Making the case for supporting broad energy efficiency programmes: impacts on household incomes and other economic benefits

: In recent years, an overly narrow focus on rebound effects has limited the extent of researcher and policy attention afforded to the wider multiple benefits of increased energy efficiency. The objective of this paper is to focus policy attention on the sustained added value to the economy that is created as result of improving energy efficiency in the residential sector. Governments around the world are committed to increasing energy efficiency more generally, but often focus public support in low income households where energy poverty is a particular concern. However, governments operate in a context of multiple objectives where energy efficiency is expected to deliver significant reductions in carbon emissions alongside sustainable economic development. We use a UK CGE model to consider the general effects of supporting increases in energy efficiency in residential energy use. Our results demonstrate that the increase in GDP, and economic activity more generally, triggered by increased energy efficiency delivers more in terms of increased household incomes than the efficiency improvement itself. We find that the more wide ranging the boost to energy efficiency, the greater the economic expansion and associated returns are likely to be, and the less the means of financing through public budgets will erode the benefits over time. efficiency programmes should be carefully considered and examined. Our results imply that a reallocation of government spending will be less distortive than requiring the household sector to pay indirectly (according to ability to pay) via income tax. However, we reserve fuller consideration of specific funding mechanisms for future research, ideally in consultation with policy decision makers the UK.


Introduction
In recent years the literature on the wider economic impacts of energy efficiency improvements has tended to focus on the issue of rebound effects. In particular, rebound studies have mainly focussed on measuring direct and indirect ( -) rebound effects using microeconomic or limited input-output economy-wide models (see for example Chitnis and Sorrell, 2015;Druckman, et al. 2011;Freire-Gonzáles, 2011). Where different household income groups are identified, emphasis has tended to be placed on how rebound effects that are driven by changes in real income following an energy efficiency improvement will be bigger the larger the share of total income that is spent on energy consumption (Chitnis et al., 2014;Murray 2013;Thomas and Azevedo, 2013).
However, certainly in colder climates like that of the UK, where lower income households tend to spend a larger share of their income on energy (Office for National Statistics, 2011Statistics, , 2012Statistics, , 2013, there are concerns over energy or fuel poverty (UK DECC, 2015). 1 This both raises a challenge for the rebound-focussed literature, in that direct rebound effects triggered by lower energy costs may in fact be a true representation of required demand (to adequately heat properties), and focuses attention on the nature of socio-economic returns from increased energy efficiency.
The latter point reflects the proposed by the International Energy Agency (IEA, 2014). In particular the current paper focuses attention on the sustained added value to the economy that is created as result of investing in increased energy efficiency. We consider this in the context of a general equilibrium argument. That is, we propose that the increase in GDP and economic activity more generally that is triggered by increased energy efficiency (here in the household sector) delivers more in terms of energy poverty reduction than the efficiency improvement itself. 2 This is through the additional return to household incomes as the economy expands. The larger and more wide-ranging the boost to household energy efficiency, the greater the economic expansion and associated returns are likely to be.
We also consider a government funding argument, that public support should be directed at helping those less able to pay for energy efficiency improvements themselves. Specifically, we consider whether economic expansion triggered by more wide ranging support of energy efficiency programmes is likely to provide sufficient payback to justify greater levels of public support. This may also provide the basis for setting energy efficiency programmes in the context of a national infrastructure argument linked to improving the quality of a c .
The remainder of the paper is structured as follows. Section 2 reviews the recent indirect and economy-wide rebound literature that has been the recent setting for considering the impacts of increased efficiency in household energy use. We focus on the extent to which wider economic expansionary and socio-economic arguments have been made. Section 3 then focuses attention on the policy context for identifying the issues outlined above, expanding on the multiple benefits, general equilibrium and public funding/national infrastructure arguments. Section 4 describes the UK CGE model that we use to consider the general effects that may be anticipated if energy efficiency increases in one or more household income groups in an economy. Section 5 details the simulation scenarios that are then implemented in Section 6, where we discuss our results. Finally, Section 7 draws conclusions and considers policy implications.

