Power from the people: opportunity cost
and income fungibility in solar homes
Andrea La Nauze
University of Melbourne
Job Market Paper∗
November 15, 2015
Abstract
As households increasingly become suppliers of goods and services such as electricity, accommodation and transport, household decision making may lead to counter-intuitive responses to price
and income. Using high-frequency electricity-meter data, I document the surprising behaviour of
households who sell excess power from their solar panels: on average when prices to sell are high,
households keep more power for their own use. I exploit a discontinuity in the opportunity cost
of consuming power when a household sells excess electricity to test whether they are attentive to
foregone revenue. I nd no evidence that households are inattentive to opportunity costs. I do nd,
however, that small uctuations in solar income cause households to keep more power for their own
use. I demonstrate that this behaviour is inconsistent with the fungibility of money: on average
solar households sell 40 percent less electricity than they would if their response to solar income
was consistent with responses to non-solar income. Moreover as solar production increases I nd
that the income eect dominates the substitution eect.
An unintended consequence of paying
higher subsidies to sell electricity may be that solar homes supply less power back to the grid.
∗
I thank Yann Burden and Billcap for providing proprietary data and Dylan McConnell for assistance with accessing
data from PVOutput.org. I also thank my advisers: David Byrne, Leslie Martin and Claudio Mezzetti. I have received
helpful comments from Peter Berck, Judson Boomhower, Jim Bushnell, Severin Borenstein, Mick Coelli, Matthew Gibson,
Lorenzo Goette, Ryan Kellogg, Arik Levinson, Guy Mayraz, Alberto Salvo and Leo Simon as well as seminar participants at UC Berkeley, Lawrence Berkeley National Lab, Melbourne University and audience members at the Australian
Conference of Economists. All errors, omissions and views are my own.
1
1
Introduction
In markets such as transport, accommodation and electricity, households increasingly sell excess
goods and capacity alongside rms (such as AirBnb for accommodation and Uber for transport).
These new exchanges complicate decision making by introducing new prices and income streams.
In these markets, if decision makers are inattentive to the opportunity cost of foregone revenue or
if they use heuristics to manage expenditure, household behaviour may be counter-intuitive.
In renewable energy, household decision making may distort the extent to which those with solar
photovoltaic (PV) panels respond to incentives to sell electricity. For example, the marginal cost
of producing electricity from installed solar panels is zero. But if households are paid to sell excess
power (electricity produced by solar panels and not consumed), the opportunity cost of consuming
it is foregone revenue.
Anecdotal evidence suggests that households may ignore or underweight
opportunity costs, particularly when the cost of production, the explicit cost of consumption, is
zero (Ariely, 2009; Thaler, 1980). Households may therefore fail to respond to an increase in the
price they receive to sell electricity. Furthermore, if solar revenue is provided to households via their
electricity account, they may spend income from solar generation disproportionately on electricity.
Such behaviour is consistent with theories of mental accounting and category budgeting, but it is
1
inconsistent with the fungibility of money.
In this paper I use high-frequency electricity meter
data to test whether the behaviour of households who sell excess electricity from their solar panels
is consistent with attention to opportunity cost and money fungibility.
This study helps shed light on a critical issue for economists and policy makers. Understanding
the relationship between opportunity costs and decision making is important, but researchers face a
challenge: opportunity costs are often invisible or impossible to measure. A laboratory environment
provides one tool for negotiating this problem, as researchers can create and observe foregone
alternatives. Laboratory and anecdotal evidence do suggest that decision makers (and academic
economists) do not consider or have trouble calculating opportunity costs (Bastiat, 1850; Thaler,
1980; Shavit et al., 2011; Phillips et al., 1991; Becker et al., 1974; Frederick et al., 2009; Ferraro and
Taylor, 2005). Ideally this research would be augmented with comparable evidence from the eld,
but there is scant evidence available.
2
I formulate a test of opportunity cost based on comparing
how households respond to forgone revenue from selling electricity, an implicit price, with how they
respond to the nancial outlay from buying electricity, an explicit price.
The second aspect of behaviour I study is how households respond to income from their solar
production. Solar income is the value of a household's endowment of solar electricity. The magnitude and predictability of solar income mean that uctuations in the ow of earnings should
have little eect on consumption of any goods. In particular, estimates of income elasticities suggest that uctuations in solar income at the hourly, daily or even monthly level should not have
a detectable eect on electricity consumption. In contrast to the life-cycle income hypothesis, a
1 Mental accounting is the theory that people allocate income to consumption or saving based on its source (Thaler,
1990). Category budgeting is the theory that individuals hold mental budgets for expenditure on items within the same
category (Heath and Soll, 1996). Expenditure and income across budgets are not considered substitutable.
2 There is some evidence that rms are attentive to the implicit price of free emission permits (Fabra and Reguant,
2014). There is also informal evidence that decision makers respond to opportunity costs in the form of explicit prices
(i.e. demand curves are downward sloping).
2
number of studies nd that the marginal propensity to consume out of minor windfall gains is high
and that consumers do respond to predictable variation in income (Jappelli and Pistaferri, 2010).
In addition, several studies demonstrate that the marginal propensity to consume diers by how
income is received(Milkman and Beshears, 2009; Beatty et al., 2014). In this paper I estimate the
sensitivity of household electricity consumption to small changes in the ow of solar income.
If
households are forward looking and treat money as fungible then they should not respond to these
uctuations and should not spend a higher proportion of their solar income on electricity than they
would non-solar income.
To explore the behaviour of solar homes I utilise a panel of 528 households for whom I observe
purchases (imports) and sales (exports) of electricity at the half-hour frequency.
At the hourly
level I match each observation to meteorological measurements of temperature and solar irradiance
(a measure of the energy being delivered from the sun). To test for responses to opportunity cost
and money fungibility, I exploit variation in both the price that a household receives to sell power
to the electricity grid (i.e. export electricity) and the price that a household pays to buy electricity
(i.e. import electricity). This sell price, called a feed-in tari, can be three times the cost of buying
from the grid. Perhaps counter-intuitively, for solar homes the opportunity cost of consuming their
own solar power can therefore be higher, not lower, than what it costs them to buy power. For
most households, the cost of consuming electricity changes discontinuously at the point at which
their solar production exceeds their consumption and at which they begin to sell their excess solar
power.
For each hour of the day, I separately identify households' response to foregone revenue
and their response to the cost of buying electricity. To do so I use level dierences in consumption
across households on either side of the discontinuity in the cost of consumption.
If households
are attentive to opportunity costs their response to foregone revenue and to the price of buying
electricity should be the same. In my empirical specication I then isolate the eect of solar income
using dierences in the gradient of consumption across households as solar production, and hence
solar income, rises.
My identication strategy uses instrumental variables to overcome three endogeneity problems.
The rst is that households can only sell electricity when their consumption is lower than their
current solar production. To address this simultaneity problem, I use the fact that for the same level
of consumption, variation in solar production will sometimes induce households to sell electricity
and sometimes induce them to buy it.
Controlling for temperature, the identifying variation is
dierences in solar production within feed-in tari group. The second identication problem arises
because the price of buying power is determined by a household's choice of pricing-plan.
To
overcome the potential selection problem I use variation in price due to spatial discontinuities
in electricity distribution zones and historical meter allocations.
Finally, because of changes in
government policy, early adopters receive higher prices to sell electricity. I use variation in mean
irradiance across location as a proxy for the productivity of solar panels to instrument for early
adoption. The identifying assumption is that the availability of sunshine aects when a household
installs solar panels because payback periods are more attractive, but it is not correlated with other
household characteristics that aect electricity consumption.
Several patterns in the data suggest that solar households may respond disproportionately to
uctuations in solar income.
First, all households consume more as their panels produce more,
3
regardless of opportunity cost. One explanation for this behaviour, consistent with neo-classical
principles, is that solar production is highest on sunny days when air conditioning demand is
simultaneously high. Another possibility is that solar households prefer to consume solar power
than electricity from the grid - perhaps because they feel less guilty about consuming energy that
is free from fossil fuels. Yet in the neighbourhood of the price discontinuity, when households rst
begin to sell power, those with a high opportunity cost consume the least. Moreover the gradient of
consumption with respect to sales of electricity is largest for those households earning the greatest
income. This descriptive evidence suggests that changes in income, and not temperature, guilt, or
inattention to opportunity cost, may cause households to consume more as they produce more.
My results formalise the descriptive evidence. The data reveal no (statistical) dierence between
how households respond to forgone revenue and how they respond to the cost of buying power;
I fail to reject the hypothesis that households respond to the opportunity cost of their electricity
consumption. I do nd, however, that households respond strongly to uctuations in their solar
income.
Solar households consume more electricity as a result of high average income (earned
over the previous 30 days). They also consume more in hours in which they earn higher income. I
argue that these income eects are too large to be consistent with money fungibility and a standard
income elasticity. The behaviour is instead consistent with behavioural models of mental accounting
and category budgeting. A household receiving an additional 1% of average weekly income in the
3
form of solar income increases their electricity consumption by 35%.
In the literature the highest
estimate of the short-run income elasticity of electricity consumption is one tenth the size (Espey
and Espey, 2004). Viewed from the perspective of sales of electricity, the results suggest households
would sell 40% more electricity if they treated solar income as fungible.
I fail to nd support for alternative explanations for the results, including heterogeneous preferences for consuming solar vs grid-based power or dierential use of air-conditioning across feed-in
tari groups.
I also nd no evidence that households respond to the net average cost of their
consumption instead of responding to marginal cost and income. I subject the results to a number of additional robustness checks including using alternative instruments, using within-household
variation only, restricting the sample to a single capital city, and adopting alternative functional
forms. The ndings survive all these checks.
My results indicate that when they are selling, a household with a high feed-in tari consumes
less because of the substitution eect (they are attentive to opportunity cost) but they consume
more because of the income eect (they violate fungibility). I demonstrate that as solar production
rises, the income eect can dominate the substitution eect. Thus as feed-in taris rise, consumption may increase whilst sales may decrease.
An unintended consequence of higher subsidies to
sell electricity may therefore be a reduction in sales by households with solar panels. Perversely,
I show that the eect of income is highest at times of peak demand when electricity is the most
valuable. These ndings suggest that lump sum subsidies may be a more ecient way to support
rooftop solar. The results also indicate that third-party ownership and power-purchase agreements
between panel owners and householders may result in increased sales of electricity at the intensive
margin.
This paper makes two distinct contributions. First, I implement a unique eld test of whether
3 A 1% change average weekly income is approximately equivalent to an 80% change in solar income.
4
households respond to opportunity cost. In contrast to laboratory and anecdotal evidence, I identify behaviour consistent with attention to opportunity cost. I do, however, document behaviour
that is inconsistent with the fungibility of money.
Milkman and Beshears (2009), Hastings and
Shapiro (2013), Beatty et al. (2014) and Abeler and Marklein (forthcoming) also demonstrate that
household expenditure violates fungibility.
In addition, Beatty et al. (2014) and Hastings and
Shapiro (2013) document large deviations between the elasticity of consumption with respect to
alternative sources of income that are consistent with category budgeting and mental accounting
and of similar magnitude to the dierences I nd.
The second contribution I make is to document household behaviour in a relatively new and
policy-relevant setting. A growing literature seeks to explore how behavioural insights might lead to
better predictions of policy impact and improve policy design (Chetty, 2015). While the literature
on the extensive margin of solar adoption is maturing (Bollinger and Gillingham, 2012; Burr, 2012;
Graziano and Gillingham, 2014; Hughes and Podolefsky, 2015; Lamp, 2014), I have yet to nd
any empirical research on the electricity consumption behaviour of solar homes (i.e. the intensive
margin).
4
This margin of behaviour is critical to understanding the impact of rooftop solar on
electricity networks and emissions.
The remainder of the paper is structured as follows. Section 2 provides background on feed-in
taris and solar PV. Section 3 outlines data sources, presents descriptive statistics and descriptive
evidence.
Section 4 discusses the empirical strategy.
Section 5 presents results and discusses
demand and supply elasticities before Section 6 concludes.
2
Rooftop solar, opportunity cost and income
2.1 Background
Solar photovoltaics have far reaching consequences for climate change and the energy sector. Residential solar has been growing rapidly around the world, most notably in Germany, California,
Hawaii and Australia.
This growth is a response both to policy support for renewable energy,
and to the rapidly declining costs of solar panels. A number of studies aim to assess the impact
of policy on adoption of rooftop solar (Burr, 2012; Bollinger and Gillingham, 2012; Graziano and
Gillingham, 2014; Hughes and Podolefsky, 2015). At the heart of the policy debate are two key
questions: (1) what is an appropriate level of support for rooftop solar? and (2) what are the most
appropriate mechanisms for subsidising and/or compensating households for supplying electricity
to the grid (see for example Baker et al. (2013); Borenstein (2008, 2015))?
A thorough under-
standing of how households respond to compensation mechanisms once their panels are installed is
required to answer these questions. At the time of writing, this was the rst known paper to study
behaviour at the intensive margin of solar production.
The combination of high penetration of rooftop solar panels, the availability of high frequency
meter data and variation in prices, make the state of Victoria, in Australia, well suited to the study
of the intensive margin of solar production. In Australia, residential rooftop solar is now widespread.
4 Baker et al. (2013) provide an overview of the economics of solar PV whilst Borenstein (2008) and Borenstein (2015)
model the costs and benets of solar PV and their distribution.
5
Generous subsidies and high electricity prices have resulted in rates of rooftop solar penetration as
high as 30% in some Australian states making it the largest per capita residential solar market in the
world (APVI, 2015).
5
Solar penetration amongst households in other jurisdictions like California
and Germany is well below 5% but rooftop solar is growing rapidly worldwide.
6
In addition to high penetration of rooftop solar, in Victoria all households are tted with smart
interval meters recording electricity ow at the half-hourly frequency. Electricity is a homogeneous
product so the physical experience of using electricity produced by solar panels is no dierent
to electricity from any other source. Energy production is a function of a PV system's capacity
and a range of external conditions.
Per unit of capacity, production is then a function of the
direction and tilt of the panels as well as seasonal and climatic factors that aect irradiation and
temperature. So, for example, panels are less ecient on hot days and when there is cloud cover.
Maximum output therefore tends to occur at midday on summer days that are clear but not hot.
The variability of solar production within and across days makes high-frequency data critical to
the study of behaviour at the intensive margin.
Variation in prices is also critical to the analysis of household behaviour. Across jurisdictions,
feed-in taris are the most widely adopted form of support for renewable energy (REN21, 2015). A
feed-in tari is a guaranteed price for electricity generated by solar panels. In Australia (as in other
major solar installing jurisdictions such as Hawaii in the United States and increasingly in Europe)
owners of solar panels are credited for electricity generation they do not consume, excess electricity
that they sell to the grid. They are charged for all electricity they buy from the grid. This system
is referred to as one of net feed-in taris.
In Australia the price a household receives to sell is
determined by enrolment in a government feed-in tari (FIT) program. FIT programs guarantee
households a given rate for their sales of electricity over a set period of time (often more than 10
years) and have been used as a mechanism to encourage solar installation. Program eligibility is
primarily a function of date of installation though other technical requirements also exist.
As the cost of solar panels has declined, so too have the subsidies available to households who
install them. Early feed-in taris were equal to or above the cost of buying electricity. More recent
feed-in taris are well below the cost of buying electricity.
Because net feed-in taris only pay
for electricity that is not consumed within the house at exactly the same time (i.e. balancing is
instantaneous), households enrolled in dierent feed-in tari programs face consumption incentives
that vary instantaneously with the level of solar production. In the next section I outline a model
of how variation this variation in solar production causes changes in price and solar income.
5 As of 2014 one in ve Australian households were generating some form of solar electricity, the vast majority from
photovoltaic (PV) panels (ABS, 2014).
There are a number of reasons for the high level of uptake.
First, Australia
has vast solar resources. As a continent Australia has the highest solar irradiance per metre in the world (Geoscience
Australia, 2010). Second, over the period 2010 to 2015 the cost of solar PV more than halved. In 2010 the cost of a
kilo-Watt (kW) was close to $AUD6000. By 2015 it was less than $AUD2500 (APVI, 2015). Third, households received a
range of overlapping state and federal government subsidies. Finally, solar PV has become more attractive as the cost of
electricity to the end-user has increased. For a Victorian household the cost of using electricity increased by more than 50
percent from 2009 to 2014 (ESC, 2015). These price increases are largely attributed to the cost of network management
and augmentation by regulated network monopolies. The combination of these factors has meant that there is now a
non-trivial number of Australian households producing and consuming electricity from rooftop solar.
6 In the U.S. rooftop solar is growing at approximately 50% p.a.(GTMR and SEIA, 2015)
6
2.2 Conceptual framework
To explore the impact of net feed-in taris on a household's hourly electricity price and solar
income I outline a very simple static model of household electricity demand in an hour. Consider a
consumer with the following well-behaved utility function for consumption of electricity in a given
hour:
U = ν(q) + g(a)
where
q
is electricity consumption in the hour and
a
(1)
is the numeraire. Households have non-solar
0
income y and an endowment of solar production in that hour of
than they produce at the same time (q
to the grid equal to
f [s − q],
where
f
s.
If they consume less electricity
< s) then they earn revenue from selling the excess electricity
is the feed-in tari (price paid for exporting or selling power).
If the household consumes more electricity than they produce at the same time then (q
they pay for electricity that they buy equal to
r[q − s],
r
where
> s)
and
is the retail cost of electricity
(price paid for importing or buying power). The household trades-o electricity consumption for
the numeraire such that their budget constraint is satised:
a = y 0 + 1(s > q) × f [s − q] − 1(q > s) × r[q − s]
where
1()
(2)
is the indicator function. Substituting in to the utility function:
U = ν(q) + g y 0 + 1(s > q) × f [s − q] − 1(q > s) × r[q − s]
Then the consumer's demand function in that hour must satisfy

ν 0 (q) − f g 0 (y 0 + f [s − q]) = 0
q(p, m) :
ν 0 (q) − rg 0 (y 0 − r[q − s]) = 0
7
(3)
:
if
if
s>q
(4)
q>s
More generally the consumer's demand function in the hour satises:
q(p, m) : ν 0 (q) − pg 0 (y 0 − pq + ps) = 0
for
According to this model the consumer responds to price
electricity in the same way they respond to the price
electricity. Solar income
electricity
s
m = ps

f
p=
r
p=f
p = r
when
when
if
s>q
if
q>s
s>q
q > s
(5)
and they are selling
and they are buying
accounts for the fact that the household has an endowment of
that is valued at current price
p.8
Note also that this household treats income as
7 These expressions are known as conditional demand functions because they are conditional on consuming at a
level above or below
s.
The consumer's unconditional demand function species the unconditional choice over whether
to consume above or below
s
as well as how much to consume given the implied price.
households with
f >r
it is never optimal to consume at
q = s.
f < r
q = s. For
For households with
the unconditional demand function also includes the possibility that the household consumes at the point
To illustrate how net feed-in taris aect marginal price
and income I focus on the conditional demand functions.
8 This income is similar to what has been called
virtual income, dierence or a rate structure discount
in the literature
on labor supply and water and electricity demand in the presence of non-linear price schedules (Olmstead et al., 2007;
7
fungible, that is an increase in solar income
m
is equivalent to an increase in non-solar income
y0.
The eect of a net feed-in tari on the household's hourly budget set it depicted in Figure 1.
Panel (a) depicts the budget set of a household who faces a feed-in tari
buying power (f
< r).
f
less than the cost of
Panel (b) depicts the budget set of a household who faces a feed-in tari
that is greater than the cost of buying power (f
> r).
f
If solar production is zero then the household
0
can buy up to y units of the numeraire or if they spend all their income on electricity they can
buy
y 0 /r
units of electricity. Now assume that a household's panels produce
s units.
If a household
sells all this solar power (and therefore consumes no electricity) they can purchase a total of
y0 + f s
units of the numeraire. Every unit of electricity they consume up to the level of solar production
s
reduces feasible expenditure on the numeraire by
q<s
is
−f .
f
units. Hence the slope of the budget set for
If on the other hand the household consumes all their solar power and spends their
entire budget on electricity they can consume
(y 0 /r) + s.
intercept of the budget set when households are selling (q
Across households both the slope and
< s)
and intercept of the budget set when households are buying (q
are very dierent while the slope
> s)
are identical.
