CAPRI Market Model

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CAPRI Market Model
Functional Forms in the CAPRI Market Model
Franziska Junker
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Behavioural functions in the CAPRI market model

• Supply
• of primary products
• of dairy products
• of oils and oil cakes
• Demand functions
• Human consumption
• Feed Use
• Processing demand

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Why does the functional form matter?

• Welfare analysis requires consistency to
  micro-theory
• Homogeneity of degree zero in prices
  (inflation does not matter/only relative price
  matter)
• Correct curvature marginal profits increasing
  in prices, marginal utility decreasing in
  quantities
• Symmetry of second derivatives
• Monotonically increasing/decreasing functions
• The functional form determines, how easily the
  model can be solved

CAPRI market model Functional forms
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Which functional forms I ?

• Normalized quadratic function

CAPRI market model Functional forms
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Which functional forms III ?Derivation of the
normalized quadratic expenditure system
CAPRI market model Functional forms
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Which functional forms II ?

• Advantages of that functional form
• Homogeneity, symmetry and correct curvature can
  be imposed globally
• Linear in prices ? constant derivatives ? easy
  for solver
• Problems
• Monotonocity not guaranteed? non-positive
  quantities are possible
• Point elasticities decrease with increasing x
• Used for
• supply of primary products
• Supply of dairy products
• Feed demand
• Demand of the processing industry

CAPRI market model Functional forms
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Supply of primary products

• Supply of agricultural output i in region r

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Supply of dairy products

• Supply of dairy products i in region r

• Balancing equations ensure that the fat and
  protein content of the raw milk is exactly used
  up for milk products

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Demand for Feed

• Demand for feed i in region r

Slope term capturing own and cross-price effects
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Demand of the processing industry

• Demand of the processing industry for product i
  in region r

• Processing demand depending on processing margin,
  defined as value per unit of raw product processed

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Which other functional forms?

• Leontief
• for supply of cakes and oils
• Generalised Leontief Expenditure System
• For human consumption

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Supply of Oils and Cake

• Supply of oils and cakes in region r

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Human consumption II

• Generalised Leontief for Human consumption
• Homogeneity in prices and income guaranteed
• if all off-diagonal elements of B are positive,
  curvature is correct ? only substitutes possible!
• Monotonicity is not guaranteed

CAPRI market model Functional forms
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Human consumption I

• Generalised Leontief for Human consumption

CAPRI market model Functional forms
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Which functional forms?
CAPRI market model Functional forms
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Thank you for your attention!
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Which functional forms II ?

• Normalised quadratic for supply, feed and
  processing demand

• Advantages of that functional form
• Linear in prices gt constant derivatives gt easy
  for solver
• Homogeneity, symmetry and curvature can be
  imposed globally
• Problems
• Monotonicity not guaranteed? non-positive
  quantities are possible
• Point elasticities decrease with increasing x

CAPRI market model Functional forms
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Which functional forms III ?
Non-symmetric normalized profit function, used
for post-model welfare analysis
Hotelling lemma
Supply functionused in market model
Supply effects are equal to symmetric matrix B?
regularity requires marginal profits not
decreasing in prices, fulfilled if matrix B
is definite? can be imposed by Cholesky
decomposition
CAPRI market model Functional forms
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Which functional forms IV ?

• Generalised Leontief for Human consumption

• Homogeneity in prices and income guaranteed
• if all off-diagonal elements of B are
  positive,curvature is correct ltgt only
  substitutive relations !
• Monotonicity is not guaranteed

CAPRI market model Functional forms
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How to find the parameters

• 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 model gt adjustment to our needs
  necessary
• In order to improve plausibility and ensure
  regularity, parameters are calibrated under
  regularity conditions
• Aim find regular parameters close to the
  original source (typically expressed as an
  elasticity)

CAPRI market model Functional forms
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How to define parameters
CAPRI market model Functional forms
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How it works for NQ case

• Search own and cross-price elasticities eij as
  close as possible to the given ones eijgiven so
  that (1) homogeneity,(2) definition of second
  derivatives, (3) symmetry,(4) and
  curvaturehold at given quantities q and prices p
• The H matrix is equal to the Bmatrix of the NQ
  for supply and feed,if the price index pn is set
  to unity in the base year

CAPRI market model Functional forms