Existing literature on the wider impacts of energy efficiency
In recent years a number of studies have analysed the impact of improved household energy efficiency using microeconomic demand systems, and input-output (IO) techniques. Their main focus has been the estimation of direct and indirect rebound effects (see for example Brännlund, et al. 2007;Chitnis and Sorrell, 2015;Druckman et al., 2011;Freire-Gonzáles, 2011;Lenzen and Dey, 2002;Mizobuchi, 2008).
More broadly, the main objective of this literature is to assess the effectiveness of energy efficiency, specifically in reducing energy use and CO2 emissions throughout the economy triggered by a reduction in final energy demand. For this reason, they estimate the rebound effect as a measure of the extent to which technically possible energy savings are eroded by economic responses.
Some of these studies have estimated energy rebound effects by considering the impacts of energy efficiency and energy saving behavioural changes across different household income groups (Chitnis et al., 2014;Murray, 2013;Thomas and Azevedo, 2013). In this context, a common finding is that the lowest income groups tend to be associated with higher rebound effects. This is for two reasons. First, lower income groups tend to spend a larger share of their income on energy. Second, the price elasticity of demand for energy goods is generally higher when income is lower, indicating that lower income households are more responsive to changes in energy price (Chitnis et al., 2014). When the price of energy in efficiency units decreases, price elastic groups respond by consuming more energy.
However, a key limitation of the approaches adopted in the aforementioned studies is to rely on models that implicitly or explicitly adopt the assumption of fixed market prices and nominal incomes. Such models are not able to capture the full set of economic responses triggered by an energy efficiency improvement that will occur as the economy adjusts to a new steady state with different spending and production decisions. Thus, they are limited in their capability to identify other potential benefits of energy efficiency (Brännlund et al., 2007;Chitnis and Sorrell, 2015;Lecca et al., 2014). Duarte et al. (2015), and Lecca et al. (2014) have estimated the impact of improving energy efficiency in household energy use using more flexible computable general equilibrium (CGE) models that incorporate IO data but permit the relaxation of the assumptions inherent in partial equilibrium and IO studies. Specifically, Lecca et al. (2014) takes the case of the UK and explores the value added of moving from a partial to a general equilibrium modelling framework (via an intermediate stage involving IO analysis) in the analysis of energy efficiency improvement. This is done by considering the impact of a 5% increase in household energy efficiency using models with different degrees of complexity calibrated on a common database. Lecca et al. (2014) initially estimate the direct rebound effect by estimating the elasticity of demand for energy goods and then derive the indirect (re-spending) rebound effects using IO techniques. They find that the indirect component of rebound is typically negative when the direct rebound is less than 100% and the economy is characterised by energy sectors that are relatively energy intensive. In their UK case study, households decrease their demand for energy and reallocate spending towards less energy intensive non-energy goods, thereby reducing both direct energy use and energy embodied in supply chains supporting consumption demand. These net negative indirect effects persist when Lecca et al. (2014) derive the full economy-wide rebound using a CGE model.
However, here the fuller economy-wide responses to the energy efficiency improvement are influenced by endogenous market price determination, nominal income and supply responses. This implies, for example, that the initial drop in demand for energy decreases the market price of energy in the short-run, exacerbating the rebound effect by amplifying the decrease in the price of energy services (for any given market price), which may be considered as the effective price of energy. However, it also negatively influences the revenue and capacity decisions of energy producing firms and, over time, their output prices (i.e. countering decreases in both the effective and market price of energy). Moreover, the increase in demand for non-energy goods puts upward pressure on domestic consumption prices, negatively influencing competitiveness of UK industries. Nonetheless, overall the Lecca et al. (2014) results show a net expansion in the UK economy, with an increase in investment, employment and household spending. However, with a fixed national labour supply, depending on how households respond to the change in cost of living given by increased energy efficiency, a sustained increase in wages may give rise to a higher price level and reduced export demand.
