Representing Heterogeneity in CGE Modeling: Application to Housing in GEMINI-E3

Representing Heterogeneity in CGE Modeling:

Application to Housing in GEMINI-E3

Alain Bernard - Ecole Polytechnique (France) Marc Vielle - Ecole Polytechnique Fédérale de

The Challenge of Long Term Climate Change

Modeling

• Starting point: there is a limited scope for GHG abatement with presently implemented or contemplated policies

• In the long run, for more ambitious targets (Factor 2, Factor

4), there is the need of a thorough change in the

structures of the economy

• Economic structures are embedded in the stock of capital

• A specific issue: the heterogeneity of productive capital

– Obviously between sectors (e. g. infrastructure capital between transport modes)

Plan of the presentation

• Some supporting figures for the French Economy • The issue of heterogeneity in the housing sector

• Its representation and calibration in the framework of a CGE model

• Results

– Profitability of insulation investments – Some policy scenarios

I. Some figures for the French economy

The total capital stock represents in value more than 5 times the annual GDP and 60 times the annual energy consumption

Two major sectors: Housing and Transport infrastructure (60% of total stock, small rate of decay)

Marginal global net productivity of capital : 3.8% (benchmark for profitable new investments)

Gross capital stock (2006, mios Euro)

Amount Rate of decay

Housing 4380 0.5% Transport infrastructure 728 1.0% of which: Roads 457 Railways 47 Other 224 Other sectors 2978 4.7% Total economy 8086

Some figures for the French economy (con’t.)

Transports and Housing represent 75% of final energy consumption and 56% of CO2 emissions (67% excluding energy transformation)

Final energy consumption and CO2 emissions by sector in 2007

Sector CO2 emissions (mios T) Final consumption (in mios TOE)

Agriculture 10 2.8 Energy transformation 70 Industry 96 37.1 Transports 136 51.6 Housing 84 70.6 Total 396 162.1

II. The issue of heterogeneity in the housing sector:

data on thermal efficiency

Very large dispersion of (reference) energy consumption according to classes (more than 75% poorly insulated)

Lack of detailed data on effective conditions of utilization and consumption LEB: Low Energy Buildings; PosEB: Positive Energy Buildings

Breakdown of the Housing Capital Stock by Thermal Performance

date of thermal Primary energy Share in total

regulation consumption stock (in m2)

(kWh/m2) Class G >450 15% Class F 331 to 450 9% Class E 231 to 330 23% Class D 151 to 230 32% Class C 2005 91 to 150 19% Class B 51 to 90 3% Class A (LEB) 2012 <50 1% Class A+ (PosEB) 2020 <0 0% Total 100%

Representing the housing sector in a CGE model

• General tool: nesting factors or demands according to a tree-structure • Calibration from the quantities and the prices in the base year

• The technical issue: prices and quantities are known at the aggregate level, not for each class of buildings

• The implemented approach: introducing an index of comfort (linked to average heating temperature) and simulating the equilibrium in the housing market

The stakes of Thermal Renovation

Catégorie de logement 1 2 3 4 5 6 7 8

Classe DPE G F E D C B A A+

Consommation référence (par m2) r1 >> r2 >> r3 >> r4 >> r5 >> r6 >> r7 >> r8

> > > > > = < <

Consommation effective c1 c2 c3 c4 c5 c6 c7 c8

Température moyenne chauffage t1 < t2 < t3 < t4 < t5 < t6 < t7 < t8

Confort u₁ u₂ u₃ u₄ u₅ u₆ u₇ u₈ Valeur immobilière p1 p2 p3 p4 p5 p6 p7 p8

Parc de logements (en m2) K₁ K₂ K₃ K₄ K₅ K₆ K₇ K₈

Transition G à B -1 1

Var. consom. Référence r2-r6

>

Var. consom. Effective c₂-c₆

< Var. consom. Temp. Constante c2-c'6

III. Modeling the housing sector in a CGE model

Nest of each type of building :

[

( )

]

1 − −

− _{+ −}

=k K C

U

Average heating temperature function of energy consumption by square m2_:

( )

Index of comfort function of temperature: q=1−c

( )

Expression of comfort in terms of the nest parameters

with :

