Natural and incentive-induced conservation in voluntary energy management programs.

I. Introduction

Energy conservation is a topic of worldwide importance. In addition to the prospect of depleted nonrenewable supplies, increased concern over environmental issues, such as air pollution and global warming, have contributed to the interest in energy conservation. The U.S., as the largest per capita user of energy, has taken the lead in promoting conservation and pollution abatement, through incentive and regulation. This climate has led to an important development in the utility industry in the last few years: the growth of "demand-side management" (DSM) programs. These voluntary programs are designed to induce the adoption of energy efficient technology (new capital) by consumers (both residential and commercial/industrial).

DSM is advocated by utility regulators, who cite factors such as the divergence of the private and social short run costs of energy (due to, e.g., the existence of environmental externalities), and the fact that the price of energy is not equal to its long run marginal cost. This means that the cost of implementing these programs may be below the cost of increasing capacity. In addition, some DSM programs are designed to flatten the load curve (power demand over time), since the cost of producing power at peak load is considerably greater than at times of normal system demands. For the consumer, it is argued that there are market imperfections which prevent adoption of energy efficient measures. These imperfections are usually attributed to the consumer's lack of knowledge concerning energy efficient technology.

Total revenue lost by the utility from a DSM program is the sum of the direct incentive cost, returned to the consumer, and the value of any lost sales. These costs may be offset by any efficiency gains in production, especially during periods of peak demand. In order to preserve the stockholders' rate of return in these regulated companies, this revenue loss is usually recovered by an increase in utility rates. To warrant this, utilities must present evidence of lost revenue due to energy savings to their regulatory commissions. These programs are becoming so large and wide-spread that by the turn of the century, it is expected that they will cost utilities over two billion dollars annually [6].

Lewis and Sappington [7] have examined the role of information for optimal regulatory policy with respect to firms offering DSM programs. They assume that firms have better information about the effect of the programs than the regulators. If the firms have good information, regulators can motivate firms to use their superior knowledge to achieve socially optimal outcomes.

Of obvious importance, then, is the estimation of the reduction in energy use resulting from these programs. This is a formidable task, as there are a number of economic and econometric problems that arise. First, the programs are voluntary - in most states by law no controlled experiments can be performed. This means that those who participate are a nonrandom sample of the population, and unless a complete model of program participation and energy savings is formulated, estimates of program savings will suffer from sample selection bias [4; 5]. Second, variable measurement is difficult, as desired conservation behavior does not necessarily equal observed conservation behavior. This means that data sets will be characterized by endogenous variables that are truncated and polytomous. Third, energy efficient capital is lumpy by nature. This means that only some households or firms faced with a reduction in the price of capital due to the DSM program will purchase new equipment. These corner solutions or lack of response smoothness make estimation difficult.

But perhaps the most important problem is that, during any observation period, a certain amount of natural conservation takes place. This conservation, concurrent with but unrelated to the DSM program confounds attempts to measure the true effect of the program. The purpose of this paper is to analyze a method of decomposing measured conservation into a natural component and an incentive-induced component. This will be done in a complete model of energy conservation and energy use that eliminates the sample selection bias due to the voluntary nature of the programs, while at the same time properly treating the truncated and polytomous variables that arise. Moreover, we propose a common statistical framework for estimating savings for the three most widely adopted (residential) DSM programs. The important observation that allows this decomposition is the fact that, in any random sample of consumers both program participants and others, unaware of the available incentives, have undertaken conservation action. Therefore, despite the fact that a controlled experiment is not possible, this form of natural experiment allows the decomposition of energy savings.

Our model and methodology is widely applicable. As another environmental example, to conserve rapidly depleting clean groundwater sources, water utilities have started to offer incentives to reduce its use (such as free low-flow shower heads). In any location where water is metered and households are billed, natural conservation may take place. The effectiveness of the program then depends upon incentive-induced savings. But the model is even more general. Consider a firm that offers workers incentives to take training. Some workers may have decided to add to their human capital without firm incentive, but these "free riders" will be counted in an evaluation of the training program.

We utilize an enriched sample of program participants and nonparticipants from a large midwestern utility. The data are of high quality as actual billing records from the utility provide information on energy use. The dependent variable in the analysis, therefore, is not subject to either measurement or reporting error, as would be the case with survey data.

The next section outlines a behavioral model for taking conservation action and for energy use. Section III describes the data and presents empirical estimates. In section IV the estimated parameters of the model are used to simulate program-induced conservation in different incentive scenarios. The last section concludes.

