stiftelsen frischsenteret for samfunnsøkonomisk forskning ragnar frisch centre for economic...
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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