The impact of price on residential demand for electricity and natural gas

Abstract

Climate change will affect the demand of many resources that households consume, including electricity and natural gas. Although price is considered an effective tool for controlling demand for many resources that households consume, including electricity and natural gas, there is disagreement about the exact magnitude of the price elasticity. Part of the problem is that demand is confounded by block pricing and the interrelated consumption of electricity and natural gas, which prevent easy estimation of price impacts. Block pricing suggests that the purchaser controls the marginal price of a commodity by the quantity purchased, turning price into an endogenous variable. Interrelated consumption indicates that demand for one resource is affected by the price of another. These complications have made difficult the estimation of the price elasticity of demand for resources and consequently the household-level impact of climate change, which will affect resource supplies. This paper evaluates statistical tools for estimating the joint demand for natural gas and electricity when both resources face a block price setting and develops estimates of own and cross price elasticity. We use data from the Federal Residential Energy Consumption Survey, along with utility price data, to estimate the household demand for electricity and natural gas in California as separate commodities. We then use a joint estimation procedure to evaluate the household demand for natural gas and electricity. Finally, we evaluate the degree to which block pricing and interrelated demand affect the price elasticity of demand for the two resources. The paper ends by noting the continuing uncertainty surrounding the use of price to manage household demand for electricity and natural gas.

Appendices

Appendix A. Price elasticity of demand in discrete continuous choice models

To understand the estimation of price elasticity of demand in a discrete continuous choice model, consider the log-log demand function, which can be written as:

$$ \begin{aligned} \ln w = & Z\delta + \beta \ln p + \lambda \ln m + \eta + \varepsilon \\ w = & w\left( {{p_k},\,y + {d_k}} \right){e^{\eta }}{e^{\varepsilon }} \\ \end{aligned} $$

(A-1)

Where $w\left( {{p_k},\,y + {d_k}} \right) = \exp \left\{ {Z\delta + \beta \ln p + \lambda \ln m} \right\}.$ The expected value of consumption must take into account that the individual might consume in any block or at any kink point. Given the assumption about the distribution of η and ε ^, the expected consumption level is:

$$ W = \mathop{\sum }\limits_{{k = 1}}^K w\left( {{p_k},\,y + {d_k}} \right){e^{{\tfrac{{\sigma_{\varepsilon }^2}}{2}}}}{e^{{\tfrac{{\sigma_{\eta }^2}}{2}}}}\pi_k^{ * } + \mathop{\sum }\limits_{{k = 1}}^{{K - 1}} {w_k}{e^{{\tfrac{{\sigma_{\varepsilon }^2}}{2}}}}{\lambda_k} $$

(A-2)

where:

$$ \begin{array}{*{20}{c}} {\pi_k^{ * } = \Phi \left( {\frac{{\ln {b_k}}}{{{\sigma_{\eta }}}} - {\sigma_{\eta }}} \right) - \Phi \left( {\frac{{\ln {a_k}}}{{{\sigma_{\eta }}}} - {\sigma_{\eta }}} \right)} \hfill \\ {{a_k} = \frac{{{w_{{k - 1}}}}}{{w\left( {{p_k},\,y + {d_k}} \right)}},\,\;\;{b_k} = \frac{{{w_k}}}{{w\left( {{p_k},\,y + {d_k}} \right)}}} \hfill \\ {{\lambda_k} = \Phi \left( {\frac{{\ln {c_k}}}{{{\sigma_{\eta }}}}} \right) - \Phi \left( {\frac{{\ln {b_k}}}{{{\sigma_{\eta }}}}} \right)} \hfill \\ {{c_k} = \frac{{{w_k}}}{{w\left( {{p_{{k + 1}}},\,y + {d_{{k + 1}}}} \right)}}} \hfill \\ \end{array} $$