II. An Econometric Model of Conservation Behavior and Energy Use

Consider a two-equation model of energy conservation behavior and energy use.(1) The first equation determines whether or not any energy conservation action (purchase of new capital equipment) is taken as well as the amount of conservation action. The observed amount of energy conservation action will not necessarily equal the desired amount, for several reasons. First, some conservation action, such as ordering a home energy audit or purchasing energy efficient appliances, is lumpy by nature. Second, it is conceivable that some households would prefer to dissave energy, that is, if it were possible they would make their homes less energy efficient and claim the capital cost difference in other goods. This is not usually possible, which means that when desired action is negative observed conservation action is zero. Therefore, depending upon the program being analyzed, observed conservation action could be dichotomous (home energy audit program), polytomous and ordered (appliance rebate program), or bounded nonnegative (subsidized loan program). That is, in the audit program, households are observed to have their homes inspected for possible conservation measures, or not to order such an audit. In the rebate program, they may do nothing, or purchase any of a discrete menu of appliances in increasing degree of efficiency (and cost). In a subsidized low-interest loan program, households may borrow money to install new equipment (but they cannot sell any existing equipment to reduce their energy efficiency).

Let [Mathematical Expression Omitted] be the per-period, desired amount of conservation action. This is the result of a utility maximization calculation over the price of energy, other goods, and the utilities associated with the consumption of the services of energy and other goods. Let [x.sub.1] be a column vector of individual, household, and housing characteristics that affect the benefits and costs of undertaking energy conservation. Let z be a column vector of program characteristics, such as the amount of a subsidy for a home energy audit or the interest rate buy-down in a loan program. Desired conservation is assumed to be a linear function of [x.sub.1] and z:

[Mathematical Expression Omitted],

where [[Beta].sub.1] and [Lambda] are unknown row vectors of parameters to be estimated and [[Epsilon].sub.1] is a random disturbance symmetrically distributed about zero, assumed to be uncorrelated with [x.sub.1] and z. Equation (1) forms the basis for the analysis of natural conservation. Some households, unaware of a utility-sponsored incentive, undertake conservation.(2) This natural conservation is undertaken, for many reasons: as new, energy efficient products become available; due to changes in relative prices; and due to changes in tastes for the services of energy. In the absence of, or unaware of utility-sponsored incentives, households have desired, expected conservation action equal to [[Beta].sub.1][x.sub.1]. The program is responsible for the marginal desired conservation action, [Lambda]z. Put another way, households are assumed to be in long run equilibrium with respect to their expenditures on the capital equipment that produces the services of energy (such as heating/cooling equipment), and in short run equilibrium with respect to their budget shares for energy and other goods. Additional (marginal) conservation is then undertaken as a result of the reasons suggested above, and the introduction of incentives (z) that change the budget set faced by households. When utility companies introduce a savings program, households may no longer be in long run equilibrium. Any marginal conservation undertaken is then attributed to the program.

Let the demand for energy be [y.sub.2]. Our focus here is on the effect on energy demand of conservation action. The price of electric energy and the prices of alternative sources of energy, traditionally part of a demand analysis, do not vary from household to household. In addition, at the level of usage of most households, the rate structure is flat. Our data are from 1989, during a period of constant (or slightly declining) energy prices, especially for the utility used here. Moreover, this is during a period of very moderate general price inflation, so that price expectations should play little role in household decisionmaking. Energy demand, therefore, is modeled as a function of the amount of conservation action taken as well as the appliance stock, number of family members and household usage patterns. Let [y.sub.1] be actual conservation action taken, and let [x.sub.2] be a vector of the remaining variables. These may be a subset of, or contain [x.sub.1]. A linear or loglinear model of energy use (the "conditional demand" model of Pard and Parti [11]) is

[y.sub.2] = [[Beta].sub.2][x.sub.2] + [Gamma][y.sub.1] + [[Epsilon].sub.2], (2)

where [[Beta].sub.2] is a (row) vector of conditional demand parameters, [Gamma] is a scalar parameter that measures the effect of conservation action on energy consumption, and [[Epsilon].sub.2] is a random disturbance, assumed uncorrelated with [x.sub.2] but possibly correlated with [[Epsilon].sub.1], and hence [y.sub.1]. Note that actual conservation, [y.sub.1], and not desired conservation, [Mathematical Expression Omitted], determines energy use. For identification the vector [X.sub.1] must contain one variable not included in [x.sub.2]. Equations (1) and (2), together with a rule for determining actual conservation from desired conservation, constitute the behavioral model with which we will evaluate program-induced and natural energy savings from conservation.

Desired conservation, [Mathematical Expression Omitted], is not observed, but what is observed is whether or not a household took action and, depending upon the program, the extent of the action taken. The way in which desired conservation is observed will depend upon the particular program. We consider in this paper three of the most commonly available residential energy conservation programs: home energy audits; energy efficient appliance rebates; and low interest loans for energy conservation. This is a natural order of analysis, following our earlier paper [9]. The three programs are ordered by the amount of information available to the analyst. In the audit program, only the fact that a household ordered an energy audit is known. The extent of conservation action, if any, is not known. In the rebate program, the choice of appliance, and hence the efficiency rating of the appliance, is known. This is ordinal information on the amount of desired conservation and the exact amount of conservation action actually undertaken. In the loan program, the amount of a loan, which is the amount of desired conservation, is known, and it is assumed that actual conservation, when it is greater than zero, is proportional to the amount borrowed.

Audit Program

Consider first an audit program. What is typically known is whether or not a household had an energy audit, and not what, if anything, was done after learning the results of the audit.(3) Define the dichotomous variable [y.sub.1] such that

[Mathematical Expression Omitted].

That is, [y.sub.1] is defined to be equal to one if the household had an audit, and zero if not. An audit is ordered if the household desires to do any conservation action. A utility-sponsored audit program usually takes the form of a free or reduced cost audit. Therefore, the incentive for undertaking conservation action in equation (1), z, is a scalar, the cost reduction offered by the program.

The probability of a household taking action with the program in place is given

[Mathematical Expression Omitted],

where F([center dot]) is the cumulative distribution function of the (symmetric) random variable [[Epsilon].sub.1]. The probability that a household will take action without the program is equal to

[Mathematical Expression Omitted].

This is a measure of the natural conservation probability. The program effect on the probability of taking conservation action is equal to the difference,

[Mathematical Expression Omitted].

If the program is indeed an inducement to taking conservation action then [Lambda]z is necessarily positive, implying D([x.sub.1], z) [greater than] 0. Note that this is the discrete analog to predicting the change in the dependent variable resulting from a change in an explanatory variable in conventional regression analysis. The program effect on desired conservation, [Mathematical Expression Omitted], is [Lambda]z, from equation (1). The expression for D arises simply because the probability of taking action is a nonlinear function of [Lambda] and z.

To calculate natural and program-induced energy conservation consider equation (2). Expected energy use is

[Mathematical Expression Omitted],

where the second equals sign is based on equations (1) and (3) and the third equals sign is by substitution from equation (5). Expected energy use without incentive (i.e., natural conservation) is given by

[Mathematical Expression Omitted].

The program effect on energy use is given by the difference:

[Mathematical Expression Omitted].

Rebate Program

In an appliance rebate program, different rebates are given for the purchase of appliances with different efficiency ("SEER") ratings, the more efficient the appliance the higher the rebate. Therefore the incentive faced by the household is a vector of the rebate levels. Consider a program with two rebate levels, one for an appliance that uses [c.sub.1] less energy than the average appliance, and a second rebate level for an appliance that uses [c.sub.2]([c.sub.2] [greater than] [c.sub.1]) less energy. A plausible model of appliance adoption in this case is given by

[Mathematical Expression Omitted]

where [a.sub.1] and [a.sub.2] are unknown threshold points. If desired conservation is less than al, no conservation action is undertaken. If desired conservation falls between the two threshold points, the lesser amount of conservation action is undertaken, while if the household's desired conservation is greater than [a.sub.2] the larger of the two conservation measures is undertaken. The threshold points can be estimated along with the parameters in the [Mathematical Expression Omitted] equation.

Expected conservation under this rebate program is:

[Mathematical Expression Omitted].

Similarly, expected natural conservation (efficient appliance purchase without incentive) is

[Mathematical Expression Omitted].

The difference between equations (12) and (11) is the expected conservation due to the program. It can be written

[Mathematical Expression Omitted],

where D([x.sub.1], z), defined in the audit program, is the increase, due to the program, in the probability of doing any conservation and [D.sub.a]([x.sub.1], z) = F([a.sub.2] - [[Beta].sub.1][x.sub.1]) - F([a.sub.2] - [[Beta].sub.1][x.sub.1] - [Lambda]z) is the increase, due to the program, in the probability that the greater amount of conservation will be undertaken. Since [c.sub.1], D, and [D.sub.a] are all positive and [c.sub.2] [greater than] [c.sub.1], the program must increase conservation. The first term on the right hand side of equation (13) is the increased savings from the effect of the program influencing nonconservers to purchase the first level efficient appliance, and the second term is the program's effect on moving those that would save from the first level to the second level.

Loan Program

In a subsidized loan program, households purchasing energy conservation equipment are given loans at below market rates. Therefore, the vector z contains the interest reduction schedule appropriate to the program. Households wishing to conserve energy buy insulation, etc., according to the equation

[Mathematical Expression Omitted].

Only the desired amount of energy conservation is observed - the desired amount of dissaving of energy is not known.

Observed spending on energy conservation with a loan program in place will estimate

E([y.sub.1]) = ([[Beta].sub.1][x.sub.1] + [Lambda]z) Pr[[[Epsilon].sub.1] [greater than] -([[Beta].sub.1][x.sub.1] + [Lambda]z)] = ([[Beta].sub.1][x.sub.1] + [Lambda]z) F([[Beta].sub.1][x.sub.1] + [Lambda]z) (15)

[TABULAR DATA FOR TABLE I OMITTED]

while in the absence of any incentives expected spending would be

[Mathematical Expression Omitted].

