Day 5: Multi-Market Models
Day 5 NotesHowitt and Msangi 1
 We have now gone through half of our taxonomy of
models – so that we can now address mkt-level
interactions in detail
St...
 We have seen how the outputs of one model can inform a
different kind of model
Static Dynamic
Micro-level
Farm productio...
 Understand the basics of a Multi-Market Model
 Consider the theoretical underpinnings of such
models – and their wide v...
 There are various types of partial-equilibrium models that try and model
interactions between markets
 They are ‘partia...
 Used for partial equilibrium analysis of the impact of changes
in prices and quantities in selected markets on other mar...
There is a wide variety of PE multi-market models. There is no standard template
for these models – they vary according to...
 Although there is a wide variety in PE model
elements – most models contain some of these
components:
◦ Price responsive...
Day 5 NotesHowitt and Msangi 9Day 5 NotesHowitt and Msangi
Factor
supply
Factor
demand
Supply
of goods
Demand
for goods
Fa...
Day 5 NotesHowitt and Msangi 10
Factor
supply
Factor
demand
Factor markets
Profit-
maximizing
producer
Prices, quantities&...
 Data Requirements
◦ Used to analyze induced substitution effects across
selected goods in response to policy and shocks
...
 We consider an inter-regional water trade
example
 Regions ( i and j ) trade good x
◦ Trading cost c
 Supply and deman...
 We can define the primal model as:
Day 5 NotesHowitt and Msangi 13
1 1
max ( ) ( 0.5 ) ( 0.5 )
0
J I
j j j j i i i i
j i...
 Calibrating Demands Using Elasticity Estimates
◦ Deriving parameters for demand and supply with only
equilibrium price a...
 We can formulate the dual of the water trade
problem
 Supply and demand (price-dependent) is
linear and given by:
Day 5...
 We can define the dual model as:
Day 5 NotesHowitt and Msangi 16
2 21 1
2 2
1 1
min ( ) ( ) ( )
0
I J
i i i i j j j j
i ...
 California Water Trade Example
 The GAMS code illustrates the dual water trading
problem
 Regions
◦ North Sacramento V...
 Another example from California – based on the
work of Kazim Konyar (1985 dissertation)
 Looks at the market for alfalf...
 The model tries to address some important gaps
that the author perceived in the literature
 Many of the existing studie...
 Therefore, Kazim Konyar built a dynamic spatial
equilibrium model that embodies 2 key elements:
◦ A spatial equilibrium ...
 Alfalfa has a number of interesting properties
◦ High in protein & palatability – means “best fodder” in
Arabic
◦ Remain...
 Therefore, the example of alfalfa combines a
number of key elements that make it
interesting
 Have to make a conscious ...
 GAMS code from Minot (2009) has been
provided as part of the course materials
 This provides a very good basis upon whi...
 This model runs without an explicit optimization
criterion (objective) – but profit- & utility-
maximizing behavior are ...
 Some key concepts that underlie the price
relationships in this model are:
◦ The CIF (cost-insurance-freight) price – wh...
 If we consider the transportation costs of
getting goods to the interior of the country:
◦ The cost of importing is abov...
 Trade is determined by price relationships:
◦ If autarky price (Pa) > IPP – country will import
◦ If autarky price falls...
 The model also considers the effects of trade
policies (taxes & quotas)
◦ Import tax raises the domestic price above CIF...
Day 5 NotesHowitt and Msangi 29
( ) ( )
Regs Regsother other
Supply inflows outflows
iMport Demand eXprt
+ −
+ = +
∑ ∑
exp...
Day 5 NotesHowitt and Msangi 30
,(X) R RR
RR
Quota X≥ ∑
,( ) R RR
RR
Quota I M≥ ∑
exp p, , ,inflows,outflows,ImTax ,ImTax
...