We can use this expression to calculate the change in expected consumption given a change in 1% of all prices in the block rate structure. For the log-log demand function given above, it can be shown (see Olmstead et al. 2007) that the elasticity is given by:

$$ \frac{1}{W}\frac{{\partial W}}{{\partial \theta }} = \frac{{\beta \left( \Sigma {\mathop{}\nolimits_{{k = 1}}^K \tfrac{{w\left( {{p_k},\,y + {d_k}} \right)}}{{{p_k}}}{\psi_k} + \Sigma \mathop{}\nolimits_{{k = 1}}^{{K - 1}} {w_k}{\chi_k}} \right) + \lambda \left( \Sigma {\mathop{}\nolimits_{{k = 1}}^K \tfrac{{w\left( {{p_k},\,y + {d_k}} \right)}}{{y + {d_k}}}{d_k}{\psi_k} + \Sigma \mathop{}\nolimits_{{k = 1}}^{{K - 1}} {w_k}{\tau_k}} \right)}}{\Omega } $$

(A-3)

with:

$$ \begin{array}{*{20}{c}} {{\psi_k} = \left( {\pi_k^{ * } - \frac{1}{{{\sigma_{\eta }}}}\left[ {\varphi \left( {\frac{{\ln {b_k}}}{{{\sigma_{\eta }}}} - {\sigma_{\eta }}} \right) - \varphi \left( {\frac{{\ln {a_k}}}{{{\sigma_{\eta }}}} - {\sigma_{\eta }}} \right)} \right]} \right)} \hfill \\ {{\chi_k} = \frac{1}{{{\sigma_{\eta }}{e^{{\sigma_{\eta }^2/2}}}}}\left( {\varphi \left( {\frac{{\ln {b_k}}}{{{\sigma_{\eta }}}}} \right) - \varphi \left( {\frac{{\ln {a_k}}}{{{\sigma_{\eta }}}}} \right)} \right)} \hfill \\ {{\tau_k} = \frac{1}{{{\sigma_{\eta }}{e^{{\sigma_{\eta }^2/2}}}}}\left( {\varphi \left( {\frac{{\ln {b_k}}}{{{\sigma_{\eta }}}}} \right)\frac{{{d_k}}}{{y + {d_k}}} - \varphi \left( {\frac{{\ln {a_k}}}{{{\sigma_{\eta }}}}} \right)\frac{{{d_{{k + 1}}}}}{{y + {d_{{k + 1}}}}}} \right)} \hfill \\ {\Omega = \mathop{\sum }\limits_{{k = 1}}^K w\left( {{p_k},y + {d_k}} \right)\pi_k^{ * } + \mathop{\sum }\limits_{{k = 1}}^{{K - 1}} {w_k}{e^{{ - \tfrac{{\sigma_{\eta }^2}}{2}}}}{\lambda_k}_{.}} \hfill \\ \end{array} $$

We can see that price elasticity is a complex function of the parameters of the model; it includes a price effect and an income effect produced by the virtual subsidy implicit in the tiered rate structure.

Analogous formulae can be derived for the linear model.

Appendix B. Formulation of linked consumption in discrete continuous choice demand models

Let us consider the following system of demand equations

$$ \begin{array}{*{20}{c}} {{x_{{1j}}} = Z{\delta_1} + {\beta_{{11}}}{p_{{1j}}} + {\beta_{{12}}}{p_{{2j}}} + {\lambda_1}{m_j} + {\varepsilon_1} + {\eta_1}} \hfill \\ {{x_{{2j}}} = Z{\delta_2} + {\beta_{{21}}}{p_{{1j}}} + {\beta_{{22}}}{p_{{2j}}} + {\lambda_2}{m_j} + {\varepsilon_2} + {\eta_2}} \hfill \\ \end{array} $$

