What does radical price change and choice reveal?

What does radical price change and choice reveal? A project by YarraValley Water and the Centre for Water Policy Management November 2016 CRICOS Provider 00115M latrobe.edu.au CRICOS Provider 00115M

Objectives The aim is to estimate the price elasticity of demand for residential water in Melbourne (serviced by Yarra Valley Water). No previous estimates in Melbourne Previous research indicates elasticity estimates vary by location Timing of the study. In 2013 July 1 prices increased by 21.7% + CPI (see YVW Annual report 2013-14). This comes after a two year period of no price increases, so provides a unique opportunity to estimate consumer's response. Also attitudinal survey provided an opportunity to estimate the elasticity controlling for a number of household characteristics. 2

Table 1: Yarra Valley Water Three Tier Pricing Scheme Residential Water Usage 2010/11 ($/kl) 2011/12 ($/kl) 2012/13 ($/kl) 2013/14 ($/kl) 2014/15 ($/kl) Block 1 (0-440 Litres/day 1.5343 1.7756 1.7756 2.5970 2.5523 Block 2 (441-880 Litres/day 1.800 20.832 2.0832 3.0469 2.9944 Block 3 (881 + Litres/day 2.6594 3.0778 3.0778 4.5017 4.4242 3

Previous literature Previous estimates of the price elasticity of demand indicate an inelastic demand for water. Meta analysis: Dalhuisenet al. (2003) report a mean price elasticity mean of -0.41 and median of -0.35 -SD of 0.81(124 studies) Sebri(2014) report a mean of -more recent study finds -0.365 and a median of -0.291 (100 studies) Key factors affecting demand and included in studies are the pricing structure, income, rainfall, temperature, household size and property size. 4

Table 2: Estimated price elasticities in Australia Author(s) Data Location Price Elasticity Method Function Hoffman, Worthington and Higgs (2006) Grafton and Kompas (2007) Grafton and Ward (2008) Panel Brisbane SR -0.588 LR -1.16 OLS Panel Sydney -0.352 OLS Linear Aggregate Sydney -0.17 OLS Linear Abrams, Sarafidis, Kumaradevan and Spaninks (2012) Panel Sydney SR -0.082 LR -0.139 GMM Linear and loglog Loglinear ICRC (2016) Panel ACT -0.14 2SLS Log-log YVW and CWPM Panel Melbourne -0.09 to -0.3 OLS, GMM, FE and FD Linear and loglinear 5

Complications Aproblem in estimation of the elasticity of demand is endogenous prices, via simultaneous shifting of demand and supply OLS estimates biased and inconsistent However water prices set administratively, but Nonlinear pricing also raises the problem of endogenous prices Kinked budget constraint (Moffitt, 1986, 1990) Structural or reduced-form approaches to dealing with nonlinear prices 6

Figure 1 Budget constraint with nonlinear pricing Q X I 3 I 2 I 1 Q K Q W 7

Complications A second estimation issue with nonlinear pricing is what price to use; marginal, average prices, both and also a difference variable (Nordin1976) This has been debated in the literature and relates to water pricing, electricity and income tax rates (see Shin 1985, Nieswiadowy and Monila 1991) A recent study (Ito 2014) on nonlinear electricity prices argues that consumers respond to average rather than marginal prices The implication is that nonlinear pricing does no have the desired impact on energy conservation 8

Econometric method Based on thedata and potential problems in estimationwe used several econometric techniques Pooled OLS: Likely to be biased and inconsistent But estimates the effects of household characteristics Fixed effects and a first difference model These models remove the household heterogeneity. More likely to be unbiased and consistent estimates. GMM model (Arellano Bond) uses lagged consumption as an instrumental variable to correct for endogeneity 9

