the town utilizes standard disc type pd water

Question

The town utilizes standard disc type PD water meters for all residential connections. These meters were warranted by the manufacturer to be accurate within two percent of actual flow for 15 years or 1.5 million gallons of usage. To assess the financial viability of the project, data was collected on 100 connections: 50 homes with "old" or out-of-warranty meters and 50 homes with "new" meters that were still in the original warranty period. For each sub-sample of the 100 accounts, two pieces of demographic data were collected: the size of the household (PEOPLE) and the size of the property (ACRE). In Texas, water consumption is highly seasonal; during the fall, winter, and early spring, usage is lowest, while during the summer, when temperatures often exceed 100 degrees, demand is significantly greater. To simplify the analysis, while still recognizing this variability, for each of the 100 accounts,two monthsof water meter readings were tabulated: August (peak period) and November (off-peak). The relevant data is shown in file Exhibit 1.xls (SpreadsheetWaterMeter)

A critical first step in our analysis is examining the demographics of the new and old meter samples; if they are not different, then we would expect the same usage patterns by the customers. In other words, if the households are the same, then, ceteris paribus, theobserved meter reading for a typical customer with a new meter should be identical to one with an old meter. Under this assumption, any deviations in the meter readings between the two samples wewould attribute to meter inaccuracy. Furthermore, we can predict the direction of the inaccuracy; we expect the reported usage of the older meters to be significantly lower (i.e. to under-report).

Assume we estimate water usage for the old meter sample using the following regression:

(1) Usage_OLD(i) = a + b*PEOPLE_i + c*ACRE_i

Similarly, assume we estimate water usage for the new meter sample using the regression:

(2) Usage_NEW(k) = α + β*PEOPLE_k + γ*ACRE_k

From these regressions, if the old meters are inaccurate and under-report the water usage then we would expect b<β, and c < γ. In addition, the estimated water loss (unbilled usage) for each house with an old meter could be estimated as:

(3) LOSS_i = α + β*PEOPLE_i + γ*ACRE_i- Usage_OLD(i).

In Lakewood Village, the average residential water rates are approximately $3.00 per 1000 gallons of usage.Thus, if the water LOSS could be billed and collected, the additional revenues for house i would be estimated to be $3.00 * LOSSi ÷ 1000.