The model and budget sets demonstrate three things: rst, the feed-in tari is the opportunity
cost of consuming a unit of electricity when a household is selling. Second, there is a kink in the
budget set at the point where consumption of electricity is equal to production of electricity (at
q = s).
These kinks mean that consumption and price are jointly determined.
In what follows
I follow a common strategy in the empirical literature to deal with this problem; I use solar
production as to instrument for whether households are buying or selling and hence which segment
of the budget set they choose to consume at. I will then compare how households respond to the
opportunity cost of foregone revenue with how they respond to the cost of buying.
The rst is
an implicit price not an actual nancial outlay, the second is an explicit price. If households are
attentive to opportunity costs then responses to these two forms of price should be the same.
Finally, solar income in a given hour is the endowment of solar production valued at current
price.
For illustrative purposes, the shift out in the budget set reects the exaggerated eect
of solar income relative to the true magnitude of non-solar income
y0.
In practice, across hours
household consumption should reect average solar income over the year and should not respond
to uctuations in the ow of income from solar production at the hourly, weekly or even monthly
level. In addition, because money is fungible, any change in consumption as a result of changes
in average solar income should still be commensurate with the response to changes in non-solar
income: money fungibility means households should treat income independent of its source. I will
use dierences in solar production and the value of that production at the hourly and monthly
level to identify the eect of solar income. I will then compare this response to the elasticity of
consumption with respect to non-solar income. Before I outline in detail how I will estimate the
responses to these forms of income and price I outline the data to be used and discuss descriptive
evidence on household behaviour.
Mott, 1990; Reiss and White, 2005).
8
3
Data and descriptive evidence
3.1 Data
This paper combines data from a number of dierent sources. These data are: interval meter data,
price data, weather and satellite data, solar production data, and household demographic data at
the census block (Statistical Area Level 1) level.
The primary data source is an unbalanced panel of half-hourly meter reads from a set of 528
Victorian households with solar panels covering the period January 2012 to June 2013. Meter data
consists of electricity exports (sales) and imports (purchases) measured in kilowatt hours (kWh).
In Australia the electricity sector has undergone substantial reform including vertical separation of
retail, distribution and production of electricity. In Victoria there is full competition for electricity
retailing services.
9
My sample of households is from a single small online-only retailer. For this
set of households I also observe postcode, distribution zone, network tari and plan type, feed-in
tari program enrolment and a Statistical Area Level 1 (SA1) identier (the smallest spatial scale
for which Census data are available).
The Victorian retail electricity market is not price regulated.
For each household I observe
meter type, distribution zone and plan choice. Using this information I match each observation to
price data from two sources. First, I use price data from the Essential Services Commission's price
comparator website for the period January 2012- June 2012. The Essential Services Commission
(ESC) is the regulatory body with oversight for retail electricity in Victoria.
10
The second source
of data I use comes directly from the retailer's website (available for July 2012-June 2013).
In
Appendix A.1 I verify the price data using invoice data from a separate set of households without
solar panels.
I use the centroid of a household's postcode to match the meter data to weather observations
from 358 Bureau of Meteorology (BoM) weather stations.
For these weather stations I observe
ground measurements of 3 hourly temperature, intra-day cloud coverage as well as daily rainfall. I
also match each household to gridded hourly solar irradiance measures derived by the BoM from
satellite observations. I observe global horizontal irradiance (GHI) and direct normal irradiance
(DNI) for 18 000 grid points across the state.
Weather and satellite data are used for two purposes.
First, they are used to construct a
measure of solar production for each hour and household in the sample and impute a measure of
consumption. Net meters collect import and export data. Consumption is equal to net imports
(imports minus exports) plus solar production. Solar production and consumption are unobserved,
latent variables. To construct a measure of solar production I utilise a separate source of hourly
solar production data covering the period January 2012-December 2013. The data are sourced from
PVoutput.org, a public website enabling individuals with solar panels to upload and share their
solar production data.
For this group of individuals I also observe system capacity, installation
date and latitude and longitude. Appendix A.2 provides further detail on the data and the method
9 Retailing services include metering and billing end-use consumers. Distribution and transmission (networks of poles
and wires) are upstream privately owned regulated natural monopolies.
10 The ESC maintains quality oversight and licenses electricity retailers.
9
11
used to predict solar production and hence impute consumption.
Second, weather data are used
as controls in the econometric model.
Table 1 presents descriptive statistics of the main variables of interest by feed-in tari program
and for the sample as a whole. The rst panel presents means and standard deviations for the raw
data. The second panel presents means and standard deviations for derived variables: consumption,
solar production and solar capacity. A household's FIT program is determined by the date at which
they installed solar panels. Actual date of installation is not observed. Households receiving the
12
Standard FIT (1:1 FIT = import price) are the earliest adopters.
Households receiving the
Provisional FIT (60 FIT =60c/kWh) installed solar before the end of 2011.
before 2012 were eligible for the Transitional FIT (25 FIT = 25c/kWh).
13
Households installing
The Minimum FIT (8
14
FIT =8c/kWh in the sample period) is open to any household installing solar from January 2013.
Thus in general households who installed earlier receive higher feed-in taris.
Average peak price is 31c/kWh while average o peak price is 14c/kWh. The mean import price
across peak and o peak between 9am and 5pm is approximately 25c/kWh (not reported). Table
1 also gives a sense for the magnitude of solar income. On average the value of solar production
(i.e.
Solar income )
is just over $20/week.
Despite producing and exporting power, households
in the sample continue to pay their electricity retailer net power charges (cost of imports minus
the revenue from exports) of $8/week.
Daily xed charges are just under $1/day so on average
households pay a weekly bill of around $15/week. Across all feed-in tari programs, on average
households continue to pay a weekly bill for electricity consumption.
To explore whether households dier on observable characteristics by feed-in tari group I use
the SA1 identier to match households to demographic information from the 2011 Australian Census and 2013 Federal Election results. Columns 1-4 of Table 2 report demographic characteristics
for each feed-in tari group, for the sample as a whole (column (5)) and for the state as a whole.
Households in dierent feed-in tari programs do not appear to live in neighbourhoods that dier
on observable characteristics. In my baseline estimates I will therefore take feed-in tari program
as exogenous. In subsequent estimations I allow for the possibility that feed-in tari program is
endogenous.
Balance on observable characteristics across households in dierent feed-in tari programs is
important for internal validity. For the purposes of external validity it is important that the sample
is representative of the broader population. There are many reasons to believe that solar households
dier to non-solar households. For example, barriers to installation on rental properties may mean
11 I permanently drop 20 households with Two Rate network tari assignment, 54 households who are estimated to
consume more than 75kWh in a single day and 2 households who record exporting overnight.
I drop any household
for whom I do not observe a postcode and I drop any observation between 9am and 5pm for which satellite irradiance
measures are not available. I also drop any date for which total estimated consumption is less than 2kWh and any hour
that estimated consumption is negative or zero.
12 Households installing from 2007-2012 were eligible for the Standard FIT. Those installing under 5 kW of capacity
(the majority) between 2009 and 2012 were allocated to other FIT programs that were open at that time hence on average
SFIT customers were earlier installers
13 All gures in the paper are in Australian dollars (AUD). Over the last 4 years the exchange rate between the US
dollar (USD) and AUD has been close to 1. As of October 2015, the exchange rate is 1 AUD = 0.73 USD
14 The obligation to fund feed-in taris also diers by program: 60 FIT and 25 FIT were funded by regulated distribu-
tors, 1:1 FIT and 8 FIT are funded by retailers. From 2013 households installing solar panels are paid a Minimum feed-in
tari where the rate is determined annually by the Essential Services Commission. As of 2015 the rate is 6c/kWh.
10
that the solar installing households are more likely to be owner-occupiers. Comparing column (5)
and (6) of Table 2 shows that relative to the state average, the sample live in neighbourhoods
with larger houses, with a greater proportion of separate dwellings and higher incomes. On the
other hand they live in neighbourhoods where there is a lower proportion of households with a
Bachelor degree, a lower proportion of houses that are owned outright and lower support for the
Australian Greens party (a measure of environmental preferences). In Appendix Table A.4 I use
the results of a national survey to show that observable characteristics at the household level do
not suggest that solar homes are a much wealthier, better educated and more environmentally
conscious sub-population (AER, 2015).
3.2 Descriptive evidence
Before I lay out the empirical strategy I highlight correlations in the data that provide suggestive
evidence on household behaviour. Figure 3a plots mean consumption across hours of the day for
households on the 60 FIT (solid line) and 8 FIT (dotted line) for very sunny days (black lines) and
very cloudy days (grey lines). Recall that peak electricity rates are approximately 25-30c/kWh. On
very sunny days households on the 60 FIT consume
more
at all hours of the day than households
on the 8 FIT. Thus households who face a high opportunity cost consume more than households
who face a low opportunity cost. On very cloudy days we observe the opposite pattern. Thus it is
not the case that 60 FIT households always consume more. Even if we just compare consumption
within FIT group, 60 FIT households consume relatively more on sunny days.
Figure 3b plots consumption against net imports (imports of electricity minus exports of electricity) within feed-in tari group. The solid line plots the consumption of households with a high
opportunity cost when they are exporting (60 FIT). The dotted line plots the consumption of
households with a low opportunity cost when they are exporting (8 FIT). The dashed line plots
the consumption of households with an intermediate opportunity cost.
15
Mean consumption in all
groups is relatively low when households are exporting, and relatively high when households are
importing. This pattern reects the fact that households only import when their consumption is
higher than their production and that peak consumption (typically around 4pm) occurs at a time
of relatively low production because of the angle of the sun. Figure 2a shows that there is a discontinuity in the cost of consumption for 60 FIT and 8 FIT households at the point at which they
begin to export (at zero net imports). In Figure 3b we see that in the region of this discontinuity
60 FIT households consume less on average than 8 FIT households (i.e there are dierences in the
level of consumption). In particular the average consumption of 60 FIT households is less than 8
FIT households in the region immediately to the left of where the discontinuity in price occurs.
Thus consumption patterns in the immediate vicinity of the discontinuity are similar to what we
would expect if households were attentive to opportunity cost: households with an opportunity
cost of 60c/kWh consume less than households with an opportunity cost of 8c/kWh.
16
15 For some in this group there is no dierence between the opportunity cost and the import price (1:1 FIT), for others
this dierence is very small (25 FIT)
16 Consumption of 60 FIT households is also lower than 25 & 1:1 FIT households however 25 FIT households consume
more than 8 FIT households; there also appear to be level dierences between 25 & 1:1 FIT households when households
are importing.
11
Figure 3b also demonstrates that as households begin to export more, the 60 FIT households
begin to consume more relative to 8 FIT households. Once households are exporting about 0.7kWh
the mean consumption of 60 FIT households begins to increase whereas the mean consumption
of 8 FIT households remains roughly constant. Figure 2b depicts the relationship between solar
income and net imports, in particular it shows dierences in the gradient of solar income as exports
increase. The pattern of gradients in consumption (Figure 3b) closely resembles these dierences.
Hence changes in solar income for these two groups appear to be highly correlated with changes in
consumption. As further evidence for the income eect note that the opportunity cost of consumption does not change for households on 1:1 FIT or on 25 FIT however as they export more, their
income increases. Figure 3b shows that consumption of this group also increases as they export
more.
The descriptive evidence points to two things: rst, that households may be attentive to opportunity costs, second, that they may have a large income elasticity. On the one hand households
who face a high feed-in tari consume more on days when the opportunity cost is highest. On the
other, their income from solar production is also highest at these times.
The observed patterns
could therefore reect a non-standard income eect. Yet as seen in both Table 1 and Figure 2b the
variation in income for solar households is small and would not be expected to cause such notable
dierences in electricity consumption. A nal explanation is that household consumption diers
across these days because of unobserved dierences that are correlated with feed-in tari program,
such as air conditioning use or a preference for consuming solar generation. In general there are a
range of reasons why the observed patterns of behaviour may not reect the causal impact of price
and income. In what follows I outline an econometric model of electricity consumption and specify
how I explore whether households respond to opportunity cost and the fungibility of money. I then
go on the discuss my identication strategy.
4
Estimation strategy
I model demand as a linear function of current price and income.
that household
i
17
At hour
h
of day
hour of day
h.
I assume
consumes:
qihd = ηh pihd + γYihd + αg + τhd + δh Wihd + ihd
The parameter
d
ηh
(6)
governs the price-sensitivity of electricity demand and is allowed to vary by
The parameter
γ
captures the eect of total income
Yihd
(solar and non-solar
income) on consumption. In this model, time-invariant household heterogeneity at the group level
is captured by the term
τhd .
αg .
Dierences in use across hours and days of the week are captured in
Consumption of electricity also varies with characteristics such as weather which are captured
in the matrix
Wihd .
The eect of weather (δh ) is assumed to depend on hour-of-day
h but for now is
17 In my base specication I treat electricity demand as static. Households may substitute electricity across days or
hours in response to prices that uctuate. Because much of the variation within an hour-of-day is cross-sectional I abstract
away from this more complicated specication of the demand function. I ensure the results are robust to allowing for
cross-price eects.
12
18
assumed to be the same across households.
consumption shocks
Demand for electricity is also subject to idiosyncratic
ihd .
4.1 Opportunity cost
To explore whether households respond to the opportunity cost of their consumption let
the dierence between the household's import rate
tari (the price for selling power) such that:
rih
∆ocihd
be
(the cost of buying power) and their feed-in
fi = rih + ∆ocihd .
Then
∆ocihd
captures the relative
dierence in opportunity cost when a household exports (sells) electricity. Thus households on the
60 FIT and paying an import price of 25c/kWh have
∆ocihd = 35c (i.e.
opportunity cost increases)
when they export. Households on the 8 FIT and with the same import price have
∆ocihd = −17c
(i.e. opportunity cost decreases) when they export. Households with a feed-in tari equal to their
import rate have
∆ocihd = 0
at all times. Then I can re-write demand as:
qihd = ηh [rih + ∆ocihd ] + γmihd + αg + τhd + δh Wihd + ihd
where
∆ocihd
= 1(sihd > qihd ) × [fi − rih ]
1(sihd > qihd )
is the indicator function
mihd
= sihd × [1(sihd > qihd ) × fi + 1(qihd > sihd ) × rih ]
αg
are distribution zone eects
In this model I capture dierences in time-invariant non-solar income at the distribution zone level
in the xed eect
αg .
To test whether households are responsive to opportunity cost I allow parameter
ηh
qihd = ηh,1 rih + ηh,2 ∆ocihd + γmihd + αg + τhd + δh Wihd + ihd
The neo-classical consumer responds to the implicit price of foregone revenue
(7)
fi = rih + ∆ocihd
the same way they respond to a change in the explicit price of buying electricity
ηh,1 = ηh,2
to vary:
rih .
in
Therefore
if consumers are attentive to opportunity cost. The null hypothesis for the test that
households are attentive to opportunity cost is:
H0 : η1,h = η2,h
∀h
(attentive to opportunity cost)
In the following subsections I outline in detail the identication of the demand parameters.
Before doing so I briey outline how I explore household responses to solar income.
18 I estimate the model using hour-of-day by heating and cooling degrees. A heating degree is a proxy for the electricity
required to heat a home. It is the positive dierence between 18C and ambient temperature. A cooling degree is a proxy
for the amount of electricity required to cool a home. It is the positive dierence between ambient temperature and 24C.
13
4.2 Solar income
In (7)
γ
captures the eect of
current
income on household consumption. To further explore how
households respond to solar income I allow consumption to be aected by two dierent measures of
income:
meihd
and
muihd .
The rst measure
meihd
accounts for the household's average hourly solar
income for the previous 30 days generated during daylight hours, hence:
meihd =
30
18
l=1
t=6
1 X 1 X
mit,d−l
30
13
This specication allows for households to respond to solar income across all hours of the day
(including overnight) and is intended to capture a very simple measure of a household's expected
or anticipated solar income. In this model cross-sectional dierences in
average dierences in solar income across households.
dierences in
meihd
meihd
identify the eect of
In the model with household-hour eects
identify anticipated changes in solar income within a household within a given
hour of the day. According to the permanent income hypothesis anticipated income should have
no eect on consumption within the household. Despite this, many studies nd that anticipated
income changes do aect consumption (Jappelli and Pistaferri, 2010) and that compared to larger
changes, small additions to income are more likely to be consumed rather than saved (Feldman,
2010).
The second measure of solar income
muihd
is intended to capture how households respond to
contemporaneous income shocks or unexpected solar income
taking the dierence between solar income in hour
h
of day
d
muihd .
I construct this measure by
and the average solar income in that
hour for the previous 30 days, hence:
30
muihd
1 X
= mihd −
mih,d−l
30
l=1
A number of papers demonstrate that household consumption responds strongly to windfall gains
and in particular that the marginal propensity to consume out of small windfall gains is higher
than out of larger windfall gains (see for example Milkman and Beshears (2009)).
Ideally I would observe variation in non-solar income equivalent to the type of variation in
solar income that I observe. Instead, I observe a time invariant measure of non solar income
at the census SA1 level.
across households.
yi
This measure is assumed to capture dierences in permanent income
If household behaviour accords with the permanent income hypothesis then
the response to expected income
meihd
(identied in the cross section) should be consistent with
responses to permanent income. To construct a conservative test of whether households treat solar
income as fungible with other money I take the largest estimate of the income elasticity of electricity
consumption from the literature. I convert this to a linear response called
γ max .
I then test the
following null hypothesis:
H0 : γ > γ max
(excessively sensitive to solar income)
A failure to reject this null hypothesis is a failure to reject that household electricity consumption
14
is excessively sensitive to solar income and consistent with households violating the fungibility of
money.
4.3 Identication
To identify the parameters of the demand function I must overcome three possible identication
problems. First, that price and income are determined simultaneously with consumption. Second,
that households choose retail price plans and third that feed-in taris are determined by when a
household installs their solar panels.
4.3.1 Simultaneity of export and consumption
A household exports power if their consumption (qihd ) is less than the total amount of electricity
their panels are producing at the same time (sihd ).
19
This means that opportunity cost and
income are determined simultaneously with consumption and hence are potentially correlated with
idiosyncratic shocks in
ihd .
Intuitively, by consuming at level
qihd
a household simultaneously
determines whether they import or export and hence what opportunity cost they face and how
much income they generate. Shocks to consumption are therefore correlated with opportunity cost
and income which are both a function of whether a household is exporting.
To overcome this simultaneity problem I use variation from contemporaneous solar production
sihd .
Within each feed-in tari group solar production is correlated with opportunity cost. Consider
a household consuming at
qihd > sihd
and with a feed-in tari below their import rate.
household's current price is the import rate and
s0ihd
such that
qihd < s0ihd
feed-in tari, hence
∆ocihd = 0.
This
An increase in solar production to
decreases the cost of their consumption because their implicit price is the
∆ocihd < 0.
Hence solar production is correlated with opportunity cost in the
neighbourhood of the price discontinuity. However while exporting decreases opportunity cost for
some households (with a feed-in tari below import rate) it increases opportunity cost for others
(with a feed-in tari above import rate). For some households, exporting leads to no change in
opportunity cost (households receiving a 1:1 feed-in tari ). Across all households the correlation
between solar production and opportunity cost may therefore be close to zero. This also means
that the direction of the bias in the estimate of
ηh,2
is unknown.
To capture the dierential eect of solar production on opportunity cost for those with an export
price above, below and equal to their import price I use solar production and an interaction between
solar production and an indicator for membership of the 60 FIT group as my set of instruments.
As I allow the response to opportunity cost to vary by hour-of-day (i.e.
I estimate a separate
parameter for each hour of the day) I also interact solar production within feed-in tari group with
indicators for hour-of-day. As with opportunity cost, current income (mihd ) is a function of whether
19 Thus the household eectively faces a non-linear or block price schedule where the level of solar production
sihd
determines the length of the block. In practice there is a dierent price schedule for every instant of the day rather than
every hour as assumed here. Smart meters separately record the ow of electricity from and to the residence and report
the cumulative ows in half hourly intervals. Thus it is possible to observe both exports and imports for the same 30
minute interval. I aggregate 30 minute meter readings to the hourly level and determine price
pihd
based on a comparison
of total exports and imports within that hour. If imports exceed exports I assign the household the import price
exports exceed imports I assign the household the feed-in tari rate
15
fi .
rih .