in which Z is a vector of explanatory variables, p _1j and p _2j are the prices of the goods and j take the value 1 if the consumption is below the kink point and the value of 2 if consumption of that good is above the kink point. m is the income of the individual and (δ, β, λ) are parameters to be estimated. Finally, (ε ₁, η ₁, ε ₂, η ₁) are error terms with the same interpretation given in Hewitt and Hanemann (1995) and Olmstead et al. (2007). The main purpose of our model is to capture correlation between the two goods. Therefore we assume that (ε ₁, ε ₂) distributes as a bivariate normal with correlation coefficient equal to ρ and mean zero. Finally, following the authors mentioned above, we assume that the rest of the error terms are independent among each other and with mean zero as well. Therefore the joint distribution of the error terms is

$$ \begin{aligned} {\varepsilon_1} = & {u_1} \\ {\varepsilon_2} = & {u_2} \\ {\varepsilon_1} + {\eta_1} = & {v_1} \\ {\varepsilon_2} + {\eta_2} = & {v_2} \\ \end{aligned} $$

$$ {f_{{{\varepsilon_1},\,{\varepsilon_2},\,{\eta_1},\,{\eta_2}}}}\sim MN\left( {0,\Sigma } \right) $$

$$ \Sigma = \left( {\begin{array}{*{20}{c}} {\sigma_1^2} & {{\sigma_{{12}}}} & 0 & 0 \\ {{\sigma_{{12}}}} & {\sigma_2^2} & 0 & 0 \\ 0 & 0 & {\sigma_{{{\eta_1}}}^2} & 0 \\ 0 & 0 & 0 & {\sigma_{{{\eta_2}}}^2} \\ \end{array} } \right) $$

where $E\left( {\varepsilon_1^2} \right) = \sigma_1^2,$ $E\left( {\varepsilon_2^2} \right) = \sigma_2^2,$ $E{\left( {{\varepsilon_1} + {\eta_1}} \right)^2} = \sigma_1^2 + \sigma_{{{\eta_1}}}^2,$ $E{\left( {{\varepsilon_2} + {\eta_2}} \right)^2} = \sigma_2^2 + \sigma_{{{\eta_2}}}^2$ and $E\left( {{\varepsilon_1}{\varepsilon_2}} \right) = {\sigma_{{12}}} = \rho {\sigma_1}{\sigma_2}.$ Furthermore $E({\varepsilon_1}\left( {{\varepsilon_1} + {\eta_1}} \right)) = \sigma_1^2,$ $E\left( {{\varepsilon_2}\left( {{\varepsilon_2} + {\eta_2}} \right)} \right) = \sigma_2^2$ $E\left( {{\varepsilon_1}\left( {{\varepsilon_2} + {\eta_2}} \right)} \right)\left( {E({\varepsilon_2}\left( {{\varepsilon_1} + {\eta_1}} \right)} \right) = E\left( {{\varepsilon_1} + {\eta_1}} \right)\,\left( {{\varepsilon_2} + {\eta_2}} \right) = {\sigma_{{12}}}$. Then

$$ {f_{{{\varepsilon_1},\,{\varepsilon_2},\,{\varepsilon_1} + {\eta_1},\,{\varepsilon_2} + {\eta_2}}}}\sim MN\left( {0,\,\hat{\Sigma }} \right) $$

$$ \hat{\Sigma } = \left( {\begin{array}{*{20}{c}} {\sigma_1^2} & {{\sigma_{{12}}}} & {\sigma_1^2} & {{\sigma_{{12}}}} \\ {{\sigma_{{12}}}} & {\sigma_2^2} & {{\sigma_{{12}}}} & {\sigma_2^2} \\ {\sigma_1^2} & {{\sigma_{{12}}}} & {\sigma_1^2 + \sigma_{{{\eta_1}}}^2} & {{\sigma_{{12}}}} \\ {{\sigma_{{12}}}} & {\sigma_2^2} & {{\sigma_{{12}}}} & {\sigma_2^2 + \sigma_{{{\eta_2}}}^2} \\ \end{array} } \right) $$