The Lecca et al. (2014) contribution helps to clarify the importance of analysing the full general equilibrium impacts of increased household energy efficiency. However, it is limited in only considering one single representative household, thereby not permitting any differentiation among household income groups. However, differences in the composition of both incomes and expenditures are likely to be crucial in influencing the distribution of the effects of economic adjustment across household income groups. Here, heterogeneity of households proves to be very important from a policy perspective. Duarte et al. (2015) also use a CGE model, this time for Spain to assess a range of energy-saving policies including increasing energy efficiency, but identifying four household income groups. They actually find that lower income household are less responsive to an energy efficiency improvement, and indeed are associated with lower rebound effects. 3 However, the main point is that, although the focus of the work is on potential reduction of CO2 emissions, D results also show that an energy efficiency improvement delivers an economic stimulus with a broader set of outcomes than reducing energy use.
In general, though, much of the rebound literature neglects the wider range of potential economic benefits associated with increased energy efficiency that have been the focus of policy community contributions such as the IAE (2014) report. In response, this paper aims to add to the energy efficiency and CGE literature in filling this gap by exploring the wider impacts of household energy efficiency improvements in more detail, and to do so with specific focus on identifying different impacts among household income groups. In particular we focus on how support of energy efficiency programmes in the household sector may be justifi macroeconomic expansion.

Broadening focus for a policy context
If we broaden focus from estimating rebound effects of increased energy efficiency more carefully to consider the processes that drive them, we implicitly turn attention to what has become known as the multiple benefits argument. While this specific terminology originates with the IEA (2014), arguments and evidence that energy efficiency will enhance economic welfare in a range of ways, including as a result of macroeconomic expansion, have been considered in other studies, notably (in terms of reflecting on the recent dominant focus on rebound effects) in the recent contribution by Gillingham et al. (2016). 4 In the current paper, we build on previous CGE studies of increased household energy efficiency to consider the wider economic impacts that fall under the multiple benefits umbrella. In particular, we focus on a general equilibrium argument that economic expansion will potentially deliver more in terms of individual household economic well-being than the initial improvement in energy efficiency. That is, when the economy expands (through increased investment, employment and output) as a result of increased and reallocated real household spending, increased incomes from employment of labour and capital services will further boost household incomes. 5 In an energy poverty context, while the expansionary process will trigger further rebound in household use (as well as in the production sector of the economy), this must be set against increased household incomes (and benefits).
Thus, one implication of this general equilibrium argument is that support of energy efficiency will deliver on more than just the outcome of reducing energy use (and related carbon emissions). Rather, by stimulating economic expansionary processes, it will further boost incomes throughout the economy and potentially deliver a level of pay back that would justify the public support required to allow the efficiency improvement to occur.
However, it may be argued that macroeconomic expansion can be delivered through other policies and that, where energy efficiency policy requires the support of the public purse, focus should be on helping those households who are currently unable to heat 6 their homes sufficiently. While the general equilibrium argument above implies that that the more wide-ranging the energy efficiency improvement, the greater will be the benefit to all households, it is necessary to consider whether restrictions on the government budget may erode the multiple benefits. That is, a government funding argument must also be considered. In the UK analysis below, we consider the context of a government that requires to maintain a fixed public sector deficit so that any support for energy efficiency programmes must be of a balanced-budget nature. That is to say that the funding for such programmes must come either from a reallocation of existing public spending or a change in tax revenues, at least in the short-term (until the costs of introducing the efficiency improvement have been recovered).