If
20
a household is importing or exporting.
Income is also clearly a function of solar production and
can be instrumented using the same set of variables. In total this gives me 14 instruments (solar
production (sihd ) and solar production within the 60 FIT group for each of 13 hours for which I
estimate the coecient
ηh,2 (Fih × sihd ))
for 14 endogenous variables.
21
As intuition for separate identication of price and income eects recall that attention to opportunity cost is consistent with level dierences in consumption in the neighbourhood of the price
discontinuity (i.e. at the point of export). Sensitivity to current income is consistent with dierences
in the gradient of consumption with respect to solar production. Finally, note that for households
receiving a 1:1 tari there is no change in opportunity cost so changes in solar production are only
associated with an income change for this group.
Figure 5a illustrates the rst stage relationship between solar production and
∆ocihd
by feed-in
tari group. To demonstrate the within-hour variation in the data Figure 4 shows the frequency
of export and import across hours of the day for two solar system sizes. Households with smaller
solar system sizes face greater within hour-of-day variation in opportunity cost. On the other hand
households with larger system sizes will face greater variation in their endowment and hence their
solar income.
Solar production is not a valid instrument if it is correlated with shocks to consumption i.e.
E(ihd |sihd ) 6= 0.
The main potential threat is the correlation between sunshine and tempera-
ture. In general sunnier days tend to be warmer and warmer days cause households to increase
consumption independent of price (for example switch on an air conditioner).
22
Recall that so-
lar production is an estimate so it should not be correlated with household level temperature or
weather shocks that are not captured in other controls. In equation (7)
eect of temperature on electricity
production
sih,d−j
23
consumption.
(i.e. solar production at hour
h
δh
captures the non-linear
As a robustness exercise I use lags of solar
of date
d − j)
as alternative instruments. The
regular pattern of irradiance throughout the day means that lagged production
poraneous production
sih,d
sih,d−j
and contem-
are highly correlated. This in turn induces correlation between
sih,d−j
and contemporaneous exports. Lags of solar production are valid instruments if they are weakly
exogenous: that is, if
E[sih,d−j ihd ] = 0.
If there is serial correlation in
ihd
(for example because
weather shocks are serially correlated) then lags need to be of an order larger than the correlation.
In practice I nd no evidence of serial correlation in
ihd
at the 24th, 48th or 72nd order lag. I
thus implement (7) using a variety of lags of solar production as instruments and present estimates
using a 48 hour lag.
20 In specications with current income shock (mu ) this is also endogenous.
ihd
21 I ensure that the results are robust to using interactions between solar production and other feed-in tari group
membership indicators including using a full set of interactions between feed-in tari group and solar production within
hour-of-day. In this specication the model has a lot more instruments than endogenous variables and although I reach
the same conclusions the instruments are not as strong. This is not unexpected in such an over-identied model.
22 Ameliorating this eect somewhat is the fact that higher temperatures reduce solar panel performance
23 The eects of temperature can easily be identied separately because of variation in ∆oc
ihd across households within
a given hour-date.
16
4.3.2 Selection of import-price plans
When a household joins the retailer they sign up to a pricing plan. Plans dier in terms of payment
facilities and billing frequency and are associated with discounts o the underlying standard rate.
24
Import prices therefore dier by plan type which is chosen by the household. Variation in import
price due to plan type is endogenous if household preferences for billing arrangements or other
characteristics aecting plan choice are correlated with consumption.
This may be the case if
large users avoid automatic payment of bills due to cash ow constraints and therefore receive
lower discounts or if larger users were more likely to select pre-payment in order to receive higher
discounts.
Once again the direction of the bias in the coecients is unclear.
To address the
endogeneity concern I present results using variation from the underlying network tari (determined
by distribution zone and meter type) as an instrument for nal import price.
As I estimate a
separate price coecient for each of the 24 hours of the day I interact the household's pre-discounted
electricity rate with indicators for hour-of-day giving me 24 instruments for 24 endogenous variables.
A household's underlying standard rate is determined by their network tari, the retailer then
oers a discount given the customer's plan choice. Network taris are regulated distribution and
transmission charges and vary across distribution zones due to dierences in capital investment
and costs of network operation. I follow Ito (2014) in taking advantage of the variation in price
arising from spatial discontinuities in electricity distribution zones. To guard against time-invariant
characteristics at the zone level I specify
αg
in (7) as a zone xed eect. As a robustness check I
then restrict the same to households living within the capital city of Melbourne.
Network taris also dier by the historical meter type of the household which was chosen
by the monopoly distribution company.
These meter types determine whether households face
prices that vary by time of day. I take this variation to be exogenous. As part of the mandatory
roll-out of smart meters, all households in the estimation sample have interval meters recording
consumption at the 30 minute frequency.
However due government regulation, their historical
meter type determines whether the household has a Single Rate or a Time of Use network tari
over the period of the sample. These network taris in turn drive variation in the retail cost of
electricity faced by a household.
This variation would be endogenous for example if households
with electric hot water or other household characteristics were historically allocated dierent meters
and this historical characteristic aected consumption today. This is unlikely as these households
were generally placed on Two Rate taris with a dedicated circuit and such households are dropped
from the sample. As a further robustness check I also restrict the sample to households only on
Time of Use electricity rates.
4.3.3 Selection of feed-in tari
Finally, feed-in tari program enrolment is a function of date of solar panel installation. Households
who installed solar panels earlier receive higher feed-in taris. As feed-in taris decline households
who consume more electricity during the day are more likely to benet from installing solar panels.
Thus underlying patterns in electricity consumption could be correlated with feed-in tari.
I
therefore allow for dierences in the hourly consumption of households on dierent feed-in taris.
24 Appendix A.1 discusses the application of discounts in more detail.
17
I also implement a model with household-by-hour eects. Even with feed-in tari program by hour
xed eects, estimates would be biased if characteristics of households that are correlated with
installation date or feed-in tari cause electricity consumption within hour to vary over time, for
example heating and cooling use or electricity to heat swimming pools.
To address the selection problem, I instrument for feed-in tari program using geographic
variation in solar productivity. In doing so I follow Duo and Pande (2007) and Lipscomb et al.
(2013) who use geographic characteristics such as the steepness of terrain as an instrument for
time and location of dam construction. Figure 7b shows that mean solar irradiance is positively
correlated with feed-in tari. Specically, it plots feed-in tari partialling out the eect of living in
25
Melbourne.
The mechanism for this instrument is as follows: feed-in taris have fallen over time
thus early adopters have higher feed-in taris. Mean solar irradiance is correlated with feed-in tari
if households who will produce more electricity from their panels (as measured by mean irradiance)
are likely to adopt earlier for example because the pay-back period is more attractive. Consistent
with this, Hughes and Podolefsky (2015) nd some evidence that Californian households in better
solar locations install PV earlier. The Melbourne indicator variable allows me to isolate variation
in solar productivity across households in otherwise similar locations. Figure A.9 in Appendix A.4
maps the distribution of mean irradiance across the state and within Melbourne.
Irradiance is
highest in the northern part of the state and lowest in coastal areas. Within Melbourne irradiance
is lowest in the eastern part of the city where elevation increases.
26
To operationalise the instrument I adopt a three step process. First, I use variation in solar
productivity due to geography and contemporaneous solar irradiance within hour to explain solar
production within feed-in tari group and hour. This generates variables
are used in the second stage to predict changes in opportunity cost
Finally
∆oc
b ihd
and
m
b ihd
F\
ih × sihd
∆ocihd
sd
ihd
which
and income
mihd .
and
are then used to estimate the parameters of the demand function.
I
cluster bootstrap to generate standard errors that account for serial correlation within household
and that account for the three step estimation process. The three step estimation strategy is:
Step 1
Zihd = β1 GHI i + β2h GHIihd + β3 M elbi + Π1 Xihd + κ1,ihd
Zihd = {Fih × sihd , sihd }
Step 2
Yihd = β4 Fih\
× sihd + β5 sd
ihd + Π2 Xihd + κ2,ihd
Yihd = {Hh × ∆ocihd , mihd }
Step 3
\
qihd = ηh,1 rih + ηh,2 ∆oc
[
ihd + γ m
ihd + δh Wihd + ihd
25 The slope of the line thus represents the correlation between irradiance and feed-in tari within location where
location is either Melbourne or Rest of state. This accounts for the fact that the cross-state variation in irradiance
dwarfs the within Melbourne variation in irradiance where most of the sample is located.
An alternative would be
to restrict the same to Melbourne or to allow the eect of irradiance to dier within Melbourne.
Neither alternative
qualitatively changes the results.
26 Melbourne is a sprawling coastal city. The eastern most boundary of the city is 75km from the central business
district whilst the western boundary is over 60km from the central business district. At the outer eastern edge elevation
rises as the city hits the Yarra Ranges.
18
where
GHI i
GHI ihd
is the average solar irradiance for household
is solar irradiance for
hour-of-day,
i
at hour
h
of day
d
M elb is an indicator for Melbourne, Xihd
equation 7 and
Hh
is an indicator for hour
h.
i
derived from satellite data. Similarly,
and is allowed to aect
Zihd
are the remaining exogenous covariates from
Note in this specication I drop zone and hour by
feed-in tari group xed eects and rely on my instruments for identication.
strategy with and without an additional set of instruments for import price
5
separately by
rih
I implement this
as outlined above.
Results
The main results are provided in Tables 3 and 4. Table 3 presents results from estimating equation
(7) and controlling for
Current income.
Table 4 presents results from allowing consumption to
Expected income ) and the dierence between
current income and average income in that hour over 30 days (Income shock ). In all models ηh,1 and
depend on average income over the previous 30 days (
ηh,2
are estimated separately. The main dierence between the Tables is the treatment of income
eects and the drop in sample size reecting the 30 day lag to construct measures of average income.
Table 3 reports results controlling for current solar income: column (1) reports results with zone
xed eects; column (2) adds hour-of-day by feed-in tari program eects; column (3) adds an
instrument for import price.
Finally column (4) adds an instrument for feed-in tari program
(and removes zone and hour of day by feed-in tari eects).
Table 4 reports results controlling
for expected and unexpected solar income as well as a measure of long run income. For a direct
comparison between income specications column (1) reports results with zone and hour-of-day by
feed-in tari xed eects.
Column (2) adds in a measure of long run income and removes zone
xed eects; column (3) controls for current solar income instead of expected and unexpected solar
income. Finally column (4) controls for household by hour of day xed eects. All standard errors
27
are clustered at the household level.
Instruments for
∆ocihd
are strong for all hours from 7am.
28
Instruments for import price and the two income variables are also strong across models.
5.1 Opportunity cost
In this section I discuss the results of the test of whether households respond to opportunity cost.
I focus on results in Table 3 however the conclusions from Table 4 are identical. This test is based
on comparing how households respond to import price with how they respond to an implicit price
or opportunity cost in the same hour of the day. If households are attentive to opportunity cost
29
then these responses should be equal. I plot coecients estimated for hours 7am-5pm.
Figure 6 plots the results presented in columns (1) and (2) of Table 3. Within each panel the top
27 Standard errors presented do not reect uncertainty from the estimate of solar production. For the results in columns
(1)-(3) in Table 3 I check that the results are robust to bootstrapping solar production jointly with the estimate of the
demand function. For column 4 standard errors are cluster bootstrapped in the three step IV strategy.
28 The strength of instruments is judged by calculating the F statistic outlined in Angrist and Pischke (2008) for
multiple endogenous variables and applying the Staiger and Stock (1997) rule of thumb. For the model instrumenting
for feed-in tari the F test is undertaken independently of the cluster bootstrap process. In this instance I assess the
strength of instruments for each of the stages.
29 All models and tests were specied with
ηh,2
coecients for hours 6am - 6pm however wide condence intervals for
these hours make plotting impractical.
19
gure plots condence intervals for the coecients. The parameter
η1,h
measures the response of
households to variation in the cost of importing electricity for each hour of daylight. The parameter
η2,h
measures the response of households to changes in the opportunity cost of their consumption.
The bottom gures of 6 plot the 90% condence interval for the dierence
η̂1,h − η̂2,h .30
Under
the null hypothesis that households are attentive to opportunity cost this dierence is zero. The
p-value for the joint signicance test that the dierence is zero in all hours is also reported.
The top of Panel 6a plots the estimates of
η1,h
and
η2,h
coecients where group eects
αg
are at
the zone level. The coecients are estimated using within and across household variation in import
and export prices. Estimated coecients are negative, signicant, and condence intervals overlap
across all hours of the day. The bottom of Panel 6a plots the condence interval for the dierence
for each hour of daylight. The null hypothesis that households respond to implicit price in the same
way they respond to the import price cannot be rejected for any hour. The p-value for the joint
signicance test is 0.35. I thus cannot reject that households are responsive to opportunity cost.
Panel 6b plots the estimates where I also allow for dierences in consumption at each hour of the day
for households within each feed-in tari program. Once again estimated coecients are negative,
signicant and not statistically dierent. I cannot reject that households are equally attentive to
implicit and explicit prices and therefore that they are attentive to opportunity cost. The eect
of adding controls for hourly consumption by feed-in tari group can be seen in the change in the
magnitude of the coecients. Controlling for underlying dierences across households in feed-in
tari group by hour I nd that households are
more
responsive to the explicit price and implicit
price of electricity consumption. This suggests there are some dierences across feed-in tari groups
in their hourly consumption proles.
In Figure 7 I present estimates instrumenting for import price using a household's pre-discounted
price. Variation in this underlying price is driven by regulated network charges and is plausibly
exogenous to household level characteristics and shocks to consumption. The bottom panel plots
the dierence between the estimated coecients. For a considerable portion of the day households
are found to respond
more
to the change in opportunity cost than to the explicit price (certainly
not evidence that households are inattentive to this change). Overall the conclusion of the test (p
value 0.309) is the same: I fail to reject that households are responsive to the change in opportunity
cost associated with exporting. Price coecients in Figure 7 and 6b dier very little in magnitude
suggesting that the selection of plan discounts does not cause a strong endogeneity problem.
The nal identication problem arises because of selection into feed-in tari program. As outlined above, I adopt a three step instrumental variables strategy using average solar irradiance as an
instrument for feed-in tari program. Higher average irradiance should lead to earlier solar adoption which determines feed-in tari program and hence export price. Results from this estimation
are presented in Figure 7b. Standard errors are cluster bootstrapped with 200 replications. The
model uses hourly irradiance to instrument for whether the household is exporting, network taris
to instrument for import price and average irradiance and a Melbourne indicator to instrument for
feed-in tari group. Note that using variation from hourly irradiance instead of solar production
also ensures these estimates are robust to dierences in solar system size. The conclusions from
30 90% condence intervals are chosen in order to be conservative in failing to reject the null hypothesis that households
are attentive.
20
this specication are unchanged: I cannot reject that households are as responsive to the implicit
price of consumption as they are to the explicit price of consumption. This leads me to conclude
that households are not inattentive to opportunity cost. The magnitude of the explicit and implicit
price coecients have reduced compared to Figure 7 but are still of larger order than those in
Figure 6a. These dierences reect both the absence of hour-by-feed-in tari eects and also the
alternative three step estimation strategy.
5.2 Solar income
I nd evidence that households are responsive to opportunity cost yet they are excessively responsive
to variation in their solar income. Table 3 shows that consumption is immediately responsive to
Current income ): income generated within the same hour. The estimated
Current income is stable across models that account for dierences in consumption at
variation in income (
eect of
each hour of the day across feed-in tari programs and that instrument for import price and for
feed-in tari program. Interpreting the coecient in column 1 of Table 4: a 10c increase in current
solar income (30% of mean solar income) will lead to a 0.1kWh increase in current consumption
(10% of day-time consumption).
31
For context a typical split system air conditioner run for an hour
would consume approximately 1.5kWh whilst a load of washing consumes approximately 1.3kWh.
32
Households may respond dierently to solar income that is anticipated relative to shocks in
income.
In Table 4 I separately identify household responses to anticipated and unanticipated
income. The estimated income eects are relatively stable across models. The variable
income
Expected
measures average hourly solar income (measured in cents) for the previous 30 days from
9am-5pm. In this specication I capture the average eect of recent income on consumption at all
hours of the day. The variable
Income shock
measures the dierence between current hourly income
and average income for that hour for the previous 30 days.
33
This income eect is current in that it
captures the within hour change in consumption associated with an unexpected change in current
solar income.
34
This latter variable therefore captures the immediate eect of an unexpected
increase in solar income averaged over all solar-producing hours.
The magnitudes of the estimated income eects are once again extreme. As for
the coecient on
Expected income
Current income
in column (1) of Table 4 suggests that a 25c increase in average
hourly solar income will lead to a 0.25kWh increase in hourly consumption. To put this in context
this is equivalent to an increase of $14 in weekly income or approximately 1% of weekly (median)
35
income measured at the census SA1 level.
Average hourly consumption across all hours is approx-
imately 0.7kWh so the implied elasticity with respect to total income is extreme. The coecient
on
Income shock
in column (1) of Table 4 suggests that an unexpected 25c increase in hourly solar
income increases consumption in that hour by 0.9kWh. Households thus appear to consume more
31 Average hourly consumption during solar producing hours is approximately 1kWh (for the full sample approximately
0.7kWh) and average solar income for the same is approximately 30c.
32 http://tools.switchon.vic.gov.au/appliance-calculator/tools-appliance-calculator
33 For hours outside of daylight
34 Estimates of
Expected income
ηh,1 − ηh,2
Income shock
is always zero.
are qualitatively unchanged using alternative specications of income including aggregating
with SA1 census level median weekly income (though this aggregated income variable is insignicant).
35 Average weekly income reported for the sample is reported in Table 2.
Expected income
is measured as the average
hourly income over the previous 30 days during the hours 9am-5pm. At the weekly level a 25c increase in
is 25*8*7 = 1400 or $14.
21
Expected income
on average when their expected income is higher, but also to consume more in specic hours when
their income is unexpectedly high.
It is also possible to compare how consumption varies in response to non-solar income measured
using cross sectional variation in census data.
to reect long run dierences in income.
Cross sectional measures of income can be taken
Expected income
is also identied o of cross sectional
variation and, if households are forward looking, can be interpreted as a long run income eect.
In Table 3 and column (1) of Table 4, zone xed eects are assumed to capture time invariant
dierences in income.
In columns (2) and (3) of Table 4 I include a measure of cross sectional
dierences in weekly income (in AUD '000) at the census SA1 level and drop zone xed eects.
In column (2) I control for expected and unexpected income. In column (3) I control for current
instead of expected and unexpected income.
income
In both columns the point estimate on
Non-solar
is positive and signicant however the magnitudes of the implied income eects are tiny
relative to the eect of solar income. Note that
Non-solar income
is measured in units of $1000
per week whereas solar income is measured in units of c/hour. Interpreting the coecient on
solar income
Non
in column (2): a $1000 increase in weekly income leads to a 0.07kWh increase in
consumption. The elasticity implied by the income coecient in column (2) is approximately 0.1
which is at the lower end of analyses of the long run eect of income on electricity consumption.
The response to solar income is well in excess of any known estimate of an income elasticity of
electricity consumption. In a meta-analysis Espey and Espey (2004) nd the mean estimated short
run income elasticity of electricity consumption is 0.28 with the highest elasticity being 3.48. The
mean of long run elasticities is around 1. The response to solar income is well above this range.
An elasticity of 1 would suggest that a 1% increase in weekly (non-solar) income (approximately
$14) would lead to a 0.007kWh increase in consumption. An elasticity of 3.48 would suggest a 1%
increase in weekly non-solar income would lead to a 0.025kWh increase in consumption. My results
indicate that if this increase in income was earned via solar production households would increase
consumption by 0.25kWh or roughly 10 times the consumption response to the same monetary
increase in non-solar income.
Beatty et al. (2014) and Abeler and Marklein (forthcoming) nd
similar discrepancies between income elasticities of consumption in home heating and gasoline
expenditures that are also consistent with violations of fungibility. More formally, translating the
elasticity of 3.48 into a linear response to a one cent increase in average weekly income leads to
γ max = 0.0002.
I emphatically fail to reject the null hypothesis that the eect of average solar
income on consumption is higher than
for
γ max
(p value
>
0.9) regardless of which estimate I choose
γ̂ .
I next isolate variation in expected and unexpected solar income within a household-hour-of-
36
day.
