biosight: quantitative methods for policy analysis: multi market models

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

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


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


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


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


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 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


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


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:


j j j j

i i i i

pd xdps xs

φ δ

α γ

= +

= +

We can define the primal model as:


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)


We can formulate the dual of the water trade problem

Supply and demand (price-dependent) is linear and given by:


j j j j

i i i i

xd a s pdxs b g ps

= +

= +

We can define the dual model as:


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.


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)


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


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


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)


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


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


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


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)


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


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


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)



( ) ( )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


,(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


biosight: quantitative methods for policy analysis: multi market models

Education

ag models

cge models

taxonomy of models

multiregion model

model interactions

model of water trade

water trade model day

multimarket modelsday