Stiftelsen frischsenteret for samfunnsøkonomisk forskning

Ragnar Frisch Centre for Economic Researchwww.frisch.uio.no

Two calibration submodels in

LIBEMOD

Sverre A.C. Kittelsen

Ragnar Frisch Centre for Economic Research

Problem 1. Calibrating final demand

• Linear demand functions not consistent outside calibration point

• Too flexible in cross-price elasticities• Corner solutions possible

– Zero demand or zero prices

• No easy period demand functions– Share functions possible for periods– Then why not use share functions for all model

final demand?

Ragnar Frisch Centre for Economic Research

Constant Elasticity of Substitution (CES) demand systems

• Flexible in structure• Consistent behaviour globally, thus also

reasonable elasticities• Exact calibration of own- and crossprice

target elasticities not possible– Because target elasticities may not be

consistent

• CES is homogenous of degree 1 – Without shift parameters, income elasticity is

allways 1

Ragnar Frisch Centre for Economic Research

CES and linear demand functions

p

x

p0

x0

Ragnar Frisch Centre for Economic Research

CES Nested Utility tree

PM o n ey

P GG a s u s ing

GG as

R GG a s n e st

P OO il u s ing

OO il

R O IO il n e st

P EE le c tric ity u s ing

S NS u m m er N ig h t

S DS u m m e r D ay

S US u m m er

W NW in te r N ig h t

W DW in te r D ay

W iW in te r

EE le c tric ity

R EE le c tric ity n e st

P CC o a l u s ing

CC o a l

R CC o a l n e st

P BB io us ing

B MB io m a ss

B FB io fu e l

B IB io

R BB io n e st

RE n erg y re la te d co n su m p tion

TU tilit y

Endogenous commoditiesExogenous commoditiesNests

- substitution parameters Nodes = Nests+Commodities

x - quantities p - prices

Goods = Nodes – {T}a - share parameters

Ragnar Frisch Centre for Economic Research

Calibration:• Demand function parameters determined by calibration

submodel:

• Some reasonableness restrictions (e.g. 0<sigma<2.5)• Calibration demand level allways on target• Income elasticities allways on target• Own price elasticities usually near target• Cross price elasticities often far from target

( )2

( )

( ) Target( ( ))j j

i ii iI i

i

j p i p ii j

I pxx xElast x

x I

Min Share Elast x Elast xs

++=

-

å

å å

Ragnar Frisch Centre for Economic Research

Problem 2: Electricity block calibration

• Unknown fuel efficiency distribution– Only average country-technology efficiency

known

• Observed behaviour deviates from optimal• Period production from each technology

unknown

Ragnar Frisch Centre for Economic Research

Unknown fuel input requirement function (inverse efficiency

distribution)

Period CapacityY

Best

0 1E

E E Emtlmjtl ml ml mtl ml mtl

t

yx y y

mlt

Ragnar Frisch Centre for Economic Research

Unknown period production by technology

Period tWinterDay WinterNight SummerDay SummerNight Sum

Technology lreservoir - pumped 5.925

run-of-river 18.375 gaspower 97.084

steamcoalpower 120.693 lignitepower 138.255

oilpower 9.438 wastepower 10.869

biopower 24.636

windpower 38.637

solarpower 6.577

GTWO 6.423 nuclear 127.690

Net import -18.293 157.423 144.996 147.005 139.167 586.309

Ragnar Frisch Centre for Economic Research

Constrained cost minimisation• Usual problem, each agent maximizes profit

• FOC:

• Calibration problem, each country minimizes short run costs

• FOC:

( ) , , .

. . technology constraints

E YE E KPR PR P inv inv Nml mt mtl mt mtl ml ml ml

t T

P y P K C c K m M l L

s t

00

Min C

s.t. technology constraints

and ,

Pml

E E E Emtmlt ml mtl

t ly y y y

10 0YE O M m T E

mt ml mtl ml mtl mul ml tl ml mtlt

P c ø y

10 0YE O M m E

mt ml mtl ml mtl mul ml tl mtlt

P c y