This reduces the magnitude of the estimated income eects but nonetheless the eects of
anticipated and unanticipated changes in solar income are large and signicant. The eect of a 25c
increase in expected solar income leads to an increase of 0.1kWh whilst a 25c income shock leads
36 Within a household-hour-of-day variation comes from Time of use rates and variation in price schedules over time.
Time of use rates charge households a lower rate for consumption at o peak times which is 11pm-7am weekdays and
Saturdays and Sundays. I observe some price variation from changes in the retailer's taris over the course of the sample
period.
These sources of variation allow me to specify models with household-hour xed eects (αih ).
I control for
hour-by-weekend/weekday eects to ensure that my results do not conate underlying dierences in weekday/weekend
demand. The parameters are therefore identied from variation in the dierence between peak and o peak rates across
households.
22
to a 0.25kWh increase in consumption. Once again, I emphatically fail to reject the null hypothesis
that the response to
Expected income
is higher than
γ max
(p value
>
0.9).
The results presented in Tables 3 and 4 constrain the eect of solar income to be the same across
hours of the day. Households may however respond very dierently to income at dierent points in
the day. The richness of the meter data also allows me to explore this heterogeneity. In Table A.5
Appendix A.5 I allow
Current income and Expected income to aect consumption dierently in each
hour of the day. In column (1) I specify zone and hour by feed-in tari program eects. In columns
(2) and (3) I specify household by hour eects. In columns (1) and (2) I nd that higher
income
Expected
across and within households increases consumption at most times of the day bar evening.
In column (2) I nd that higher
Expected income
reduces night time and morning consumption
within a household. This is consistent with households substituting consumption away from night
time and towards daylight hours. Focusing on the hourly impact of
Current income
I nd that the
eects are largest in the late afternoon. These results indicate that consumption is most responsive
to income at times of peak consumption and not at times of peak production. This contrasts to
37
price responsiveness which tends to peak towards the middle of the day.
In the next section I
discuss and rule out several feasible alternative explanations for the observed patterns of behaviour
before I go on to discuss mechanisms.
5.3 Alternative explanations
The results already presented suggest that households respond to the opportunity cost of foregone
revenue but they are overly sensitive to the income their panels generate. In this section I briey
consider and rule out three other explanations for the estimated eects.
First, I rule out an
explanation that household preferences for consuming solar-generated power over grid-based power
are correlated with export price.
Second, I rule out that the results are an artefact of using
predicted consumption as my dependent variable. Finally, I explore and rule out the possibility
that households respond to the average cost of their electricity and not to marginal prices and
income.
Households who install solar panels are motivated to do so by a concern for the environment.
In Victoria over the period in which households in the sample installed their solar panels the
payback periods of the investment were not suciently attractive as to merit installation on purely
nancial grounds (though this is rapidly changing, Grattan (2015)).
Consumption of electricity
post-adoption may therefore be aected by a concern for the environment. One possibility is that
households derive greater utility from consuming solar generation than grid-based generation. This
could result from a perception that the environmental impacts of consuming solar generation are
lower (or vice versa that the environmental impacts of consuming grid-based generation are higher).
In reality the environmental impact of consumption depends on the marginal emissions that the
exported generation would displace, so it is by no means true that substituting consumption to
times when panels are producing does reduce emissions. Regardless of the true emissions impact,
household perception of their impact may suggest that it is better to consume their own solar power
37 I nd weak evidence that income earned during the day aects consumption that evening and nd no eect on
consumption overnight. I also nd no evidence of cross price eects on consumption overnight: households who face a
high average price during the day do not consume more overnight.
23
or they may feel less guilty about consuming power they know has been generated by their panels
and not by coal.
The opportunity cost of consuming solar exports is high for some households and low for others. One might expect a preference for consuming solar power to result in a uniform increase in
consumption regardless of the implicit price. This would tend to result in a rejection of the null
hypothesis that they are responsive to opportunity cost.
However I nd that households do re-
spond to foregone revenue as the cost of their consumption. This is preliminary evidence that a
preference for consuming solar generation does not confound the results. To do so, it must be that
there is correlation between feed-in tari group and preferences for consuming solar generation.
Because earlier adopters tend to receive higher export prices, there may be reason to suspect such
a correlation exists. As solar income is a linear function of solar production within each feed-in
tari group (at least given a household is exporting) it is not possible to identify the eect of solar
income separately to the eect of solar production within feed-in tari group. Instead I implement
three strategies to address the concern that feed-in tari group may be correlated with preferences
for consuming solar vs grid-based electricity. In each of these strategies I impose that households
are attentive to opportunity cost and estimate a single price response within each hour.
38
In column (1) of Table 5 I demonstrate that the results hold even when I control directly for solar
production and allow solar production to aect early adopters dierently. I dene early adopters to
be households in the 1:1 FIT and the 60 FIT programs. As discussed earlier, the 25 FIT and 8 FIT
programs were for households installing solar panels from 2012 and 2013 respectively. To account
for the endogeneity of price and solar income I use a combination of instruments: hourly irradiance,
lagged solar production and hourly lagged solar production within the 60 FIT group as well as using
underlying variation in import prices from network tari assignment. Identication of price and
income parameters comes from variation across households for a given level of solar production. I
nd that on average solar production is associated with higher electricity consumption but there
is no statistical dierence in the eect for early adopters.
The income eect remains of similar
magnitude to earlier estimates.
In column (2) of Table 5 I allow a household's consumption to be aected by whether their panels
are producing or not and I allow this eect to be dierent for households with dierent export prices.
If preferences for consuming solar production are present then these eects should be reected in a
dierence in consumption when panels switch on.
39
Furthermore if these preferences render solar
income endogenous we should see the largest eect for households who have the highest export
price and earn the highest income (the 60 FIT group).
I instrument for hourly price and solar
income using interactions between feed-in tari and solar production and variation from network
taris.
I nd that across feed-in tari groups, households consume more when their panels are
switched on and that the eect of panels switching on is large. I do not, however, nd any evidence
that this eect diers for the 60 FIT group.
The third strategy is to allow household consumption during solar producing hours to be aected
by whether they are importing electricity.
If households have a preference
for
consuming solar
38 Doing so means I require fewer instruments and am therefore less likely to be subject to weak instrument problems.
39 In practice panels are almost always running at midday even for high levels of cloud. The eect will thus be identied
from panels operating or not operating at the start and end of daylight hours. As solar production is an estimate I make
sure the results are robust to a number of cut-o points to dene the indicator variable "not producing".
24
generation then they should have a preference
against
consuming when they need to import power.
Crucially for the estimation of the income eect, if this preference is correlated with export price,
then the estimated reduction in consumption when importing should be largest for households
with the highest export price. The results reported in column (3) of Table 5 indicate that 8 FIT
households consume more when they are importing electricity from the grid but 60 FIT households
do not consume less than the average household.
In this specication I instrument for hourly
price and solar income using interactions between feed-in tari and solar production and using
underlying variation in import prices from network tari assignment. I also instrument for whether
40
a household is importing during daylight hours using this set of plausibly exogenous variables.
Across these three strategies I nd no evidence consistent with a correlation between export price
or early adoption and a preference for consuming solar power over grid-based power.
If households do have a preference for consuming solar generation then the exclusion restriction
that allows me to use solar production as an instrument is problematic. A separate concern may
be that I use solar production to determine a household's consumption. Appendix A.3 discusses
the implications of prediction error in solar production for estimation of the demand function.
Intuitively, prediction error represents random dierences between actual and predicted output
(such as shading) that cannot be explained by the solar production model. The disturbances in
the solar production model are assumed to be uncorrelated with the predictors of that model. This
implies that the solar prediction is also orthogonal to those disturbances. If this assumption holds
then prediction error does not cause an endogeneity problem.
As further evidence I re-estimate the model using net imports instead of predicted consumption
as the dependent variable. Solar production then becomes an explanatory variable:
nihd = β1 sihd + ηh pihd + γmihd + αg + δh Wihd + ωihd
where
ωihd
(8)
is a new disturbance term. I compare this model to estimates of the demand model in
(6) with consumption as the dependent variable. In both models the price and income variables
are instrumented using interactions between irradiance and its lags and feed-in tari. Results of
the net demand model and the consumption model are presented in columns (1) and (2) of Table
6.
In practice though minor dierences exist the parameters across these two models are very
similar. Unlike consumption, net imports are observed directly from the meter data. The fact that
the results are almost identical suggests that the estimates are not an artefact of the consumption
prediction.
The nal possibility I consider is that households may be responding to average net cost and
not to marginal price and opportunity cost. Ito (2014) demonstrates that households faced with
non-linear prices respond to average not marginal price.
Households on net feed-in taris eec-
tively face a non-linear price: once consumption exceeds production there is a discrete jump in a
household's eective price. One possibility is therefore that households respond to their average
bill for electricity (revenue minus cost per unit of consumption) and not to marginal price and
opportunity cost. To explore this possibility I include average bill as an explanatory variable in
equation 7. If households respond to average net cost instead of the opportunity cost and income
40 Whether a household is importing is determined simultaneously with consumption which renders it endogenous
25
then income and opportunity cost should be insignicant. Instead I nd that allowing households
to respond to average bill does not change the conclusions. As further evidence that households do
not respond to net average cost, Figure 8 shows the t of two alternative models. On the left hand
side are predictions using the baseline model used to test opportunity cost and fungibility. On the
right hand side are predictions using a model assuming instead that households respond to the
average net cost of their electricity. The opportunity cost and income model clearly outperforms
the net average cost model in explaining observed consumption. In the next section I demonstrate
that the tests of attention to opportunity cost and excess sensitivity to income are also robust to
a number of key identication assumptions.
5.4 Further robustness
The results are robust to a number of basic checks including alternative specications of the demand
function and the test of opportunity cost, dropping solar installations greater than 5kW in capacity,
restricting the sample to Melbourne only and using a dierent imputed solar system size or model of
solar production. The conclusions are also robust to splitting the same into weekdays and weekends
and to allowing for cross-price eects in electricity consumption within and across days. Results
of these robustness checks are not presented for brevity. In this section I outline robustness checks
that address some of the main threats to my identication strategy.
The results presented in columns 2 and 3 of Table 3 (and Table 4) are robust to dierences in
regular patterns of consumption across feed-in tari groups. Then the parameters are identied if
there are no characteristics of households that are correlated with consumption and feed-in tari
group that cause deviations from this regular pattern of use.
One potential such characteristic
is air-conditioning. Air-conditioning use varies over time, is energy intensive and uctuates with
weather. If having and using air-conditioning is correlated with feed-in tari program enrolment
then the parameters are not identied.
In column (4) of Table 3 I instrument for feed-in tari
program and use solar irradiance as an instrument for whether a household is exporting. Another
strategy to demonstrate that my results are robust to this possibility is to allow households within
feed-in tari groups to respond dierently to temperature in the form of heating and cooling degrees.
In Appendix A.5 I report results allowing temperature responses to dier by feed-in tari group
whilst retaining zone and hour-of-day by feed-in tari group eects and instrumenting for import
price. The conclusion remains the same: households appear to be as responsive to implicit prices
as they are to explicit prices and they respond strongly to changes in income.
The next robustness check focuses on the possibility that the interaction terms between solar
production and feed-in tari group are not valid instruments. The instrument is invalid if solar
production is correlated with contemporaneous shocks to consumption. To address this concern
I use a 48 hour lag of solar production instead of contemporaneous solar production as a set of
instruments.
Results of this specication are presented in column (2) of Table A.6 (I also nd
that the conclusions do not change when I use irradiance (measured using satellite data) or its lags
instead of production). I also estimate models including an indicator for above average cloudiness
in each hour of the day.
This indicator controls for the possibility that sunshine (rather than
temperature) is correlated with electricity use for example because on cloudy or rainy days people
26
tend to stay inside and use more appliances. The results hold. The results also hold if I control
for the eect of irradiance within each feed-in tari group (thus allowing households to respond
dierently to sunshine) and if I control for measures of cloud.
This gives condence that solar
production is a valid instrument in that the correlation between solar production and sunshine
does not render production endogenous. Having ruled out alternative explanations and outlined a
number of checks to the robustness of the results I next move on to discuss possible mechanisms
behind the observed income eects.
5.5 Mechanisms
Several hypotheses for the mechanisms underlying the observed income eects can be mounted and
several discounted. For example, households could be myopic or have trouble forecasting their solar
income. However myopia does not explain the magnitude of the response. The fact that households
also respond strongly to temporary shocks may also indicate projection bias. Consistent with this
hypothesis, Lamp (2014) nds that the the decision to adopt solar panels is aected by temporary
shocks to sunshine. However projection bias again does not explain either the magnitude of the
response or the fact that households respond both to anticipated and unanticipated income.
Existing evidence also suggests consumers engage in mental accounting, category budgeting,
suer from reference dependence and are inuenced by labelling. Both mental accounting and category budgeting are models of decision making in which consumers use heuristics to manage income
and expenditure.
Households who engage in mental accounting allocate income to consumption
or saving based on its source (Thaler, 1990) (for example small windfalls are more likely to be
spent rather than saved). Households who engage in category budgeting hold mental budgets for
expenditure on items within the same category and track these categories separately (Heath and
Soll, 1996). Changes in expenditure or income in one account may have larger eects within that
account than would be expected if consumers treated all expenditure as substitutable.
Feldman (2010) nds evidence for mental accounting in responses to lump sum versus incremental tax rebates. Beatty et al. (2014) and Abeler and Marklein (forthcoming) nd evidence that
labelling aects spending patterns and Hastings and Shapiro (2013) nd that households violate
the fungibility of money in response to dierential shifts in the price of dierent grades of gasoline.
I nd that solar income causes households to consume more electricity on average. This nding is
consistent with category budgeting: income earned from exporting electricity is spent on electricity. However I also nd that households consume more within this category at the very same time
that they benet from small income gains. If households are engaging in category budgeting this
suggests that category budgets may be both time and product specic. Such behaviour would also
be consistent with non standard discounting such as present bias. It may also result from salience
eects.
Dierences in the salience of solar income across and within days may help to explain the
electricity consumption of solar households. Hastings and Shapiro (2013) following Bordalo et al.
(2013) use a model of salience to explain violations of fungibility in gasoline purchases.
In this
model households place greater weight on more salient attributes of a decision. In electricity, Gilbert
and Gra Zivin (2014) nd evidence that time-varying salience aects expenditure in household
27
electricity consumption over the course of a billing cycle.
In Table A.5 I show solar households
tend to consume more during the day when their average solar income over for the previous 30
Expected income on consumption overnight is negative. This
latter result is consistent with households substituting electricity towards daylight hours when the
days is high and that the eect of this
salience of solar income is likely to be highest.
Regardless of the underlying model, the fact that households appear to spend a very high
proportion of solar income on electricity consumption during daylight hours and within the period
that it is made has signicant implications for policy. In the next section I discuss the implications
of these results more directly. In particular I discuss how to interpret the responses in terms of
policy relevant parameters: elasticities of consumption and export.
5.6 Price elasticities and policy implications
Having established that households respond to implicit prices I can now treat the feed-in tari as
a price and discuss price elasticities. To do so I return to the results of estimating (6) which are
reported in the rst column of Table 6.
Following Reiss and White (2005) I take the price elasticity of consumption to be the percentage
change in consumption resulting from a one percent change in a household's
current marginal price.
The total change in consumption also includes the eect of a change in solar income as this is also
aected by a marginal price change. Let
i
at hour
h
of day
d,
C
θihd
be the price elasticity of consumption for household
then:
C
=
θihd
where
pihd
pihd ∂qihd
qihd ∂pihd
is the household's current marginal price. Substituting in for the second term:
C
=
θihd
pihd
[ηh + γsihd ]
qihd
The price elasticity of demand is increasing in
γ
and
sihd < −
Once
(9)
sihd > − ηγh
sihd
(10)
such that it is only negative if:
ηh
γ
(11)
a household's consumption increases following an increase in marginal price.
Of importance to policy makers is not just the price elasticity of consumption, but also the
price elasticity of electricity exports to the grid. A household exports what they do not consume
i.e. the dierence between solar production and consumption:
xihd = sihd − qihd |sihd − qihd > 0.
X
Let θihd be the price elasticity of export, then:
X
θihd
=
fihd
[−ηh − γsihd ]
xihd
(12)
where once again this is a conditional elasticity, it assumes that the price change does not induce a
28
41
household to alter whether they are currently exporting.
Columns 2 and 3 of Table 6 report the
mean price elasticity of consumption and export for each hour of the day. To construct the mean
elasticities for each hour of the day I average over households and dates. All estimates in Table 6
are cluster bootstrapped to generate standard errors.
Figure 9 shows how the price elasticities of consumption and export vary over the course of
the day (panel a) and across levels of solar production (panel b). The solid line plots the mean
consumption elasticity whilst the dashed line plots the mean export elasticity.
During daylight
both consumption and export are most price elastic during the middle of the day. Over all hours
consumption is most price elastic overnight (from 12am to 5am consumption is highly elastic).
Panel b shows that for low levels of solar production the price elasticity of consumption is
negative.
However as solar production increases the magnitude of the price elasticity decreases.
This change reects the additional income caused by increases in solar production. In fact, the price
elasticity of consumption becomes positive once solar production exceeds approximately 2kWh. At
this point the income eect associated with an increase in price dominates the substitution eect.
As would be expected the export elasticity follows a similar pattern.
solar production an increase in the feed-in tari leads to a
decrease
After a threshold level of
not an increase in exports.
Subsidies designed to increase exports of electricity may therefore have the unintended consequence
of reducing exports at the intensive margin.
To underline the importance of accounting for the response of solar homes to the income produced by their panels, Figure 10 plots computed price elasticities (panel (a)) and consumption
predictions (panel (b)) assuming income eects consistent with the highest income elasticity in
the literature (3.58). As would be expected, without income eects mean consumption elasticities
are negative regardless of the level of solar production and vice versa, mean export elasticities
are all positive regardless of the level of solar production.
In panel (b), without income eects
consumption of 60 FIT households is predicted to be lowest on sunny days and consumption of 8
FIT households is predicted to be highest on sunny days and well in excess of 60 FIT households.
This contrasts with patterns of actual consumption previously discussed in Figure A.8: 60 FIT
households consume more on sunny days relative to cloudy days, and consume more than 8 FIT
households on sunny days. Viewed from the perspective of exports, the results suggest households
would export 40% more electricity if they treated solar income as fungible and had an income
elasticity consistent with the largest estimate from the literature.
These results have important implications for the structure of feed-in taris. In Figure 9 Panel a
shows that at 4pm the price elasticity of consumption and export cannot be distinguished from zero.
This is despite the fact that the coecient on price at 4pm (hour 16) is highly signicant. This is
particularly pertinent as peak network demand usually occurs around 4pm. Exports of electricity
at 4pm therefore have the highest value.
However increasing the price paid to households for
electricity exports at 4pm to reect this value may have little eect on exports because of the
41 In general in non-linear price environments it is also possible that a non-marginal price change will aect consumption
even without a change in marginal price. In the solar setting however this is not the case. If a household is currently
exporting electricity (their current price is the feed-in tari ) then a change to the import price has no immediate eect on
current price or income and hence has no eect on consumption. The opposite is also the case, if a household is currently
importing electricity then a change to the feed-in tari has no immediate eect on either price or income hence has no
eect on consumption.
29
income eect.
Indeed the elasticities in Panel b suggest that proposals to match export prices
to wholesale electricity market prices may have the perverse eect of decreasing exports at times
42
when they are most valuable.
Systems of gross feed-in taris that pay households dierent rates
for all electricity produced and charge households for all electricity consumed, and systems of net
metering that charge households only for net electricity imported may do no better. Both gross
feed-in taris and net-metering may cause anomalous behaviour as they still cause increases in
solar income as solar production rises.
The results in fact suggest that policy instruments that
succeed in breaking the link between solar income, solar production and electricity consumption
may result in an increase in exports at the intensive margin. Mechanisms to nance or subsidise
rooftop solar such as lump sum subsidies and power purchase agreements for third party owned
solar panels may therefore be more ecient instruments.
6
Conclusions
Just as Uber drivers become suppliers of transportation services, households who install solar
panels become suppliers of electricity. This electricity can be consumed by the household for free
or exported to the grid for revenue. Solar production therefore changes the opportunity cost of a
household's consumption whilst also generating income. In such environments, decision making is
complex and household responses to these new forms of price and income may be counter-intuitive.