 Now we will look at several things in the
model:
◦ Talk through the model to understand the equations
◦ Compare the mode...
of 31

Biosight: Quantitative Methods for Policy Analysis: Multi Market Models

Biosight: Quantitative Methods for Policy Analysis: Multi Market Models
Published on: Mar 3, 2016
Published in: Education      
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Transcripts - Biosight: Quantitative Methods for Policy Analysis: Multi Market Models

  • 1. Day 5: Multi-Market Models Day 5 NotesHowitt and Msangi 1
  • 2.  We have now gone through half of our taxonomy of models – so that we can now address mkt-level interactions in detail Static Dynamic Micro-level Farm production models Resource management models Macro-level Multi-market equilibrium models Growth models
  • 3.  We have seen how the outputs of one model can inform a different kind of model Static Dynamic Micro-level Farm production models Resource management models Macro-level Multi-market equilibrium models Growth models Derived factor demands Benefit functionSupply response Decision rule
  • 4.  Understand the basics of a Multi-Market Model  Consider the theoretical underpinnings of such models – and their wide variety  Look at some specific examples: ◦ Consider a model of water trade in which the inter- regional trade model is specified in primal and dual forms ◦ Manipulate the model and calibrate demands with elasticities from prior estimates ◦ Consider a multi-good, multi-region model in which there is more policy content related to trade – and in which the optimization criterion are not as obvious as in the water trade model Day 5 NotesHowitt and Msangi 4
  • 5.  There are various types of partial-equilibrium models that try and model interactions between markets  They are ‘partial-equilibrium’ b/c they don’t try and capture all the transactions and financial flows that happen within an economy  They try and focus on the markets of interest and represent supply, demand and trade – and how various policies and drivers of change might affect those Day 5 NotesHowitt and Msangi 5 Single region Multiple regions Single good Very simple – single demand and supply curve We will look at a spatial equilibrium model Multiple goods The SWAP example was similar to this – can be any single- country model The most common type – we will look at an example with 4 goods & 6 regions
  • 6.  Used for partial equilibrium analysis of the impact of changes in prices and quantities in selected markets on other markets  The analyst may not want to consider the entire economy and how the macro-level balances occur at the level of national accounts (like CGE models) – but some models do allow for more economy-wide perspective than others (for particular goods/markets) ◦ Examples:  Poverty and distributional impact of commodity price policies  Distributional impacts of subsidies and taxes  Distributional impacts of tariffs and quotas  Impacts of changes in prices of imported or exported commodities  Evaluation of external shocks and policies on individual sectors of the economy Day 5 NotesHowitt and Msangi 6
  • 7. There is a wide variety of PE multi-market models. There is no standard template for these models – they vary according to the needs of the analyst  Some models ignore factor markets entirely – while others try and model the key ones like labor or fertilizer (for ag models)  Some models ignore the flows of revenues between production activities and consumer households and the interventions of government – while others try and capture the payment of wages to households, the revenue from taxes to government (and its transfers to households), or the share of production profits that are captured by households  Some build their structure very closely on theory (in the demand & supply of both goods & factors) – while others are completely ad-hoc in their specification  The underlying paradigm of optimization is still there – although it might not be modeled as explicitly as what we’ve seen so far Day 5 NotesHowitt and Msangi 7
  • 8.  Although there is a wide variety in PE model elements – most models contain some of these components: ◦ Price responsiveness & flexibility ◦ Multi-agent representation (producers, consumers, etc) ◦ Trade (or non-tradeability) of goods & factors ◦ Tend to be at a more macro-level compared to the models that we’ve been looking at, so far Day 5 NotesHowitt and Msangi 8
  • 9. Day 5 NotesHowitt and Msangi 9Day 5 NotesHowitt and Msangi Factor supply Factor demand Supply of goods Demand for goods Factor markets Product markets Profit- maximizing producer Prices, quantities & trade of factors Prices, quantities& trade of products Non-ag income Agricultural profit Hhold income Hhold characteristics Population Per capita Hhold income factor income Demand technologies, Fixed factors
