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, accommo-

dation 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 e�ect dominates the substitution e�ect. 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 accessingdata from PVOutput.org. I also thank my advisers: David Byrne, Leslie Martin and Claudio Mezzetti. I have receivedhelpful 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 partici-pants at UC Berkeley, Lawrence Berkeley National Lab, Melbourne University and audience members at the AustralianConference 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

inconsistent with the fungibility of money.1 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 mag-

nitude and predictability of solar income mean that �uctuations in the �ow of earnings should

have little e�ect on consumption of any goods. In particular, estimates of income elasticities sug-

gest that �uctuations in solar income at the hourly, daily or even monthly level should not have

a detectable e�ect on electricity consumption. In contrast to the life-cycle income hypothesis, a

1Mental 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.

2There 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 di�ers 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 di�erences 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 speci�cation I then isolate the e�ect of solar income

using di�erences in the gradient of consumption across households as solar production, and hence

solar income, rises.

My identi�cation 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

di�erences in solar production within feed-in tari� group. The second identi�cation 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 a�ects when a household

installs solar panels because payback periods are more attractive, but it is not correlated with other

household characteristics that a�ect 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) di�erence 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 e�ects 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

form of solar income increases their electricity consumption by 35%.3 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 prefer-

ences for consuming solar vs grid-based power or di�erential 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 num-

ber 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 e�ect (they are attentive to opportunity cost) but they consume

more because of the income e�ect (they violate fungibility). I demonstrate that as solar production

rises, the income e�ect can dominate the substitution e�ect. Thus as feed-in tari�s rise, consump-

tion 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 e�ect 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 e�cient 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

3A 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 iden-

tify 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 di�erences 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

tari�s 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. Res-

idential 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.

4Baker et al. (2013) provide an overview of the economics of solar PV whilst Borenstein (2008) and Borenstein (2015)model the costs and bene�ts 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 di�erent

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 a�ect irradiation and

temperature. So, for example, panels are less e�cient 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 tari�s 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 tari�s. 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 tari�s were equal to or above the cost of buying electricity. More recent

feed-in tari�s are well below the cost of buying electricity. Because net feed-in tari�s only pay

for electricity that is not consumed within the house at exactly the same time (i.e. balancing is

instantaneous), households enrolled in di�erent 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.

5As of 2014 one in �ve Australian households were generating some form of solar electricity, the vast majority fromphotovoltaic (PV) panels (ABS, 2014). There are a number of reasons for the high level of uptake. First, Australiahas vast solar resources. As a continent Australia has the highest solar irradiance per metre in the world (GeoscienceAustralia, 2010). Second, over the period 2010 to 2015 the cost of solar PV more than halved. In 2010 the cost of akilo-Watt (kW) was close to $AUD6000. By 2015 it was less than $AUD2500 (APVI, 2015). Third, households received arange of overlapping state and federal government subsidies. Finally, solar PV has become more attractive as the cost ofelectricity to the end-user has increased. For a Victorian household the cost of using electricity increased by more than 50percent from 2009 to 2014 (ESC, 2015). These price increases are largely attributed to the cost of network managementand augmentation by regulated network monopolies. The combination of these factors has meant that there is now anon-trivial number of Australian households producing and consuming electricity from rooftop solar.

6In 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 tari�s 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) (1)

where q is electricity consumption in the hour and a is the numeraire. Households have non-solar

income y0 and an endowment of solar production in that hour of s. If they consume less electricity

than they produce at the same time (q < s) then they earn revenue from selling the excess electricity

to the grid equal to f [s− q], where f 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 > s) and

they pay for electricity that they buy equal to r[q − s], where r 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 satis�ed:

a = y0 + 1(s > q)× f [s− q]− 1(q > s)× r[q − s] (2)

where 1() is the indicator function. Substituting in to the utility function:

U = ν(q) + g(y0 + 1(s > q)× f [s− q]− 1(q > s)× r[q − s]

)(3)

Then the consumer's demand function in that hour must satisfy7 :

q(p,m) :