In this paper I develop and implement a test of whether solar households are inattentive to
opportunity cost and whether they are excessively sensitive to the income that their panels generate.
Using high frequency meter data, I exploit the discontinuity in price when a household sells their
excess solar production to implement a test of opportunity cost. I separately identify the response
of consumption to small changes in solar income using dierences in gradients of consumption as
solar production rises.
I fail to reject that households respond equally to the implicit price of consumption when
exporting as they do to the explicit price of electricity when importing. I thus conclude that there
is no evidence that households are inattentive to opportunity cost; they do not treat solar generation
as free. I also demonstrate that households are extremely sensitive to the income generated by their
solar panels; the same monetary increase in income, delivered via solar production, would result in
10 times the increase in electricity consumption had that income come from another source.
The degree of sensitivity to small changes in solar income cannot be explained in a traditional
neo-classical model of behaviour with fungibility however it can be explained by appealing to models
of mental accounting and category budgeting. The estimated income eects help to explain the
puzzling observation that households on high feed-in taris consume more as they export more,
despite the high opportunity cost of doing so.
My ndings also have immediate implications for the design of subsidies for household-scale
renewable energy programs. In the rst paper to study household behaviour following the adoption of solar panels, I demonstrate that exports of solar power may actually decrease as export
subsidies rise. Mechanisms that seek to separate income eects from realised electricity production
42 Wholesale electricity prices are volatile and in Australia reach peak prices on hot summer afternoons.
30
and exports, such as lump sum installation subsidies, may therefore be a more ecient means of
supporting household-scale renewable energy.
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33
The Journal of
Figures
Figure 1: A solar household's budget set
(a) Export price (f ) < import price (r )
(b) Export price (f ) > import price (r )
y0+ fs’ Other goods Other goods y0+ fs y0+ fs' y0+ fs y0 y0 s y0/r s' (y0/r) + s (y0/r) + s’ y0/r s Electricity (y0/r) + s s' (y0/r) + s’ Electricity Figure shows hypothetical budget sets for two solar households. Panel (a) depicts the budget set for a household with a feed-in tari (f ) is
less than the retail cost of electricity (r). Panel (b) depicts the budget set for a household whose feed-in tari is more than the retail cost of
electricity. Solar production levels s < s0 , non solar income y0 and retail cost r are the same across households. Other goods is the numeraire.
Figure 2: Price and income
(b) Income
(a) Price
2
60
60 FIT
Mean hourly solar income ($)
Mean hourly price (c/kWh)
60 FIT
40
1:1 &
25 FIT
20
1.5
1
1:1 FIT
& 25 FIT
.5
8 FIT
8 FIT
0
0
2
1
Exports (kWh)
0
1
Imports (kWh)
2
2
1
Exports (kWh)
0
1
Imports (kWh)
2
Panel (a) plots mean price (pihd ) across net imports (import (purchases) - export (sales)) by feed-in tari group. Panel (b) plots mean solar
income across net imports by feed-in tari group. Negative net import indicates a household is exporting electricity. 1:1 FIT (households
receive the same feed-in tari as their import rate) and 25 FIT have been combined.
34
Figure 3: Consumption patterns
(b) Net import
(a) Sunny and cloudy days
60 FIT
1.2
Sunny days
Mean hourly consumption (kWh)
Mean hourly consumption (kWh)
8 FIT
1
.8
Cloudy days
1.5
1:1 FIT &
25 FIT
1
60 FIT
8 FIT
8 FIT
.6 60 FIT
7
.5
8
9
10
11
12
1
Hour of day
2
3
4
5
2
Exports (kWh)
1
0
1
Imports (kWh)
Panel (a) plots mean consumption across hours of the day for very sunny days and very cloudy days for 8 FIT and 60 FIT households. Panel
(b) plots mean consumption across net imports (import (purchases) - export (sales)) for all groups. 1:1 FIT (households receive the same
feed-in tari as their import rate) and 25 FIT have been combined.
Figure 4: Frequency of export/import
Figure shows the relative frequency of import (buying)/export (selling) by each hour of the day for small (below median size) and larger (above
median size) solar systems.
35
Figure 5: Instrument relevance
(a) Production and opportunity cost
(b) Irradiance and feed-in tari
40
40
Feed−in tariff (residual)
30
∆oc (c/kWh)
20
10
0
20
0
−20
−10
−40
0
1
2
3
4
Solar production (kWh)
60 FIT
1:1 & 25 FIT
5
6
4000
4500
5000
5500
Mean irradiance
8 FIT
60 FIT
1:1 & 25 FIT
8 FIT
Panel (a) plots mean changes in opportunity cost (∆ocihd ) across levels of solar production (sihd ) for each feed-in tari group. Panel (b)
plots the correlation between feed-in tari and average irradiance partialling out the average irradiance of Melbourne. In each gure, size of
markers indicates weight of observations within each feed-in tari group.
36
Figure 6: Baseline estimates
(b) Within hour×FIT, zone
(a) Within zone
7
8
9
Hour−of−day
11
12
1
2
3
4
5
7
η2 (∆oc)
9
η1 (import price)
Coefficient estimate
−.05
0
−.1
10
Hour−of−day
11
12
1
2
3
4
5
4
5
η2 (∆oc)
η1 − η2
.06
0.354
p value of joint significance test =
0.771
7
8
9
10
11
12
1
2
3
4
−.06
−.03
Difference
0
.03
p value of joint significance test =
Difference
0
.03
.06
η1 − η2
−.03
−.06
8
Coefficient estimate
−.1
−.05
0
η1 (import price)
10
5
Hour−of−day
7
8
9
10
11
12
1
2
3
Hour−of−day
The top row of gures plot 90% condence intervals for coecients ηh1 (coecient on import price rih ) and ηh2 (coecient on relative
opportunity cost ∆ocihd ). The bottom row of gures plot 90% condence intervals for the dierence ηh1 − ηh2 . Under the null hypothesis
of attention to opportunity cost this dierence is zero. Standard errors clustered at household level. ∆ocihd is instrumented using hourly
interactions between feed-in tari program and solar production. All models are estimated with hour by day-of-week eects and hour by
heating and cooling degrees. Panel (a) has zone xed eects, panel (b) has zone xed eects and feed-in tari by hour-of-day xed eects.
37
Figure 7: Additional instruments
(a) Import price IV
7
8
9
Hour−of−day
11
12
1
2
3
4
5
7
η2 (∆oc)
9
10
Hour−of−day
11
12
1
2
3
4
5
4
5
−.1
Coefficient estimate
−.05
0
η2 (∆oc)
η1 − η2
.06
0.309
p value of joint significance test =
0.825
7
8
9
10
11
12
1
2
3
4
−.06
−.03
Difference
0
.03
p value of joint significance test =
Difference
0
.03
.06
η1 − η2
−.03
−.06
8
η1 (import price)
Coefficient estimate
−.1
−.05
0
η1 (import price)
10
(b) Export price IV
5
Hour−of−day
7
8
9
10
11
12
1
2
3
Hour−of−day
The top row of gures plot 90% condence intervals for coecients ηh1 (coecient on import price rih ) and ηh2 (coecient on relative
opportunity cost ∆ocihd ). The bottom row of gures plot 90% condence intervals for the dierence ηh1 − ηh2 . Under the null hypothesis of
attention to opportunity cost this dierence is zero. Standard errors clustered at household level. In panel (a) ∆ocihd is instrumented using
hourly interactions between feed-in tari program and solar production. Panel (a) has zone xed eects and feed-in tari by hour-of-day xed
eects and instruments for import price. Panel (b) instruments for feed-in tari program, ∆ocihd and import price using the method outlined
in section 4.3.3.
38
Figure 8: Opportunity cost vs average net cost
(b) Average (net) cost model
2.5
Predicted: opportunity cost/income
Predicted: net cost
Consumption (kWh)
1
1.5
0
.5
Consumption (kWh)
1
1.5
.5
0
2012w1
Actual
2
Actual
2
2.5
(a) Opportunity cost model
2012w26
2013w1
2012w1
2012w26
Date
2013w1
Date
Figure shows the weekly average of predicted hourly consumption from 7am to 5pm for two alternative models. On the left hand side is the
model used to test opportunity cost and fungibility. On the right hand side is a model assuming that household respond to the average net
cost of their electricity (revenue - cost per kWh of consumption). Both models are estimated with hour by day-of-week eects, hour by heating
and cooling degrees and zone xed eects.
Figure 9: Price elasticities
(b) Mean elasticity by production
(a) Mean elasticity by hour
Figure shows mean price elasticities of demand and supply over hours of the day (a) and for levels of solar production (b) and 90 percent
condence intervals. Estimates are cluster bootstrapped to generate standard errors. For each household and hour of the sample elasticities
are calculated according to equations (9) and (12) in Section 5.6. The solid line plots the mean demand elasticity for each hour of the day (a)
or level of solar production (b). The dashed line plots the mean supply elasticity for each hour of the day (a) or level of solar production (b).
Price elasticities account for both substitution and income eects resulting from price changes.
39
Figure 10: Price elasticities and predicted consumption without income eects
(b) Predicted consumption
(a) Mean elasticity by production
Panel (a) shows mean price elasticities of consumption and export for levels of solar production and 90 percent condence intervals assuming
that households do not respond to their solar income. Estimates are cluster bootstrapped. For each household and hour of the sample
elasticities are calculated according to equations (9) and (12) in Section 5.6. The solid line plots the mean consumption elasticity for level of
solar production. The dashed line plots the mean export elasticity for each level of solar production. Panel (b) shows predicted consumption
assuming no income eects for 60 FIT and 8 FIT households on very sunny versus very cloudy days.
40
7
Tables
Table 1: Descriptive statistics
(1)
(2)
(3)
(4)
(5)
1:1 FIT
60 FIT
25 FIT
8 FIT
Full sample
Observed
Export price (c/kWh)
Peak import price (c/kWh)
O peak import price (c/kWh)
Import (kWh)
Export (kWh)
Power cost ($/week)
Temperature (C)
2
Irradiance (W/m )
Melbourne
22.28
60
25
8
31.28
(5.139)
(0)
(0)
(0)
(17.75)
29.63
31.25
31.69
29.63
31.18
(2.706)
(2.570)
(1.887)
(3.602)
(2.537)
12.32
14.46
16.05
9.434
14.51
(8.709)
(5.850)
(4.204)
(8.114)
(6.048)
0.472
0.473
0.493
0.484
0.486
(0.272)
(0.271)
(0.276)
(0.268)
(0.273)
0.244
0.123
0.179
0.160
0.165
(0.198)
(0.0961)
(0.130)
(0.121)
(0.128)
7.257
3.562
9.237
13.87
8.375
(14.03)
(14.38)
(10.74)
(8.874)
(12.12)
16.25
15.37
15.26
13.99
15.15
(2.350)
(2.148)
(2.434)
(2.484)
(2.418)
476.7
445.7
455.6
378.2
442.9
(94.24)
(96.29)
(105.5)
(72.57)
(102.0)
0.720
0.850
0.687
0.684
0.730
(0.458)
(0.359)
(0.464)
(0.468)
(0.445)
Derived
Consumption (kWh)
Production (kWh)
Capacity (kW)
Solar income (c/hour 9am-5pm)
Solar income ($/week)
Households
0.816
0.676
0.741
0.689
0.720
(0.373)
(0.314)
(0.332)
(0.307)
(0.327)
0.674
0.387
0.501
0.454
0.474
(0.432)
(0.212)
(0.280)
(0.262)
(0.278)
2.760
1.782
2.270
2.513
2.205
(1.549)
(0.845)
(1.044)
(1.216)
(1.087)
34.91
45.06
29.24
13.15
31.19
(21.46)
(28.42)
(16.25)
(6.682)
(21.81)
25.70
31.18
20.49
9.007
21.78
(17.01)
(20.10)
(11.77)
(4.889)
(15.58)
26
133
291
78
528
Columns report mean values across all hours (except Irradiance, FIT price and Solar income ) by feed-in tari groups and for the
sample as a whole (column 5). Standard deviation in brackets. Exports are sales of electricity, imports are purchases of electricity. Customers
on the 1:1 FIT have an export price equal to their import price at the time of export. FIT price is average FIT price per unit of exports.
For households on a time of use rate Peak is 7am-11pm Monday to Friday. For households on a single rate, Peak is all hours. Irradiance is
mean global horizontal irradiance from 9am-5pm. Solar income is mean hourly solar income from 9am-5pm. Melbourne is an indicator for
whether the household is in the Greater Melbourne Metropolitan Area. Consumption, Production, Capacity and Solar income are estimates.
See Appendix A2 for details on how these variables are constructed.
Notes:
41
Table 2: Neighbourhood demographics
Household size 3.09
Bedrooms
Separate dwelling
Age
FT employed
Degree
Weekly income
Home ownership
High Green vote
Households
(1)
(2)
(3)
(4)
(5)
(6)
60 FIT
1:1 FIT
25 FIT
8 FIT
Full sample
State
2.97
2.94
2.90
2.95
2.89
(0.44)
(0.44)
(0.44)
(0.45)
(0.42)
(1.77)
3.36
3.17
3.24
3.20
3.22
3.04
(0.56)
(0.56)
(0.57)
(0.58)
(0.53)
(0.52)
0.91
0.84
0.87
0.85
0.86
0.79
(0.21)
(0.21)
(0.21)
(0.21)
(0.20)
(0.27)
35.48
36.77
36.97
36.37
36.76
38.00
(6.37)
(6.33)
(6.41)
(6.57)
(6.01)
(6.27)
0.42
0.40
0.40
0.40
0.40
0.38
(0.09)
(0.09)
(0.09)
(0.10)
(0.09)
(0.09)
0.12
0.19
0.15
0.18
0.17
0.18
(0.10)
(0.10)
(0.10)
(0.10)
(0.09)
(0.12)
1352.00
1466.41
1372.81
1388.96
1397.88
1338.07
(485.72)
(481.04)
(487.88)
(501.96)
(458.63)
(497.48)
0.34
0.36
0.33
0.33
0.34
0.35
(0.15)
(0.15)
(0.15)
(0.16)
(0.15)
(0.14)
0.28
0.51
0.40
0.45
0.44
0.50
(0.52)
(0.52)
(0.53)
(0.54)
(0.50)
(0.50)
131
25
285
77
518
Columns 1-5 report the mean across households using census SA1 level characteristics with the standard deviation in brackets clustered
at census SA1 level. SA1 identiers are missing for 11 households. Column (6) shows the mean and standard deviation across Victoria weighted
by SA1 population. Household size is number of residents. FT employed is proportion of working age population in full time employment.
Degree is proportion of post-school population with a bachelor's degree. Home ownership is proportion of population owning their home
outright. High Green vote indicates above median primary vote for the Australian Greens in the 2013 federal election.
Notes:
42
Table 3: Baseline results
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
Import price
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
oc
oc
oc
oc
oc
oc
oc
oc
oc
oc
oc
oc
oc
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
hour 0
(1)
(2)
(3)
(4)
Within zone
+ hour×FIT
+ import price IV
+ export price IV
-0.019
∗∗∗
(0.006)
∗∗∗
-0.018
(0.006)
∗∗∗
-0.019
(0.005)
-0.005
(0.006)
-0.005
(0.006)
-0.004
(0.006)
-0.006
(0.005)
hour 2
-0.004
(0.004)
-0.004
(0.004)
-0.002
(0.004)
-0.003
(0.004)
hour 3
-0.002
(0.004)
-0.002
(0.004)
-0.001
(0.004)
-0.002
(0.004)
hour 4
-0.002
(0.004)
-0.001
(0.004)
0.000
(0.004)
-0.001
(0.004)
hour 5
-0.005
(0.004)
-0.004
(0.004)
-0.002
(0.004)
-0.004
(0.004)
hour 6
0.003
(0.009)
0.003
(0.009)
0.003
(0.009)
-0.014
(0.361)
∗∗∗
(0.003)
-0.002
(0.004)
∗
(0.006)
∗∗∗
(0.003)
hour 7
-0.013
∗∗∗
(0.003)
-0.013
hour 8
-0.012
∗∗∗
(0.003)
-0.015
hour 9
-0.017
∗∗∗
(0.004)
hour 10
-0.022
∗∗∗
(0.004)
hour 11
-0.027
∗∗∗
(0.004)
hour 12
-0.031
∗∗∗
(0.004)
hour 13
-0.031
∗∗∗
(0.004)
hour 14
-0.030
∗∗∗
(0.004)
hour 15
-0.026
∗∗∗
(0.004)
hour 16
-0.026
∗∗∗
(0.005)
hour 17
-0.025
∗∗∗
(0.006)
(0.006)
∗∗∗
-0.028
∗∗∗
-0.049
∗∗∗
-0.068
∗∗∗
-0.076
∗∗∗
-0.074
∗∗∗
-0.061
∗∗∗
-0.041
∗∗∗
-0.032
∗∗∗
-0.027
∗∗
-0.015
(0.006)
-0.004
hour 18
hour 19
hour 20
-0.014
∗∗
-0.003
-0.008
∗∗
(0.004)
∗∗
-0.008
∗∗
-0.008
(0.006)
(0.006)
(0.006)
-0.007
(0.006)
(0.005)
(0.008)
(0.010)
(0.010)
(0.010)
(0.008)
(0.006)
(0.006)
(0.007)
(0.003)
0.006
(0.006)
-0.031
(0.003)
0.006
∗∗∗
(0.006)
-0.034
0.032
(0.040)
(0.012)
-0.000
(0.012)
(0.008)
-0.107
(2.438)
∗∗
(0.017)
-0.036
∗∗∗
(0.006)
-0.020
∗
(0.011)
(0.010)
(0.010)
-0.027
∗
(0.016)
(0.005)
(0.014)
∗∗∗
-0.037
∗∗∗
-0.068
∗∗∗
-0.090
∗∗∗
-0.100
∗∗∗
-0.098
∗∗∗
-0.082
∗∗∗
-0.057
∗∗
-0.036
(0.008)
-0.016
(0.018)
-0.016
(0.018)
(0.037)
0.043
(0.043)
0.042
(0.043)
hour 18
0.007
Observations
∗∗∗
-0.015
hour 17
∗∗∗
(0.003)
(0.006)
(0.004)
0.014
(0.003)
∗∗
∗∗∗
-0.037
∗∗∗
-0.068
∗∗∗
-0.090
∗∗∗
-0.100
∗∗∗
-0.099
∗∗∗
-0.082
∗∗∗
-0.057
∗∗
-0.036
(0.004)
∗∗∗
-0.013
∗∗∗
-0.019
∗∗∗
-0.025
∗∗∗
-0.029
∗∗∗
-0.030
∗∗∗
-0.029
∗∗∗
-0.026
∗∗∗
-0.023
∗∗∗
-0.023
Current income
0.005
∗∗
(0.039)
hour 16
(0.008)
0.005
(0.003)
0.001
hour 15
(0.008)
(0.005)
0.031
hour 14
(0.010)
∗
-0.016
(0.004)
(0.009)
hour 13
-0.012
0.003
(0.034)
hour 12
(0.010)
-0.020
(0.003)
0.001
hour 11
(0.014)
∗
-0.035
0.002
0.024
hour 10
(0.017)
∗∗
-0.046
(0.004)
(0.004)
(0.004)
(0.003)
(0.003)
(0.003)
(0.003)
(0.003)
(0.001)
1121548
∗∗
(0.019)
∗∗∗
(0.012)
-0.002
-0.004
∗∗
∗∗∗
-0.050
-0.012
-0.005
-0.008
(0.020)
(0.012)
(0.010)
(0.022)
∗∗
(0.005)
(0.004)
∗∗∗
-0.036
-0.048
(0.005)
(0.004)
-0.025
(0.013)
0.002
-0.004
(0.006)
(0.007)
∗
-0.004
-0.006
∗∗∗
(0.011)
-0.011
-0.023
(0.007)
hour 22
-0.027
(0.009)
-0.012
(0.006)
hour 21
hour 23
(0.004)
∗∗∗
-0.023
∗∗∗
-0.049
∗∗∗
-0.071
∗∗∗
-0.078
∗∗∗
-0.075
∗∗∗
-0.061
∗∗∗
-0.036
∗∗∗
-0.020
hour 7
hour 9
(0.006)
hour 1
hour 6
hour 8
∗∗∗
-0.022
-0.015
0.017
∗∗∗
(0.013)
(0.015)
(0.015)
(0.015)
(0.013)
(0.010)
(0.001)
1121548
0.017
∗∗∗
(0.013)
(0.015)
-0.034
(0.017)
∗∗∗
(0.016)
∗∗∗
(0.015)
∗∗∗
(0.013)
∗∗
(0.011)
(0.015)
-0.046
(0.015)
-0.044
(0.013)
-0.036
(0.010)
(0.014)
(0.001)
1121548
-0.027
-0.022
∗∗∗
-0.053
-0.142
0.011
(0.023)
∗∗
-0.043
∗∗∗
(0.015)
(0.019)
(0.096)
(0.002)
1122914
Notes: Dependent variable is hourly electricity consumption. Import price is the cost of buying electricity, export price is the price received to sell electricity. ∆oc
is the dierence between export and import prices for a household who is exporting (selling). Current income is current hourly solar income in cents. Standard
errors clustered at household level in parentheses. Signicance of coecients: ∗ p < 0.1,∗∗ p < 0.05,∗∗∗ p < 0.01. In columns (1) to (3) ∆oc and Current income
are instrumented using hourly interactions between feed-in tari program and solar production. All models are estimated with hour by day-of-week eects and hour
by heating and cooling degrees. Column (1) has zone xed eects, column (2) adds hour by feed-in tari eects, column (3) adds an instrument for import price.
