Greenhouse Gas Abatement Cost Curves of the Residential Heating Market: A Microeconomic Approach

Abstract

In this paper, we develop a microeconomic approach to deduce greenhouse gas abatement cost curves of the residential heating sector. Our research is based on a system dynamics microsimulation of private households’ investment decisions for heating systems to the year 2030. By accounting for household-specific characteristics, we investigate the welfare costs of different abatement policies in terms of the compensating variation and the excess burden. We investigate two policies: (i) a carbon tax and (ii) subsidies on heating system investments. We deduce abatement cost curves for both policies by simulating welfare costs and greenhouse gas emissions to the year 2030. We find that (i) welfare-based abatement costs are generally higher than pure technical equipment costs; (ii) given utility maximizing households a carbon tax is the most welfare-efficient policy and; (iii) if households are not utility maximizing, a subsidy on investments may have lower marginal greenhouse gas abatement costs than a carbon tax.

Appendices

Appendix 1: Specification of Annual Heating Costs and Cost Implications of Policies

As stated in Sect. 3.2, annual heating costs of a household of category n and a technology j, modernized in period y are a function of the investment costs $i_{n,j,y}$, the energy consumption $e_{n,j,y}$, the energy price $p_{j,y}$, plus, in the case of policies being introduced, a tax payment $T_j$ or a lump-sum subsidy $S_j$:

$$\begin{aligned} c_{n,j,y} = f(i_{n,j,y}, e_{n,j,y}, p_{j,y}, T_j, S_j) \end{aligned}$$

(39)

The total annual heating costs are derived as follows,:

$$\begin{aligned} c_{n,j,y} = (i_{n,j,y}-S_j)*a_{r,l} + o_{n,j,y} + e_{n,j,y}*(p_{j,y} + T_j) \end{aligned}$$

(40)

with $o_{n,j,y}$ being the fixed operation and maintenance costs of a technology and $a_{r,l}$ being the annuity factor.

Thus, a lump-sum subsidy $S_j > 0$ decreases annual heating costs $c_{n,j,y}$ by decreasing the costs of the initial investment. A tax payment $T_j > 0$ for each unit of consumed energy increases annual heating costs. The tax payment per unit of energy consumed $T_j$ is derived from the carbon tax $\tau$ times technology-specific conversion factor $CF_j$, i.e., $T_j = \tau *CF_j$.

The energy consumption $e_{n,j,y}$, e.g. gas consumption, is derived from the heating demand $H_{n}$, which varies by household category, and the technology specific use efficiency $\epsilon _{n,j,y}$. The use efficiency depends on technology j, the household category n and the time of installation y (to account for technological progress). Thus:

$$\begin{aligned} e_{n,j,y} = \frac{H_{n}}{\epsilon _{n,j,y}} \end{aligned}$$

(41)

Therefore, the lower the efficiency and the higher the heating demand, the higher is the energy consumption.

Table 2 Data and sources

Table 3 Energy prices

Appendix 2: Assumptions and Data

Starting point of the model calculations in DIscrHEat is a detailed overview of the current German building stock of private households in 2010. We distinguish single and multiple dwellings and six vintage classes. Each of those building classes has an average net dwelling area and a specific heat energy demand ($\hbox {kWh}/\hbox {m}^2\hbox {a}$). Additionally, we include data on the distribution of heating systems in each building class.

To simulate the future development of the German building stock (i.e. the installed heating technologies and the buildings’ insulation level), DIscrHEat accounts for new buildings and demolitions. Furthermore, we assume that a certain percentage of buildings has to install a new heating system. Those modernization rates are given exogenously. IWU/BEI (2010) show that in Germany, investments into new heaters mostly take place when mendings or replacements need to be done. Therefore, we assume that heater replacements only take place according to empirical rates of the last years based on IWU/BEI (2010) (Tables 2, 3, 4, 5, 6, 7, 8, 9, 10).

