Dafne economic model

www.dafne-project.eu
@dafne_project
DECISION ANALYTIC FRAMEWORK TO EXPLORE THE
WATER-ENERGY-FOOD NEXUS IN COMPLEX TRANSBOUNDARY
WATER RESOURCES OF FAST DEVELOPING COUNTRIES.
Funded under the H2020 Framework
Programme of the EU, GA No. 690268
WP4: Task 4.1
Professor Phoebe Koundouri
Research Coordinator ICRE8
(AUEB, LSE)
Dr. Ebun Akinsete
Senior Researcher, ICRE8
Lecturer Nikolaos Englezos,
Senior Researcher, ICRE8 , UniPi
Dr. Xanthi I. Kartala,
Senior Researcher, ICRE8, AUEB

Work Package 4
Task 4.1
Models of Development of the
Economy

3
Work Package 4
STAGES OF ANALYSIS:
• Natural Resources, Socio-Economic, Institutional Characterization
• Mathematical Model of People’s Behaviour, NR stocks & flows
• Empirical/Econometric Model
• Data Collection (revealed/stated preference data)
• Empirical Models Application & Estimation
• Analysis of Results
• Policy Recommendations

8
Work Package 4
Structure
&
Processes
Environmental
Functions
Human
Benefits Anthropocentric
Values
Use Non-Use
Values Values
Total Economic Value
Use Value Non Use Value
Actual Use
Value
Option
Value
Existence
Value
For Others
Direct Use
Value
Indirect
Use Value
Bequest
Value
Altruistic
Value
Environment
Warm
Glow

9
Work Package 4
- TEV: systematic tool for considering full range of impacts on human welfare.
- TEV: reflects the preferences of individuals.
- Preferences can be studied and estimated by stated & revealed preference methods .
- TEV: essential for resource allocation and policy making.

Modelling social, economic and institutional
developments [ Months: 1 – 30]
10
Work Package 4
• Task 4.1: Models of Development of the Economy (M1-M16)
Leader: ICRE8. Partners: ACCESS, UNZA, UEM
• Task 4.2: Models and Principles of Water Governance (M6-M24)
Leader: UABDN. Partners: UO, POLIMI, ACCESS, UNZA, UEM
• Task 4.3: Models of Environmental Policy (M8-M20)
Leader: IWMI. Partners: EM-ETHZ, ICRE8, KU LEUVEN
• Task 4.4: Models of Demographic, Cultural and Social
Developments (M10-M25)
Leader: UO. Partners: UNZA, UEM, ACCESS, ICRE8

Modelling social, economic and institutional
developments [ Months: 1 – 30]
11
Work Package 4
Participation per Partner
Partner number and short name WP4 effort
ETH Zürich 19.00
POLIMI 5.00
ICRE8 18.00
UNIABDN 14.00
UOS 10.00
IWMI 8.00
ACCESS 11.00
UNZA 18.00
UEM 9.00
TOTAL 112.00

Modelling Economic Developments
12
Work Package 4: Task 4.1 (M1-16)
The modelling of economic and social processes and environmental policy
under the W-E-F nexus perspective.
o The sectors associated with each case study, will correspond to a model with
economic characteristics of such as total employment, production output of the
energy and food sectors, volume of water use.
o Environmental indicators will be used, for example lack of urban water
supplies, and lack of access to clean water (WP2).
o Each model will accommodate different relevant scenarios, as required for the
development of a robust DAF (WP5).
o The models will capture the interdependencies between two neighbouring,
possibly different, economies that share the same resource.
o The models will support changes in the technological level and the principle of
sustainable development.
o The models will be validated against data and indicators provided by WP2.
o Sensitivity analysis will be also used for robustness assessment.

Content of Deliverable
• 1. Introduction
1.1. Description of the Economic Development in the Zambezi
River Basin. (i) Angola, (ii) Botswana, (iii) Malawi, (iv) Mozambique,
(v) Namibia, (vi) United Republic of Tanzania, (vii) Zambia, (viii) Zimbabwe.
• 2. Estimation of the Production Functions of the Economic Model by Sector .
2.1. Mathematical Tools: Production Functions.
2.2. Data Collection.
2.3. Description of the indices by sector related to ecosystem services.
2.4. Statistical Analysis.
2.5. Results.
• 3. Formulation of the Economic Development Model .
3.1. Modelling of Economic Developments under WEF nexus perspective.
3.2. Generalization of the Model in the River Basin Water Sharing Case
(i) Non Cooperative Approach, (ii) Cooperative Approach
• 4. Conclusion
4.1. Summary of results 13

14
Estimation of Sector Specific Production Functions
For each country, we focus on the 5 Core Water-Dependent Economic Sectors:
• Agriculture (including aquaculture)
• Mining (Industry)
• Energy Production
• Tourism
• Residential Water Supply
Related to the following ecosystem services:
• Provisioning Services: Water, Food
• Regulating Services: Flood prevention, Erosion control
• Supporting (Habitat ) Services: Biodiversity
• Cultural (Recreational) Services: Tourism

15
Definition of Production Functions
Production function: the relationship that describes how inputs like
capital and labor are transformed into output.

