Skip to main content

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Notes

  1. 1.

    United Nations Conference on Environment and Development.

  2. 2.

    See for example Train (2003) for an overview of discrete choice approaches on which we base our framework.

  3. 3.

    Because GHG abatement costs for insulation measures are so high in Germany, for simplification, we exclude the households’ decisions on thermal insulation from our analysis.

  4. 4.

    Reasons are versatile but are mainly due to the long-term investment character of heating systems and the fact that the investment costs will always be higher than future energy savings (see IW Köln 2012). Hence, in the model, households only invest when they have to. Thus, in the model, they are randomly drawn according to the modernization rates. As a result, household decisions are static during every period (only the building stock evolves dynamically).

  5. 5.

    We do not consider the impact of policy measures on the number of investments, but only on the structure of heating system choices. Therefore, the annual heating system costs, accounting for investment costs and future energy savings, are relevant for the heating system choices. However the split of investment costs and future energy savings is irrelevant. Based on IWU/BEI (2010), we argue that households only change their heating system when it is broken. Therefore a static discrete choice model is appropriate in this analysis.

  6. 6.

    We assume that households do not have perfect foresight and that they have bounded rationality. Hence, only current energy prices are included in their considerations, and future energy price developments are not accounted for.

  7. 7.

    For more details, “Appendix 1” shows a more detailed specification of the annual heating costs \(c_{n,j,y}\) and the impact of \(T_j\) and \(S_j\).

  8. 8.

    The logit model with its elasticities is a standard approach to model the diffusion of technologies. See for instance Geroski (2000).

  9. 9.

    For detailed mathematical derivations and explanations of logit and conditional logit models see McFadden (1974) and Train (2003).

  10. 10.

    Analyzing the development of the German heat market over the last 60 years indicates that this is a realistic assumption and that changes resulting from the cost advantages of new heating systems take place only inertially and based on the number of heating systems of that type that are already installed (BDH 2010; IWU BEI 2010). The inertia of the heating system stock results from the long life spans of the heating systems and the fact that heaters are only exchanged when they are broken. Adoption rates of heating systems that already have a large market share are much higher. The proportional substitution pattern of conditional logit models is often criticized. In the case of the homogenous good heat, it seems, however to be appropriate. See for instance Train (2003) for a detailed discussion of the substitution patterns of logit models.

  11. 11.

    We use the annual heating costs per unit of heat demand in kilowatt hour (kWh) \(c_{n,j}\) because we are interested in a normalized impact of costs on the choice of a heating system irrespective of the different dwellings’ total heat demand. As such, we can make them comparable for all buildings. We further assume that all households of category n have the same dwelling characteristics.

  12. 12.

    See “Appendix 2”.

  13. 13.

    By tendency, newer buildings c.p. have a lower heat demand.

  14. 14.

    The significance of the cost estimate is only at 10 % because the estimation is based on our own dataset, including simplified cost assumptions. For some specific households, additional costs apart from heating system costs (e.g. switching costs such as costs for network connections etc.) may be of importance. Data on these costs is not available. Braun (2010) estimates a more detailed discrete choice model for the German heating market, however, only focusing on household characteristics. Our paper’s focus is not on the estimation itself. If better data were available, the same approach of deriving marginal \(\text {CO}_2\) abatement curves could be implemented based on improved and more detailed choice estimations.

  15. 15.

    For instance, Dieckhöner (2012) shows that households with higher income rather live in single dwellings.

  16. 16.

    The carbon tax is a hypothetical policy which is not implemented currently.

  17. 17.

    For the assumed emissions of the energy carriers, see Table 4. We assume that no tax is levied on biomass.

  18. 18.

    This limitation of the analysis leads to an underestimation of the GHG reduction effect of the tax. Assuming price elastic heating demand, a tax would have a negative effect on energy demand and therefore a positive one on GHG reduction.

  19. 19.

    This assumption leads to an underestimation of the excess burden. This means that the investment costs of heating systems and energy prices are not influenced by the demand changes of the residential heating sector. We assume that the residential sector demand is too small to have an impact on energy prices. The producers of heating systems in Germany sell all types of heaters. Thus, they do not depend on a specific system and would adapt their product composition according to the changing demand conditions.

  20. 20.

    Tra (2010) provides an application of this discrete choice equilibrium framework to the valuation of environmental changes.

  21. 21.