Methods Functional form of model: A linear function A log-linear function typically the preferred form in water demand studies Using the survey data to form a panel (unbalanced): Average price (with 3 lags), household income, household size split into adults and children, rainfall per quarter (in ml) and average temperature (quarter), lagged consumption and a summer dummy. Additional household characteristics swimming pool, rainwater tank, drip watering system, garden size, vegetable garden and evaporative cooling. 10

Data The data: Benchmark survey 949 respondents, after dropping outliers and missing data finished with a panel of 715 households over 16 quarters from Q3 2011 to Q2 2015. Average price = estimated Billed amount / Billed usage (We reconstructed the billed amount or total cost from usage data) Also modelling the change in marginal price Other variables included Same variables were not significant e.g. outdoor spa and information on tap type, washing machine, Net Annual Value. 11

Figure 2 Quarterly mean usage (Kl) 60 50 40 30 20 10 0 12 01-Jul-11 01-Sep-11 01-Nov-11 01-Jan-12 01-Mar-12 01-May-12 01-Jul-12 01-Sep-12 01-Nov-12 01-Jan-13 01-Mar-13 01-May-13 01-Jul-13 01-Sep-13 01-Nov-13 01-Jan-14 Mean Usage Kl 01-Mar-14 01-May-14 01-Jul-14 01-Sep-14 01-Nov-14 01-Jan-15 01-Mar-15 Aggregate mean usage by Quarter (Kl)

Figure 3 Average temperature and rainfall by quarter 35 30 25 20 15 10 5 0 400 350 300 250 200 150 100 50 0 13 01-Jan-15 01-Jul-11 01-Sep-11 01-Nov-11 01-Jan-12 01-Mar-12 01-May-12 01-Jul-12 01-Sep-12 01-Nov-12 01-Jan-13 01-Mar-13 01-May-13 01-Jul-13 01-Sep-13 01-Nov-13 01-Jan-14 01-Mar-14 01-May-14 01-Jul-14 01-Sep-14 01-Nov-14 C 01-Mar-15 ml per quarter Average Temperature Rainfall

0 Average Price $/Kl 50 100 150 Figure 4 Quarterly demand for residential water 0 100 200 Billed Usage Kl/Quarter 300 400 14

Figure 5 Quarterly demand for residential water (log of usage) Average Price $/Kl 0 50 100 150 0 2 4 6 Log of Billed Usage 15

Results Pooled OLS estimator (similar model to Hoffman et a. 2006) This was modelled with a lagged dependent variable Variables not significant and dropped included outdoor spa and information on tap type, washing machine type, dual flush toilet. Essentially not enough variation in the data. White test provides evidence of heteroskadiscitiy Linear vs log-linear Log-linear has higher R 2 compared to linear model. Coefficients generally have the correct sign. The price variables are significant often to two lags. Some of the lagged price variables are positive, which is more the nature of lags e.g. change in seasons. 16

Results Model comparisons (linear v log-linear) Model (1) Model (2) Model (3) Model (4) Linear levels Linear levels Log-linear Log-linear Average price Marginal price Average price Marginal price Lag of Usage 0.619 *** 0.575 *** 0.710 *** 0.669 *** Price -0.586 *** -4.671 *** -0.0349 *** -0.157 *** Price 1 lag 0.238 *** 0.909 * 0.0223 *** 0.0564 *** Price 2 lags 0.0333-1.371 *** -0.000253-0.0144 * Price 3 lags -0.0851-2.688 *** -0.000443-0.0529 *** Income 0.258 0.176 0.00487 * 0.00429 Rainwater Tank -1.060-1.132 * -0.00942-0.0189 Swimming Pool 4.840 *** 4.164 *** 0.0599 *** 0.0477 ** Garden size 1.816 *** 1.945 *** 0.0195 ** 0.0224 *** Vegetable Garden 1.006 0.800 0.0216 * 0.0208 * Drip Watering System 3.216 *** 3.492 *** 0.0450 *** 0.0534 *** Evaporative cooler 0.782-0.107 0.0228 ** 0.00147 Number of Adults 3.823 *** 2.703 *** 0.0717 *** 0.0558 *** Number of Children 1.598 *** 0.714 ** 0.0371 *** 0.0244 *** Average Max Temperature 1.038 *** 0.496 *** 0.0222 *** 0.00924 *** Rainfall 0.0384 *** 0.0165 * 0.000767 *** 0.000415 ** Summer D 6.742 *** 11.41 *** 0.0924 *** 0.252 *** Constant -33.21 *** -5.130 0.139 * 0.777 *** N 6310 6310 6310 6310 Adj-R-Squared 0.586 0.597 0.790 0.746 17

