regions is exploited in later sections to estimate household-level demand. We refer the reader to Appendix 2 for additional validations conducted on the temperature and rainfall data.

# **SECTION IV: Modeling Demand for Energy Services**

The model makes use of the data from the household survey of electricity-consuming appliance ownership and use in order to estimate a model of the demand for energy services. It captures the wellknown fact that electricity is a derived demand. Specifically, a household’s overall demand for electricity is derived from the demand for an energy service provided by an electricity-consuming capital good such as a light bulb, fan, air conditioner, etc. Moreover, the amount of electricity consumed to provide a fixed quantity of electricity services, say an hour computer use, is uncertain because of back- ground factors such as the background temperature and intensity of use of the appliance. Let equal the households demand for energy service in hours of use per day within the billing cycle, and ii uu 1 2 )<sup>′</sup> equal the vector of energy services demand for the N services that the household consumes. Let equal the household’s electricity consumption in kilowatt-hours (kWh) per day during uu ss= NN (uu , uu , ... , uu the billing cycle. EE A household’s demand for a vector of energy services is related to its use of electricity during the bill cycle through the electricity production function, . This function characterizes the technological relationship between the vector of energy services a household consumes and the electricity use they require. This function also depends on EE = oo (ss, AA, εε), a vector of weather and household characteristics that impacts how the vector of energy services demand translates into electricity AA consumption, and , a random variable that is unobserved by the household and the researcher that captures the uncertain amount of electricity, , used by a household that consumes the vector of energy services, . εε EE Let ss equal the potentially nonlinear price schedule that the household faces, where is the marginal price paid at electricity consumption level . Let 0 equal household’s pp(nn) EE pp(nn) total bill for the billing cycle under the nonlinear price schedule for consumption level, . Note nn TT (EE) = ∫pp(nn) ccnn the includes the fixed charge, if one exists, that must be paid regardless of the household’s billing pp(nn) EE cycle-level consumption of electricity. pp(nn) Assume the household consumes a composite “outside” good beside electricity, and that the household has a preference function, which depends on the vector of energy services xx, demanded by the household, its daily demand for during the billing cycle and observable UU (ss, xx, AA, υυ) characteristics of the household and the weather conditions the household faces, , and υ is a vector of unobservable household characteristics. Note that different elements of xx are likely to enter and . The household’s budget constraint is equal to T AA , where is the price of and is the household’s daily income during the billing cycle. We normalize AA xx UU (ss, xx, AA, υυ) oo (ss, AA, εε) (EE) + pp xx ≤ MM all magnitudes to daily values in within the billing cycle because billing cycles have different lengths. xx pp xx MM The household’s budget constraint is nonlinear for two reasons. The first is because of the increasing block price schedule . The second is because the household consumes a vector of electricity-consuming services, , which translates into the household’s billing cycle-level electricity use, E, through a potentially nonlinear function, pp(nn) . ss 11 EE = oo (ss, AA, εε)