price elasticities and link the ownership of price elastic (or inelastic) appliances to household income. One example is Reiss and White (2005).<sup>7</sup> A conditional demand model assumes the difference in households’ price sensitivities is purely driven by the difference in households’ appliance holdings. In other words, households with the same appliance portfolio will exhibit the same level of price sensitivity.<sup>8</sup> This assumption is somewhat contentious because price sensitivities are also likely to be affected by the existing consumption levels of the appliances. For example, when the electricity price increases, rich households may adjust by restricting space heating or cooling to rooms which are frequently used; while households who already restrict the usage of electricity space heating or cooling to the minimum level may have less room to further cut down its consumption.

Different from previous studies, I develop a model that explicitly estimates the income-based heterogeneity in price elasticities by incorporating interaction terms of price and income. Conditional on appliance ownership, dwelling and household characteristics, the model estimates intra-household differences in price sensitivities that are driven by existing consumption quantities, habits and other psychological forces which may all be related to household income levels. The empirical strategy is discussed in the following section.

# **III. Model**

# _Electricity Demand_

Electricity is not consumed directly. In the residential sector, demand for electricity is derived from the demand for services provided by durable electrical appliances. To summarize this demand behavior, two types of decisions are involved. The first is the decision about whether and when to buy or replace an electricity-consuming appliance, given its technical and economic characteristics; and the second decision is about the frequency and intensity of the use of the appliance. In the short run, consumers adjust the utilization rate of the existing capital-stock in response to new levels of prices. While in the long run, both utilization behavior and the composition of household appliance holdings are variable. Therefore, long-run price elasticities tend to be much larger than short-run elasticities.

The key difference between long-run and short-run demand is whether the appliance stock is held constant. To estimate short-run demand elasticities, I therefore incorporate household-level appliance holdings as fixed variables in the demand function and leave appliance replacement

> 7 Reiss and White (2005) find that electric space heating or air conditioning exhibit much higher electricity price elasticity than other appliances. After calculating price elasticity for each household conditional on the appliance stock, they find low-income households have greater price sensitivity than high-income households in California. They suggest that this is because there is a weak correlation between household income and ownership of price sensitive appliances, and that it may be the case that households tend to substitute toward more price-inelastic electricity uses as income rises.

> 8 Empirically, a conditional demand model estimates the statistical average price elasticity averaged across households who own the appliance.

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