Column (4) adds instruments for feed-in tari program based on measures of solar productivity (see section 4.3.3) and is estimated without zone or feed-in tari
group eects. Sample size dierence in column (4) reects the cluster-bootstrap routine. Strength of instruments is judged using the F test for weak instruments
with multiple endogenous variables outlined in Angrist and Pischke (2008). Instruments are strong for ∆ocihd from 7am to 5pm. All income and import price
instruments (columns (3) and (4)) are also strong.
Table 4: Expected and unexpected solar income
(1)
Within zone + hour×FIT
Import price × hour 0
Import price × hour 1
Import price × hour 2
Import price × hour 3
Import price × hour 4
Import price × hour 5
Import price × hour 6
Import price × hour 7
Import price × hour 8
Import price × hour 9
Import price × hour 10
Import price × hour 11
Import price × hour 12
Import price × hour 13
Import price × hour 14
Import price × hour 15
Import price × hour 16
Import price × hour 17
Import price × hour 18
Import price × hour 19
Import price × hour 20
Import price × hour 21
Import price × hour 22
Import price × hour 23
(2)
Within hour×FIT
(3)
(4)
Within hour × household
-0.027∗∗∗
-0.011
-0.011∗
-0.009
-0.008
-0.011∗
-0.017
-0.017∗∗∗
-0.018∗∗∗
-0.034∗∗∗
-0.063∗∗∗
-0.073∗∗∗
-0.073∗∗∗
-0.069∗∗∗
-0.057∗∗∗
-0.041∗∗∗
-0.035∗∗∗
-0.024∗∗∗
-0.009∗∗
0.002
0.003
0.006∗
0.007∗∗∗
-0.040∗∗∗
(0.007)
(0.007)
(0.006)
(0.006)
(0.006)
(0.006)
(0.011)
(0.005)
(0.005)
(0.007)
(0.011)
(0.013)
(0.013)
(0.012)
(0.010)
(0.008)
(0.008)
(0.006)
(0.005)
(0.005)
(0.003)
(0.003)
(0.003)
(0.008)
-0.028∗∗∗
-0.012∗
-0.011∗
-0.010∗
-0.009
-0.012∗∗
-0.019∗
-0.017∗∗∗
-0.018∗∗∗
-0.035∗∗∗
-0.063∗∗∗
-0.074∗∗∗
-0.074∗∗∗
-0.069∗∗∗
-0.058∗∗∗
-0.041∗∗∗
-0.036∗∗∗
-0.024∗∗∗
-0.010∗∗
0.001
0.003
0.006∗
0.007∗∗∗
-0.041∗∗∗
(0.007)
(0.007)
(0.006)
(0.006)
(0.006)
(0.006)
(0.011)
(0.005)
(0.005)
(0.007)
(0.011)
(0.013)
(0.013)
(0.012)
(0.010)
(0.008)
(0.008)
(0.006)
(0.005)
(0.005)
(0.003)
(0.003)
(0.003)
(0.008)
-0.021∗∗∗
-0.004
-0.004
-0.002
-0.002
-0.005
-0.004
0.001
-0.003
-0.009∗∗
-0.019∗∗∗
-0.024∗∗∗
-0.027∗∗∗
-0.026∗∗∗
-0.026∗∗∗
-0.020∗∗∗
-0.016∗∗∗
-0.009∗
-0.000
0.000
0.004
0.007∗∗
0.008∗∗∗
-0.035∗∗∗
(0.006)
(0.007)
(0.005)
(0.004)
(0.004)
(0.005)
(0.010)
(0.005)
(0.004)
(0.005)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.005)
(0.005)
(0.005)
(0.006)
(0.004)
(0.004)
(0.003)
(0.008)
-0.025∗∗
-0.028∗∗∗
-0.027∗∗
-0.026∗∗
-0.033∗∗
-0.020∗∗
0.019
-0.002
-0.002
-0.004
-0.013∗∗
-0.020∗∗∗
-0.023∗∗∗
-0.021∗∗∗
-0.018∗∗∗
-0.012∗∗∗
-0.011∗∗∗
-0.008∗∗∗
0.000
0.002
-0.004∗∗∗
-0.003∗∗
-0.003∗
-0.027∗∗
(0.010)
(0.011)
(0.011)
(0.012)
(0.013)
(0.009)
(0.018)
(0.002)
(0.003)
(0.005)
(0.006)
(0.006)
(0.006)
(0.005)
(0.005)
(0.004)
(0.004)
(0.003)
(0.003)
(0.003)
(0.002)
(0.002)
(0.001)
(0.012)
oc × hour 6
oc × hour 7
oc × hour 8
oc × hour 9
oc × hour 10
oc × hour 11
oc × hour 12
oc × hour 13
oc × hour 14
oc × hour 15
oc × hour 16
oc × hour 17
oc × hour 18
-0.101
-0.060∗∗∗
-0.034∗∗∗
-0.051∗∗∗
-0.082∗∗∗
-0.087∗∗∗
-0.089∗∗∗
-0.085∗∗∗
-0.069∗∗∗
-0.053∗∗∗
-0.048∗∗∗
-0.050∗∗∗
-0.055
(0.063)
(0.012)
(0.007)
(0.010)
(0.014)
(0.016)
(0.015)
(0.014)
(0.013)
(0.010)
(0.013)
(0.015)
(0.035)
-0.103
-0.062∗∗∗
-0.035∗∗∗
-0.052∗∗∗
-0.083∗∗∗
-0.088∗∗∗
-0.090∗∗∗
-0.086∗∗∗
-0.070∗∗∗
-0.054∗∗∗
-0.049∗∗∗
-0.051∗∗∗
-0.057
(0.064)
(0.012)
(0.007)
(0.010)
(0.014)
(0.016)
(0.015)
(0.014)
(0.013)
(0.010)
(0.013)
(0.015)
(0.035)
0.021
-0.001
-0.008∗
-0.013∗∗
-0.019∗∗∗
-0.026∗∗∗
-0.030∗∗∗
-0.031∗∗∗
-0.031∗∗∗
-0.028∗∗∗
-0.026∗∗∗
-0.028∗∗∗
-0.003
(0.041)
(0.010)
(0.005)
(0.005)
(0.005)
(0.003)
(0.003)
(0.003)
(0.004)
(0.004)
(0.006)
(0.009)
(0.037)
0.048
-0.000
0.006
-0.001
-0.014∗
-0.025∗∗∗
-0.030∗∗∗
-0.028∗∗∗
-0.020∗∗∗
-0.011∗
-0.011
-0.017∗∗∗
0.010
(0.092)
(0.006)
(0.006)
(0.008)
(0.008)
(0.007)
(0.007)
(0.007)
(0.007)
(0.006)
(0.007)
(0.006)
(0.024)
Expected income
Income shock
Non-solar income
Current income
0.012∗∗∗
0.039∗∗∗
(0.001)
(0.004)
0.012∗∗∗
0.039∗∗∗
0.070∗∗
(0.001)
(0.004)
(0.035)
0.004∗∗∗
0.010∗∗∗
(0.001)
(0.001)
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
Observations
795038
795038
0.081∗∗
0.014∗∗∗
(0.039)
(0.001)
795038
795038
Notes: Dependent variable is hourly electricity consumption. Import price is the cost of buying electricity, export price is the price received to sell electricity. ∆oc
is the dierence between export and import prices for a household who is exporting (selling). Current income is current hourly solar income in cents. Expected
income is the average solar income from solar production during daylight hours for the previous 30 days in cents. Income shock is the dierence between hourly
solar income and average solar income for that hour for the previous 30 days in cents. Non-solar income is weekly income from census data in $000/week. Standard
errors clustered at household level in parentheses. Signicance of coecients: ∗ p < 0.1,∗∗ p < 0.05,∗∗∗ p < 0.01. ∆oc, Current income and Income shock are
instrumented using hourly interactions between feed-in tari program and solar production. All models are estimated with hour by day-of-week eects and hour by
heating and cooling degrees. Column (1) has zone xed eects, and feed-in tari by hour xed eects, columns (2) and (3) have hour by feed-in tari eects, column
(4) has household-hour xed eects. Compared to Table 3 lower sample sizes reect creation of income measure using 30 days of lagged solar income. Strength of
instruments is judged using the F test for weak instruments with multiple endogenous variables outlined in Angrist and Pischke (2008). Instruments for ∆ocihd are
strong for all models between 7am and 5pm. Instruments for Income shock and Current income are also strong.
Table 5: Preferences for solar
(1)
(2)
(3)
Within zone + hour×FIT
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
∗∗∗
hour 0
-0.018
(0.005)
∗∗∗
-0.022
(0.006)
∗∗∗
-0.022
(0.006)
hour 1
-0.003
(0.006)
-0.005
(0.006)
-0.006
(0.006)
hour 2
-0.002
(0.004)
-0.003
(0.004)
-0.003
(0.004)
hour 3
-0.000
(0.004)
-0.002
(0.004)
-0.002
(0.004)
hour 4
0.001
(0.004)
-0.001
(0.004)
-0.001
(0.004)
hour 5
-0.002
(0.004)
-0.004
(0.004)
-0.004
(0.004)
hour 6
0.004
(0.008)
-0.000
(0.006)
0.005
(0.007)
0.001
(0.005)
-0.000
(0.005)
hour 7
∗
(0.004)
∗∗
(0.005)
∗∗∗
(0.008)
-0.015
∗∗∗
(0.010)
-0.023
∗∗∗
(0.012)
-0.030
∗∗∗
(0.013)
-0.034
∗∗∗
(0.013)
-0.035
∗∗∗
(0.011)
-0.034
∗∗∗
(0.008)
-0.029
-0.008
hour 8
-0.010
hour 9
-0.027
hour 10
-0.054
hour 11
-0.071
hour 12
-0.075
hour 13
-0.070
hour 14
-0.054
hour 15
-0.032
∗∗
(0.003)
∗∗∗
(0.004)
-0.019
∗∗∗
(0.004)
-0.029
∗∗∗
(0.003)
-0.037
∗∗∗
(0.003)
-0.041
∗∗∗
(0.003)
-0.042
∗∗∗
(0.003)
-0.040
∗∗∗
(0.003)
-0.035
∗∗∗
(0.004)
-0.028
∗∗∗
(0.005)
-0.019
-0.007
∗∗
(0.005)
∗∗∗
(0.007)
∗∗∗
(0.009)
∗∗∗
(0.010)
∗∗∗
(0.010)
∗∗∗
(0.010)
∗∗∗
(0.010)
∗∗∗
(0.009)
∗∗∗
(0.007)
∗∗∗
(0.006)
-0.010
hour 16
-0.011
(0.007)
-0.024
hour 17
-0.003
(0.007)
-0.014
hour 18
0.007
(0.006)
0.006
(0.005)
0.001
(0.005)
hour 19
-0.003
(0.005)
-0.007
(0.005)
-0.004
(0.006)
hour 20
0.003
(0.003)
0.002
(0.004)
0.003
(0.004)
hour 21
0.005
(0.003)
0.005
(0.003)
0.005
∗∗
(0.003)
0.006
∗∗∗
(0.006)
-0.033
∗
(0.005)
0.017
∗
(0.099)
0.048
(0.130)
hour 22
0.006
hour 23
-0.030
Current income
0.009
Solar production (kWh)
0.194
Solar production
Producing
Producing
×
×
×
eary adopter
Importing
(0.003)
0.006
∗∗∗
(0.007)
-0.034
∗∗∗
(0.001)
0.021
60 FIT
-0.063
(0.062)
8 FIT
-0.042
(0.072)
∗∗∗
Producing
Importing
∗∗
0.738
×
×
(0.003)
∗∗∗
(0.007)
∗∗∗
(0.004)
(0.032)
60 FIT
-0.057
(0.075)
8 FIT
0.144
∗
(0.074)
1.224
(0.813)
Importing
Observations
(0.003)
∗∗
1045624
1121548
1121548
Dependent variable is hourly electricity consumption. Standard errors clustered at household level in parentheses. Signicance of coecients: ∗ p <
∗∗
0.1,
p < 0.05,∗∗∗ p < 0.01. Current income is current hourly solar income in cents, early adopter is an indicator variable for households in 1:1 FIT and 60
FIT feed-in tari programs (the earliest installers of solar panels), Producing is Importing is an indicator variable for household is producing or buying electricity
from the grid respectively. All models are estimated with hour by day-of-week eects, hour by heating and cooling degrees, hour by feed-in tari eects and zone
eects. In column (1) income and price variables are instrumented using hourly irradiance, 2 day lagged solar production, 2 day hourly lagged solar production
interacted with FIT group, and underlying network taris. In columns (2) and (3) instruments for price variables, income and import interactions are hourly
interactions between feed-in tari program and solar production and underlying network taris. Instrument strength is judged using the F test for weak instruments
with multiple endogenous variables outlined in Angrist and Pischke (2008). Instruments for price and income are strong for all hours. Instruments for Importing
interactions are also strong. Sample size dierence in column (1) reects dropped observations due to lagged instruments.
Notes:
Table 6: Price coecients and elasticities
Net import
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
Price
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
hour 0
(1)
(2)
(3)
(4)
Coecients
Coecients
Consumption elasticity
Export elasticity
∗
-0.021
(0.011)
(0.010)
hour 2
∗∗
-0.021
∗
-0.020
hour 3
-0.020
hour 1
hour 4
Consumption
∗∗
-0.026
∗
-0.021
(0.011)
(0.010)
(0.011)
∗∗
-0.021
∗
-0.020
(0.012)
-0.020
(0.013)
∗∗
-0.026
∗
-1.589
(0.887)
(0.788)
(0.011)
∗∗
-1.808
∗
-1.818
(0.012)
-1.787
(1.111)
(0.013)
∗∗
-2.402
(1.003)
(1.175)
hour 5
-0.013
(0.009)
-0.013
(0.009)
-1.228
(0.896)
0.373
(0.335)
hour 6
0.010
(0.015)
0.010
(0.014)
1.311
(1.548)
-1.279
(1.549)
hour 7
-0.003
(0.002)
-0.003
hour 8
0.001
(0.004)
∗
(0.002)
-0.097
(0.185)
0.060
(0.207)
-0.001
(0.003)
0.335
(0.308)
-0.318
(0.253)
-0.005
(0.289)
hour 9
-0.002
(0.005)
hour 10
-0.009
(0.006)
-0.013
∗∗
(0.006)
-0.021
hour 11
-0.016
(0.004)
0.194
(0.414)
-0.115
∗∗∗
(0.004)
-0.396
(0.343)
0.321
∗∗∗
(0.004)
-0.899
∗∗∗
(0.004)
-1.098
∗∗∗
(0.004)
-0.880
∗∗∗
(0.004)
-0.739
∗∗∗
(0.004)
∗∗
(0.004)
-0.134
(0.196)
0.164
∗∗∗
(0.003)
-0.208
(0.145)
0.391
(0.269)
-0.002
(0.003)
0.041
(0.114)
-0.154
(0.248)
-0.003
(0.004)
-0.044
(0.159)
hour 12
-0.019
∗∗∗
(0.006)
-0.025
hour 13
-0.017
∗∗∗
(0.006)
-0.023
hour 14
-0.015
∗∗∗
(0.005)
-0.020
hour 15
-0.011
∗∗∗
(0.004)
-0.015
∗
(0.004)
∗∗∗
(0.003)
hour 16
hour 17
hour 18
hour 19
hour 20
-0.007
-0.008
-0.001
(0.003)
-0.002
(0.004)
-0.004
∗∗∗
(0.001)
-0.009
-0.010
0.750
∗∗∗
(0.265)
0.710
∗∗
(0.223)
-0.466
∗∗
(0.001)
-0.212
∗
(0.012)
∗∗∗
(0.000)
hour 22
-0.003
∗∗
(0.001)
-0.003
∗
(0.012)
∗∗∗
(0.000)
1045908
0.781
(0.272)
-0.202
-0.003
-0.022
0.008
(0.298)
∗∗∗
(0.001)
(0.001)
0.006
∗∗∗
∗∗
∗∗
Current income
0.642
(0.001)
-0.003
-0.022
(0.275)
∗∗∗
-0.004
hour 21
hour 23
∗∗∗
∗∗∗
(0.082)
∗∗
(0.087)
∗∗
(0.101)
∗
(0.829)
-0.233
-1.469
(0.223)
∗∗∗
(0.184)
∗∗∗
(0.195)
∗∗∗
(0.220)
∗∗∗
(0.245)
∗∗
(0.251)
0.509
(0.288)
1045908
Column (1) dependent variable is hourly net imports (imports (purchases) of electricity minus exports (sales) of electricity). Column (2) dependent variable
is hourly electricity consumption. Columns (1) and (2) report coecients and standard errors from a cluster bootstrap routine with 100 replications. Signicance
of coecients: ∗ p < 0.1,∗∗ p < 0.05,∗∗∗ p < 0.01. Price variables and Current income are instrumented using hourly interactions between irradiance and feed-in
tari and lagged irradiance and feed-in tari. Both models are estimated with household by hour eects, hour by day-of-week eects and hour by heating and
cooling degrees. Compared to Table 3 lower sample size reects the use of lagged irradiance as an instrument. Current income is the contemporaneous value of
the solar endowment at current prices. For each household and hour of the sample the elasticity of consumption and export are calculated according to equations
(9) and (12) in Section 5.5 using price and income coecients from column (2). Means of elasticities are reported in column (3) (consumption elasticity) and (4)
(export elasticity). Strength of instruments is judged using the F test for weak instruments with multiple endogenous variables outlined in Angrist and Pischke
(2008). Price instruments are all strong except for 6am. Income instrument is also strong.
Notes:
A
Appendix
A.1 Retail prices
To construct price data I use three sources of information.
Firstly, I use price data from the
Essential Services Commission's price comparator website for the period January 2012- June 2012.
The Essential Services Commission (ESC) is the regulatory body for retail electricity in Victoria.
The ESC requires retailers to provide it with information on one available plan on 30 June each
year.
Prior to January 2013, the retailer's underlying rates did not dier across plans.
Plans
only diered in the discounts and features (e.g. direct debit, quarterly vs monthly billing) made
available. Secondly, I use plan and price information (available for July 2012-June 2013) from the
retailer's website. Most price increases occur at the start of the calendar year. However due to the
introduction of a national carbon tax in 2012, retailers increased their retail rates in July of 2012.
This increase in rates occurred on July 1 2012 across all of the retailer's plans. In January 2013 the
retailer kept rates of all but one plan xed. The nal source of price information comes from invoice
data provided by the retailer.
I use the invoice data from a separate set of households without
solar panels to estimate prices over the relevant period and compare these to the two sources of
price information. This comparison gives condence that the publicly available rates are indeed
the rates applied across the customer base.
