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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
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
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
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
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
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
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
Day 5 NotesHowitt and Msangi 9Day 5 NotesHowitt and Msangi
Factor supply
Factor demand
Supply of goods
Demand for goods
Factor markets Product marketsProfit-
maximizing producer
Prices, quantities & trade of factors
Prices, quantities& trade of products
Non-ag income
Agricultural profit
Hhold income
Hhold characteristics
PopulationPer capita Hhold income
factor income
Demand
technologies,Fixed factors
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 xNT NE w x
, ,k k kw x NE
dkx
s sh kh k
hN x x=∑ ( )Π
Some models allow households to sell certain factors of production (labor) and receive income from them
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 Janvrybook
Day 5 NotesHowitt and Msangi 11
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 xdps xs
φ δ
α γ
= +
= +
We can define the primal model as:
Day 5 NotesHowitt and Msangi 13
1 1max ( ) ( 0.5 ) ( 0.5 )
0
J I
j j j j i i i ij i
ij iji j
i ijj
j iji
ij
F xd xd xs xs
c x
subject toxs x
xd x
x
φ δ α γ= =
= + − +
−
=
=
≥
∑ ∑
∑∑
∑
∑
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
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 pdxs b g ps
= +
= +
We can define the dual model as:
Day 5 NotesHowitt and Msangi 16
2 21 12 2
1 1min ( ) ( ) ( )
0
I J
i i i i j j j ji j
j i ij
F b g ps a s pd
subject topd ps c
γ δ= =
= + − +
− − ≤
∑ ∑
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
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
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
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
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
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
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
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
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
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
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
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
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
Day 5 NotesHowitt and Msangi 30
,(X) R RRRR
Quota X≥∑
,( ) R RRRR
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
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