The key issue, then, is whether the resulting expansion is still large enough to compensate for the impacts of falling government expenditure (in the areas where spending is reduced) or the distortions triggered by increasing tax rates in part(s) of the economy. In turn, this is again likely to depend on how extensive the efficiency improvement is and what type and level of spending activity (the trigger for demand-led expansion) occurs as a result of freed up (and increased) household (real) disposable incomes. If the efficiency improvement is limited to low income households, it must be recognised that these households are (a) a more limited source of spending power, and (b) less sensitive to the wage and capital incomes generated by economic expansion, given their greater 4 Chan and Gillingham (2015) also provide an analytical exposition of how rebound effects will have positive economic welfare implications at the microeconomic level. 5 As we show in the CGE simulations reported in Section 6, where there is any constraint on the supply-side of the economy (e.g. restricted national labour supply) a demand-led expansion will put upward pressure on prices and potentially damage competitiveness. While this may benefit household incomes through higher wage rates, any loss in competitiveness will limit the extent of economic expansion over time. Where the expansion is triggered by increased energy efficiency this may be mitigated if households reflect the change in their cost of living in wage demands. However, we do not explore this issue at this stage. 6 Or, in the context of warmer climates, to cool. dependence upon publicly funded benefits. Stimulating higher income households, on the other hand, may free up much more spending on non-energy goods and services and deliver greater benefits through increased wage and capital incomes. 7 This latter point may ultimately support a national infrastructure argument. If it can be shown that the economic stimulus generated by support of wider-ranging energy efficiency programmes is likely to deliver sufficient pay back to justify the initial levels of funding required, then arguments for strategic investment in energy efficiency can be more solidly made. On this basis, the type of quite generalised analysis we offer below is intended as a first step in impacting policy discussion around focussing attention on the broader value added/benefits of, for example, making buildings more energy efficient.

Model and data
We simulate the economy-wide and macroeconomic impacts of improving household energy efficiency using a variant of the UK CGE model UK-ENVI. 8 For the specific application in this paper, we assume that investments are made by profit maximising forward-looking agents while (here five) representative households (distinguished as income quintile groups) are myopic. This intended to capture the notion that consumers often assumed by economic modellers. In particular, households tend to be rather myopic, in contrast to firms, and base their spending decisions more on current income availability rather than on future discounted utility of consumption. 9 In the following sections we provide a description of the main characteristics of the model. 10

Consumption
We model the consumption decision of five representative households h as follows: (1) In (1) total consumption C is a function of income YNG, savings SAV, income taxes HTAX, and taxes on consumption CTAX.
At each period in time, each household allocates its consumption between energy used for residential purposes, EC, and non-energy and transport goods and services (including fuel use in personal transportation), TNEC, according to the following constant elasticity of substitution (CES) function: ( 2) In is the elasticity of substitution in consumption, and measures the extent to which consumers substitute residential energy consumption, EC, for non-energy and transport consumption, TNEC, (0,1) is the share parameter, and is the efficiency parameter for residential energy consumption. For simplicity (and in the absence of better information), in all households we impose a value, 0.61, for that is the long-run elasticity of substitution between energy and non-energy estimated by Lecca et al. (2014). 11 The consumption of residential energy includes electricity, gas and coal, as shown in Figure 1, although the share of coal consumed by households represents less than 0.01% of total energy consumption. Within the energy bundle, given that we do not focus on inter-fuel substitution in the analysis below, we impose a small but positive elasticity.

Production and investment
The production structure is characterised by a capital, labour, energy and materials (KLEM) nested CES function. As we show in Figure 2, the combination of labour and capital forms value added, while energy and materials form intermediate inputs. In turn, the combination of intermediate and value added forms total output in each sector.