The invoice data contains information on total billable amount and kWh for the period exclusive
of plan discounts. To verify the above retail prices for customers with a Single Rate" meter (on a
at rate tari ) I estimate the following equation:
Iit = P riceP eriodj × Distributord × [β1jd Daysit + β2jd (kW hit × M eterim × P lani )] + eit
where
Iit
Distributord
is the invoice amount (pre-discounts and tax) at billing period
is the distribution zone of customer
of billing days in the period,
kW hit
i
which is time invariant,
rounding error. The estimates of
respectively.
β1jd
and
β2jd
i.
The error term
eit
for customer
Daysit
is the billable kWh of the household and
are respectively the meter type and plan of customer
t
(13)
i,
is the number
M eteri
and
P lani
represents billing and
are the estimated daily charges and per kWh prices
43
43 Plan discounts are applied to subsequent bill.
47
To reect the change in prices between June and July 2012 and from January 1 2013 for
customers on Plan 6 I estimate prices from the invoice data separately for plans and over three
periods. This will also verify that prior to January 2013, the retailer's underlying rates were the
same across plans. Table A.2 reports prices estimated from equation 13 applied to customers on
at rate taris (Single Rate" customers). Empty cells refer to combinations of plan, zone, meter
and period where there were insucient observations. The reported prices are very close to the
prices reported in TableA.1 for Single Rate" customers. The exception is prices for the period 1
zone 4 where there are insucient households to identify daily charges and consumption charges
(peak rate) separately.
The invoice data does not separate billable kWh into peak and o peak.
To verify rates of
customers on Time of Use" and Two Rate" plans I rely on being able to match interval data with
invoice data. For the subset of customers for whom I have a high quality match, I am then able to
apportion the total kWh consumed into peak and o peak. As this subset is much smaller than the
full invoice sample I then estimate prices as per (13) except that I collapse plans 1-5 into a single
plan. Estimated prices are reported in Table A.3. Once again empty cells indicate combinations
with insucient data. In general the estimated prices are in line with the observed prices in Table
A.1.
The prices reported in Table A.1 and estimated in Tables A.2 and A.3 are pre-discounted
prices. When a customer joins the retailer they choose a price plan. Each plan diers in available
payment methods (for example a customer can elect to be billed xed instalments in advance
with quarterly reconciliation, they can alternatively elect to have their bill direct debited from
a nominated account). Plans also dier in discounts o a customer's allocated charge (based on
their meter type and distribution zone). Some discounts are conditional on the retailer receiving
payment on time and are credited onto a household's subsequent bill. I assume that customers make
decisions with respect to their plan's discounted price.
44
In practice I instrument for retail price
using the underlying rates from Table A.1 which are determined by network tari assignments on
the part of the distributor (each zone has a local monopoly regulated distributor). I do so to allay
two possible concerns: rst that plans are chosen by households and therefore may be correlated
with other household characteristics. Second, as noted I do not observe the household's perceived
44 Some customers are also oered an additional 5% discount o of imported peak electricity above 500kWh in a billing
month (eectively a declining block tari ). I do not include this discount in a household's import price. Ito (2014) shows
that consumers faced with a non-linear price respond to average prices and not marginal prices. In this instance the 5%
discount on consumption makes very little dierence to the average peak price a household pays, I therefore ignore it and
assume that household's respond to the regular plan price.
48
price (which in fact may dier from their actual price because they may intend but fail to pay their
bill on time), instead I use their discounted price. Hence there may be error in the price variable.
Once again this error may be correlated with household characteristics. My instrument uses the
plausibly exogenous allocation of households to network taris to overcome these two identication
problems.
Table A.1: Publicly available prices
Tari type
Distributor
(1)
(2)
(3)
All plans: 30 June 2012
All plans: 1 July 2012
Plan 6: 1 January 2013
Peak
O peak
Daily
Peak
O peak
Daily
Peak
O peak
Daily
Single Rate
Zone 1
18.5
.
60
22
.
70
24.5
.
70
Time of Use
Zone 1
23.75
12.5
60
28.5
15.5
70
30
17
70
Two Rate
Zone 1
19.5
12
60
23
16
70
25
16.5
70
Single Rate
Zone 2
20.5
.
70
25.5
.
80
27.5
.
80
Time of Use
Zone 2
27
13
70
33
17
80
35
18.5
80
Two Rate
Zone 2
20.5
13
70
25.5
17
80
27.5
18.5
80
Single Rate
Zone 3
22
.
70
25.5
.
80
28
.
80
Time of Use
Zone 3
28.5
13
70
32
16
80
35.5
18.5
80
Two Rate
Zone 3
23
12
70
26.5
16.5
80
29
17.5
80
Single Rate
Zone 4
22
.
65
26
.
80
28.5
.
85
Time of Use
Zone 4
26
16
65
31
18.5
80
33.5
22
85
Two Rate
Zone 4
24
14.5
65
28
19
80
31
20
85
Single Rate
Zone 5
20.5
.
70
25
.
80
27.5
.
80
Time of Use
Zone 5
27
13
70
33
16
80
35
18.5
80
Two Rate
Zone 5
20.5
13
70
25
16
80
27.50
18.5
80
Prices are exclusive of Goods and Services Tax (GST) and plan discounts.
Pre July 2012 prices are sourced from the Essential Service Commission.
Post July 2012 prices are sourced directly from the retailer's website.
49
Table A.2: Estimated prices: single rate tari type
(1)
Period 1
(2)
(3)
Period 2
Period 3
Peak rates ($/kWh)
Zone 1
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Zone 2
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Zone 3
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Zone 4
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
Zone 5
Plan 1
Plan 2
Plan 3
Plan 4
Plan 5
Plan 6
0.184
(0.001)
0.185
(0.000)
0.185
(0.001)
0.183
(0.001)
0.185
(0.002)
0.185
(0.000)
0.216
(0.000)
0.211
(0.000)
0.218
(0.001)
0.215
(0.000)
0.215
(0.001)
0.218
(0.000)
0.212
(0.000)
0.221
(0.000)
0.222
(0.000)
0.222
(0.000)
0.221
(0.002)
0.244
(0.000)
0.205
(0.001)
0.205
(0.001)
0.205
(0.001)
0.205
(0.001)
0.205
(0.003)
0.205
(0.001)
0.252
(0.001)
0.252
(0.001)
0.248
(0.001)
0.247
(0.001)
0.252
(0.002)
0.247
(0.001)
0.256
(0.001)
0.256
(0.000)
0.256
(0.000)
0.257
(0.001)
0.257
(0.002)
0.273
(0.001)
0.220
(0.002)
0.220
(0.001)
0.220
(0.001)
0.220
(0.002)
.
(.)
0.220
(0.001)
0.257
(0.001)
0.256
(0.000)
0.258
(0.001)
0.257
(0.001)
0.258
(0.003)
0.260
(0.000)
0.254
(0.001)
0.254
(0.000)
0.255
(0.000)
0.255
(0.000)
0.254
(0.004)
0.272
(0.000)
.
(.)
0.146
(0.002)
.
(.)
.
(.)
.
(.)
.
(.)
0.269
(0.004)
0.264
(0.001)
0.260
(0.003)
0.239
(0.001)
.
(.)
0.257
(0.002)
0.253
(0.001)
0.252
(0.000)
0.254
(0.000)
0.257
(0.001)
0.254
(0.002)
0.265
(0.000)
0.205
(0.002)
0.205
(0.001)
0.205
(0.001)
0.205
(0.001)
0.205
(0.002)
0.205
(0.001)
0.249
(0.001)
0.249
(0.000)
0.250
(0.000)
0.251
(0.001)
0.249
(0.002)
0.248
(0.000)
0.251
(0.001)
0.250
(0.000)
0.251
(0.000)
0.251
(0.000)
0.250
(0.002)
0.272
(0.000)
Daily charge ($/day)
Zone 1
Zone 2
Zone 3
Zone 4
Zone 5
0.599
(0.003)
0.697
(0.006)
0.697
(0.005)
2.084
(0.023)
0.7
(0.004)
0.736
(0.001)
0.796
(0.004)
0.77
(0.003)
0.748
(0.00842)
0.782
(0.003)
Observations
38966
Standard errors in parentheses
Period 1: January 1 2012-June 30 2012
Period 2: July 1 2012-December 30 2012
Period 3: January 1 2013-June 30 2013
Estimated using invoice data only
50
0.686
(0.001)
0.786
(0.003)
0.806
(0.002)
0.873
(0.003)
0.796
(0.002)
Table A.3: Estimated prices: multiple tari types
(1)
(2)
(3)
(4)
(5)
Zone 1
Zone 2
Zone 3
Zone 4
Zone 5
Peak rates ($/kWh)
Single Rate
Plans 1-5
Period 1
Period 2
Period 3
Plan 6
Period 1
Period 2
Period 3
Time of Use
Plans 1-5
Period 1
Period 2
Period 3
Plan 6
Period 1
Period 2
Period 3
Two Rate
Plans 1-5
Period 1
Period 2
Period 3
Plan 6
Period 1
Period 2
Period 3
0.186
(0.002)
0.229
(0.001)
0.223
(0.001)
0.186
(0.001)
0.238
(0.001)
0.247
(0.001)
0.205
(0.004)
0.258
(0.002)
0.256
(0.002)
0.205
(0.002)
0.254
(0.002)
0.275
(0.002)
0.219
(0.007)
0.261
(0.002)
0.255
(0.002)
0.219
(0.002)
0.265
(0.001)
0.278
(0.001)
.
()
.
()
0.250
(0.025)
.
()
0.270
(0.021)
0.285
(0.005)
0.205
(0.004)
0.259
(0.003)
0.251
(0.003)
0.205
(0.002)
0.256
(0.001)
0.273
(0.002)
0.265
(0.019)
0.250
(0.004)
0.270
(0.004)
0.237
(0.003)
0.260
(0.002)
0.283
(0.003)
.
()
.
()
.
()
.
()
.
()
.
()
0.286
(0.018)
0.336
(0.017)
0.323
(0.015)
0.297
(0.009)
0.314
(0.004)
0.368
(0.005)
.
()
.
()
.
()
.
()
.
()
.
()
.
()
.
()
.
()
0.240
(0.304)
0.162
(0.020)
0.636
(0.010)
0.275
(0.016)
0.214
(0.012)
0.202
(0.005)
0.169
(0.003)
0.238
(0.002)
0.250
(0.003)
.
()
.
()
.
()
.
()
0.344
(0.034)
.
()
0.221
(0.029)
0.271
(0.007)
0.264
(0.005)
0.203
(0.007)
0.275
(0.002)
0.284
(0.002)
.
()
.
()
.
()
.
()
.
()
0.436
(0.020)
.
()
.
()
.
()
.
()
.
()
.
()
O peak rates ($/kWh)
Time of Use
Plans 1-5
Period 1
Period 2
Period 3
Plan 6
Period 1
Period 2
Period 3
Two Rate
Plans 1-5
Period 1
Period 2
Period 3
Plan 6
Period 1
Period 2
Period 3
0.112
(0.013)
0.216
(0.003)
0.201
(0.003)
0.129
(0.003)
0.216
(0.002)
0.207
(0.003)
.
()
.
()
.
()
.
()
.
()
.
()
0.128
(0.016)
0.158
(0.013)
0.151
(0.011)
0.112
(0.006)
0.184
(0.003)
0.160
(0.004)
.
()
.
()
.
()
.
()
.
()
.
()
.
()
.
()
.
()
0.183
(0.113)
0.266
(0.006)
.
()
.
()
0.179
(0.012)
0.196
(0.013)
0.129
(0.005)
0.162
(0.003)
0.165
(0.004)
.
()
.
()
.
()
.
()
.
()
.
()
0.100
(0.026)
0.165
(0.007)
0.166
(0.009)
0.112
(0.009)
0.162
(0.002)
0.171
(0.003)
.
()
.
()
.
()
.
()
.
()
.
()
.
()
.
()
.
()
.
()
.
()
.
()
Daily charge ($/day)
Period 1
Period 2
Period 3
0.594
(0.010)
0.590
(0.007)
0.668
(0.006)
Observations
0.700
(0.023)
0.716
(0.016)
0.784
(0.018)
0.712
(0.018)
0.732
(0.011)
0.797
(0.011)
7585
Standard errors in parentheses
Period 1: January 1 2012-June 30 2012
Period 2: July 1 2012-December 30 2012
Period 3: January 1 2013-June 30 2013
Estimated using invoice data and interval data
51
0.779
(0.041)
0.656
(0.230)
0.851
(0.049)
0.700
(0.015)
0.708
(0.013)
0.798
(0.015)
A.2 Solar production
For households on net feed-in taris, smart meters record half hourly exports and imports of electricity. Total electricity consumption and total electricity generation are not observed. Without
additional metering infrastructure however there is no way of observing solar production or household consumption. Instead, I rely on an estimate of solar production. Using this estimate I then
back out an estimate of household consumption. My estimate of solar production is derived from
an empirical model of observed solar output for a separate sample of solar PV installations. Using
this auxiliary sample I rst run a regression to explain observed solar output with a set of right
hand side variables. I then use the estimated coecients from this regression to predict production
in my main sample. I then combine this estimate with the observed import and export data to
generate an estimate of consumption.
To construct my model of solar production I use data from the three sources. The rst is from
the organisation PVOutput. PVOutput is a free and publicly available online service allowing users
to upload, track and compare their solar production. Data is uploaded in 5 minute intervals. I
construct a panel of solar production over 2012-2013 for 358 installations across Victoria. I analyse
production at the hourly level for installations with less than 6kW of rated capacity.
45
For each
installation I also observe latitude and longitude and system characteristics.
The second source of information is weather and satellite data from the Bureau of Meteorology
(BoM). I match each site of the PV Output data to gridded hourly solar irradiance data derived
from satellite observations
46
by the BoM over the period 2012-2013. The BoM uses satellite imagery
to derive estimates of global horizontal irradiance and direct normal irradiance. Global horizontal
irradiance (GHI) measures the intensity of solar energy falling on a horizontal surface (BoM, 2013).
GHI is measured in
W atts/m2 .
I also match PV Output sites to 3 hourly temperature observations
from over 200 weather stations across the state. I interpolate 3 hourly temperature observations
to generate an hourly temperature series.
Finally as a comparison exercise I use estimates of solar production from the National Renewable
Energy Laboratory's (NREL) PV Watts Calculator.
The calculator provides hourly engineering
estimates of solar production based on a yearly set of data derived from each calendar month over
45 I construct an hourly series from cumulative energy production. My production series therefore starts for the second
hourly observation of output for each installation-date.
I also drop any date for which an installation has a missing
production observation.
46 I also observe 1 minute solar irradiance data for Melbourne and Mildura
52
more than 15 years. The online calculator uses this data and dened user inputs to calculate solar
production for every hour of a representative year. I compare predictions from my model of solar
production to PV Watts estimates for default settings for Melbourne.
My rst step is to estimate a model to explain solar production in the PVOutput.org data using
a set of right-hand side variables that I also observe for my main sample of solar households. Figure
A.1 shows the distribution of actual production per kW of capacity for the PV Output sample.
The baseline model is:
sihd = β1h GHIihd + β2h T empihd + β3hs [Ss × Latitudei ] + β4hs [Ss × Longitudei ] + ihd
where
sihd
is solar output per kW of capacity for installation
horizontal irradiance at the same frequency,
T empihd
indicator variables for season. I allow each
β
i
at hour
h
d, GHI
of date
is ambient temperature and
Ss
coecient to dier by hour-of-day.
(14)
is global
is a series of
GHI
captures
regular variation in solar irradiance caused by movement of the sun as well as hour-to-hour variation
caused by atmospheric conditions such as cloud (BoM, 2013). Ambient temperature aects how
eciently PV panels can convert irradiance to power.
Finally latitude and longitude aect the
angle and intensity of the sun at a given hour in a given season. I specify the dependent variable as
production per kW of capacity following the scaling implied by PV Watts estimates across system
sizes. This means that
sihd ∈ [0, 1]
and the dependent variable is a fractional variable. Papke and
Wooldridge (1996) outline the methodological issues associated with modelling fractional variables.
In particular, estimating (14) using Ordinary Least Squares (OLS) will likely lead to predictions of
sihd
outside the unit interval. To ensure that predictions lie on the interval I then implement the
47
zero-one-inated beta (ZOIB) regression model developed by (Cook et al., 2008).
To validate the models I randomly select
20% of the PVOutput sites to set aside for the purposes
of validation. This validation sample is not used to estimate parameters. I use estimated parameters
to predict solar output for both estimation and validation samples.
Histograms of actual and
47 The ZOIB regression model was developed to model fractional variables with positive mass at the boundaries of the
unit interval (Cook et al., 2008). The model assumes that the response variable takes on a mixed discrete-continuous
distribution. The discrete component of the mixed distribution models the probability of observations at the boundary
points of the interval, whilst the continuous component models the conditional mean of the data on (0,1). In the ZOIB
model the continuous component of the mixed distribution is a beta distribution whilst the discrete component is governed
by a logistic distribution. The model allows the eect of exogenous variables on the probability of observing boundary
values to dier from their eect on the conditional mean in the interval (0,1).
In the present context this eectively
allows a dierent data generating process to determine observations of zero production. I use the same set of explanatory
variables for the continuous and discrete components however allow the coecients of these variables to dier.
53
predicted production for the OLS model for the estimation sample and for the validation sample
are shown in panels (a) and (b) of Figure A.2. The
R2
value for the estimation is 0.9 suggesting
that the stylised model in 14 explains 90% of the variation in actual production. I nd that
predictions are within the
94% of
95% prediction interval for both the estimation sample and the validation
sample. Despite this, the model has some trouble correctly predicting very low solar production
and results in predictions of
sihd
below zero. Figure A.4 shows predicted solar production per kW
of capacity using the ZOIB model.
This performance of the zoib model is worse in the region
of zero production. The median prediction error for the OLS model with production censored at
zero is 0.009 (standard deviation 0.14).
The median prediction error for the zoib model is 0.14
(standard deviation 0.14). In what follows I therefore use the OLS model and censor production
per unit of capacity at zero. As further evidence of the ability of the model to predict variation
in solar production, Figure A.5 shows actual and predicted production per kW of capacity for a
single household in the validation sample over a single week. The household was selected by taking
the median account number within the randomly chosen validation sample. The week was chosen
as the median week for this household. The model does very well at picking uctuations in solar
production across days.
The benet of using high resolution temperature and satellite data can be seen a comparison of
how the model performs relative to engineering estimates based on historic averages. In Figure A.3
I plot the distribution of predictions from the PV Watts Calculator. Average historical observations
explain
70%
of the variation in actual production. For the validation sample, Figure A.6 shows
average hourly predicted versus actual production per kW of capacity for each model by season.
The model does well at predicting the mean of production out of sample.
I use the estimated parameters of the OLS model to generate a prediction of solar production for
the main sample. A histogram of estimated solar production per kW of capacity is shown in panel
(a) of Figure A.7.
48
I then use the interval data to derive an estimate of solar system size. To do so
I take the maximum observed export for each household. I assume a household's maximum export
is approximately
70% of system capacity.49
Using this measure of capacity I then assign households
48 As noted this predicted is censored at zero.
49 The NREL PV Watts calculator's default losses from soiling, shading and other system imperfections is set at
14%.
This does not include the eects of temperature, angle and inverter eciency. The NREL predictions have a maximum
output per kW of 0.89 whilst in the PVOutput.org sample maximum output per kW is 1. This could however be due
to measurement error. Maximum production of observed solar panels is typically
the maximum export to be
70%
80%
of capacity (Jones, 2012). I take
of total capacity to reect the possible dierence between export and consumption.
Conclusions do not dier if I take the maximum export to reect approximately
80%
of capacity. However doing so leads
to a higher frequency of negative estimated consumption. In the solar production data I nd no evidence that output per
unit of capacity and per unit of irradiance is lower for earlier adopters. In fact the correlation between output per unit of
54
50
to one of 9 common system sizes: 1 kW,1.5 kW, and 2kW-8kW in 1 kW increments.
of households in each solar system category is depicted in panel (b) of Figure A.7.
shows consumption and total production (per kW output
×
The number
Figure A.8
system size) by hour once again by
season. Missing data points correspond to hours in seasons where no measures of GHI are available.
Production and consumption follow expected patterns across hours of the day and seasons of the
year. Figure A.8 also plots net imports (imports of electricity minus exports of electricity) used to
construct the measure of consumption (Consumption = Net import + Production).