ν ′(q)− fg′(y0 + f [s− q]) = 0 if s > qν ′(q)− rg′(y0 − r[q − s]) = 0 if q > s (4)More generally the consumer's demand function in the hour satis�es:

q(p,m) : ν ′(q)− pg′(y0 − pq + ps) = 0 for p =

f if s > qr if q > s (5)According to this model the consumer responds to price p = f when s > q and they are selling

electricity in the same way they respond to the price p = r when q > s and they are buying

electricity. Solar income m = ps accounts for the fact that the household has an endowment of

electricity s that is valued at current price p.8 Note also that this household treats income as

7These expressions are known as conditional demand functions because they are conditional on consuming at alevel above or below s. The consumer's unconditional demand function speci�es the unconditional choice over whetherto consume above or below s as well as how much to consume given the implied price. For households with f < rthe unconditional demand function also includes the possibility that the household consumes at the point q = s. Forhouseholds with f > r it is never optimal to consume at q = s. To illustrate how net feed-in tari�s a�ect marginal priceand income I focus on the conditional demand functions.

8This income is similar to what has been called virtual income, di�erence or a rate structure discount in the literatureon 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 e�ect 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� f less than the cost of

buying power (f < r). Panel (b) depicts the budget set of a household who faces a feed-in tari� f

that is greater than the cost of buying power (f > r). If solar production is zero then the household

can buy up to y0 units of the numeraire or if they spend all their income on electricity they can

buy y0/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 +fs

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 f units. Hence the slope of the budget set for

q < s is −f . If on the other hand the household consumes all their solar power and spends theirentire budget on electricity they can consume (y0/r) + s. Across households both the slope and

intercept of the budget set when households are selling (q < s) are very di�erent while the slope

and intercept of the budget set when households are buying (q > 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 re�ects the exaggerated e�ect

of solar income relative to the true magnitude of non-solar income y0. In practice, across hours

household consumption should re�ect 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 di�erences in solar production and the value of that production at the hourly and monthly

level to identify the e�ect 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.

Mo�tt, 1990; Reiss and White, 2005).

8

3 Data and descriptive evidence

3.1 Data

This paper combines data from a number of di�erent 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) identi�er (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

9Retailing services include metering and billing end-use consumers. Distribution and transmission (networks of polesand wires) are upstream privately owned regulated natural monopolies.

10The ESC maintains quality oversight and licenses electricity retailers.

9

used to predict solar production and hence impute consumption.11 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

Standard FIT (1:1 FIT = import price) are the earliest adopters.12 Households receiving the

Provisional FIT (60 FIT =60c/kWh) installed solar before the end of 2011.13 Households installing

before 2012 were eligible for the Transitional FIT (25 FIT = 25c/kWh). The Minimum FIT (8

FIT =8c/kWh in the sample period) is open to any household installing solar from January 2013.14

Thus in general households who installed earlier receive higher feed-in tari�s.

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 di�er on observable characteristics by feed-in tari� group I use

the SA1 identi�er to match households to demographic information from the 2011 Australian Cen-

sus 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 di�erent feed-in tari� programs do not appear to live in neighbourhoods that di�er

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 di�erent 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

di�er to non-solar households. For example, barriers to installation on rental properties may mean

11I permanently drop 20 households with Two Rate network tari� assignment, 54 households who are estimated toconsume more than 75kWh in a single day and 2 households who record exporting overnight. I drop any householdfor whom I do not observe a postcode and I drop any observation between 9am and 5pm for which satellite irradiancemeasures are not available. I also drop any date for which total estimated consumption is less than 2kWh and any hourthat estimated consumption is negative or zero.

12Households 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 averageSFIT customers were earlier installers

13All �gures in the paper are in Australian dollars (AUD). Over the last 4 years the exchange rate between the USdollar (USD) and AUD has been close to 1. As of October 2015, the exchange rate is 1 AUD = 0.73 USD

14The obligation to fund feed-in tari�s also di�ers 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-intari� 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 elec-

tricity) 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 re�ects 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 dis-

continuity 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 di�erences 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

15For some in this group there is no di�erence between the opportunity cost and the import price (1:1 FIT), for othersthis di�erence is very small (25 FIT)

16Consumption of 60 FIT households is also lower than 25 & 1:1 FIT households however 25 FIT households consumemore than 8 FIT households; there also appear to be level di�erences between 25 & 1:1 FIT households when householdsare 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 di�erences in the gradient of solar income as exports

increase. The pattern of gradients in consumption (Figure 3b) closely resembles these di�erences.

