Past studies have estimated residential demand for water and electricity in isolation, but these goods are often used as joint inputs in household production activities. As such, separately estimating electricity and water demand may lead to biased demand parameter estimates. If prices are positively correlated and goods are complements, ignoring cross-price effects will exaggerate own-price elasticity estimates, leading to inaccurate revenue and conservation forecasts. Moreover, understanding the water-electricity demand relationship will allow for synergistic conservation strategies. We propose a joint estimation procedure using 3-Stage-Least-Squares-Fixed-Effects (3SLS-FE) to highlight linkages between water and electricity and conclude that water demand, in particular, appears less own-price elastic when cross-prices are included in the demand system. Results from our study region suggest that water and electricity are gross complements (with an average cross-price elasticity of approximately $-0.1$). A simple simulation is included to highlight how omitting cross-price elasticities may lead to inaccurate forecasting and suboptimal decisions.

过去的研究估计居民对水和电的需求是孤立的，但是这些商品通常用作家庭生产活动的联合投入。这样，分别估计电力和水需求可能导致有偏的需求参数估计。如果价格呈正相关，而商品是互补，则忽略交叉价格效应将夸大自身价格弹性估计，从而导致收入和保护预测不准确。此外，了解水电需求关系将有助于采取协同的保护策略。我们提出了一种使用3级最小二乘固定效应（3SLS-FE）的联合估算程序，以突出水电之间的联系，并得出结论，特别是对水的需求，当需求系统中包含交叉价格时，自身价格弹性较小。我们研究区域的结果表明，水和电是总的补充（平均交叉价格弹性约为$-0.1$）。包括一个简单的模拟，以突出说明忽略交叉价格弹性如何可能导致不正确的预测和次优决策。