Condition of consistency: individual comfort curves must coïncide with the global one (in fact be enveloped by the latter)

Competitive equilibrium in the housing market

• Theorem : With a continuum of classes, market equilibrium is such that the expenditure functions have a linear envelop going through the origin

• Corollary : the price of comfort is constant

• NB: this approach is analogous to the bid-rent curve of the urban monocentric model (Nash equilibrium)

• The two « envelop » conditions determine completely the equilibrium, i. e. the rent, the energy consumption, the average heating temperature and the comfort for each class of buildings (and the parameters of the nests)

Total expenditure of the consumer : D = rK + πC

Lemma : for each class of building, the log-derivative of the expenditure function at the equilibrium is equal to 1 :

Competitive equilibrium of the housing market -results by unit of capital G F E D C B A (LCB) A+ (PosEB) Capital 1 1 1 1 1 1 1 1 Rent 0.891 0.928 0.981 1.032 1.071 1.105 1.137 1.169 Energy consumption 0.176 0.168 0.145 0.113 0.085 0.058 0.030 0.000 Temperature 13.7 14.6 15.9 17.1 18.1 19 20.0 22 Total expenditure 1.068 1.096 1.126 1.146 1.156 1.163 1.167 1.169 Comfort 0.913 0.938 0.963 0.980 0.989 0.995 0.998 1 μ 0.33500 0.75224 1.48210 2.48979 3.69159 5.55663 5.55663 θ 0.90055 0.95487 0.99166 0.99951 0.99999 1.00000 1 k 1.14454 1.10037 1.05111 1.02196 1.01002 1.00411 1.00312 1

The rent (value of capital) is increasing with the level of thermal performance The same for temperature, comfort and total expenditure

Effective energy consumption on the contrary is decreasing with the level of thermal performance

The range of effective energy consumption (1 to 6) is much smaller than the range of theoretical consumption (1 to 13)

Comfort Index Curve 0.7 0.75 0.8 0.85 0.9 0.95 1 10 12 14 16 18 20 22

Average heating temperature

Comfort Index

Class G Class F Class E Class D Class C Class B Class A Envelop Curve

Total housing expenditure in function of comfort 1.05 1.07 1.09 1.11 1.13 1.15 1.17 1.19 1.21 1.23 0.9 0.925 0.95 0.975 1 Comfort Index

Total housing charges (rent and heating

)

Class G Class F Class E Class D Class C Class B Class A Class PosEB Envelop Curve

The Rebound Effect

Theoretical and Effective Energy Consumption - The Rebound Effect

G F E D C B A Energie+ Average

(LCB) (PosEB)

Theoretical consumption 0.355 0.287 0.205 0.138 0.094 0.058 0.027 0 0.189

(at reference temperature)

Effective consumption 0.176 0.168 0.145 0.113 0.085 0.058 0.030 0 0.128

Average heating temperature 13.7 14.6 15.9 17.1 18.1 19 20.0 22 16.3

Confort index 0.914 0.938 0.963 0.980 0.989 0.995 0.998 1 0.965

Transition to class B

Theoretical energy decrease 0.297 0.229 0.147 0.080 0.035 0.000 -0.031

Effective energy decrease 0.118 0.110 0.087 0.055 0.027 0.000 -0.028

Rebound effect 1 60.3% 52.0% 41.1% 30.9% 23.1% 8.8%

Cons. Const. Temperature 0.029 0.034 0.041 0.048 0.053 0.058 0.064 Rebound effect 2 50.4% 41.5% 29.4% 17.9% 8.8% 0.0% -9.9%

Main teachings and conclusions

• General conclusion: Importance of taking into account the heterogeneity of capital for a relevant analysis of rigidities in the structures of the economy

• A more specific one: insulation investments are not very profitable under present conditions

– Even with thermal regulation (RT 2012 and RT2020), a high carbon (Quinet) and subsidies to insulation investments, Factor 4 in the housing sector appears out of reach

– Energy price increases after 2030 not contemplated in present scenarios may further help the 2050 target

• Not taken into account: changes in the energy mix (biomass, heat networks), technical progress in energy efficiency (Heat pumps)

• A major uncertainty: the energy mix in electric generation (nuclear)