This is the natural conservation. In this case both the size and the probability of undertaking any natural conservation is different without a program. The difference between equations (16) and (15) is the expected expenditure on conservation due to the program. It can be written

[Mathematical Expression Omitted]

where D([x.sub.1], z) is defined as in the audit program. The first term on the right hand side of the equation is the product of expected natural conservation and the incremental probability of saving, due to the program, while the second term is the product of incremental saving and the probability of saving under a program. As was the case for the audit and rebate programs expected energy savings is simply [Gamma] times this difference.

The formulas for the decomposition of total energy savings into natural and program-induced components for all three programs are presented in Table I.

III. Data, Estimation, and Empirical Results

The data used to estimate the parameters of the model and decompose energy conservation represent an advantageous combination of market data, the actual energy used by households, merged with demographic and attitudinal variables from surveys. This combination is unusual and with it the problem of self-reported consumption information that plagues demand studies is avoided. For each of the three programs separately offered to consumers, a mail survey was conducted of a random sample who had participated in a program to collect housing characteristics and demographic data. This sample was enriched by similarly surveying a random sample of nonparticipants. Since the combined set of observations is not, therefore, a random sample of the population, weighting is necessary for consistent estimation. We used the weighted exogenous sampling maximum likelihood (WESML) estimator introduced by Manski and Lerman [8], adapted to the conservation models used here by Ozog and Waldman [10]. From utility billing records monthly electricity (kWh) consumption for both groups was merged with the survey data, as well as program tracking data, which provided details on the actions undertaken by participants as part of the program.

The audit program was designed to offer advice tailored to individual customer needs. The audit consisted of either an analysis of a single conservation measure, a walk-through audit, or a computerized analysis of the home, calculating the simple payback for each conservation option. The cost of this service, which would normally be about $50, was given free to participating customers. The appliance rebate program was designed to provide incentives to encourage customers to choose more efficient technologies when purchasing appliances. During 1989 (the target year), residential customers were eligible for rebates on several appliances which included refrigerators (which account for approximately 20% of residential electricity consumption), room air conditioners, and electric water heaters. The refrigerator rebate program is analyzed here, where two rebate levels of $25 and $50 were offered. The loan program offered financial assistance to residential customers. A customer could borrow as little as $750 or as much as $5,000. The assistance consisted of an interest rate buy-down (of 2.5%), no money down, no collateral needed, and up to 60 months to repay the loan.

The key variable in the conservation adoption equation is the incentive offered by the utility. This is the program inducement, the reduction in price associated with conservation when done under the program. Incentive in the audit and rebate programs is the value of the incentive relative to income, if the household was aware that an incentive was being offered. In the loan program Incentive is the loan buy-down rate, again if the household was aware of the program. If the household was unaware of the program, the incentive variable was zero, as the household perceived that it must bear the total cost of conservation. The statistical decomposition of energy savings into natural and program-induced components depends upon the existence of households that conserved without any program. Utilities are required by their public service commissions to market conservation programs to all their customers (that is, they are not allowed to experiment). It is, therefore, crucial to this analysis that some households are unaware of the existence of a utility-sponsored conservation program, and that the program is marketed to customers in such a way that this variable is exogenous. For our purposes, it is fortunate that the marketing of DSM to customers is done in a way that leaves a substantial number of customers unaware of the program. In our data, 38%, 23%, and 30% of those in the supplementary random samples were unaware of the audit, rebate, and loan programs, respectively. Because of the importance of this variable, we now examine the question of its exogeneity.

Marketing of DSM programs is typically done through billing envelope inserts, and occasionally through media advertising. It may be reasonable to assume that a random sample of the population of utility customers takes the time to read the advertisements in their billing envelope, or happens to be exposed to the media advertising. On the other hand, it may be that customers who know of the programs are more educated, more energy conscious, or are looking for opportunities to conserve energy. This would call into question our identifying information: the exogeneity of the awareness status of each household. To examine this question we did two things. First, in Tables II and III we present descriptive statistics for all three programs on the full sample and the subsamples of aware and unaware households. Table II shows that for each program, there is little difference in the mean values of the exogenous variables between individuals aware of the program and individuals unaware of the program. In fact, for most variables the mean values are nearly identical, in the sense that differences are typically in the range of one-third to one-tenth of one standard deviation. In addition, differences seem to be somewhat randomly distributed across programs. For example, those unaware of the availability of reduced cost audits have higher incomes than those aware of the incentive, while the situation is reversed for the other two programs. As another example, for the audit subsamples those unaware are more likely to use electricity for space heating but less likely to use electricity for water heating. Energy use differences fall in the one-third to one-tenth of one standard deviation range, but since energy is a dependent variable in the second equation of our models these differences may be more meaningful. Here, it is reassuring to note that there is no pattern to these differences. That is, for the audit and loan programs, unaware individuals consume, on average, more than aware individuals. However, this observation is reversed for the rebate program (where the difference is particularly small). Based upon the impressionistic evidence presented in Table II, it can be concluded that the subsamples of unaware and aware individuals are reasonably similar, which lends support to the assumption that program awareness is exogenous.