Hence changes in solar income for these two groups appear to be highly correlated with changes in

consumption. As further evidence for the income e�ect note that the opportunity cost of consump-

tion 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 op-

portunity 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 re�ect a non-standard income e�ect. 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

di�erences in electricity consumption. A �nal explanation is that household consumption di�ers

across these days because of unobserved di�erences 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 re�ect 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 identi�cation strategy.

4 Estimation strategy

I model demand as a linear function of current price and income.17 At hour h of day d I assume

that household i consumes:

qihd = ηhpihd + γYihd + αg + τhd + δhWihd + �ihd (6)

The parameter ηh governs the price-sensitivity of electricity demand and is allowed to vary by

hour of day h. The parameter γ captures the e�ect 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 αg. Di�erences in use across hours and days of the week are captured in

τhd. Consumption of electricity also varies with characteristics such as weather which are captured

in the matrixWihd. The e�ect of weather (δh) is assumed to depend on hour-of-day h but for now is

17In my base speci�cation I treat electricity demand as static. Households may substitute electricity across days orhours in response to prices that �uctuate. Because much of the variation within an hour-of-day is cross-sectional I abstractaway from this more complicated speci�cation of the demand function. I ensure the results are robust to allowing forcross-price e�ects.

12

assumed to be the same across households.18 Demand for electricity is also subject to idiosyncratic

consumption shocks �ihd.

4.1 Opportunity cost

To explore whether households respond to the opportunity cost of their consumption let ∆ocihd be

the di�erence between the household's import rate rih (the cost of buying power) and their feed-in

tari� (the price for selling power) such that: fi = rih + ∆ocihd. Then ∆ocihd captures the relative

di�erence 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 + δhWihd + �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 e�ects

In this model I capture di�erences in time-invariant non-solar income at the distribution zone level

in the �xed e�ect αg.

To test whether households are responsive to opportunity cost I allow parameter ηh to vary:

qihd = ηh,1rih + ηh,2∆ocihd + γmihd + αg + τhd + δhWihd + �ihd (7)

The neo-classical consumer responds to the implicit price of foregone revenue fi = rih + ∆ocihd in

the same way they respond to a change in the explicit price of buying electricity rih. Therefore

ηh,1 = ηh,2 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 identi�cation of the demand parameters.

Before doing so I brie�y outline how I explore household responses to solar income.

18I estimate the model using hour-of-day by heating and cooling degrees. A heating degree is a proxy for the electricityrequired to heat a home. It is the positive di�erence between 18C and ambient temperature. A cooling degree is a proxyfor the amount of electricity required to cool a home. It is the positive di�erence between ambient temperature and 24C.

13

4.2 Solar income

In (7) γ captures the e�ect of current income on household consumption. To further explore how

households respond to solar income I allow consumption to be a�ected by two di�erent measures of

income: meihd and muihd. The �rst measure m

eihd accounts for the household's average hourly solar

income for the previous 30 days generated during daylight hours, hence:

meihd =1

30

30∑l=1

1

13

18∑t=6

mit,d−l

This speci�cation 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 di�erences in meihd identify the e�ect of

average di�erences in solar income across households. In the model with household-hour e�ects

di�erences in meihd 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 e�ect on consumption within the household. Despite this, many studies �nd that anticipated

income changes do a�ect 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 muihd. I construct this measure by

taking the di�erence between solar income in hour h of day d and the average solar income in that

hour for the previous 30 days, hence:

muihd = mihd −1

30

30∑l=1

mih,d−l

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 yi

at the census SA1 level. This measure is assumed to capture di�erences in permanent income

across households. If household behaviour accords with the permanent income hypothesis then

the response to expected income meihd (identi�ed 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 γmax. I then test the

following null hypothesis:

H0 : γ > γmax

(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 Identi�cation

To identify the parameters of the demand function I must overcome three possible identi�cation

problems. First, that price and income are determined simultaneously with consumption. Second,

that households choose retail price plans and third that feed-in tari�s 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. This

household's current price is the import rate and ∆ocihd = 0. An increase in solar production to

s′ihd such that qihd < s′ihd decreases the cost of their consumption because their implicit price is the

feed-in tari�, hence ∆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 di�erential e�ect 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

19Thus the household e�ectively faces a non-linear or block price schedule where the level of solar production sihddetermines the length of the block. In practice there is a di�erent price schedule for every instant of the day rather thanevery hour as assumed here. Smart meters separately record the �ow of electricity from and to the residence and reportthe cumulative �ows in half hourly intervals. Thus it is possible to observe both exports and imports for the same 30minute interval. I aggregate 30 minute meter readings to the hourly level and determine price pihd based on a comparisonof total exports and imports within that hour. If imports exceed exports I assign the household the import price rih. Ifexports exceed imports I assign the household the feed-in tari� rate fi.