Results Elasticities The price elasticities range from -0.3 to -0.13 suggesting inelastic demand in line with other studies. This suggests that a 10 per cent increase in price leads to a 3 per cent reduction in usage. Household size is an important determinant of water usage more so than income, which was only significant at the 10% level in one of the model runs. 18

Results Elasticities (Model comparisons) Model (1) Model (2) Model (3) Model (4) Linear levels Average price Linear levels Marginal price Log-linear Average price Log-linear Marginal price Price -0.1308-0.1661-0.3129-0.2236 Price1lag 0.0532 0.3233 0.2002 0.0804 Price2lag 0.0074-0.0487-0.0022-0.0205 Price3lag -0.0190-0.0956-0.0039-0.0755 Income 0.0230 0.0158 0.0050 0.0044 Number of Adults 0.1928 0.1363 0.0416 0.0324 Number of Children 0.0369 0.0164 0.0098 0.0064 19

Results: Estimators comparison Model (1) Pooled OLS Model (2) Fixed Effects Model (3) First Differences Model (4) GMM Lagged usage 0.710 *** 0.193 *** AvPrice -0.0349 *** -0.0368 *** -0.0346 *** -0.0316 *** AvPrice1lag 0.0223 *** -0.00528 *** -0.00128 0.00714 *** AvPrice2lag -0.000253-0.000596 0.00109 0.00171 AvPrice3lag -0.000443 0.000239 0.00236 ** 0.000520 Income 0.00487 * 0.750 *** Rainwater Tank -0.00942 Swimming Pool 0.0599 *** Garden size 0.0195 ** Vegetable Garden 0.0216 * Drip Watering System 0.0450 *** Evaporative cooler 0.0228 ** Number of Adults 0.0717 *** Number of Children 0.0371 *** Rainfall 0.000767 *** 0.000290 * 0.00148 *** 0.000709 *** Av Max Temperature 0.0222 *** 0.00370 * 0.0123 *** 0.00998 *** Summer D 0.0924 *** 0.179 *** 0.147 *** 0.162 *** Constant 0.139 * 3.746 *** N 6310 6310 5816 5816 Adj-R-squared 0.790 0.370 Rho 0.7624 20

Results estimators comparisons Different estimators The fixed effects model washes out the household heterogeneity and estimates time varying parameters. The parameter rho indicates 76 per cent of variation is due to household specific heterogeneity. The first differences model is a first differenced equation, which again washes out household heterogeneity. The GMM model (similar to the model used in Abrams et al. 2012) indicates that income is significant a dynamic panel model.. Each estimator gives a similar average price coefficient and significance. Summer also significant 21

Results comparison of different households Standalone-houses vs units/apartments Log-linear depending on type of dwelling, smaller sample of units/apartments Many characteristics not significant or relevant for units. Price variable significant at the 1% level. Number of adults still significant at 5% level, but not the number of children. Elasticities Similar price elasticities between dwelling types. A negative income elasticity although coefficient not significant. 22

Results comparison of different households Owners vs renters Many of the dwelling characteristics not significant or relevant for renters. Price variable significant at the 1% level. Summer dummy and rainfall not significant for renters. Elasticities Price elasticity positive for renters this reflects that the average price does not include fixed costs. In this case the more usage the greater the prices because of the increase block tariff. Price elasticity for owners same as for stand-alone houses suggesting the a 10% increase in price there is a 0.9% decrease in water usage. 23