Table II. Descriptive Statistics by Program Awareness

                      Unaware                      Aware
Variable          Mean      Std. Dev.          Mean      Std. Dev.

AUDIT                (n = 189)                    (n = 311)

Energy        4358.753       3314.950      3560.512       2930.992
Twoyear          1.682          0.811         1.582          0.729
Age             42.579         30.887        45.133         31.382
Income          33.439         19.646        32.668         19.351
Singfam          0.809          0.393         0.877          0.328
Sp_heat          0.063          0.244         0.035          0.185
Wt_heat          0.317          0.466         0.331          0.471
Dwt_heat         0.317          0.466         0.379          0.486
Cook             0.703          0.502         0.691          0.502
Dry              0.629          0.484         0.675          0.475
Ffref            0.936          0.580         0.938          0.520
Replace          0.095          0.294         0.360          0.480
Often            2.800          0.660         2.800          0.704
Farm             0.042          0.201         0.045          0.207
Night            2.346          1.184         2.922          1.361

REBATE                (n = 132)                    (n = 443)

Energy        3974.137       2301.195      4054.129       2236.550
Twoyear          1.698          0.786         1.499          0.656
Age             40.786         32.475        42.396         29.885
Income          32.284         19.349        34.508         17.036
Singfam          0.780          0.415         0.873          0.332
Sp_heat          0.045          0.209         0.022          0.148
Wt_heat          0.325          0.470         0.273          0.446
Dwt_heat         0.272          0.447         0.367          0.482
Cook             0.666          0.561         0.731          0.492
Dry              0.659          0.491         0.672          0.469
Ffref            0.848          0.559         1.088          0.502
Replace          0.113          0.318         0.149          0.356
Often            2.910          0.742         2.951          0.614
Farm             0.045          0.209         0.047          0.212
Night            2.478          1.179         2.580          1.166

LOAN                  (n = 177)                    (n = 409)

Energy        4037.033       3204.327      3403.603       2667.873
Twoyear          1.666          0.784         1.582          0.714
Age             42.380         29.454        44.740         31.345
Income          31.384         16.289        37.571         17.539
Singfam          0.779          0.415         0.880          0.325
Sp_heat          0.050          0.220         0.019          0.138
Wt_heat          0.282          0.451         0.202          0.402
Dwt_heat         0.322          0.468         0.430          0.495
Cook             0.672          0.548         0.667          0.525
Dry              0.615          0.487         0.650          0.482
Ffref            0.926          0.584         0.997          0.482
Replace          0.101          0.303         0.489          0.500
Often            2.854          0.651         2.865          0.647
Farm             0.045          0.208         0.041          0.199
Night            2.422          1.113         2.950          1.352
Table III. Descriptive Statistics

Variable          Mean      Std. Dev.       Minimum        Maximum

AUDIT

Audit           0.4520         0.4982        0.0000         1.0000
Energy       3862.2474      3102.7628       147.898    320294.4730
Incentive       0.0266         0.0288        0.0000         0.1000
Twoyear         1.6205         0.7624        1.0000         4.0000
Age            44.1680        31.1894        2.0000       150.0000
Income         32.9600        19.4472       10.0000        90.0000
Singfam         0.8520         0.3555        0.0000         1.0000
Sp_heat         0.0460         0.2097        0.0000         1.0000
Wt_heat         0.3260         0.4692        0.0000         1.0000
Dwt_heat        0.3560         0.4793        0.0000         1.0000
Cook            0.6960         0.5021        0.0000         2.0000
Dry             0.6580         0.4791        0.0000         2.0000
Ffref           0.9380         0.5429        0.0000         3.0000
Replace         0.2600         0.4391        0.0000         1.0000
Often           2.8004         0.6876        1.0000         7.0000
Farm            0.0440         0.2053        0.0000         1.0000
Night           2.7047         1.3259        0.0000         8.0000

REBATE

Level           0.5757         0.5669        0.0000         2.0000
Energy       4035.7659      2249.7835     1005.0112     13380.0520
Incentive       2.8257         2.4554        0.0000        10.0000
Twoyear         1.5450         0.6930        1.0000         4.0000
Age            42.0267        30.4781        1.0000       150.0000
Income          0.3400         0.1760       10.0000        90.0000
Singfam         0.8522         0.3552        0.0000         1.0000
Sp_heat         0.0278         0.1646        0.0000         1.0000
Wt_heat         0.2852         0.4519        0.0000         1.0000
Dwt_heat        0.3461         0.4761        0.0000         1.0000
Cook            0.7165         0.5091        0.0000         3.0000
Dry             0.6696         0.4745        0.0000         2.0000
Ffref           1.0330         0.5253        0.0000         3.0000
Replace         0.1409         0.3482        0.0000         1.0000
Often           2.9419         0.6456        1.0000         4.0000
Farm            0.0470         0.2117        0.0000         1.0000
Night           2.5573         1.1688        0.0000         7.0000