Using the marginal distribution and the conditional distribution expression of this distribution, that is ${f_{{{\varepsilon_1},\,{\varepsilon_2},\,{\varepsilon_1} + {\eta_1},\,{\varepsilon_2} + {\eta_2}}}} = {f_{{{\varepsilon_1} + {\eta_1},\,{\varepsilon_2} + {\eta_2}}}} * {f_{{{\varepsilon_1},\,{\varepsilon_2}/\left( {{\varepsilon_1} + {\eta_1}} \right),\,\left( {{\varepsilon_2} + {\eta_2}} \right)}}}$ we can characterize all possible consumption patterns. The marginal distribution is

$$ {f_{{{\varepsilon_1} + {\eta_1},\,{\varepsilon_2} + {\eta_2}}}}\sim NB\left( {0,\,\bar{\Sigma }} \right) $$

$$ \bar{\Sigma } = \left( {\begin{array}{*{20}{c}} {\sigma_1^2 + \sigma_{{{\eta_1}}}^2} & {{\sigma_{{12}}}} \\ {{\sigma_{{12}}}} & {\sigma_2^2 + \sigma_{{{\eta_2}}}^2} \\ \end{array} } \right) $$

while the conditional distribution is

$$ {f_{{{\varepsilon_1},\,{\varepsilon_2}/\left( {{\varepsilon_1} + {\eta_1}} \right),\,\left( {{\varepsilon_2} + {\eta_2}} \right)}}} $$

where we use the following property of a partitioned matrix of normal distribution given the mean vector and the matrix of variance and covariance given by

$$ \mu = \left[ {\begin{array}{*{20}{c}} {{\mu_1}} \\ {{\mu_2}} \\ \end{array} } \right] $$

$$ \Sigma = \left[ {\begin{array}{*{20}{c}} {{\Sigma_{{11}}}} & {{\Sigma_{{12}}}} \\ {{\Sigma_{{21}}}} & {{\Sigma_{{22}}}} \\ \end{array} } \right] $$

the mean of the variables i conditional on variables j is given by

$$ {\mu_{{i/j}}} = {\mu_i} + {\Sigma_{{ij}}}\Sigma_{{jj}}^{{ - 1}}\left( {{x_j} - {\mu_j}} \right) $$

and the conditional variance is given by

$$ {\Sigma_{{i/j}}} = {\Sigma_{{ii}}} - {\Sigma_{{ij}}}\Sigma_{{jj}}^{{ - 1}}{\Sigma_{{ji}}} $$

Using this equation we found that

$$ {f_{{{\varepsilon_1},\,{\varepsilon_2}/\left( {{\varepsilon_1} + {\eta_1}} \right),\,\left( {{\varepsilon_2} + {\eta_2}} \right)}}}\sim NM\left( {{\mu_{{i/j}}},\,\Omega, \,\hat{\rho }} \right) $$

$$ {\mu_{{i/j}}} = \left( {\begin{array}{*{20}{c}} {\tfrac{1}{{1 - {\rho^2}}}\left[ {\rho_1^2{v_1} - {\rho^2}\left( {{v_1} - \tfrac{{\sigma_{{{\eta_1}}}^2}}{{{\sigma_{{12}}}}}{v_2}} \right)} \right]} \\ {\tfrac{1}{{1 - {\rho^2}}}\left( {\rho_2^2{v_2} - {\rho^2}\left( {{v_2} - \tfrac{{\sigma_{{{\eta_2}}}^2}}{{{\sigma_{{12}}}}}{v_1}} \right)} \right)} \\ \end{array} } \right) $$

$$ \Omega = \left( {\begin{array}{*{20}{c}} {\sigma_{{{\eta_1}}}^2\left( {\sigma_1^2\left( {\sigma_2^2 + \sigma_{{{\eta_2}}}^2} \right) - \sigma_{{12}}^2} \right)} & {{\sigma_{{12}}}\sigma_{{{\eta_1}}}^2\sigma_{{{\eta_2}}}^2} \\ {{\sigma_{{12}}}\sigma_{{{\eta_2}}}^2\sigma_{{{\eta_1}}}^2} & {\sigma_{{{\eta_2}}}^2\left( {\sigma_2^2\left( {\sigma_1^2 + \sigma_{{{\eta_1}}}^2} \right) - \sigma_{{12}}^2} \right)} \\ \end{array} } \right) $$