15

a household is importing or exporting.20 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 coe�cient ηh,2 (Fih × sihd)) for 14 endogenous variables.21

As intuition for separate identi�cation of price and income e�ects recall that attention to op-

portunity cost is consistent with level di�erences in consumption in the neighbourhood of the price

discontinuity (i.e. at the point of export). Sensitivity to current income is consistent with di�erences

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) δh captures the non-linear

e�ect of temperature on electricity consumption.23 As a robustness exercise I use lags of solar

production sih,d−j (i.e. solar production at hour h of date d − j) as alternative instruments. Theregular pattern of irradiance throughout the day means that lagged production sih,d−j and contem-

poraneous production sih,d 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.

20In speci�cations with current income shock (muihd) this is also endogenous.21I 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 withinhour-of-day. In this speci�cation the model has a lot more instruments than endogenous variables and although I reachthe same conclusions the instruments are not as strong. This is not unexpected in such an over-identi�ed model.

22Ameliorating this e�ect somewhat is the fact that higher temperatures reduce solar panel performance23The e�ects of temperature can easily be identi�ed separately because of variation in ∆ocihd 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 di�er in terms of payment

facilities and billing frequency and are associated with discounts o� the underlying standard rate.24

Import prices therefore di�er 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 a�ecting 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 coe�cients 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 coe�cient 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

o�ers a discount given the customer's plan choice. Network tari�s are regulated distribution and

transmission charges and vary across distribution zones due to di�erences 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 e�ect. As a robustness check I

then restrict the same to households living within the capital city of Melbourne.

Network tari�s also di�er 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 tari�s 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 di�erent meters

and this historical characteristic a�ected consumption today. This is unlikely as these households

were generally placed on Two Rate tari�s 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 tari�s. As feed-in tari�s decline households

who consume more electricity during the day are more likely to bene�t from installing solar panels.

Thus underlying patterns in electricity consumption could be correlated with feed-in tari�. I

therefore allow for di�erences in the hourly consumption of households on di�erent feed-in tari�s.

24Appendix A.1 discusses the application of discounts in more detail.

17

I also implement a model with household-by-hour e�ects. Even with feed-in tari� program by hour

�xed e�ects, 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 Du�o 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�. Speci�cally, it plots feed-in tari� partialling out the e�ect of living in

Melbourne.25 The mechanism for this instrument is as follows: feed-in tari�s have fallen over time

thus early adopters have higher feed-in tari�s. 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 F̂ih × sihd and ŝihd whichare used in the second stage to predict changes in opportunity cost ∆ocihd and income mihd.

Finally ∆ôcihd and m̂ihd 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 = β1GHIi + β2hGHIihd + β3Melbi + Π1Xihd + κ1,ihd

Zihd = {Fih × sihd, sihd}

Step 2

Yihd = β4 ̂Fih × sihd + β5ŝihd + Π2Xihd + κ2,ihd

Yihd = {Hh ×∆ocihd,mihd}

Step 3

qihd = ηh,1rih + ηh,2∆̂ocihd + γm̂ihd + δhWihd + �ihd

25The slope of the line thus represents the correlation between irradiance and feed-in tari� within location wherelocation is either �Melbourne� or �Rest of state�. This accounts for the fact that the cross-state variation in irradiancedwarfs the within Melbourne variation in irradiance where most of the sample is located. An alternative would beto restrict the same to Melbourne or to allow the e�ect of irradiance to di�er within Melbourne. Neither alternativequalitatively changes the results.

26Melbourne is a sprawling coastal city. The eastern most boundary of the city is 75km from the central businessdistrict whilst the western boundary is over 60km from the central business district. At the outer eastern edge elevationrises as the city hits the Yarra Ranges.