    See Appendix 1 for a more detailed derivation. Income effects are not accounted for because Braun (2010) shows that the marginal effects of income are low in the German heating market controlling for further household characteristics. The marginal effects are not even significant for all heating system choices. Moreover, income is highly correlated with the dwelling type. Dieckhöner (2012) shows that households with higher income rather live in single dwellings than in multiple dwellings. In addition, she shows that households with higher income spend more on insulation and thus live predominantly in dwellings with lower heat demand. Hence, controlling for the dwelling type approximates the impact of differences in income. This approach assumes a constant marginal utility of income denoted by \(\frac{1}{\beta }\). Torres et al. (2011) investigate the sensitivity of mistaken assumptions about the marginal utility of income and their impacts on the welfare measures in Monte Carlo experiments. They find that mistaken assumptions about the marginal utility of income can amplify misspecifications of the utility function. However, throughout all misspecification cases analyzed, they find an underestimation of the compensating variation (referred to as ’compensating surplus’ in their paper). Thus, the analysis conducted in this paper assuming a constant marginal utility of income is conservative and might even underestimate the compensating variation (and excess burden).

  22. 22.

    See Allcott and Greenstone (2012). There are further typical barriers in the heating market that constrain utility-maximizing behavior of households such as the landlord-tenant problem.

  23. 23.

    The utility maximizing approach to model the diffusion process is still appropriate as long as the household choice pattern is not be affected by public policies. However, in the case of households misoptimizing the evaluation of the compensating variation does not reflect real consumer losses and costs to society.

  24. 24.

    In Appendix 1, we provide a sensitivity analysis assuming a discount rate of 3 %.

  25. 25.

    Technology based approaches to determine GHG abatement curves would imply even lower costs since they neglect household characteristics and therefore household preferences.

  26. 26.

    The paper’s results are to be underestimates of the true efficiency gains from using a carbon tax. In reality, households are more heterogeneous than in the presented simplified approach.

  27. 27.

    In 2, we provide a sensitivity analysis assuming a discount rate of 3 %.

  28. 28.

    Please note that the group with the construction period 1949–1978 includes so many buildings because it covers the longest time period. There was no further differentiation of construction periods in the data. In the two vintage classes 1996–2000 and 2001–2004 there were almost no newly installed heating systems in 2010 because of the 15-year lifetime of heating systems on average in Germany.

Abbreviations

GHG:

Greenhouse gas

\(\text {CO}_2\)-eq:

\(\text {CO}_2\)-equivalent

DIscrHEat:

DIscrete choice HEat market model

References

  1. Allcott H, Greenstone M (2012) Is there an energy efficiency gap? J Econ Perspect 26(1):3–28

    Article  Google Scholar 

  2. ARGE Kiel (2010) Wohnungsbau in Deutschland 2011—Modernisierung oder Bestandsersatz. Arbeitsgemeinschaft für zeitgemäßes Bauen, Kiel

  3. Auerbach A (1985) The theory of excess burden and optimal taxation. In: Auerbach AJ, Feldstein M (eds) Handbook of public economics, vol 1. North-Holland, New York, pp 61–127

  4. Ballard C, Medema S (1993) The marginal efficiency effects of taxes and subsidies in the presence of externalities—a computational general equilibrium approach. J Public Econ 52:199–216

    Article  Google Scholar 

  5. Baumol WJ (1972) On taxation and the control of externalities. Am Econ Rev 62(3):307–322

    Google Scholar 

  6. BDH (2010) Trends und Herausforderungen im Wärmemarkt—Marktentwicklung Wärmeerzeuger 1999–2009. http://bdh-koeln.de/uploads/media/100126_bdh-pm-folien_pk.pdf (09/23/2014)

  7. Berry S (1994) Estimating discrete-choice models of product differentiation. RAND J Econ 25(2):242–262

    Article  Google Scholar 

  8. Berry S, Levinsohn J, Pakes A (1995) Automobile prices in market equilibrium. Econometrica 63(4):841–890

    Article  Google Scholar 

  9. Bovenberg AL, de Mooij RA (1994) Environmental levies and distortionary taxation. Am Econ Rev 84(4):1085–1089

    Google Scholar 

  10. Bovenberg AL, Goulder L (1996) Optimal environmental taxation in the presence of other taxes: general-equilibrium analyses. Am Econ Rev 86:985–1000

    Google Scholar 

  11. Braun FG (2010) Determinants of households’ space heating type: a discrete choice analysis for German households. Energy Policy 38(10):5493–5503

