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Appendix A incorporating Data from Prob~em-Centered Research on incentives and information in Formal Demand Models Problem-oriented studies can investigate the effect of the size and type of incentives, of qualitative factors in the context of the incentive, and of different ways of offering information about energy efficiency. When such studies produce quantitative results, those results can be incorporated into formal energy demand models. This appendix presents a method for using such data in discrete choice models. The typical state-of-the-art residential energy model includes equations that predict household purchases of new energy-efficient systems (appliances, heating equipment, retrofit of existing homes, thermal performance of new homes). Typically, these are discrete choice models to reflect the finite number of options consumers face for each class of purchase decision. For example, a model may define eight choices of water heaters (the combinations of two size classes, two fuels, and two levels of insula- tion). The choice models that predict what fraction of each equipment type is purchased might be of the form: (Si/Sl) = aO + alpeUi/eff i + a2Ci + - alpeUl/effl ~ a2C1 ' where Si is the fractional share of new water heaters sold that are of type i, S1 is the fractional share of type 1 water heaters, Pe is the price of electricity, Ui is annual hours of use of type i water heaters, effi is the energy efficiency of type i water heaters, Ci is the cost to the consumer of type i water heaters, U1 is the annual hours of use of type 1 water heaters, eff1 is the energy efficiency of type 1 water heaters and C1 is the cost of type 1 water heaters. The coefficients al and a2 represent the weights of operating and capital 117

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118 costs in the choice; together, they determine the implicit discount rate for energy efficiency in purchases of new water heaters. Predicted values of equipment purchases are used to project stocks of energy-using equipment. These stocks are then used in conditional demand models to estimate household energy demand.2 Studies of variables that affect appliance choice yield findings that can be used to adjust either the coefficient a2 or the equipment cost Ci in the purchase choice models. For example, information on consumer preference among different levels and types of incentives, stratified by type of consumer (e.g., by household income or educa- tion of household head) can be used to determine indif- ference curves, along which households are indifferent to choices such as those between rebates and loans (Figure A-1). These indifference curves can be converted to implicit discount rates to yield equations of the form: a2 = f(incentive type and level, household characteristics). Such equations, which may vary with the type of purchase decision, can be used to determine the coefficient a2, which can then be used in the purchase choice model. Alternatively, the same kinds of findings might be used to estimate a parameter a3 for some dummy vari- able, such as rebate versus loan or presence of an waif d is the implicit discount rate for choices among water heaters with different efficiency levels, g is the consumer's expectation of future Growth rates in fuel . . . price, L is the expected lifetime of the water heater, and U is the expected annual hours of water heater usage, then the relationship between the coefficients and d is a2/a1 = (d - g)/u[1 - e~(d-g)L] . If g is close to zero and L is large, then a2/a1 = d/U. 2 The present discussion does not incorporate possible effects of appliance efficiency on U. subsequent appliance usage. In practice, purchase of a more efficient piece of equipment is likely to lead to greater use of that equipment than would occur with purchase of a less effici- ent unit. This occurs because higher efficiency leads to lower operating costs.

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