  • 10. Day 5 NotesHowitt and Msangi 10 Factor supply Factor demand Factor markets Profit- maximizing producer Prices, quantities& trade of factors Households factor income Profit fcn: , , : , , k k k k k k T w NE x NT NE w x , ,k k kw x NE d kxs s h kh k h N x x=∑ ( )Π  Some models allow households to sell certain factors of production (labor) and receive income from them
  • 11.  Data Requirements ◦ Used to analyze induced substitution effects across selected goods in response to policy and shocks ◦ Multi-market models involve a system of equations representing a sub-set of the economy ◦ Examples:  Disaggregate income and/or consumption data across households  Supply and demand functions for all markets in the model (and cross-effects)  Specify model closure (domestic and rest-of-world markets)  Mathematical specification mapping endogenous variables into the income and consumption of households and other markets  See the discussion in Chapter 11 of Sadoulet & De Janvry book Day 5 NotesHowitt and Msangi 11
  • 12.  We consider an inter-regional water trade example  Regions ( i and j ) trade good x ◦ Trading cost c  Supply and demand (quantity-dependent) is linear and given by: Day 5 NotesHowitt and Msangi 12 j j j j i i i i pd xd ps xs φ δ α γ = + = +
  • 13.  We can define the primal model as: Day 5 NotesHowitt and Msangi 13 1 1 max ( ) ( 0.5 ) ( 0.5 ) 0 J I j j j j i i i i j i ij ij i j i ij j j ij i ij F xd xd xs xs c x subject to xs x xd x x φ δ α γ = = + − + − = = ≥ ∑ ∑ ∑∑ ∑ ∑ 
  • 14.  Calibrating Demands Using Elasticity Estimates ◦ Deriving parameters for demand and supply with only equilibrium price and quantity data in the base year for the model, and an estimate of the elasticity from a previous econometric study.  Using derived demands from programming models ◦ Given what we covered in Day 1 and 2 – we know that if we have a well-specified production model for agriculture that captures the decision-maker’s response to resource availability adequately – we can use the shadow values that come out of that model to derive our demand curve for that factor of production – which could be water (among others) Day 5 NotesHowitt and Msangi 14
  • 15.  We can formulate the dual of the water trade problem  Supply and demand (price-dependent) is linear and given by: Day 5 NotesHowitt and Msangi 15 j j j j i i i i xd a s pd xs b g ps = + = +
  • 16.  We can define the dual model as: Day 5 NotesHowitt and Msangi 16 2 21 1 2 2 1 1 min ( ) ( ) ( ) 0 I J i i i i j j j j i j j i ij F b g ps a s pd subject to pd ps c γ δ = = = + − + − − ≤ ∑ ∑
  • 17.  California Water Trade Example  The GAMS code illustrates the dual water trading problem  Regions ◦ North Sacramento Valley ◦ Southern San Joaquin Valley ◦ Bay Area ◦ Los Angeles  The model maximizes the net social benefit of water trade, taking into account transfer costs. Day 5 NotesHowitt and Msangi 17
  • 18.  Another example from California – based on the work of Kazim Konyar (1985 dissertation)  Looks at the market for alfalfa in California (which is an important feed crop for dairy, esp)  He builds a multi-region model ◦ 15 producing regions in California ◦ 4 consuming regions ◦ 13 deficit regions ◦ He wants to account for the heterogeneity across space  He uses a dynamic spatial equilibrium model to capture the market interactions and perennial acreage response of alfalfa (in response to price) Day 5 NotesHowitt and Msangi 18
  • 19.  The model tries to address some important gaps that the author perceived in the literature  Many of the existing studies were incomplete ◦ Only looked at the demand or supply – but not both ◦ The few that did have both – were only suitable for short-term (one year ahead) predictions ◦ Most of them left livestock & feed demand completely out of the picture  The California-wide (CARM) model of UC Berkeley used a programming approach but ◦ Treated alfalfa as an annual crop ◦ Was purely static ◦ Had aggregate (statewide) demand that could not capture the regional price differences Day 5 NotesHowitt and Msangi 19
  • 20.  Therefore, Kazim Konyar built a dynamic spatial equilibrium model that embodies 2 key elements: ◦ A spatial equilibrium model of alfalfa trade ◦ Dynamic acreage response equations that respond to prices from the equilibrium model  Therefore the model solves fwd recursively ◦ Given a price in period t  get acreage in period t+1 (from response function)  which determines the price in t+1  leads to new prices in t+2, etc…..  The model is solved forward in this recursive fashion for 11 years Day 5 NotesHowitt and Msangi 20