16
• Mathematically, we estimate each sector’s i=1,2,…,5 specific production function as:
GDP (sector i) = F (Technological Capital Input; Labor Input; Natural Capital Input),
where
- Data on Technological Capital, labor and natural capital are collected from national and
regional accounts
- Data should be time series (over time), but also yearly panels of regional data points
would be valuable so that we can do panel data econometrics that are more robust.

17
Data Collection
• For each Core Water-Dependent Economic Sector i = 1,2…,5, we gathered
data on Natural Capital using Environmental Indices as approximations
of both quality and quantity.
• At first, we define all the relative indices that we will use per sector
(see the table below).
• Secondly, we try to gather these data using manydatabases as:
1. Food and Agriculture Organization of United Nations (FAOSTAT, AQUASTAT)
2. ILO (International LABOR Organization)
3. The World Bank data
4. The World Bank Group: Climate Change Knowledge Portal For
Development Practitioners and Policy Makers
5. The United Nations Statistics Division
6. Unesco World Heritage list
7. OpenDataSoft
8. Environment & Climate Change Data Portal

18
Data Collection
• Additionally, we gathered a lot of information from Input-Output (IO) Tables
that we have in our disposal from the Eora multi-region input-output table
(MRIO) database.
• This database provides a time series of high resolution IO tables with
matching environmental and social satellite accounts for 187 countries (to
190 in some datasets).
• The Eora MRIO features:
➢ 187 individual countries represented by a total of 15,909 sectors
continuous coverage for the period 1990-2012
➢ 35 types of environmental indicators covering air pollution, energy
use, greenhouse gas emissions, water use, land occupation, N and
P emissions.

19
Data Collection
• We have 13 IO tables, each for the time period 2000-2013 for all the 8
countries under investigation.
• These tables have 2946 rows and column with massive information each.
• For example the table of Angola for 2000 has the form:
• https://www.dropbox.com/home/F%20ICRE8%20Proposals%20%26%20Pr
ojects/icre8.funded.projects/H2020-IP-
DAFNE/ModelIntegration.Meeting?preview=IO_AGO_2000_BasicPrice.tab
.xlsx

20
Indices Per Sector
Common Factors
GVA temperature
LABOR rainfall
CAPITAL Habitats (by country’s scores
determined by how close or
far countries are to targets)
Water use CO2 emissions
Energy use NO2 emissions
Water quality
(Nitrogen emissions
exportable to water bodies)
floods/droughts
(estimated damage or people
killed or total affected),
Freshwater withdrawals Unesco World Heritage list.
Common Factors

21
Indices Per Sector
Sector Factors
Land use (agricultural
area, arable land,
permanent crops, total
area equipped for
irrigation), forest
AGRICULTURE soil erosion/degradation
agricultural production,
fishery production,
aquaculture production
use of pesticides
/fertilizers
Raw materials (bio-mass)
Sector Factors
energy for renewable resources
MINING raw materials (construction
material, and total fossil fuel)
Sector Factors
Energy energy for renewable resources
dam capacity
Sector Factors
International tourism,
expenditures
Tourism number of arrivals
Terrestrial Conservation Areas
Sector Factors
Residential Water
Supply
access to clean water

22

Estimation of Sector Specific Demand Functions
• By econometric methods, we estimate the production (output)
per each specific sector i = 1,2…,5, against the obtained data, such as, on water
quantity on labor etc.
• Collapsing all the variables, except for the water quantity to their means,
we obtain the equation:
where
= marginal contribution of the water to the production of sector i
= maximum willingness-to-pay (WTP) by sector i for each unit of water
= price of the water for sector i = .
• Hence, we obtain the demand function (curve) for each sector i :
• By integration of this curve, we obtain the Social Benefit function
of each sector i .
23
,iY
,iw ,iL
ˆ ( ) ,i i iY f w
ˆ ( )i if w
ip
ˆ ( )i i ip f w
,iw
 iSB

24
• Our model will describe the water allocation between the Upstream (U)
and the Downstream (D) country, as indicated in our case studies.
• We will focus on two different cases :
➢ without any cooperation in water sharing
➢ with cooperation in water and hydropower sharing.
• Water sharing:
✓ the upper riparian country has the right to unilaterally divert water,
✓ the downstream country’s freshwater availability partially depends on the water
usage in the upstream country.
• The 5 sectors are ordered via their demand function per country.
• As increases over time due to decreasing water availability, water demand for
each of these economic sectors reaches zero sequentially, i.e. intersect
• We denote by the exit time of the j-th sector, j = 1,2…,5,
thus time is divided into 5 exit stages, per country h = U, D .
Model for River Basin Water Sharing
ip
h
jT
ˆ (0) .if 