LOAN

Loan_amt        1.3980         1.6969        0.0000         5.1750
Energy       3594.9294      2852.6927       60.4844     20294.4730
Incentive       0.6980         0.4595        0.0000         1.0000
Twoyear         1.6075         0.7366        1.0000         4.0000
Age            44.0278        30.7805        2.0000       130.0000
Income         35.7023        17.3916       10.0000        90.0000
Singfam         0.8498         0.3575        0.0000         1.0000
Sp_heat         0.0290         0.1680        0.0000         1.0000
Wt_heat         0.2270         0.4192        0.0000         1.0000
Dwt_heat        0.3976         0.4898        0.0000         1.0000
Cook            0.6689         0.5323        0.0000         4.0000
Dry             0.6399         0.4840        0.0000         2.0000
Ffref           0.9761         0.5158        0.0000         3.0000
Replace         0.3720         0.4838        0.0000         1.0000
Often           2.8620         0.6486        1.0000         4.0000
Farm            0.0427         0.2023        0.0000         1.0000
Night           2.7907         1.3070        0.0000         7.0000

Second, we examined the exogeneity of awareness in the audit program using a Hausman-type specification test suggested by Grogger [3]. Since subsample differences seem to be minor and not systematic in any way, we chose the audit program since the test is most straightforward in probit analysis. The test, as with any Hausman test, involves a comparison of two estimates: one consistent and efficient under the null hypothesis (exogeneity), and the other consistent under the alternative. If awareness is exogenous, the ML estimates presented in Table IV are consistent and efficient. But an alternative to ML in the probit model is nonlinear least squares. For the audit program, [Mathematical Expression Omitted] in equation (1) is observed as the dichotomous [y.sub.1] in equation (3). The expectation of [y.sub.1] is the probability [Mathematical Expression Omitted] is positive, given in equation (4):

E([y.sub.1]) = F([[Beta].sub.1][x.sub.1] + [Lambda]z), (18)

where awareness is one of the variables in [x.sub.1]. Define [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. The nonlinear least squares estimator is the set of estimates that solves

[Mathematical Expression Omitted].

If it is suspected that a variable in v is endogenous, a nonlinear instrumental variable estimator can be calculated, provided an instrument can be found. A plausible instrument for awareness is education, reported as the number of years of schooling (in categories). With the remaining variables assumed to be measured without error, the nonlinear instrumental variable estimator, [Mathematical Expression Omitted] solves

[Mathematical Expression Omitted],

where [w.sub.i] equals [v.sub.i] except education replaces awareness, and W is the matrix containing all the [w.sub.i]. This estimator, while not efficient, is consistent under any hypothesis concerning awareness. This suggests the Hausman test of the null hypothesis of exogeneity,

[Mathematical Expression Omitted],

where k is the index of awareness and [Mathematical Expression Omitted] (.) is the estimated variance of the estimator. This statistic is distributed [Mathematical Expression Omitted] under the null hypothesis of exogeneity of awareness. For the audit subsample, H = 0.146, well below the 90% critical value of 2.71. Therefore, the null hypothesis of exogeneity cannot be rejected in our data.

Other factors assumed to affect the decision to conserve include: the self-reported likelihood that the family will continue to live in the house in two years (Twoyear, coded as 1 if the answer is definitely, 2 if probably, 3 if probably not, and 4 if definitely not); the age of the structure (Age); total household income, reported in categories, recoded to the category midpoint, in $000 (Income); dichotomous variables indicating whether the structure is a single family home (Singfam); whether or not electricity is used for space heating (Sp_heat), water heating (Wt_heat), and clothes drying (Dry), cooking (Cook); whether or not the household had recently replaced or added an electric hot water heater (Dwt_heat); ownership of a frost-free refrigerator (Ffree); whether or not the household had recently replaced their main heating system (Replace); and whether or not the household is a farm (Farm). Additional variables include the number of household members at home during the night (Night); and the percentage of total heating met by supplemental heating, (Supheat). The specification of the conservation equation varies slightly because the factors that are influential in the decision-making process differ across the type of conservation action. Since obtaining loans for the purchase of conservation equipment and having one's home audited emphasize changes to the structure of the house, such as the installation of more insulation, undertaking these actions is expected to be a function of housing characteristics. This is not the case for the rebate program.(4)

The determinants of total household demand for electricity are assumed to be independent of the type of program under investigation, so that the specification of the electricity demand equation is identical across programs. Electricity use during the heating season (measured in 1000's of kilowatt hours) is partly determined by whether the conservation action was undertaken (Conserve), which is either a dummy variable for the audit program denoting whether or not an audit was undertaken; one of two values (representing purchase of a new refrigerator) for the appliance rebate program; or the loan amount for purchasing conservation measures for the loan program. Electricity use is further determined by the exogenous variables Age, Income, Singfam, Sp_heat, Wt_heat, Dwt_heat, Dry, Ffree, and Night. Energy use is not a function of weather, typical in these types of models, as this is a cross-sectional analysis and there is no geographic dispersion of the households. The self-reported size of the house, a potentially important variable, is typically measured with error and was missing for a significant portion of our samples. In addition, house size is highly correlated with income, so that the income variable should capture some of this effect.