The estimation of the discrete choice model is based on data on the distribution of energy carriers chosen by a number of building type categories in 2010, characteristics of these building types and the heating system costs. The dwelling stock comprises six different vintage classes, differentiates between single/double and multiple dwellings and three different insulation levels (heat demand levels) per house type vintage class combination. Due to a lack of data for the diffusion of energy carriers per insulation level, we include the average heat demand per dwelling category in our discrete choice estimation. However, we account for the different insulations in our simulation model. Thus, our data comprises twelve different representative dwelling types with different heat demand, heating system costs and distributions of heating systems chosen in 2010. Out of this aggregated data, we generate our data set which represents the number of buildings that changed their heating system in 2010 differentiated by dwelling type with the respective characteristics. Heating system costs are derived using the data listed in the tables below. Additionally, a fixed interest rate of 6 % and an assumed household’s planning horizon of 15 years determine the annuity factor.²⁷ An overview of all data sources is provided in Table 2.

Table 4 $\text {CO}_2$ emissions of energy carriers

Table 5 Dwelling stock

Table 6 Cost assumptions

Table 7 Subsidies on heating system investment

Table 8 Heat demand per insulation level

Table 9 Modernization rates

Table 10 Distribution of new heaters installed in 2010

Appendix 3: Sensitivity Analysis of the Assumed Interest Rate

In the following, we provide a sensitivity analysis assuming an interest rate of 3 %. Figure 7 illustrates the welfare-based GHG abatement cost curves (i.e., based on the excess burden) for each of the three policies for an interest rate of 3 % (dashed lines) and 6 % (solid lines). Interestingly, the welfare-based GHG abatement costs decrease for a lower interest rate. The explanation is that less carbon intensive, but capital-intensive technologies such as heat pumps or biomass heaters become relatively cheaper compared to, e.g., gas-fired heaters. Therefore, abatement costs decrease. However, in the case of a subsidy, the opposite holds. This reason is that the subsidy, which is paid lump-sum when the investment is made becomes less valuable since the interest rate is lower.

Fig. 7

Marginal excess burden of GHG abatement for different interest rates

Appendix 4: Discrete Choice Model-Statistics, Welfare Measurement and Tests

Figure 8 presents the structure of newly installed heating systems in Germany in 2010 across different dwelling types and their total annual heating costs in Euro. The groups contain dwellings of the same type with the same year of construction, housetype (single/double or multiple and average insulation status/heat demand). The frequency of each group in the sample is indicated by the area of the circles.²⁸ Analyzing these heating system choices leads to the assumptions that the annual costs of a heating system might have an impact on the households’ heating system choices. Yet, costs are not the only driver. In addition, the heating system choice differs systematically across the different dwelling types and the buildings’ vintage class.

Fig. 8

Costs and frequency of energy carriers installed in different dwellings in 2010

Table 11 presents the summary statistics of our discrete choice estimation.

Table 11 Summary statistics

Later works on random utility models of discrete choice or mixed logit models (McFadden and Train 2000; Train 2003) or the approach presented by Berry et al. (1995), Berry (1994) and others point out that the approaches presented in McFadden (1974, (1976) neglect product heterogenity. We assume, that this might be true for products such as cars but is not valid in the case of heating systems installations since the product heat energy is a rather homogenous good. In addition, especially the approach of Berry et al. (1995) accounts for price endogeneity and price formation on the market level by demand and supply. Our analysis sets its focus on energy consumption neglecting supply and is thus a partial analysis of the residential heat market. Further, we do not deal with price endogeneity as we assume that energy prices are not determined by the residential energy demand: the price of oil and gas is influenced by global supply and demand effects and other sectors such as power generation, transport or industry sectors rather than private households’ heat demand. We also assume the price of biomass to be exogenous because the final biomass consumption of the residential sector accounted for 16 % of German and only 3 % of the European primary biomass production and there is still a significant unused biomass potential (Eurostat 2011; European Commission 2007). Another often mentioned problem with the presented approach is the Independence of Irrelevant Alternatives (IIA) assumption, which we test for (see the last section of this Appendix).

1.1 Computation of the compensating variation

Small and Rosen (1981) introduce a methodology to determine the aggregated compensating variation for discrete choice models and overcome the difficulty of the demand function aggregation and the discontinuity of the demand functions. We apply a generalization of this apporoach to determine the compensating variation $CV_n$ of the representative household n based on McFadden (1999) associated with a changing of $V_{n,j}$ resulting from introducing a policy.