$$ \hat{\rho } = \frac{{{\sigma_{{12}}}\sigma_{{{\eta_2}}}^2\sigma_{{{\eta_1}}}^2}}{{\sqrt {{\sigma_{{{\eta_1}}}^2\left( {\sigma_1^2\left( {\sigma_2^2 + \sigma_{{{\eta_2}}}^2} \right) - \sigma_{{12}}^2} \right)}} \sqrt {{\sigma_{{{\eta_2}}}^2\left( {\sigma_2^2\left( {\sigma_1^2 + \sigma_{{{\eta_1}}}^2} \right) - \sigma_{{12}}^2} \right)}} }} $$

in which ${\rho_1} = \tfrac{{E\left( {{\varepsilon_1}\left( {{\varepsilon_1} + {\eta_1}} \right)} \right)}}{{{\sigma_1}\sqrt {{\sigma_1^2 + \sigma_{{{\eta_1}}}^2}} }} = \tfrac{{{\sigma_1}}}{{\sqrt {{\sigma_1^2 + \sigma_{{{\eta_1}}}^2}} }}$ and ${\rho_2} = \tfrac{{E\left( {{\varepsilon_2}\left( {{\varepsilon_2} + {\eta_2}} \right)} \right)}}{{{\sigma_2}\sqrt {{\sigma_2^2 + \sigma_{{{\eta_2}}}^2}} }} = \tfrac{{{\sigma_2}}}{{\sqrt {{\sigma_2^2 + \sigma_{{{\eta_2}}}^2}} }}$ and ${v_1} = \left( {{\varepsilon_1} + {\eta_1}} \right)$ and ${v_2} = \left( {{\varepsilon_2} + {\eta_2}} \right).$

In addition, using these distributions and the properties of the normal distribution we can build the likelihood function for each individual, including nine possible combinations, as we do not have sample separability with a two error term (Hewitt, 1993). For example, consider the case that both levels $\left( {\bar{x}_1^1,\,\bar{x}_2^1} \right)$ of consumption are below the kink points (x ₁₁, x ₂₂), then we have that

• $\bar{x}_1^1 < {x_{{11}}}$ and $\bar{x}_2^1 < {x_{{22}}}$ which is characterized by ${\varepsilon_1} + {\eta_1} = {v_1} = {x_{{11}}} - \bar{x}_1^1,$ ${\varepsilon_2} + {\eta_2} = {v_2} = {x_{{22}}} - \bar{x}_2^1$, ${\varepsilon_1} \leqslant {x_{{11}}} - \bar{x}_1^1$ and ${\varepsilon_2} \leqslant {x_{{22}}} - \bar{x}_2^1.$ Then contribution to the likelihood function of this component is given by