  • 21.  Alfalfa has a number of interesting properties ◦ High in protein & palatability – means “best fodder” in Arabic ◦ Remains in the field 3-5 yrs (or 6-7 in N Calif) ◦ Get the 1st cutting 6 months after establishment  Some interesting feedbacks in management ◦ The # cuttings/yr affects the stand life – get more yld with frequent cuttings but need to re-establish sooner ◦ Cutting just b/f bloom gives best quality (high in digestible protein & other nutrients) – but this weakens the stand and leads to lower yield in future ◦ Alfalfa is water intensive ◦ Fixes N & improves soil structure/drainage –therefore it is rotated with other crops ◦ But this rotation also benefits alfalfa (re: pest, disease) Day 5 NotesHowitt and Msangi 21
  • 22.  Therefore, the example of alfalfa combines a number of key elements that make it interesting  Have to make a conscious choice of what to model ◦ The perennial nature of the crop – and implications for land use (wrt other crops in the field) ◦ The nutrient/water interactions & properties ◦ The trade-offs in yield (harvest intensity) vs frequency of re-establishment -- or that between harvest timing and the future yield effects  Read the dissertation to get the details Day 5 NotesHowitt and Msangi 22
  • 23.  GAMS code from Minot (2009) has been provided as part of the course materials  This provides a very good basis upon which to understand a multi-market model which has: ◦ Multiple goods ◦ Multiple regions ◦ Regional trade ◦ International trade ◦ Trade policy instruments Day 5 NotesHowitt and Msangi 23
  • 24.  This model runs without an explicit optimization criterion (objective) – but profit- & utility- maximizing behavior are assumed to prevail, and certain no-arbitrage conditions are maintained  Like the spatial equilibrium trade model, the model allows for differences in prices across regions which determines the flow of goods  The 7th regions is the “World” which allows you to consider the effects exchange rates and trade policy Day 5 NotesHowitt and Msangi 24
  • 25.  Some key concepts that underlie the price relationships in this model are: ◦ The CIF (cost-insurance-freight) price – which is the LR equilibrium import prices that puts an upper bound on prices at the port ◦ The FOB (free-on-board) price which is the LR export price that puts a lower bound on prices @ port ◦ These are the key prices at the border which are linked to the international price (and policy) Day 5 NotesHowitt and Msangi 25
  • 26.  If we consider the transportation costs of getting goods to the interior of the country: ◦ The cost of importing is above CIF –> (CIF + TC = import parity price), which defines the relevant upper bound on prices within the interior ◦ The price received for exports originating from the interior are lower than the FOB -> FOB-TC = export parity price which is the new lower bound on prices in the interior ◦ The regional prices move relative to IPP/EPP Day 5 NotesHowitt and Msangi 26
  • 27.  Trade is determined by price relationships: ◦ If autarky price (Pa) > IPP – country will import ◦ If autarky price falls in b/w IPP and EPP (i.e. IPP>Pa>EPP) – then no trade occurs ◦ If autarky price falls below the EPP – exports occur  Therefore, the price relationships within the model endogenize the flows of trade – similar to the spatial equilibrium model we saw Day 5 NotesHowitt and Msangi 27
  • 28.  The model also considers the effects of trade policies (taxes & quotas) ◦ Import tax raises the domestic price above CIF ◦ Export tax lowers the domestic price below FOB ◦ Quotas on imports serve to restrict domestic supply and raises prices – like an implicit tax on imports ◦ Quotas on exports serve to raise domestic supply and lower prices – like an implicit tax on exports  Both the explicit and implicit import & export taxes are treated in the model (the implicit ones coming from quotas are endogenous, whereas the ones determined by explicit policy are fixed) Day 5 NotesHowitt and Msangi 28
  • 29. Day 5 NotesHowitt and Msangi 29 ( ) ( ) Regs Regsother other Supply inflows outflows iMport Demand eXprt + − + = + ∑ ∑ exportImreg MP TC Tax P+ + ≥ portImM im regP TC Tax P+ + ≥ ( , y)DDemand f P= ( )SSupply f P= ,regionR R RR regionRRP TC P+ ≥ Domestic market balance Export price relationships Import price relationships Domestic demand Domestic supply Domestic trade price relationships
  • 30. Day 5 NotesHowitt and Msangi 30 ,(X) R RR RR Quota X≥ ∑ ,( ) R RR RR Quota I M≥ ∑ exp p, , ,inflows,outflows,ImTax ,ImTax , reg orts im ortsX M P Demand Supply ( )1x worldP NER P t= × × − ( )1M worldP NER P t= × × + , , , ( ), ( ),TC,t, NERM X worldP P P Quota I Quota X Quota on exports Effect of export tax on effective FOB price Quota on imports Effect of import tax on effective CIF price Endogenous variables Fixed parameters
  • 31.  Now we will look at several things in the model: ◦ Talk through the model to understand the equations ◦ Compare the model that reads in data using the usual “table” format to the one that uses the GDX utility to read in data directly from Excel ◦ Run the model ◦ Look at the outputs ◦ Do some experiments – to test the behavior of the model Day 5 NotesHowitt and Msangi 31