We have the distribution of the energy carriers j chosen based on the following:

$$\begin{aligned} P_{n,j} = \frac{e^{ V_{n,j}}}{\sum _{i}e^{ V_{n,i}}} \end{aligned}$$

(42)

To compute the consumer surplus based on the utility in the no-policy case and the policy case we get:

$$\begin{aligned} \int _0^{V_{n,j}^{\text {no policy}}}P_{n,j}dV_{n,j} \end{aligned}$$

(43)

and

$$\begin{aligned} \int _0^{V_{n,j}^{\text {policy}}}P_{n,j}dV_{n,j} \end{aligned}$$

(44)

Thus, for the difference in consumer surpluses of the two scenarios we get:

$$\begin{aligned} \int _{V_{n,j}^\text {no policy}}^{V_{n,j}^{\text {policy}}}P_{n,j}dV_{n,j} = \left[ \ln {\sum _i{\frac{e^{\alpha _j + \beta c_{n,j} + \gamma _{1,j}z_{1,n} + \gamma _{2,j}z_{2,n}}}{\beta }}}\right] _{V_{n,j}^\text {no policy}}^{V_{n,j}^\text {policy}} \end{aligned}$$

(45)

To compute the compensating variation of household n $CV_n$, we need to find the amount of money $CV_n$ that compensates the costs caused by the policy measures to keep the utility at the ’without policy’ level. Thus, the following equation based on McFadden (1999) must hold for the compensating variation $CV_n$ of household n for each period y:

$$\begin{aligned} \ln {\sum _j{\frac{e^{\alpha _j + \beta (c_{n,j}^{\text {policy}}- CV_n) + \gamma _{1,j}z_{1,n} + \gamma _{2,j}z_{2,n}}}{\beta }}} = \ln {\sum _i{\frac{e^{\alpha _i + \beta c_{n,j}^{\text {no policy}} + \gamma _{1,j}z_{1,n} + \gamma _{2,j}z_{2,n}}}{\beta }}} \end{aligned}$$

(46)

We have a constant $\beta$ over all alternatives, so the formula by Small and Rosen (1981) to compute the compensating variation in our logit model can easily be derived:

$$\begin{aligned} CV_{n}= \frac{1}{\beta } \left[ ln\sum _{j}exp\left( V_{n,j}^{\text {policy}}\right) - ln \sum _{j}exp\left( V_{n,j}^{\text {no policy}}\right) \right] \end{aligned}$$

(47)

The division by $\beta$ translates the utility into monetary units. This formula by Small and Rosen (1981) depends on certain assumptions: the goods considered are normal goods, the representatives in each group (households with the same dwelling characteristics) are identical with regard to their income, the marginal utility of income $\beta$ is approximately independent of all costs and other parameters in the model, income effects from changes of the households’ characteristics are negligible, i.e. the compensated demand function can adequately be approximated by the Marshallian demand function.

1.2 Hausman–McFadden Test

We conduct tests of Hausman and McFadden (1984) to make sure the Independence of Irrelevant Alternatives (IIA) assumption holds. We therefore reestimate the model presented in Table 1 by dropping different alternatives i. For instance one could assume that the choice of a heating technology depends rather on fossile versus non-fossile fuels than on the different energy carriers presented. Thus, we first drop the alternative biomass, oil, and heatpump in seperate tests, and then both biomass and oil and both oil and heatpump. We compare these estimators with those of our basic model.

Under H0 the difference in the coefficients is not systematic. The test statistic is the following:

$$\begin{aligned} t = (b- \beta )'(\Omega _b - \Omega _{\beta })^{-1} (b -\beta ),\quad \text {with} \; t \sim \chi ^2(1) \end{aligned}$$

(48)

b is the cost coefficient of the reduced estimations dropping alternatives and $\Omega _b$ and $\Omega _{\beta }$ are the respective estimated covariance matrices.

Table 12 shows the results:

Table 12 Hausman–McFadden test of IIA

The results show that IIA cannot be rejected.