Identification in simultaneous equations models with limited and discrete dependent variables follows similar rules as in conventional equation systems. A necessary condition for identification of the parameters of an equation that contains an endogenous variable is the exclusion of at least one exogenous explanatory variable. Energy use is logically not a function of Incentive or Twoyear, so each model is overidentified. Table III contains descriptive statistics of the variables used in both the participation and energy-use equations.

Estimation is accomplished by treating equations (1), (2), and either (3) (audit program), (10) (rebate program), or (14) (loan program) as a system and using full information maximum likelihood. The stochastic specification and the likelihood functions maximized are presented in the appendix. In addition to the usual questions of parameter identification, simultaneous equation models with limited and discrete dependent variables are subject to certain coherency conditions [2; 12]. These conditions are met by the three sets of two-equation models estimated.

The coefficient estimates are presented in Table IV. With respect to the conservation action [TABULAR DATA FOR TABLE IV OMITTED] equation, households who faced the incentives offered by the program had a statistically significant increase in the probability of undertaking the conservation action, as the coefficients of Incentive are positive with large asymptotic t-ratios. Planning to move from the house reduced this probability, although this coefficient is not as precisely measured. Those in older houses were more likely to take action, while the results for Income, Singfam, Homenight and the appliance usage variables were mixed. In the energy-use equation, the important variable from a policy perspective is the conservation action variable (Conserve), where the coefficient indicates the energy savings associated with conservation. That is, the coefficient is an estimate of the change in kilowatt hours consumed associated with the change in capital. All three types of action resulted in a statistically significant energy savings. The other variables in the electricity use equation enter as expected, with most being positive and statistically significant. For the audit model, the estimated savings associated with having an audit were 1,962 kWh. This represents a savings of approximately 51 percent, but this large percentage is misleading. Since the conservation measures promoted by an energy audit primarily impact the energy used for space heating, we expect this program to produce savings primarily for those customers who use electricity for space heating. The mean consumption for households who use electricity for space heating is much larger than average, so that the percentage savings for these households is closer to 20 percent.

Table V. Estimated Average Conservation

Program                           Total     Program     Natural

A. At program incentive level:

Audit                            185.73      131.45       54.28
Rebate                           252.99       98.92      154.07
Loan                             248.77      237.04       11.73

B. At twice incentive level:

Audit                            457.74      403.46       54.28
Rebate                           358.35      204.28      154.07
Loan                             606.46      594.73       11.73

C. At half incentive level:

Audit                             96.24       41.95       54.28
Rebate                           200.95       46.88      154.07
Loan                             113.56      101.83       11.73

Note: From Table I, with explanatory variables set at means.

In the rebate model, the estimate of the effect of purchasing a new energy-efficient refrigerator was a savings of 430 kWh, a savings of approximately 11 percent. For the loan model, the estimated savings are a function of the size of the loan (in $1000s). The estimated savings is 478 kWh/$1,000. An average loan amount of $1,398 for the sample implies an average savings of 668 kWh, or about 19 percent of energy use.

These estimates are of the total savings associated with undertaking conservation action, regardless of whether the savings occurred as part of the DSM program. That is, these estimates include both program-induced savings and natural conservation. In Table V (part A.) we apply the techniques presented in section II (and Table I) to decompose the total savings estimates into program-induced and natural conservation. The three programs vary widely as to the energy savings. The largest average program-induced savings per participant occur in the loan program, while the lowest average program-induced savings occur in the rebate program. Notice that ignoring the decomposition between natural and program-induce savings would overstate all three programs, as well as leading to the erroneous conclusion that the rebate program resulted in the largest energy savings.

The model and parameter estimates may be used to simulate scenarios based on the incentive level for each program. For example, Table V (parts B and C) present the results associated with alternatively doubling and halving the incentive. Since the signs of the important estimated parameters agree with a priori expectations, doubling the incentive causes an increase in the program-induced savings. Since energy savings from natural conservation do not depend upon the incentive, there is no change in the third column of Table V. Responses are highly nonlinear, since total and program-induced savings depend upon the probability of conservation as well as the effect of conservation on energy use. All three programs display an elastic response to doubling the incentive, for example, there is a 207% increase in savings with the audit program. When the incentive amount is halved, the program-induced savings in each program declines. The program-induced savings associated with the audit program declines the most relative to the existing incentive. The program-induced savings for all programs at half the original incentive rate are less than half of the savings under the original rate.