25
• We assume that
➢ water flow is stochastic and
➢ uncertainty in the flow of water can be attributed to climate change
• The total renewable fresh water resources in the upstream country, , evolve
through time according to:
where
➢ is a standard Wiener process, and
➢ can be considered as the volatility of water flow in the upstream country.
• The total per capita freshwater utilization in the upstream country is denoted by
per sector i .
• Consider the rate of water utilization of country h as per each sector i.
• The total per capita freshwater utilization in the upstream country can be exhibited
in mathematical form as
The Proposed Model
U
W
, (1)U U U U
tdW W dz
U
tz
U

U
iw
h
ia
. (2)i i
U U U
w a W
, (1)U U U U
tdW W dz

26
• The water availability in the downstream country depends on
➢ water consumption in the upstream,
➢ and runoff R
• The runoff of the downstream country, denoted by R, is also stochastic in the model
and follows by
where is a standard Wiener process.
• The water availability in the downstream country for the j-th exit stage is
• The water withdrawal in the downstream country per sector i for the j-th exit stage is
The Proposed Model
5
11 + , . (4)D U U U U
j i j j
i j
W W R T t T 

 
    
 

(3)R R
tdR Rdz
R
tz
5
, 11 + , . (5)D D U U U U
i j i i j j
i j
w W R T t T  

  
     
   


27
• The stock of water in the downstream area, where hydropower is
produced, is denoted by S.
• The state equation can be represented for the (j,k)-th exit stage as:
where S(0) is an initial condition.
• Here O denotes the outflow and evaporation of water from this area.
• We also assume that water reserves exceed a minimum (critical) level i.e.
• If the constraint is binding, then the scarcity value of water will be positive.
The Proposed Model
5 5
1
1
1 1 + , and
(6)
D U U U U
jk i i j j
i k i j
D D
k k
dS W R Odt T t T
T t T
  
 

   
        
    
 
 
,S
. (7)S S

28
• Consider the social benefit function of water consumption w per sector i :
• The total cost function of withdrawing water from the river at rate α is denoted by
• We consider that as water becomes increasingly scarce in the economy, areas which
store water receive benefits.
• We denote the net consumer surplus or economic benefit from hydropower
generation per sector i by
where S is the corresponding stock of water in the downstream area.
The Proposed Model
 , , .h
iSB w h U D
   / , , .h h
i iTC TC w W h U D  
( ), , ,h
iH S h U D

29
• Non Cooperative: absence of any agreement between countries.
• Problem of Upstream Country: maximizes its own net benefit (NB) per sector i
where the maximization is as follows:
subject to:
➢ the Upstream country water resources equation of (1).
Non Cooperative: Water Sharing
( ) ( ),U U U U U
i i i i iNB SB w TC  
1
5 5 5
1 1
max max .
U
j
UU U
j
T
U U r U
j iT
j j i j
J J E e NB d
 



  
 
   
 
  

30
• The downstream water consumption depends on:
➢ inflow from the upstream,
➢ runoff,
but enjoys economic benefits from hydropower.
• Problem of Downstream Country: based on the given availability of water, it
maximizes its own net benefit (NB) per sector i and exit stage (j,k)
subject to:
➢ the Upstream country water resources equation of (1),
➢ the runoff flow equation of (3),
➢ the stock of water (state) in the downstream area equation of (6),
➢ the stock reserves constraint of (7).
Non Cooperative: Water Sharing
, , ,, ( ) ( ) ( ),D D D D D D
i i j ii j ik j k iNB SB w H S TC   
   1 1
5 5 5 5 5
, , ,
1 1 1 1
max max .D D
U U D D
j j k k
D D r D
j k i j k
j k j k i kT t T T t T
J J E e NB d
 

 

        
 
  
 
 
  

31
• Cooperative: agreement between countries for water and hydropower sharing.
• The Downstream country offers a discounted price for hydropower exports to the
Upstream country, in exchange for greater transboundary water flow.
• Problem of Upstream Country: maximizes its own net benefit (NB) per sector i and
exit stage (j,k)
subject to: same equations as with the Downstream country.
Cooperative: Water and Hydropower Sharing
 , , ,( ,) ( ),U U
j k i j k
U U U U U
i i i i iiNB SB w TCH S   
   1 1
5 5
,
1 1
5 5 5
, ,
1 1
max max ,
U U D D
j j k k
U Uk j k
k k
U U r U
j i
j j i jT t T T t T
J J E e NB d
 

 

        
 
  
 
 
  

32
• Solution: utilize a differential Stackelberg Leader-Follower game.
• The Upstream country represents the Leader and moves first, a priori knowing that
the Follower (Downstream) country observes its actions and moves accordingly.
• First, we find the solution to the Follower’s problem of maximizing its payoff function.
• Then, using the Follower’s reaction function, the Leader’s objective function is
maximized.
• We assume that the respective countries use Markovian perfect strategies.
• The Markovian perfect strategies determine a subgame perfect equilibrium.
• The optimal strategies define an equilibrium set of decisions dependent on
previous actions.
Cooperative: Water and Hydropower Sharing

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