18

where GHIi is the average solar irradiance for household i derived from satellite data. Similarly,

GHIihd is solar irradiance for i at hour h of day d and is allowed to a�ect Zihd separately by

hour-of-day, Melb is an indicator for Melbourne, Xihd are the remaining exogenous covariates from

equation 7 and Hh is an indicator for hour h. Note in this speci�cation I drop zone and hour by

feed-in tari� group �xed e�ects and rely on my instruments for identi�cation. I implement this

strategy with and without an additional set of instruments for import price rih as outlined above.

5 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

depend on average income over the previous 30 days (Expected income) and the di�erence between

current income and average income in that hour over 30 days (Income shock). In all models ηh,1 and

ηh,2 are estimated separately. The main di�erence between the Tables is the treatment of income

e�ects and the drop in sample size re�ecting 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 e�ects; column (2) adds hour-of-day by feed-in tari� program e�ects; 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� e�ects). 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 speci�cations column (1) reports results with zone and hour-of-day by

feed-in tari� �xed e�ects. Column (2) adds in a measure of long run income and removes zone

�xed e�ects; 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 e�ects. All standard errors

are clustered at the household level.27 Instruments for ∆ocihd are strong for all hours from 7am.

Instruments for import price and the two income variables are also strong across models.28

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

then these responses should be equal. I plot coe�cients estimated for hours 7am-5pm.29

Figure 6 plots the results presented in columns (1) and (2) of Table 3. Within each panel the top

27Standard errors presented do not re�ect 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 thedemand function. For column 4 standard errors are cluster bootstrapped in the three step IV strategy.

28The strength of instruments is judged by calculating the F statistic outlined in Angrist and Pischke (2008) formultiple endogenous variables and applying the Staiger and Stock (1997) rule of thumb. For the model instrumentingfor feed-in tari� the F test is undertaken independently of the cluster bootstrap process. In this instance I assess thestrength of instruments for each of the stages.

29All models and tests were speci�ed with ηh,2 coe�cients for hours 6am - 6pm however wide con�dence intervals forthese hours make plotting impractical.

19

�gure plots con�dence intervals for the coe�cients. 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% con�dence interval for the di�erence η̂1,h − η̂2,h.30 Underthe null hypothesis that households are attentive to opportunity cost this di�erence is zero. The

p-value for the joint signi�cance test that the di�erence is zero in all hours is also reported.

The top of Panel 6a plots the estimates of η1,h and η2,h coe�cients where group e�ects αg are at

the zone level. The coe�cients are estimated using within and across household variation in import

and export prices. Estimated coe�cients are negative, signi�cant, and con�dence intervals overlap

across all hours of the day. The bottom of Panel 6a plots the con�dence interval for the di�erence

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

signi�cance 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 di�erences in consumption at each hour of the day

for households within each feed-in tari� program. Once again estimated coe�cients are negative,

signi�cant and not statistically di�erent. I cannot reject that households are equally attentive to

implicit and explicit prices and therefore that they are attentive to opportunity cost. The e�ect

of adding controls for hourly consumption by feed-in tari� group can be seen in the change in the

magnitude of the coe�cients. Controlling for underlying di�erences 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 di�erences across feed-in tari� groups

in their hourly consumption pro�les.

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 di�erence between the estimated coe�cients. 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 coe�cients in Figure 7 and 6b di�er very little in magnitude

suggesting that the selection of plan discounts does not cause a strong endogeneity problem.

The �nal identi�cation problem arises because of selection into feed-in tari� program. As out-

lined 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 adop-

tion 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 tari�s

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 di�erences in solar system size. The conclusions from

3090% con�dence intervals are chosen in order to be conservative in failing to reject the null hypothesis that householdsare attentive.

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this speci�cation 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 coe�cients have reduced compared to Figure 7 but are still of larger order than those in

Figure 6a. These di�erences re�ect both the absence of hour-by-feed-in tari� e�ects 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

variation in income (Current income): income generated within the same hour. The estimated

e�ect of Current income is stable across models that account for di�erences in consumption at

each hour of the day across feed-in tari� programs and that instrument for import price and for

feed-in tari� program. Interpreting the coe�cient 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 di�erently 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 e�ects are relatively stable across models. The variable Expected

income measures average hourly solar income (measured in cents) for the previous 30 days from

9am-5pm. In this speci�cation I capture the average e�ect of recent income on consumption at all

hours of the day. The variable Income shock measures the di�erence between current hourly income

and average income for that hour for the previous 30 days.33 This income e�ect 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 e�ect of an unexpected

increase in solar income averaged over all solar-producing hours.