  $$ \mathop{\smallint }\limits_{{ - \infty }}^{{{x_{{11}}} - \bar{x}_1^1}} \mathop{\smallint }\limits_{{ - \infty }}^{{{x_{{22}}} - \bar{x}_2^1}} {f_{{{\varepsilon_1},\,{\varepsilon_2},\,{\varepsilon_1} + {\eta_1},\,{\varepsilon_2} + {\eta_2}}}}(.)d{\varepsilon_2}d{\varepsilon_1} = \mathop{\smallint }\limits_{{ - \infty }}^{{{x_{{11}}} - \bar{x}_1^1}} \mathop{\smallint }\limits_{{ - \infty }}^{{{x_{{22}}} - \bar{x}_2^1}} {f_{{{\varepsilon_1} + {\eta_1},\,{\varepsilon_2} + {\eta_2}}}} * {f_{{{\varepsilon_1},\,{\varepsilon_2}/\left( {{\varepsilon_1} + {\eta_1}} \right),\,\left( {{\varepsilon_2} + {\eta_2}} \right)}}}(.)d{\varepsilon_2}d{\varepsilon_1} $$
  $$ {f_{{{\varepsilon_1} + {\eta_1},\,{\varepsilon_2} + {\eta_2}}}} * \mathop{\smallint }\limits_{{ - \infty }}^{{{x_{{11}}} - \bar{x}_1^1}} \mathop{\smallint }\limits_{{ - \infty }}^{{{x_{{22}}} - \bar{x}_2^1}} {f_{{{\varepsilon_1},\,{\varepsilon_2}/\left( {{\varepsilon_1} + {\eta_1}} \right),\,\left( {{\varepsilon_2} + {\eta_2}} \right)}}}d{\varepsilon_2}d{\varepsilon_1} $$

Because we know all the distributions, we can evaluate the value of this expression. Similar expressions, although more complicated in some cases, can be derived for each consumption pattern and included in the likelihood function.

Appendix C. Estimation of parameters for analyzing consumption in discrete continuous choice demand models

Estimating the parameters related to linked consumption of resources in a discrete continuous choice demand model requires constructing a likelihood function that represents the probability that each resource experiences the consumption pattern observed in the overall sample. The characteristics of the likelihood function depend both on the assumptions about the distribution of the error terms of the models and on the price structure consumers face. For example, let us call w ^* the optimal level of consumption, and assume that the two error terms are independent and normally distributed with mean zero and variance as σ _η and σ _ε . Here the contribution to the likelihood function of an individual in a uniform price system would be:

$$ {l_i} = \ln \left( {\frac{1}{{\sqrt {{2\pi }} \left( {{\sigma_n} + {\sigma_{\varepsilon }}} \right)}}\exp \left( { - \frac{1}{2}{{\left( {\frac{{\ln w - \ln w*}}{{{\sigma_{\eta }} + {\sigma_{\varepsilon }}}}} \right)}^2}} \right)} \right) $$

(C-1)

The likelihood function for increasing block prices is more complicated. If there are K blocks, then there exist K – 1 kinks in the budget set; let’s call them W _k . For each block there exists a virtual income ỹ _k  = y + d _k that enables individuals to consume inside this block. In order to define d_k and therefore the virtual income, we must remember that people pay different marginal prices for different units of consumption. Referring again to Fig. 1 in the main paper, people pay only p1 for units below W ^*. Therefore there is an implicit benefit of p2 – p1 for each unit consumed in that range. Because higher levels of consumption are associated with higher marginal prices, a subsidy is created for the initial quantities, which can be consumed at a lower marginal price. Then:

$$ {d_k} = \left\{ {\begin{array}{*{20}{c}} {0\quad \quad \quad \quad \quad \quad \quad if\;\;k = 1} \hfill \\ {\sum\nolimits_{{j - 1}}^{{k - 1}} {\left( {{p_{{j + 1}}} - {p_j}} \right){w_k}\,if} \,k > 1} \hfill \\ \end{array} } \right. $$

(C-2)

To build the likelihood function, we must consider the probability that consumption lies in each segment defined by all the K blocks and the K – 1 kinks. Following Olmstead et al. (2007), the likelihood function is:

$$ \ln \left[ {\sum\limits_{{k = 1}}^K {\left( {\frac{1}{{\sqrt {{2\pi }} }}\frac{{\exp \left( { - s_k^2/2} \right)}}{{{\sigma_v}}}} \right)\left( {\Phi \left( {{r_k}} \right) - \Phi \left( {{n_k}} \right)} \right) + \sum\limits_{{k = 1}}^{{K - 1}} {\left( {\frac{1}{{\sqrt {{2\pi }} }}\frac{{\exp \left( { - u_k^2/2} \right)}}{{{\sigma_{\varepsilon }}}}} \right)\left( {\Phi \left( {{m_k}} \right) - \Phi \left( {{t_k}} \right)} \right)} } } \right] $$

