CAPRI Market Model

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CAPRI Market Model
Current elasticity sourcesand parameter
calibration Wolfgang Britz
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Which functional forms?
CAPRI market model Functional forms
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What is parameter calibration?

• The process of defining parameters of behavioral
  functions (e.g. a supply function) at given
  quantities and prices ( the so-called
  calibration point)
• As only one point is given, a classical
  estimation is not possible (no variance in
  explanatory variables ..)
• Instead, a priori information is used, typically
  point price (and income) elasticities
• Similarities to system estimations as parameters
  for all products are defined simultaneously
  (often under regularity constraints)
• Leads to a Non-Linear Optimization Problem(find
  the best parameters under constraints ..)

CAPRI market model Functional forms
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How to find the parameters in CAPRI ..

• The CAPRI market model is synthetic
• Parameters are not estimated by CAPRI team,but
  borrowed from literature or other models
• These sources used data bases, product
  definitions, functional forms etc. different from
  the CAPRI market modelgt adjustment to our needs
  necessary
• Aim of the calibration process
• Find regular parameters close to the original
  source (typically expressed as an elasticity)
• Ensure that resulting simulation behavior is
  robust

CAPRI market model Functional forms
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How to derive robust parameters ..

• Ensure regularity coherence with behavioral
  assumptions (profit maximizing producers and
  utility maximizing consumers)
• Ensures that direction of change are in line with
  common sense
• Ensures convex solution space for the market
  model
• ensures that a gradient based solver has a
  theoretical chance to find a solution
• if convexity is global, ensures that the solution
  will be unique
• Allows welfare analysis
• Introduce bounds regarding absolute size and sign
  of certain elasticities to ensure plausible size
  of simulation responses

CAPRI market model Functional forms
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How does it work in practise

• Point elasticities must be expressed as functions
  of the functional parameters at given prices and
  quantities
• Regularity conditions are expressed based on the
  point elasticities (e.g. homogeniety ? sum of own
  and cross price elasticities is zero)

CAPRI market model Functional forms
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How to define parameters
CAPRI market model Functional forms
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The case of supply
Elsaticities are now expressed as a function of
the parameters (here nqs), prices and production
CAPRI market model Functional forms
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How it works for supply

• Search own and cross-price elasticities eij as
  close as possible to the given ones eijgiven so
  that
• (1) homogeneity,
• (2) definition of elasticities,
• (3) symmetry,
• (4) and curvature
• hold at given quantities production and prices
  ppri

CAPRI market model Functional forms
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Additional safeguards for supply

• Ensure that price elasticities are between /-10
• Ensure that cross-effects between cereals are
  negative
• Possible improvements
• Check for changes in total land used (or land for
  groups of activities), based on yield and yield
  elasticities
• or for labor or water requirements
• Further contributions weight deviations from
  given elasticities based on a priori-knowledge
  (e.g. t-statistics of elasticities)
• Analyze parameters from other global models
  (FAPRI, FAO, IFPRI ..)

CAPRI market model Functional forms
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Additional safeguards for final demand

• Remember
• Generalized Leontief Expenditure System is used
• Calculation of price and income elasticities
  somewhat more demanding than in the NQ case
• Adding up of income elasticities necessary as
  further regularity constraint
• Functional forms ensures curvatures, however at
  the price of excluding Hicksian complementarity
• Ensure that total calorie input is increasing
  with income, however, with low rates at high
  incomes
• Ensure that price elasticities are between /-10
• Ensure that income elasticities are not below
  -0.1

CAPRI market model Functional forms
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Improvements for final demand

• Possible improvements
• Again, reflect quality of information (e.g.
  t-statistics for elasticities)
• Include estimates of own price and income
  elasticities for groups of food products form
  ERS/USDA
• Check GTAP data base ..

CAPRI market model Functional forms
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Additional safeguards for feed demand

• The elasticities are substitution elasticities
  for given levels of calorie demand from animal
  production
• The cross-effects with animal production are
  hence expressed by a linear up-and-down scaling
  of total calorie demand from animal production
• The calorie demand per animal production quantity
  produced is calibrated ex post to given
  production and given feed demand
• For any price change, protein and calorie
  deliveries must (almost) stay constant

CAPRI market model Functional forms
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Additional safeguards for feed demand
CAPRI market model Functional forms
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Current sources for elasticities ..

• The so-called Food Demand Model of the FAO,
  which estimates income elasticities for a
  selected range of food products for many
  countries
• The elasticities used in the World Food Model
  of the FAO (which covers all countries, but just
  13 products)
• For the EU, rather old system estimations from
  literature (however supply elasticities are only
  determine the convergence speed between the
  supply and demand part)
• Feed demand elasticities for Germany feed
  industry estimated some years back, used for
  other countries as well

CAPRI market model Functional forms
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• Thanks for your attention

CAPRI market model Functional forms