Results comparison of households Model (1) Model (2) Model (3) Model (4) Stand-alone Units Owners Renters Lagged usage 0.692 *** 0.818 *** 0.670 *** 0.802 *** AvPrice -0.0356 *** -0.0289 *** -0.0354 *** 0.191 *** AvPrice1lag 0.0214 *** 0.0256 *** 0.0200 *** -0.0913 * AvPrice2lag 0.000720-0.00506 ** -0.000998-0.130 AvPrice3lag -0.000950 0.00185-0.00111 0.0734 Income 0.00564 * -0.00126 0.00348 0.0147 Rainwater Tank -0.0156-0.0148-0.0244 ** 0.0563 Swimming Pool 0.0613 *** 0.0671 *** 0.0490 Garden size 0.0152 * 0.00179 0.0207 ** 0.0213 Vegetable Garden 0.0186 * 0.0131 0.0272 ** -0.00175 Drip Watering System 0.0446 *** 0.0362 0.0410 *** -0.0305 Evaporative cooler 0.0182 0.0212 0.0199 * 0.0394 Number of Adults 0.0715 *** 0.0532 ** 0.0682 *** 0.0588 *** Number of Children 0.0365 *** 0.0271 0.0379 *** 0.0337 ** Av Max Temperature 0.0226 *** 0.0200 *** 0.0226 *** 0.0262 *** Rainfall 0.000668 *** 0.00129 *** 0.000663 *** 0.000831 Summer D 0.102 *** 0.00750 0.0991 *** 0.0686 Constant 0.249 *** -0.144 0.360 *** -0.545 * N 5297 716 5601 699 Adj R-squared 0.767 0.808 0.795 0.790 24

Results Elasticities dwelling types Model (1) Model (2) Model (3) Model (4) Stand-alone Units Owners Renters AvPrice -0.0914-0.0744-0.0911 0.4906 AvPrice1lag 0.0550 0.0658 0.0513-0.2348 AvPrice2lag 0.0018-0.0130-0.0025-0.3338 AvPrice3lag -0.0024 0.0047-0.0028 0.1887 Income 0.0058-0.0012 0.0035 0.0152 Number of Adults 0.0415 0.0309 0.0039 0.0341 Number of Children 0.0096 0.0072 0.0100 0.0089 N 5297 716 5601 699 25

Summary Demand is found to be inelastic This is found using different estimators. Across Dwelling types but not when accounting for renters (use Marginal price) Other key determinants of water consumption: Household characteristics such as garden size and swimming pool. The size of the household. Household income in the pooled OLS model is not significant. Seasonal variation as picked up by the summer variable. 26

Table 3 Summary statistics of variables Variable Count Mean sd min max Log Billed usage 11253 3.484603.6999926 0 5.932245 Billed usage (Kl) 11440 40.13977 29.76123 0 377 Billed amount ($/quarter) 11440 250.6856 156.3248-2033.06 1741.35 Total cost ($/quarter) 11440 281.3342 145.3623 0 2107.392 Marginal Price ($/Kl) 11253 1.428.8818219.3037 2.597 Average Price ($/Kl) 11253 8.962852 8.00437 2.859612 157.5075 Income 8560 3.596262 1.7428 1 7 Rainwater Tank 10704 1.31988.4664518 1 2 Swimming Pool 10704 1.091181.2878796 1 2 Garden size 10704 1.898356.7203228 1 3 Vegetable Garden 10704 1.41704.4930927 1 2 Drip Water System 10704 1.252616.4345328 1 2 Evaporative cooler 11344 1.335684.4722499 1 2 Number of Adults 11440 2.025175.796484 0 8 Number of Children 11440.9272727 1.175689 0 6 Average Max Temp ( C) 11440 21.055 4.651484 15.43 28.73 Rainfall (ml) 11440 160.175 61.34025 54.8 344.2 27

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