Following Hayashi (1982), we derive the optimal time path of investment by maximising the value of firms , subject to a capital accumulation function , so that: 11 However, we have conducted sensitivity analysis where we introduce different values for different household income groups. In particular, we introduced higher values for lower household income groups and vice versa. In comparison to the results reported in Section 4, we find that a higher elasticity triggers a larger rebound effect overall and in the households with higher elasticity. While the impact on overall GDP is not much changed (slightly reduced in the short run), as may be expected, there is a larger boost to disposable income in those groups with a higher elasticity, while the share of income spent on energy falls by less. (3) In (3), , is private investment, is the adjustment cost function with and is depreciation rate. The solution of the optimisation problem gives us the law of motion of the shadow price of capital, T path of investment (Hayashi, 1982).
where the real consumption (after tax) wage is negatively related to the rate of unemployment (Blanchflower and Oswald 2009). In (4), is the real take home wage, is a parameter calibrated to the steady state, is the elasticity of wage related to the level of unemployment , and is the income tax rate. The working population is assumed to be fixed and exogenous.

Government
The Government collects taxes and spends the revenue on a range of economic activities. We constrain the Government to maintain a constant budget balance. The aggregate fiscal deficit is taken to be fixed, so that any changes are constrained to be balanced budget in nature. The given fiscal deficit is maintained by either adjusting taxation or expenditure as illustrated in Equation (5): where (5) In (5) GOVBAL is the government budget which is equal to the difference between government income GY, and government spending GEXP. GY is given by the share d_gof capital income KY that is transferred to the Government, Indirect business taxes, IBT, revenues from labour income LY at the FE I GOVBAL we assume to be fixed in our present analysis.
We initially assume that the Government absorbs the budgetary impacts of any change in the economy by adjusting expenditure and keeping household income tax rates fixed. However, as explained below, we explore other cases, including where the Government fixes its expenditure and adjusts the income tax rate.

Dataset: income disaggregation and energy use
We calibrate the UK-ENVI CGE model on the UK Social Accounting Matrix for 2010. 12 The data has 30 different productive sectors including 4 main energy supply industries that encompass the supply of coal, refined oil, gas and electricity. We identify UK households, the UK Government, imports, exports and transfers to and from the rest of the World (ROW). As noted above, we disaggregate the household sector into 5 household income quintiles (HG), using the UK Living Costs and Food Survey. The income bands are described and related to weekly gross incomes in Table 1. Table 2 shows residential energy spending (on electricity, gas and coal) for each household as percentage of total energy consumption and of total consumption spending.
As would be expected for a country with a colder climate like the UK, lower income household groups spend a greater share of their budget on energy. Moreover, the energy expenditure is mostly for residential (heating and lighting) use. As income increases, the share of energy in total expenditure decreases, and spending on fuels for transport increases.

Simulation Scenarios
As explained above (Section 3), the aim of the simulations in this paper is consider the general effects of delivering increased energy efficiency in different household income groups. For this reason, we focus on specifying and explaining simple and transparent scenarios, rather than attempting to detail and conduct simulations of particular policy options. We derive the impact of an illustrative 10% improvement in household residential energy use by exploring three main Scenarios. Each scenario is divided into two sub-scenarios: first, a, where we assume that the energy efficiency improvement occurs in all households, regardless of their income; then, b, where we assume that efficiency improves only in the energy use of the lowest income quintile household. From above, the latter case is identified as a priority focus for public spending where energy poverty is an issue of policy concern.
In Scenario 1 we explore the impact of a 10% costless (and exogenously determined) improvement in household residential energy efficiency. This builds on the work of Lecca et al. (2014), extending that analysis to explore how the implications of the efficiency enhancement differ across the five income quintiles, and focussing only on energy used for heating and lighting (i.e. excluding refined fuel used in personal transportation).
In Scenarios 2 and 3 we consider in broad terms different options for how Government may fund the increase in energy efficiency. Given that we do not have information about the likely cost of increasing household energy efficiency by 10% in UK, we simplify by assuming that the Government compensates for the difference in household energy expenditure before and after the efficiency increase, for a limited time period (5 years). This is done by including in the expenditure items of its own budget, as shown in Equation (6).