    Article  Google Scholar 

  12. Buildings Performance Institute Europe (BPIE) (2011). Europe’s buildings under the microscope—a country-by-country review of the energy performance of buildings. http://www.bpie.eu/eu_buildings_under_microscope.html. 23 Sept 2014

  13. Cremer H, Gahvari F, Ladoux N (2003) Environmental taxes with heterogeneous consumers: an application to energy consumption in France. J Public Econ 87:2791–2815

    Article  Google Scholar 

  14. Destatis (2008) Bauen und Wohnen—Mikrozensus—Zusatzerhebung 2006. Fachserie 5 Heft 1, Statistisches Bundesamt

  15. Destatis (2010a) Bauen und Wohnen—Baugenehmigungen/Baufertigstellungen von Wohn- und Nichtwohngebäuden (Neubau) nach Art der Beheizung und Art der verwendeten Heizenergie. Lange Reihen ab 1980, Statistisches Bundesamt

  16. Destatis (2010b) Bauen und Wohnen—Bestand an Wohnungen. Fachserie 5 Reihe 3, Statistisches Bundesamt

  17. Destatis (2010c) Gebäude und Wohnungen—-Bestand an Wohnungen und Wohngebäuden, Abgang von Wohnungen und Wohngebäuden. Lange Reihen ab 1969–2009, Statistisches Bundesamt

  18. Diamond P, McFadden D (1974) Some uses of the expenditure funtion in public finance. J Public Econ 3:3–22

    Article  Google Scholar 

  19. Dieckhöner C (2012) Does subsidizing investments in energy efficiency reduce energy consumption? Evidence from Germany. EWI Working Paper 12/17

  20. European Commission (2007) Accompanying document to the Communication from the Commission to the Council and the European Parliament—Renewable Energy Road Map—Renewable energies in the 21st century: building a more sustainable future—Impact Assessment. Commission Staff Working Document SEC 2006:1719

  21. Eurostat (2011) Eurostat statistics database: renewable energy primary production: biomass, hydro, geothermal, wind and solar energy. http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=nrg_107a&lang=en, 23 Sept 2014

  22. Fullerton D, Metcalf G (1998) Environmental taxes and the double-dividend hypothesis: did you really expect something for nothing? Chicago-Kent Law Rev 73:221–256

    Google Scholar 

  23. Geroski P (2000) Models of technology diffusion. Res Policy 29:603–625

    Article  Google Scholar 

  24. Goulder LH (1995) Environmental taxation and the double dividend: a reader’s guide. Int Tax Public Finance 2(2):157–183

    Article  Google Scholar 

  25. Hausman J, McFadden D (1984) Specification tests for the multinomial logit model. Econometrica 52(5):1219–1240

    Article  Google Scholar 

  26. Huntington H (2011) The policy implications of energy-efficiency cost curves. Energy J 32(Special Issue 1):7–22

    Google Scholar 

  27. Leipzig IE (2009) Vollkostenvergleich Heizsysteme 2009. Informationen für Verbraucher, Leipziger Institut fr Energie GmbH, Leipzig

  28. IEA (2011) Energy balances of OECD countries 2011. International Energy Agency, Paris

  29. IPCC (2007) Climate change 2007: the physical science basis. The Fourth Assessment Report of the Intergovernmental Panel on Climate Change, IPCC

  30. IW Köln (2010) Wohngebäudesanierer Befragung 2010. Technical Report, KFW/Institut der deutschen Wirtschaft Köln

  31. IW Köln (2012) Energetische Modernisierung des Gebäudebestandes: Herausforderungen fr private Eigentümer. Technical Report, Institut der deutschen Wirtschaft Köln

  32. IWU (2013) Energetische Sanierung des Gebudebestandes privater Haushalte. Technical Report, Institut Wohnen und Umwelt

  33. IWU BEI (2010) Datenbasis Gebäudebestand. Datenerhebung zur energetischen Qualität und zu den Modernisierungstrends im deutschen Wohngebäudebestand, Institut Wohnen und Umwelt (IWU) / Bremer Energie Institut (BEI)

  34. Kavgic M, Mavrogianni A, Mumovic D, Summerfield A, Stevanovic Z, Djurovic-Petrovic M (2010) A review of bottom-up building stock models for energy consumption in the residential sector. Build Environ 45(7):1683–1697

    Article  Google Scholar 

  35. Llavador H, Roemer JE, Silvestre J (2011) A dynamic analysis of human welfare in a warming planet. J Public Econ 95:1607–1620

