046
Drip irrigation 2.053 ** 0.792 0.010
Pool 7.806 * 2.414 0.001
Consider supply 2.534 * 1.085 0.020
Consider price 8.152 * 1.435 0.000
Temperature n.a n.a. n.a.
Very low 3.654 * 0.609 0.000
Low 3.773 * 0.510 0.000
Average 1.015 *** 0.539 0.060
Northwest -0.445 1.316 0.735
Southwest -3.123 *** 1.626 0.055
Southeast -2.012 1.253 0.108
Constant 6.849 *** 3.226 0.034
Rho 0.253 0.033 0.000

 Mean Value ([bar.X])

Variable Market Experimental

Price 1.950 1.800
Budget 1821.096 35.250
Age 50.680 54.273
Education 14.909 14.965
Gender (Male = 1) 0.518 0.535
Household Size 2.231 2.256
Native Albuquerquean 0.266 0.256
Own home 0.826 0.814
Years there 12.614 12.198
Hispanic 0.266 0.256
Native American 0.048 0.047
Protestant 0.517 0.535
Non-denominational 0.024 0.023
Other religion 0.072 0.070
DNR religion 0.072 0.070
Attend services? 0.784 0.791
Republican 0.387 0.372
Independent 0.053 0.070
Other political 0.024 0.023
 affiliation
DNR political affiliation 0.097 0.090
Risk averse 0.266 0.256
Risk seeking 0.325 0.349
Low flow toilet rebate 0.067 --
Landscape rebate 0.005 --
Low flow shower 0.441 0.442
Low flow toilet rebate 0.936 0.953
Automatic sprinklers 0.295 0.302
Drip irrigation 0.248 0.256
Pool 0.024 0.023
Consider supply 0.728 0.721
Consider price 0.121 0.116
Temperature 58.054 --
Very low -- 0.150
Low -- 0.286
Average -- 0.470
Northwest 0.095 0.093
Southwest 0.054 0.070
Southeast 0.193 0.186
Constant -- --
Rho -- --

Note: DNR, did not report.

* Significant at 1%; ** significant at 5%; *** significant at 10%.

TABLE 7
Statistically Significant Variables and Direction of Impact

Variable

Economic
 * Price (-)
 * Budget (+)

Demographic
 * Education (+)
 * Gender (1 if male) (+)
 * Native Albuquerquean (+)
 * Own home (-)
 * Protestant (+)
 * Non-denominational Christian (+)
 * Did not report religious affiliation (+)
 * Republican (-)
 * Other political affiliation (-)
 * Did not report political affiliation (-)

Technology
 * Automatic sprinklers (+)
 * Drip irrigation (-/+)
 * Pool (-/+)

City quadrant
 * Southwest (-)

Attitudes
 * Consider supply (+)
 * Consider price (+)

Risk preferences
 * Risk seeking (+)

Climate
 * Average temperature (market data) (+)
 * Very low precipitation (experimental data) (+)
 * Low precipitation (experimental data) (+)
 * Average precipitation (experimental data) (+)