In order to keep the budget balanced when EC varies, the Government can either reduce its current expenditure, GEXP, or increase its income, GY. In the sixth period (year) after the efficiency improvement, we consider that it has been completely paid for and Equation (6) is replaced by its standard version described in (5). 13 Following this approach, in Scenario 2 we assume that a 10% household energy efficiency enhancement is funded via a temporary reallocation of Government spending. This effectively means that for five years the Government has to decrease its expenditure on other goods and services in order to spend on energy efficiency, while ensuring that the government balance is maintained in each period.
In Scenario 3 we assume that a 10% household energy efficiency improvement is funded through a temporary rise in income tax. This implies that the Government is able to hold its current spending constant while balancing the budget through additional revenue. The focus on income tax is motivated in terms of the energy efficiency improvement being beneficial to households so that paying through tax provides an indirect way of having the household sector as a whole pay for increased efficiency in dwellings. However, there are distributional implications because higher income households pay more tax. Moreover, where only the lowest income household benefits from the energy efficiency improvement, the implication is that this is largely paid for by other households. In terms of the impacts on any economic expansion, introducing a change in income tax has important implications. This is because it triggers a change in supply side behaviour through the wage bargaining process, given that the after-tax or take-home wage, which is the focus of the bargaining process, is directly impacted. Table 3 shows the short and long-run impacts on key macroeconomic and energy use variables of a costless 10% increase in UK household energy efficiency for the two sub-scenarios: a. where the energy efficiency improvement occurs in all households (All HG); b. where efficiency improves only in the energy use of the lowest income quintile households (HG1).

Costless improvement in household energy efficiency
We report the results as percentage changes from the base year (SAM 2010) values, with the shortrun results referring to the first period (year) after the energy efficiency improvement takes place and the long-run referring to a conceptual time period where the capital stock is fully adjusted to a new steady-state equilibrium. Remember from Section 4 that we assume a fixed national labour supply, with a pool of unemployed labour and wage bargaining where there is a negative relationship between the unemployment rate and real after tax wage.
Beginning with Scenario 1a, where all UK households increase efficiency in residential energy, the first column in Table 3 shows that in the short run the switch in household expenditure away from spending on energy for heating and lighting towards other types of consumption has a small expansionary impact on the economy. Total GDP, consumption (disposable income after savings), employment, and investment increase by 0.03%, 0.52%, 0.05% and 1.14% respectively. As the sectors involved (directly or indirectly) in supplying goods and services where demand has increased expand (off-set by contractions in energy supply chains), there is a corresponding stimulus to labour demand. This causes the unemployment rate to decrease by 0.82% while the nominal wage increases by 0.42%, which, with a CPI increase of 0.32%, equates to the 0.09% increase in the real wage. However, the increase in the CPI does lead to a decrease in total export demand of 0.49% while imports increase by 0.7%.
Total household residential energy consumption falls by 2.35%, which, taking into account how a full range of economy-wide adjustments impact household income and consumption, is a large (76.5%) rebound on the 10% potential energy savings. That total household energy rebound is higher reflects increased spending on refined fuels for personal transportation. However, that the full economy-wide rebound is proportionately smaller (just under 69.9%) reflects that there is a net decrease in energy use on the production side of the economy (due to the contraction in energy supply activity).
The long-run results for Scenario 1a, reported in the second column in Table 3, show household energy use remaining below its base-year value. That rebound effects are smaller in the long-run than in the short-T in energy supply on energy prices and consumption and production choices. There is a further (less energy-intensive) expansion in GDP, with a long run increase of 0.16%. The expansion in the long run is greater than in the short run because the ability for all production sectors to adjust capacity allows a greater response to the net positive demand stimulus from increase real household income reallocated to other goods and services. However, given that the total labour force is assumed to be fixed, there is a fall in the unemployment rate generating an increase in the real wage. This, in turn, puts continued (but declining) upward pressure on all commodity prices and reduces competitiveness so that there is a lasting decrease in export demand (-0.37%). The third and fourth columns of Table 3 show the corresponding results if we limit the increase in energy efficiency to the lowest income quintile, Household Group 1 (HG1). The long-run results are qualitatively the same as found in Scenario 1a, but the scale of both the economic expansion and the contraction in total household energy use is much smaller. In the short-run, crowding out effects impacting exports and disinvestment in the energy supply sectors actually causes a very small net negative impact in GDP (-0.001%). 14 The core issue is that the lowest income quintile, where spending power is directly boosted by the energy efficiency improvement, is only a very small source of consumption expenditure in the UK economy. This group is also not a huge beneficiary of increased labour and capital income when the expansion occurs. This means that further induced limited in the very small expansion reported. 15  Table 3 show that the long-run GDP increase under Scenario 1b is only around 10% of what is realised when all households improve their energy efficiency.