    Article  Google Scholar 

  36. Madlener R (1996) Econometric analysis of residential energy demand: a survey. J Energy Lit 2:3–32

    Google Scholar 

  37. Mansur ET, Mendelsohn R, Morrison W (2008) Climate change adaptation: a study of fuel choice and consumption in the US energy sector. J Environ Econ Manag 55(2):175–193

    Article  Google Scholar 

  38. Mayshar J (1990) On measures of excess burden and their application. J Public Econ 43(3):263–289

    Article  Google Scholar 

  39. McFadden D (1976) Quantal choice analysis: a survey. Ann Econ Soc Meas 5:349–368

    Google Scholar 

  40. McFadden D (1999) Computing willingness-to-pay for transport improvements. In: Moore J, Riezman R, Melvin J (eds) Trade, theory and econometrics: essays in honour of John S. Chipman. Routledge, London

  41. McFadden D, Train K (2000) Mixed MNL models with discrete response. J Appl Econ 15(5):447–470

    Article  Google Scholar 

  42. McFadden DL (1974) Conditional logit analysis of qualitative choice behavior. Academic Press, New York, pp 105–142

    Google Scholar 

  43. McKinsey & Company, Inc. (2009) Unlocking energy efficiency in the U.S. economy. McKinsey Global Energy and Materials, McKinsey & Company, Inc

  44. Michelsen CC, Madlener R (2012) Homeowners’ preferences for adopting innovative residential heating systems: a discrete choice analysis for Germany. Energy Econ 34(5):1271–1283

    Article  Google Scholar 

  45. Morris J, Paltsev S, Reilly J (2008) Marginal abatement costs and marginal welfare costs for greenhouse gas emissions reductions: results from the EPPA model. Report No. 164, MIT Joint Program on the Science and Policy of Global Change

  46. Nordhaus WD (2011) Estimates of the social cost of carbon: background and results of the RICE-2011 model. Cowles Foundation Discussion Paper

  47. Öko-Institut eV (2011) Global emission model for integrated systems (GEMIS). http://www.oeko.de/service/gemis/en/index.htm. 29 August 2011

  48. Pearce D (2003) The social cost of carbon and its policy implications. Oxford Rev Econ Policy 19(3):362–384

    Article  Google Scholar 

  49. Rehdanz K (2007) Determinants of residential space heating expenditures in Germany. Energy Econ 29(2):167–182

    Article  Google Scholar 

  50. Small KA, Rosen HS (1981) Applied welfare economics with discrete choice models. Econometrica 49(1):105–130

    Article  Google Scholar 

  51. Stadler M, Kranzl L, Huber C, Haas R, Tsioliaridou E (2007) Policy strategies and paths to promote sustainable energy systems—the dynamic Invert simulation tool. Energy policy 35(1):597–608

    Article  Google Scholar 

  52. Stern N (2007) The economics of climate change. Cambridge University Press, Cambridge

    Book  Google Scholar 

  53. Swan LG, Ugursal VI (2009) Modeling of end-use energy consumption in the residential sector: a review of modeling techniques. Renew Sustain Energy Rev 13(8):1819–1835

    Article  Google Scholar 

  54. Torres C, Hanley N, Riera A (2011) How wrong can you be? Implications of incorrect utility function specification for welfare measurement in choice experiments. J Environ Econ Manag 62:111–121

    Article  Google Scholar 

  55. Tra C (2010) A discrete choice equilibrium approach to valuing large environmental changes. J Public Econ 94:183–196

    Article  Google Scholar 

  56. Train K (2003) Discrete choice methods with simulation. Cambridge University Press, Cambridge

    Book  Google Scholar 

  57. UBA (2015) Kohlendioxid-emissionen. https://www.umweltbundesamt.de/daten/klimawandel/treibhausgas-emissionen-in-deutschland/kohlendioxid-emissionen

Download references

Acknowledgments

We would like to thank Felix Höffler, Christian Growitsch, Sebastian Kranz, Heike Wetzel and Andreas Peichl for their helpful comments and suggestions.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Harald Hecking.

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.Footnote 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
figure7

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.Footnote 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
figure8

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).

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.

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.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Löffler, C., Hecking, H. Greenhouse Gas Abatement Cost Curves of the Residential Heating Market: A Microeconomic Approach. Environ Resource Econ 68, 915–947 (2017). https://doi.org/10.1007/s10640-016-0052-0

Download citation

Keywords

  • Greenhouse gas abatement costs
  • Heat market
  • Household behavior
  • Pigou tax

JEL Classification

  • C35
  • C61
  • Q47
  • Q53
  • R21