This approach can be extended to investigate all of the possible range of incentives [ILLUSTRATION FOR FIGURE 1 OMITTED]. This figure shows the program-induced conservation as the incentive level changes from near zero to 1.6 times the actual incentive rate. The loan program yields the highest savings per customer throughout the range of incentives graphed, while whether the rebate or audit program produces greater savings depends upon the size of the incentive.

The average savings per consumer may be misleading, however. A more meaningful calculation may be the program-induced savings per dollar incentive. This is shown in Figure 2. From this figure, the rebate program is the most effective (i.e., the highest savings per dollar incentive) except at very high levels of incentive.

IV. Conclusions

The production and consumption of energy has significant negative environmental impacts. Coal fired electrical generation plants produce greenhouse gases and other forms of air pollution. Nuclear plants produce radioactive wastes. Therefore conserving energy enhances the environment. While government at various levels is involved with pollution controls, pollution permits, etc., the utility industry is currently engaged in a massive campaign to conserve energy. The evaluation of costs and benefits of these programs depends upon real (incentive-induced) savings. Naive estimates of program savings include concurrent natural savings, that is, savings that would have occurred in the absence of any incentive. In this paper we analyzed a method of decomposing measured conservation into a natural component and an incentive-induced component. This was done in a complete model of energy conservation and energy use that eliminated the sample selection bias due to the voluntary nature of the programs and at the same time properly treated the truncated and polytomous variables that arose. A common statistical framework for estimating savings for the three most widely adopted DSM programs was used. The important observation that allowed this decomposition was the fact that, in any random sample of consumers both program participants and those unaware of the available incentives undertook conservation action. Therefore, despite the fact that a controlled experiment is not possible, this form of natural experiment allowed the decomposition of energy savings.

Estimates were obtained of the total savings associated with undertaking conservation action. Using the methodology developed in the paper total savings was decomposed into program-induced and natural conservation. Ignoring the decomposition between natural and program-induce savings would have overstated all three programs and led to incorrect conclusions regarding the relative value of the programs. All three programs displayed elastic responses to changing the incentive. The rebate program proved to be the most cost effective, that is, it had the highest savings per dollar incentive.

Appendix

Assume ([[Epsilon].sub.1], [[Epsilon].sub.2]) [similar to] N(0, [Sigma]), where [Sigma] = ([[Sigma].sub.ij]), with density function f([center dot], [center dot]). Let [Phi]([center dot], [center dot]; w) be the density of a bivariate normal random vector with zero mean and covariance matrix W. Let the univariate normal density and distribution function be [Phi]([center dot]) and [Phi]([center dot]), respectively.

Since the estimation sample is chosen by augmenting those that participated in the program by a random sample of nonparticipants, we used the weighted exogenous sampling maximum likelihood (WESML) estimator introduced by Manski and Lerman [8]. This estimator is easy to program and provides consistent (although not efficient) parameter estimates. All computation was done on a 486-DX50 personal computer using the MAXLIK applications package of the GAUSS programming language. These programs are available from the authors at cost on request.

In the audit program, since the amount of conservation action is not observed, [[Sigma].sub.11] is normalized to unity. Let [Theta] be a vector of parameters that include [[Beta].sub.1], [[Beta].sub.2], [Gamma], [Lambda] and [Sigma]. The likelihood for the audit program system of equations is

[Mathematical Expression Omitted].

For the rebate program [a.sub.1] is normalized to 0 and [a.sub.2] is added to the vector of unknown parameters. The likelihood is

[Mathematical Expression Omitted].

For the loan program, note that the reduced form of equations (1) and (2) is

[Mathematical Expression Omitted].

Define [Omega] equal to the reduced form covariance matrix:

[Mathematical Expression Omitted],

and further define

u[prime] = [[y.sub.1] - [[Beta].sub.1]x, [y.sub.2] - ([[Beta].sub.2] + [Gamma][[Beta].sub.1])[prime]x], and [Mu] = ([y.sub.2] - [[Beta][prime].sub.2]x)/[[Sigma].sub.2].

Then the likelihood is

[Mathematical Expression Omitted].

We thank an anonymous referee for clearing up an important point on an earlier draft. Any remaining errors are, of course, our own.

1. Dubin and McFadden [1] examine electricity demand in a model of appliance portfolio choice.

2. We ignore the possibility that households anticipate the time when a utility will offer an incentive program and delay energy conservation behavior. This issue will become important as utilities continue to offer and renew programs.

3. To the extent that households respond differently to the suggestions of the auditor, this variable is measured with error.

4. Specifically, the decision to undertake an audit or to obtain a loan for energy conservation measures is a function of the age of the house, while this variable is not expected to influence the decision to receive a rebate for an energy-efficient refrigerator.

References

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