Comparison of the results in scenarios 1a and 1b reported in Table 4 show that residential energy use in the lowest household income group falls most, as does the share of consumption spending on this energy use, when the efficiency improvement is targeted only in HG1. This is because the rebound in energy use is smaller where there is a more limited boost to household income. However, Table 3 has shown that the total reduction in UK households and economy-wide energy use is smaller (i.e. rebound is larger) under Scenario 1b when the efficiency improvement is limited to HG1. This is because the other households do not experience an improvement in efficiency and slightly increase their energy consumption with the (very limited) economic expansion.
The conclusion that can be drawn is that more extensive energy efficiency stimuli can deliver a fuller set of desired outcomes. This includes achieving reductions in energy use through energy efficiency and (by implication from reduced energy use) carbon reduction targets, boosting household income in low (and other) income households, along with wider economic expansion. However, so far we have not given any consideration to how increased energy efficiency may be funded. Therefore, in the next section, we report on extended simulations where we incorporate a basic consideration of the impacts of applying some treatment of cost via the public budget.

Basic options for funding improvements in household energy efficiency via the Government budget
First, let us consider the case of effecting some payment for the introduction of the energy efficiency improvement through a temporary reallocation of government expenditure, in the manner detailed above in Section 5 (Scenarios 2a and 2b). 16 The main impact of the required reduction in Government spending in other areas of the economy is a short run contraction in economic activity (reflected in the GDP results over time in Figure 3). The contraction in activity actually continues for less than the assumed 5-year period of required reallocation of government expenditure. This is because firms are forward looking (i.e. they know that the contraction in spending will end) and they adjust their investment plans accordingly.
At the level of the different household income groups, in Scenario 2a, where all households improve their energy efficiency, the short-run impact is a slightly smaller boost to consumption (disposable income net of savings) but with the gap relative to the no cost Scenario 1a being larger in higher income groups where labour and capital incomes are more important. In Scenario 2b, where energy efficiency only increases in the lowest income quintile, the impact for HG1 remains more or less unchanged relative to Scenario 1b. However, all other groups now experience a slight contraction in their income used for consumption (-0-01% in HG2&3 and -0.02% in HG4&5).
The key finding, however, is that the long-run results under Scenarios 2a and 2b are unchanged relative to the costless case in Scenarios 1a and 1b. 16 The long run results under Scenarios 2 and 3 are generally not very different to what is observed in Scenario 1 so we do not provide equivalent tables, instead focussing on key results in the figures below. On the other hand, when we consider the case of a temporary increase in the income tax rate (Scenarios 3a and 3b) there are more marked changes in the nature of the results. First, as noted in Section 5, the change in income tax brings about a change in the supply side of the economy. This is because the increase in taxation reduces the take home wage, causing workers to demand higher salaries, putting upward pressure on the real wage and thereby impacting costs faced by all firms. While Figure 3 shows a very close convergence in long-run GDP under Scenario 3a, there are some minor differences in the long-run impacts on GDP, investment and employment/unemployment. However, there is a greater impact on results when the energy efficiency improvement is limited to HG1 in Scenario 3b. First, Figure 4 shows that there is a small contraction in GDP that lasts into the long run (-0.005%). This implies that the increase in energy efficiency in HG1 does not provide a sufficient economic stimulus to demand to deliver a long-run expansion in the presence of the adverse supply-side shock that is delivered via the induced rise in wage demands. 17 Moreover, while the impact on income used for consumption is very similar in Scenario 3b (as compared to 3a) under the government spending and tax options for HG1 (only slightly worse under the latter), it is very different for all the other household income groups. Initially, given that they pay more income tax, HG2-5, effectively pay for the increase in HG1 energy efficiency through their increased tax contributions. However, over time, even once the tax rate returns to its original level, the other groups continue to pay through the greater impact on their disposable (net of savings) incomes from the economic contraction. This is shown in Figure 5. N the highest income quintile, HG5. This is due to the fact that income from ownership of capital (most important in HG5) is adversely affected in this scenario due to more limited investment activity.
