1. Linking the TIMES model for Spain to a dynamic macroeconomic IO model:
Some initial thoughts
Sevilla, 2017
Kurt Kratena CESAR

2. Overview
Development of the DYNK (DYnamic New Keynesian) model for Spain: new K,L,E,M database (SUT, 1995 – 2010)  estimation of production model
Link between the TIMES and the DYNK model: Technologies of electricity/heat generation in TIMES – physical Energy Balances – K,L,E,M production block in the DYNK model
Specific link: deriving elasticity of substitution K/E and other parameters from stochastic simulations with the TIMES model
Analytical potential of the approach and further research

3. The new K,L,E,M database for Spain
SUT Spain, 1995 – 2010 (INE), Classification 2 and 3 digits NACE, but structural breaks: , , , 2010  consistent data set for agriculture/mining/manufacturing/construction/trade (not for the rest of services), 1995 – 2007.
Construction of price indexes for E(nergy) and M(aterials): domestic price (Spain) and import price (INE, EUROSTAT, WIOD,…)
Import price: weighted output price of countries of origin (Estadísticas del comercio exterior español, Encuesta de Comercio Internacional de Servicios)
1995 – 2010: Tabla de destino de la producción interior (QDeg,s,a), Tabla de destino de las importaciones(QIMeg,s,a)
Price of domestic/imported goods previously calculated (pDg,a & pIMg,a)
Non-energy goods (g):
pMs,a= ∑g(QDg,s,a+QIMg,s,a)/∑g[(QDg,s,a/pDg,a)+(QIMg,s,a/pIMg,a)], Price of M
Energy goods (eg):
pEs,a= ∑eg(QDeg,s,a+QIMeg,s,a)/∑eg[(QDeg,s,a/pDeg,a)+(QIMeg,s,a/pIMeg,a)] , Price of E

4. The new K,L,E,M database for Spain
Construction of price indexes for L(abor) and K(= capital)
From SUT (Tabla de destino) Spain: Remuneración de asalariados (QLs,a), Puestos de trabajo equivalentes a tiempo completo, Asalariado (Ns,a)
Wage rates: ws,a=QLs,a/ Ns,a  Index of wage rates, 1995=100: pLs,96=100*ws,95/ws,96
Price of K: user costs of capital (interest rate r = 0.04 and depreciation rates dj by industry (EUKLEMS)): user cost in industry j = pINV,j (r + dj)
User costs: pINV,j (r + dj)  Index of user costs, 1995=100: pK
Price of investment, pINV,j: multiplying the row vectors of domestic (pD) and import prices (pIM) with the investment matrices: pINV = pIM[mK,D * BK]+ pD[(1-mK,D)* BK]
Capital input matrix ESP (industry/commodity classification of SUT/ESP): One matrix for domestic (D) and one for imported (IM) parts: BK,D = mK,D * BK and BK,D = (1-mK,D)* BK, where mK,D is the import share by commodity

5. The K,L,E,M model block within the DYNK model
Factor demand for E and M is split up into IO columns by „Use structure matrices“ SE and SM for domestic and imported goods.
Factor demand for K drives investment by industry, which with matrices [mK,D * BK] and [(1-mK,D)* BK] is converted into the IO investment vector
Factor demand for L determines wage income (part of disposable household income by quintiles)
Other model blocks: private consumption (durables/nondurables, energy), trade (Armington for final and intermediate demand), wage curves (industry/occupation), public sector

6. Linking the K,L,E,M data to TIMES & Energy Balance (IEA)
K,L,E,M dataset: Factor shares in all industries (j) are defined by:
Link to TIMES: involves all factor shares in electricity sector (NACE 401), technologies p differ by investment costs (K), operation & maintainance costs (L and M), and energy costs (E).
Link to Energy Balance: involves factor share for energy costs (E) in electricity sector
General data link (for TIMES & Energy Balance): the factor share at the K,L,E,M level vi is the weighted sum of the products of output shares by technology wq,p and the cost share by technology, vi,p.
Data from Energy Balance: physical data by technology (more aggregate than the TIMES technologies): output electricity and input energy (main producers) from/of k energy types in TJ  conversion efficiency ( = physical input coefficient)

7. Linking the K,L,E,M data to TIMES & Energy Balance (IEA)
Link between monetary flows (Tabla de Destino) and physical flows (Energy Balance): implicit prices: monetary/physical data by technology (all k energy type inputs, electricity output).
Cost share energy, vE( p) = (1/conversion efficiency) * (pE,p/ pEl), where pE,p is the implicit price of the energy type (k) used in technology (p) and pEl is the imlicit output price of electricity.
Linking of vE (p) to vE: Multiplying this cost share vE,p with the corresponding output share wE (p,q) and summing up gives the energy cost share of the K,L,E,M dataset:
Inter-fuel substitution: At a second nest, the input of the energy bundle E is split up into k energy types
Consistent data set (no structural break in classification):

8. K,L,E,M data set: Factor cost shares in electricity

9. K,L,E,M data set: Factor cost shares in electricity

10. Energy Balance: Output shares in electricity production

11. Energy Balance: Efficiency in electricity production

12. Linking the K,L,E,M data to TIMES: Some theory
Translog model for K,L,E,M and for inter-fuel substitution: the explicit cost share of energy
For some technologies (p) vE = 0 and vK is significantly higher than the average (wind, PV)
Decomposition of the price parameters (giE, i.e. reaction of (mainly) vE, vE,i, and vK to changes in prices of energy type k):
When pE,k changes: changes of vE,i  new aggregate price pE  changes in wE (p,q) can be related to changes in pE,k and pE.

13. Linking the K,L,E,M data to TIMES: Some theory
Stochastic simulations with TIMES: changes in pE,k and measuring the
output share reaction
The second term is equal to the cost share of the technology vi(p)
Bataille et al. (2006) suggest creating ‚pseudo‘ data by these stochastic simulations for regression analysis. Alternative: directly calculating the Translog parameters by applying the identity
This term is part of the derivation of the substitution elasticity (most important for policy analysis: between K and E)
Simulation of a long-run scenario without price changes with TIMES: decomposition of the autonomous change in the share (technology trend):

14. Linking the K,L,E,M data to TIMES: Some theory
Interpreting the average change in wE (p,q) between 1995 and 2007 completely as trend
Applying
This gives a negative autonomus energy efficiency increase (AEEI)
(dvi/dt) = , mainly due to the large increase in the output share of natural gas.

15. Analytical potential and future research
Finalizing the K,L,E,M database after 2007 and estimation of Translog-model (K,L,E,M and inter-fuel substitution)
Linking Translog model to TIMES and derivation of elasticity of substitution & comparison to values of estimated Translog model  journal article/conference presentation
Rebuilding the full DYNK model: new IO database, external trade, private consumptIon (quintiles)
Model simulations with the linked model (full new DYNK): different scenarios for renewables in electricity generation: (i) funding schemes, (ii) new diffusion of technologies, (iii) price instruments  projects for Ministry (?) on the future of renewables in Spain