Residential water demand and water waste in Taiwan

Abstract

Residential water demand has long been an important topic of empirical research. How to estimate water waste, however, has rarely been touched. Using the stochastic frontier approach, this article jointly estimates the residential demand for water and water waste in Taiwan, where water resources are scarce and unevenly distributed throughout the island and across seasons. The empirical results confirm that residential water demand is closely related to household characteristics and the overuse of water is affected by environmental variables. The estimated price and income elasticities are below 0.1 in absolute value. The estimated amount of wasted water is around 83 L per capita per day, which is roughly 1/3 of the actual water consumption. It is also shown that overlooking the waste of water use results in an over-estimation of the subsistence water requirement.

Appendix

The probability density functions

The probability density function (pdf) of ω is equal to:

$$f\left( \omega \right) = \frac{{\frac{1}{{\sigma_{\omega } }}\phi \left( {\frac{\omega }{{\sigma_{\omega } }}} \right)}}{{1 - \varPhi \left( {\frac{{ - \delta^{\prime}Z}}{{\sigma_{\omega } }}} \right)}}$$

(6)

where ϕ(·) and Φ(·) are the pdf and cumulative distribution function of the standard normal random variable, respectively. The pdf of the composed error ɛ can be expressed as:

$$f\left( \varepsilon \right) = \frac{{\varPhi \left( { - B} \right)}}{{\sigma \varPhi \left( {\frac{{\delta^{\prime}Z}}{{\sigma_{\omega } }}} \right)}}\phi \left( {\frac{\varepsilon }{\sigma }} \right)$$

(7)

where $- B = \frac{{\delta^{\prime}Z\sigma^{2} + \sigma_{\omega } \varepsilon }}{{\sigma_{v} \sigma_{\omega } \sigma }}$ and σ ² = σ ² _v  + σ ² _ω . On the basis of Eq. (7), the corresponding log-likelihood function is readily derived and can be applied to estimate the parameters in Eqs. (3) and (4).