We have run a specific sensitivity scenario where we increase the size of the energy efficiency improvement in HG1 to see what is required to produce a positive GDP result over the long-run under the income tax funding scenario. We find that a 12% boost to the residential energy use in HG1 is sufficient to deliver a net positive (0.0003%) increase in GDP over the long run, with the positive result emerging from period 11. However, the net negative impact on disposable income in the other household groups persists, albeit to a lesser extent. We find that, where we have an income tax funding arrangement as above, a doubling of the efficiency improvement in HG1 residential energy use to 20% is required to remove the long-run negative impacts on the disposable income of all other groups. Below this, the highest income household remains most affected, for example with only HG5 losing out over the long run where the efficiency improvement in HG1 is 19%. Figure 5: Short-run and long-run % change in disposable income from a 10% increase in residential energy efficiency in household quintile 1 funded via an increase in income tax.
Overall, the results above suggest that imposing a cost for increasing energy efficiency via the public However, if the economic expansion is sufficiently big, the long-run outcome is one of net gain in broader economic impacts. When the efficiency improvement is targeted only in the lowest income households this does deliver the desired outcomes for that group, but it weakens the economic expansion, while the need for (and nature of) public funding through the government budget becomes much more important.

Conclusions and policy implications
Many recent economic modelling studies of increased energy efficiency have tended to focus on the issue of rebound effects. However, in considering economy-wide rebound in particular, some studies have identified economic expansion resulting from increased energy efficiency as the driver of M B IEA (2014). Here, we have focused our attention on how the economic expansion may provide a justification for public/government support of energy efficiency programmes.
Specifically, we have used an illustrative CGE modelling analysis for the UK to consider the general effects of government support of domestic energy efficiency programmes. We have raised the question of whether only low income households should be aided in improving their energy efficiency, or whether there is sufficient return through expansion to justify potentially supporting wider ranging programmes. A key point that we have raised is that many governments are committed to the support of energy efficiency programmes but may focus this in low income households. However, Governments tend to have a wider set of desired outcomes, including reduced energy use and carbon emissions, but also in terms of reducing poverty (including but not limited to energy poverty) and increasing economic well-being, in part through GDP and employment growth.
In considering scenarios where support is provided only for the lowest income households to increase their energy efficiency, our findings suggest that it is likely to be difficult to meet all of objectives simultaneously through limited support of households that are significantly less connected to the wider economy than others (in terms of their level of spending and their sources of income). Our own results suggest that in order to stimulate economic activity by this route quite large proportionate increases in residential energy efficiency in low income household need to be achieved. In contrast, where the introduction of increased energy efficiency is spread over all (or at least a wider range) of households, even where there is a cost to supporting energy efficiency improvements, the return via the impacts of economic expansion is likely to provide what justification for support.
However, our findings suggest that the means of providing support for energy efficiency programmes should be carefully considered and examined. Our results imply that a reallocation of government spending will be less distortive than requiring the household sector to pay indirectly (according to ability to pay) via income tax. However, we reserve fuller consideration of specific funding mechanisms for future research, ideally in consultation with policy decision makers particularly within the UK.