The magnitudes of the estimated income e�ects are once again extreme. As for Current income

the coe�cient on Expected 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)

income measured at the census SA1 level.35 Average hourly consumption across all hours is approx-

imately 0.7kWh so the implied elasticity with respect to total income is extreme. The coe�cient

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

31Average hourly consumption during solar producing hours is approximately 1kWh (for the full sample approximately0.7kWh) and average solar income for the same is approximately 30c.

32http://tools.switchon.vic.gov.au/appliance-calculator/tools-appliance-calculator33For hours outside of daylight Income shock is always zero.34Estimates of ηh,1 − ηh,2 are qualitatively unchanged using alternative speci�cations of income including aggregating

Expected income with SA1 census level median weekly income (though this aggregated income variable is insigni�cant).35Average 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 Expected incomeis 25*8*7 = 1400 or $14.

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on average when their expected income is higher, but also to consume more in speci�c 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. Cross sectional measures of income can be taken

to re�ect long run di�erences in income. Expected income is also identi�ed o� of cross sectional

variation and, if households are forward looking, can be interpreted as a long run income e�ect.

In Table 3 and column (1) of Table 4, zone �xed e�ects are assumed to capture time invariant

di�erences in income. In columns (2) and (3) of Table 4 I include a measure of cross sectional

di�erences in weekly income (in AUD '000) at the census SA1 level and drop zone �xed e�ects.

In column (2) I control for expected and unexpected income. In column (3) I control for current

instead of expected and unexpected income. In both columns the point estimate on Non-solar

income is positive and signi�cant however the magnitudes of the implied income e�ects are tiny

relative to the e�ect 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 coe�cient on Non

solar income in column (2): a $1000 increase in weekly income leads to a 0.07kWh increase in

consumption. The elasticity implied by the income coe�cient in column (2) is approximately 0.1

which is at the lower end of analyses of the long run e�ect 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

γmax = 0.0002. I emphatically fail to reject the null hypothesis that the e�ect of average solar

income on consumption is higher than γmax (p value > 0.9) regardless of which estimate I choose

for γ̂.

I next isolate variation in expected and unexpected solar income within a household-hour-of-

day.36 This reduces the magnitude of the estimated income e�ects but nonetheless the e�ects of

anticipated and unanticipated changes in solar income are large and signi�cant. The e�ect of a 25c

increase in expected solar income leads to an increase of 0.1kWh whilst a 25c income shock leads

36Within 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 andSaturdays and Sundays. I observe some price variation from changes in the retailer's tari�s over the course of the sampleperiod. These sources of variation allow me to specify models with household-hour �xed e�ects (αih). I control forhour-by-weekend/weekday e�ects to ensure that my results do not con�ate underlying di�erences in weekday/weekenddemand. The parameters are therefore identi�ed from variation in the di�erence between peak and o� peak rates acrosshouseholds.

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 γmax (p value > 0.9).

The results presented in Tables 3 and 4 constrain the e�ect of solar income to be the same across

hours of the day. Households may however respond very di�erently to income at di�erent 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 a�ect consumption di�erently in each

hour of the day. In column (1) I specify zone and hour by feed-in tari� program e�ects. In columns

(2) and (3) I specify household by hour e�ects. In columns (1) and (2) I �nd that higher Expected

income 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

e�ects 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

price responsiveness which tends to peak towards the middle of the day.37 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 brie�y

consider and rule out three other explanations for the estimated e�ects. 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 su�ciently attractive as to merit installation on purely

�nancial grounds (though this is rapidly changing, Grattan (2015)). Consumption of electricity

post-adoption may therefore be a�ected 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

37I �nd weak evidence that income earned during the day a�ects consumption that evening and �nd no e�ect onconsumption overnight. I also �nd no evidence of cross price e�ects on consumption overnight: households who face ahigh 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 oth-

ers. 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 e�ect of solar

income separately to the e�ect of solar production within feed-in tari� group. Instead I implement

three strategies to address the concer