(C-3)

with:

$$ \begin{array}{*{20}{c}} {v = \eta + \varepsilon } \hfill & {{t_k} = \left( {\ln {w_k} - \ln w_k^{*}} \right)/{\sigma_{\eta }}} \hfill \\ {\rho = corr\left( {v,\rho } \right),} \hfill & {{r_k} = \left( {{t_k} - \rho {s_k}} \right)/\sqrt {{1 - {\rho^2}}} } \hfill \\ \end{array} $$

$$ \begin{array}{*{20}{c}} {{s_k} = \left( {\ln {w_i} - \ln w_k^{*}} \right)/{\sigma_v}} \hfill & {{m_k} = \left( {\ln {w_k} - \ln w_{{k + 1}}^{*}} \right)/{\sigma_{\eta }}} \hfill \\ {{u_k} = \left( {\ln {w_i} - \ln {w_k}} \right)/{\sigma_{\varepsilon }}} \hfill & {{n_k} = \left( {{m_{{k - 1}}} - \rho {s_k}} \right)/\sqrt {{1 - {\rho^2}}} } \hfill \\ \end{array} $$

where $_k^{ * }$ is the optimal consumption on block k, w _k is consumption at kink point k.

Appendix D: Data sets for estimating residential energy demand

Discrete continuous choice (DCC) modeling has been relatively rare in the literature because it requires consumer-level information. To protect customer privacy, U.S. electric and natural gas utilities historically have restricted the availability and use of customer-level information regarding utility consumption. Utilities strictly limit access to information about a household from which researchers could derive basic factors that influence consumption (e.g., house size, number of household members, number and types of appliances).

For this study we collected large sets of data on household natural gas and electricity consumption.

4.1 D.1 Household electricity and natural gas data

One public source of residential energy use data is the Residential Energy Consumption Survey (RECS), performed every 4 years by the Energy Information Administration (EIA) of the U.S. Department of Energy. RECS is a sample survey that provides household-level information on home energy uses and costs, based on a combination of actual utility bills and household survey information. A subset of these data was identified for California. The latest public use files, from survey year 2001, contain data for 541 California households. The EIA releases a public use file that includes annual consumption and expenditures for electricity, natural gas, and other fuels both in total and as estimated by end use, as well as descriptions of household demographics, equipment and appliances, and various energy use practices. These data can be used to estimate electricity and natural gas elasticities for California, via the construction of monthly estimated bills, as Reiss and White (2005) did for electricity using 1993 and 1997 RECS data. Supplemental data on natural gas and electricity use in California households are available through the Residential Appliance Saturation Survey, covering five participating utilities in 2003, including California’s three largest investor-owned utilities.⁴

4.2 D.2 Processing of natural gas and electricity data

In order to recover the gas and electricity prices faced by households sampled for the 1993 and 1997 RECS, we used a database constructed by Reiss and White (2005), wherein each individual in the survey was matched to a NOAA weather station. Using GIS techniques, each weather station was assigned a ZIP code and city, then matched to its corresponding natural gas provider. Data on the areas supplied by natural gas providers, as well as prices for 1993 and 1997, were obtained from the websites of the providers and by contacting provider personnel. Data on electricity prices were obtained from the database provided by Reiss and White (2005). Because natural gas prices were obtained only for single-family households, we discarded RECS data on consumers who reported living in condominiums or multi-unit houses, as well as those who did not pay their utility bills. We also discarded records of individuals who reported having no natural gas supplied to their households. Because some socioeconomic variables have different ranges or do not match between the 1993 and 1997 survey years, we had to transform some of them to make the answers comparable and discard others. Given that RECS reports annual energy consumption, we calculated average natural gas prices for each household.