The conclusion from the test of opportunity cost and the sensitivity of consumption to solar
income do not change when alternative estimates of solar system size or alternative models of
solar production are used. Appendix A.3 discusses how measurement error in solar production and
consumption would enter into the estimation and its implications for the coecients of interest.
Figure A.1: Actual production
PV Output Sample
Histogram of actual hourly solar output per kW for PVOutput.org sites.
capacity per unit of irradiance and installation date is -0.0187. Thus I nd no systematic correlation between eciency
of panels and age of panels.
50 These system sizes were chosen to match system sizes covered on the solar comparison website Solar Choice
(www.solarchoice.net.au).
In reality potential production is a function of total panel capacity and inverter size.
To-
tal panel size is the sum of individual PV modules which may not scale to the increments imposed in the measure of solar
size. Similarly, I can allow solar size to be a continuous function of observed maximum export. This does not change
the estimated results however it restricts my ability to implement specications with system size xed eects.
PVOutput.org data the most common solar system sizes are approximately 1.5, 3 and 5kW.
55
In the
Figure A.2: Predicted and actual production
Ordinary Least Squares
(a) Predicted production
(b) Predicted production
estimation
validation
Figure on left is a histogram of predicted hourly solar output per kW for PVOutput.org sites in the estimation sample
using the OLS model described above.
Figure on right is a histogram of predicted hourly solar output per kW for
PVOutput.org sites from the randomly chosen validation sample. Households in the validation sample were not used to
estimate the parameters of the OLS model.
Figure A.3: Predicted production
NREL
Histogram of predicted hourly solar output per kW using NREL calculator.
56
Figure A.4: Predicted and actual production
Zero-one inated beta
(a) Predicted production
(b) Predicted production
estimation
validation
Figure on left is a histogram of predicted hourly solar output per kW for PVOutput.org sites in the estimation sample
using the zero one inated beta model (ZOIB). Figure on right is a histogram of predicted hourly solar output per kW
for PVOutput.org sites from the randomly chosen validation sample. Households in the validation sample were not used
to estimate the parameters of the ZOIB model.
Figure A.5: Predicted and actual production for a singe household-week
Figure shows one week of production observations and predicted production for a single household from the validation
sample using the OLS model. Households in the validation sample were not used to estimate the parameters of the OLS
model. The household was picked using the median account number and the week was similarly picked using the median
date for this household. Dashed lines represent the 95 percent prediction interval.
57
Figure A.6: Predicted and actual production by season
Validation sample
(a) Summer
(b) Autumn
(c) Winter
(d) Spring
Figures show predicted and actual production per kW by season for the PVOutput.org validation
sample. Households in the validation sample were not used to estimate the parameters of the
OLS model.
Figure A.7: Predicted production and solar size
Main sample
(b) Distribution of predicted solar size
(a) Predicted production per kW
Figures show predicted production per kW and solar capacity (kW) for the main sample of solar
households with electricity meter data (imports and exports of electricity).
58
Figure A.8: Production, consumption and net imports by season
Main sample
(a) Summer
(b) Autumn
(c) Winter
(d) Spring
Figures show predicted consumption and production by season for the main sample of solar households and net imports from electricity meter data. Consumption = Net import + Production
59
A.3 Prediction error
In practice I do not observe electricity consumption, instead I observe net imports of electricity
nihd
(where
nihd < 0 when a household is exporting).
Consumption is net imports plus unobserved
solar production. To estimate my model of household demand I use an estimate of solar production
ŝihd .
Appendix A.2 outlines in detail how the measure of solar production is constructed. For each
hour of the sample an estimate of solar output per kW of capacity is constructed. If
output per kW and
ŝihd
sihd
is actual
is estimated output then:
sihd = ŝihd + τihd
Actual solar production is then given by:
sihd = ci sihd = ci ŝihd + ci τihd
= ŝihd + ξihd
where
ci
51
is solar capacity.
I interpret this measurement error as random dierences between
actual solar output and predicted output for example arising from unobserved shading of solar
panels. These random dierences are orthogonal to predicted production so that
E(ξihd |ŝihd ) = 0.
Actual demand is given by:
qihd = nihd + ŝihd + ξihd
= ηh pihd + γmihd + αg + δh Wihd + ωihd
where
qihd is true (unobserved) consumption and ξihd is measurement error.
consumption
q̂ihd = nihd + ŝihd
and estimated income
Now dening estimated
m̂ = pŝ:
q̂ihd = ηh pihd + γ mˆihd + αg + δh Wihd + ihd
where
51 ξ
ihd
ihd = γpξihd + ωihd − ξihd
= ci τihd
is a combined error term.
implies that measurement error is heteroskedastic. As outlined in Appendix A.2 solar capacity
also an estimate which may also be measured with error. For simplicity here I assume
60
ci
is observed.
ci
is
Then
ηh,1 , ηh,2
and
γ
are estimated from the following equation:
q̂ihd = ηh,1 rih + ηh,2 ∆ocihd + γ m̂ihd + αg + δh Wihd + ihd
Identication relies on interactions between solar production
∆ocihd
and
mihd .
no correlation between
ξihd
and
instruments for
I assume that
ŝihd
ŝihd
ŝihd
(15)
and feed-in tari
is an unbiased estimate of
and importantly no correlation between
validity of solar production as in instrument then hinges on
is shorthand for the remaining explanatory variables in (15).
Fi
sihd
ξihd
being valid
and there is
pihd .
The
where
Xihd
and
E(ωihd |ŝihd , Xihd ) = 0
I control directly for the eect of
weather on consumption and as a robustness exercise I use lags of solar production and irradiance
as alternative instruments.
61
A.4 Supplemental gures
Figure A.9: Mean irradiance by Statistical Area 2
(a) Statewide
(b) Within Melbourne
Figure shows mean irradiance (global horizontal irradiance in Watts/m2 ) within Statistical Area 2 regions across Victoria (panel a) and within
Melbourne panel (b). Colours represent quantiles of mean irradiance.
62
A.5 Supplemental tables
Table A.4: Solar representativeness
Household size
Bedrooms
Separate dwelling
Age
FT employed
Degree
Weekly income
Capital city
Air conditioning
Insulation
Energy saving devices
Households
(1)
(2)
(3)
Solar
Non-solar
Dierence
2.58
2.55
0.03
(1.17)
(1.29)
(0.05)
3.40
3.02
(0.37)
(0.46)
0.94
0.72
(0.24)
(0.45)
57.02
51.28
(13.15)
(14.55)
0.26
0.31
(0.44)
(0.46)
(0.02)
0.30
0.33
-0.03
(0.46)
(0.47)
(0.02)
1357.22
1311.14
46.08
(0.22)
(0.36)
(37.33)
0.48
0.54
(0.50)
(0.50)
0.84
0.71
(0.37)
(0.46)
0.95
0.85
(0.22)
(0.36)
0.43
0.33
(0.50)
(0.47)
2543
759
0.37
∗∗∗
(0.04)
0.23
∗∗∗
(0.02)
5.74
∗∗∗
(0.59)
-0.05
-0.07
∗∗∗
∗∗∗
(0.02)
0.13
∗∗∗
(0.02)
0.10
∗∗∗
(0.01)
0.10
∗∗∗
(0.02)
Means and standard deviations (in brackets) reported in columns (1) and (2). Column (3) reports dierence in means and standard
error of the dierence in brackets. ∗ p < 0.1,∗∗ p < 0.05,∗∗∗ p < 0.01: indicates dierence between solar households and non-solar households
is statistically signicant at the given level. Survey data are from the Australian Energy Regulator (AER, 2015). Household size is number of
residents, FT employed is whether respondent is employed, Degree is whether respondent has a Bachelor's degree. Capital city is resides in a
capital city. Energy saving devices indicates the household has energy saving devices.
Notes:
63
Table A.5: Heterogeneity of income eects
Expected income
Current income
(1)
(2)
(3)
Within zone, hour × FIT
Within hour × household
Import price × hour 0
-0.021∗∗∗
(0.006)
-0.015
(0.010)
-0.021∗
(0.011)
Import price × hour 1
-0.005
(0.006)
-0.021∗∗ (0.010) -0.022∗∗ (0.010)
Import price × hour 2
-0.004
(0.004)
-0.022∗
(0.012)
-0.020∗
(0.011)
Import price × hour 3
-0.002
(0.004)
-0.022∗
(0.013)
-0.019
(0.012)
Import price × hour 4
-0.001
(0.004)
-0.028∗∗ (0.013) -0.026∗∗ (0.012)
Import price × hour 5
-0.004
(0.004)
-0.014
(0.009)
-0.013
(0.009)
Import price × hour 6
-0.007
(0.014)
0.026
(0.020)
0.031
(0.035)
Import price × hour 7
-0.001
(0.005)
0.000
(0.002)
0.005
(0.003)
Import price × hour 8
-0.004
(0.005)
0.002
(0.004)
-0.006∗
(0.003)
Import price × hour 9
-0.015∗
(0.008)
0.001
(0.006)
0.003
(0.006)
Import price × hour 10 -0.043∗∗∗
(0.012)
-0.008
(0.006)
0.016
(0.010)
Import price × hour 11 -0.061∗∗∗
(0.013)
-0.018∗∗∗ (0.005)
0.017∗∗
(0.008)
Import price × hour 12 -0.068∗∗∗
(0.013)
-0.022∗∗∗ (0.006)
0.007
(0.008)
Import price × hour 13 -0.070∗∗∗
(0.013)
-0.023∗∗∗ (0.006)
-0.005
(0.009)
Import price × hour 14 -0.064∗∗∗
(0.012)
-0.025∗∗∗ (0.005) -0.034∗∗∗ (0.008)
Import price × hour 15 -0.042∗∗∗
(0.008)
-0.019∗∗∗ (0.004) -0.051∗∗∗ (0.010)
Import price × hour 16 -0.032∗∗∗
(0.008)
-0.016∗∗∗ (0.004) -0.069∗∗∗ (0.011)
Import price × hour 17 -0.015∗∗∗
(0.005)
-0.009∗∗∗ (0.003) -0.024∗∗∗ (0.009)
Import price × hour 18
-0.003
(0.004)
-0.000
(0.003)
0.005
(0.006)
Import price × hour 19
0.001
(0.005)
0.002
(0.003)
-0.001
(0.004)
Import price × hour 20
0.003
(0.003)
-0.003∗∗ (0.001) -0.004∗∗∗ (0.002)
Import price × hour 21
0.006∗∗
(0.003)
-0.002
(0.001) -0.003∗∗ (0.001)
Import price × hour 22 0.008∗∗∗
(0.003)
-0.002
(0.001) -0.003∗∗ (0.001)
Import price × hour 23 -0.035∗∗∗
(0.008)
-0.014
(0.013)
-0.022∗
(0.013)
∆ oc × hour 6
-0.034
(0.092)
0.042
(0.079)
0.035
(0.061)
∆ oc × hour 7
-0.004
(0.012)
0.006
(0.007)
0.023∗∗
(0.010)
∆ oc × hour 8
-0.008
(0.008)
0.014∗
(0.008)
-0.003
(0.006)
∆ oc × hour 9
-0.022∗
(0.013)
0.006
(0.009)
0.010
(0.011)
∆ oc × hour 10
-0.056∗∗∗
(0.017)
-0.006
(0.008)
0.031∗∗
(0.015)
∆ oc × hour 11
-0.075∗∗∗
(0.017)
-0.021∗∗∗ (0.007)
0.029∗∗
(0.011)
∆ oc × hour 12
-0.086∗∗∗
(0.017)
-0.028∗∗∗ (0.007)
0.014
(0.010)
∆ oc × hour 13
-0.090∗∗∗
(0.017)
-0.029∗∗∗ (0.008)
-0.001
(0.013)
∆ oc × hour 14
-0.082∗∗∗
(0.016)
-0.029∗∗∗ (0.008) -0.045∗∗∗ (0.012)
∆ oc × hour 15
-0.063∗∗∗
(0.013)
-0.023∗∗∗ (0.007) -0.083∗∗∗ (0.016)
∗∗∗
∆ oc × hour 16
-0.059
(0.016)
-0.021∗∗∗ (0.008) -0.122∗∗∗ (0.021)
∆ oc × hour 17
-0.055∗∗∗
(0.016)
-0.020∗∗∗ (0.006) -0.055∗∗∗ (0.021)
∆ oc × hour 18
-0.046
(0.035)
0.004
(0.023)
0.023
(0.023)
∗∗∗
∗∗∗
Income shock
0.015
(0.001)
0.008
(0.001)
Income × hour 0
0.004∗∗∗
(0.002)
-0.003
(0.002)
Income × hour 1
0.004∗∗∗
(0.001)
-0.001
(0.001)
Income × hour 2
0.002∗∗
(0.001)
0.001
(0.001)
Income × hour 3
0.002∗∗
(0.001)
0.001
(0.001)
Income × hour 4
0.002∗∗
(0.001)
0.001
(0.001)
Income × hour 5
0.002∗∗
(0.001)
0.001
(0.001)
Income × hour 6
0.007
(0.006)
-0.003
(0.005)
-0.016
(0.075)
Income × hour 7
0.005∗∗∗
(0.001)
-0.005∗∗∗ (0.001)
-0.010
(0.008)
Income × hour 8
0.009∗∗∗
(0.002)
-0.005∗∗ (0.002) 0.011∗∗∗ (0.003)
Income × hour 9
0.014∗∗∗
(0.002)
-0.002
(0.002)
0.004
(0.004)
Income × hour 10
0.020∗∗∗
(0.003)
0.001
(0.002)
-0.001
(0.003)
Income × hour 11
0.024∗∗∗
(0.002)
0.009∗∗∗ (0.003)
-0.001
(0.002)
Income × hour 12
0.026∗∗∗
(0.002)
0.012∗∗∗ (0.003)
0.001
(0.002)
Income × hour 13
0.027∗∗∗
(0.002)
0.014∗∗∗ (0.003)
0.004∗
(0.002)
Income × hour 14
0.028∗∗∗
(0.002)
0.020∗∗∗ (0.003) 0.012∗∗∗ (0.002)
∗∗∗
Income × hour 15
0.025
(0.002)
0.022∗∗∗ (0.003) 0.024∗∗∗ (0.004)
Income × hour 16
0.022∗∗∗
(0.002)
0.023∗∗∗ (0.003) 0.042∗∗∗ (0.007)
Income × hour 17
0.017∗∗∗
(0.002)
0.014∗∗∗ (0.003) 0.025∗∗∗ (0.009)
Income × hour 18
0.012∗∗∗
(0.002)
0.009∗∗
(0.004)
-0.003
(0.012)
Income × hour 19
0.010∗∗∗
(0.003)
0.001
(0.003)
Income × hour 20
0.002
(0.002)
-0.003
(0.002)
Income × hour 21
0.001
(0.001)
-0.005∗∗∗ (0.002)
Income × hour 22
0.000
(0.001)
-0.004∗∗ (0.002)
Income × hour 23
0.005∗∗
(0.002)
-0.005
(0.003)
Observations
795038
795038
1121548
Notes: Dependent variable is hourly electricity consumption. In columns (1) and (2) Income × hour is Expected income in each hour, in
column (3) Income × hour is Current income in each hour. Current income is current hourly solar income in cents. Expected income is the
average solar income from solar production during daylight hours for the previous 30 days in cents. Income shock is the dierence between
hourly solar income and average solar income for that hour for the previous 30 days in cents. Standard errors clustered at household level in
parentheses. Signicance of coecients: ∗ p < 0.1,∗∗ p < 0.05,∗∗∗ p < 0.01. ∆oc and Current income are instrumented using hourly interactions
between feed-in tari program and solar production. Import price is also instrumented using variation from network taris. All models are
estimated with hour by day-of-week eects and hour by heating and cooling degrees. Column (1) has hour by feed-in tari program and zone
xed eects, columns (2) and (3) have household-by-hour eects. Instrument strength is judged using the F test for weak instruments with
multiple endogenous variables outlined in Angrist and Pischke (2008). All import price and income instruments are strong. Instruments for
∆ocihd are strong from 7am to 5pm. Sample size dierences reect lags used in construction of Expected income.
Table A.6: Robustness to temperature and choice of instruments
Temperature robustness
Lagged solar IV
(1)
(2)
Within zone, hour × FIT
Import price × hour 0
Import price × hour 1
Import price × hour 2
Import price × hour 3
Import price × hour 4
Import price × hour 5
Import price × hour 6
Import price × hour 7
Import price × hour 8
Import price × hour 9
Import price × hour 10
Import price × hour 11
Import price × hour 12
Import price × hour 13
Import price × hour 14
Import price × hour 15
Import price × hour 16
Import price × hour 17
Import price × hour 18
Import price × hour 19
Import price × hour 20
Import price × hour 21
Import price × hour 22
Import price × hour 23
-0.021∗∗∗
-0.005
-0.002
-0.001
0.000
-0.002
0.001
-0.002
-0.007∗∗
-0.015∗∗∗
-0.025∗∗∗
-0.031∗∗∗
-0.033∗∗∗
-0.033∗∗∗
-0.029∗∗∗
-0.020∗∗∗
-0.014∗∗∗
-0.006
0.004
0.002
0.004
0.007∗
0.008∗∗∗
-0.034∗∗∗
(0.006)
(0.006)
(0.004)
(0.004)
(0.004)
(0.004)
(0.008)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.004)
(0.005)
(0.005)
(0.005)
(0.006)
(0.004)
(0.003)
(0.003)
(0.007)
-0.019∗∗∗
-0.004
-0.002
-0.001
0.001
-0.002
0.006
-0.002
-0.010∗∗
-0.030∗∗∗
-0.069∗∗∗
-0.098∗∗∗
-0.106∗∗∗
-0.102∗∗∗
-0.082∗∗∗
-0.046∗∗∗
-0.027∗∗∗
-0.008
0.002
-0.004
0.003
0.005∗
0.007∗∗
-0.030∗∗∗
(0.006)
(0.006)
(0.004)
(0.004)
(0.004)
(0.004)
(0.012)
(0.005)
(0.004)
(0.008)
(0.013)
(0.017)
(0.017)
(0.017)
(0.013)
(0.008)
(0.009)
(0.008)
(0.006)
(0.005)
(0.003)
(0.003)
(0.003)
(0.006)
oc × hour 6
oc × hour 7
oc × hour 8
oc × hour 9
oc × hour 10
oc × hour 11
oc × hour 12
oc × hour 13
oc × hour 14
oc × hour 15
oc × hour 16
oc × hour 17
oc × hour 18
0.020
-0.009
-0.015∗∗∗
-0.022∗∗∗
-0.029∗∗∗
-0.035∗∗∗
-0.039∗∗∗
-0.039∗∗∗
-0.038∗∗∗
-0.033∗∗∗
-0.030∗∗∗
-0.032∗∗∗
-0.024
(0.032)
(0.007)
(0.004)
(0.005)
(0.005)
(0.005)
(0.005)
(0.005)
(0.005)
(0.005)
(0.006)
(0.008)
(0.024)
0.044
-0.000
-0.019∗∗∗
-0.049∗∗∗
-0.097∗∗∗
-0.127∗∗∗
-0.138∗∗∗
-0.135∗∗∗
-0.112∗∗∗
-0.076∗∗∗
-0.049∗∗
-0.014
0.060
(0.055)
(0.016)
(0.006)
(0.013)
(0.018)
(0.022)
(0.022)
(0.021)
(0.018)
(0.013)
(0.020)
(0.031)
(0.058)
Current income
0.015∗∗∗
(0.001)
0.021∗∗∗
(0.001)
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
Observations
1121548
1045568
Dependent variable is hourly electricity consumption. Standard errors clustered at household level in parentheses. Signicance of coecients: ∗ p <
0.1,∗∗ p < 0.05,∗∗∗ p < 0.01. All models are estimated with hour by day-of-week eects, hour by heating and cooling degrees, zone xed eects and hour by feed-in
tari program eects. In column (1) instruments for ∆oc and Current income are interactions between feed-in tari program and current solar production. In
column (2) instruments for ∆oc and Current income × hour are 48 hour lagged interactions between feed-in tari program and solar production. Instrument
strength is judged using the F test for weak instruments with multiple endogenous variables outlined in Angrist and Pischke (2008). Instruments for ∆ocihd are
strong from 7am to 5pm. Instruments for import price and income are all strong. Sample size dierences reect use of lagged solar production as an instrument.
Notes: