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What does radical price change and choice

reveal?

A project by Yarra Valley Water and the Centre for Water

Policy Management

November 2016

2La Trobe University

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.


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


Previous literature

� Previous estimates of the price elasticity of demand indicate an

inelastic demand for water.

� Meta analysis:

Dalhuisen et 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.


Table 2: Estimated price elasticities in Australia

Author(s) Data Location Price Elasticity Method Function

Hoffman,

Worthington and

Higgs (2006)

Panel Brisbane SR -0.588

LR -1.16

OLS Linear

and log-

log

Grafton and

Kompas (2007)

Panel Sydney -0.352 OLS Linear

Grafton and Ward

(2008)

Aggregate Sydney -0.17 OLS Linear

Abrams, Sarafidis,

Kumaradevan and

Spaninks (2012)

Panel Sydney SR -0.082

LR -0.139

GMM Log-

linear

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 log-

linear


Complications

� A problem 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 non-

linear prices


Figure 1 Budget constraint with nonlinear pricing

I3

I2

I1

QX

QWQK


Complications

� A second estimation issue with nonlinear pricing is what price

to use; marginal, average prices, both and also a difference

variable (Nordin 1976)

� 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


Econometric method

� Based on the data and potential problems in estimation we

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


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.


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 re-

constructed 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.


Figure 2 Quarterly mean usage (Kl)

0

10

20

30

40

50

60

01-J

ul-

11

01-S

ep-1

1

01-N

ov-1

1

01-J

an-1

2

01-M

ar-1

2

01-M

ay-1

2

01-J

ul-

12

01-S

ep-1

2

01-N

ov-1

2

01-J

an-1

3

01-M

ar-1

3

01-M

ay-1

3

01-J

ul-

13

01-S

ep-1

3

01-N

ov-1

3

01-J

an-1

4

01-M

ar-1

4

01-M

ay-1

4

01-J

ul-

14

01-S

ep-1

4

01-N

ov-1

4

01-J

an-1

5

01-M

ar-1

5

Mea

n U

sag

e K

l

Aggregate mean usage by Quarter (Kl)


Figure 3 Average temperature and rainfall by quarter

0

50

100

150

200

250

300

350

400

0

5

10

15

20

25

30

35

01

-Ju

l-1

1

01

-Se

p-1

1

01

-No

v-1

1

01

-Ja

n-1

2

01

-Ma

r-1

2

01

-Ma

y-1

2

01

-Ju

l-1

2

01

-Se

p-1

2

01

-No

v-1

2

01

-Ja

n-1

3

01

-Ma

r-1

3

01

-Ma

y-1

3

01

-Ju

l-1

3

01

-Se

p-1

3

01

-No

v-1

3

01

-Ja

n-1

4

01

-Ma

r-1

4

01

-Ma

y-1

4

01

-Ju

l-1

4

01

-Se

p-1

4

01

-No

v-1

4

01

-Ja

n-1

5

01

-Ma

r-1

5

ml p

er

qu

art

er

C°

Average Temperature Rainfall


Figure 4 Quarterly demand for residential water

05

01

00

15

0

Ave

rag

e P

rice

$/K

l

0 100 200 300 400Billed Usage Kl/Quarter


05

01

00

15

0A

ve

rag

e P

rice

$/K

l

0 2 4 6Log of Billed Usage

Figure 5 Quarterly demand for residential water (log of usage)


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 R2 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.


Results – Model comparisons (linear v log-linear)

Model (1) Model (2) Model (3) Model (4)

Linear levels

Average price

Linear levels

∆Marginal price

Log-linear

Average price

Log-linear

∆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


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.


Results – Elasticities (Model comparisons)


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


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


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


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.


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.


Results – comparison of households


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


Results – Elasticities dwelling types


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


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.


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

Thank you

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