What is the TOA-MD Model?
Basic Concepts and an Example
John Antle
Roberto Valdivia
Agricultural and Resource Economics
Oregon State University
www.tradeoffs.oregonstate.edu
What is the TOA-MD Model?
• The TOA-MD Model is a unique simulation tool for multidimensional impact assessment that uses a statistical description
of a heterogeneous farm population to simulate the adoption and
impacts of a new technology or a change in environmental
conditions.
• TOA-MD is designed to simulate what would be observed if it
were possible to conduct a controlled experiment. In this
experiment, a population of farms is offered the choice of
continuing to use the current or “base” production system
(System 1), or choosing to adopt a new system (System 2).
• In fact it is never possible to carry out such ideal experiments, so TOA-MD is
designed to utilize the available data to attain the best possible approximation,
given the available time and other resources available to conduct the analysis.
• Additionally, TOA-MD is designed to facilitate analysis of the inevitable
uncertainties associated with impact assessment.
• There are two components in the TOA-MD analysis:
• First, the model simulates the proportion of farms that would adopt a
new system (system 2), and the proportion that would continue to use the
“base” system (system 1)
• Second, based on the adoption rate of the system 2, the TOA-MD model
simulates selected economic, environmental and social impact indicators
for adopters, non-adopters and the entire population.
• How is the TOA-MD simulation approach related to the
experimental and non-experimental statistical approach to impact
assessment (estimation of “treatment effects”)?
• The underlying conceptual model is very similar: economic agents (farms
in this case) self-select into “treatment” or choose to adopt a technology
(or adapt to an exogenous change such as climate change), and related
“outcomes” occur to those self-selected into “treatment” (adoption)
• For “ex post” assessment the simulation approach can be used together
with experimental methods to parameterize the model and simulate
outcomes of interest, including both “mean” indicators and other
“threshold” indicators such as poverty rates and indicators based on other
quantifiable outcomes. It can also be used to simulate “policy relevant”
effects, such as technology adoption induced by payments for ecosystem
services.
• For “ex ante” assessment, where statistical methods cannot be used, the
simulation approach provides a “laboratory” to explore potential impacts,
using various types of available data to construct the future
“counterfactual,” e.g., the impacts of and adaptation to climate change.
TOA-MD approach: modeling systems
used by heterogeneous populations
A system is defined in terms of
household, crop, livestock and
aquaculture sub-systems
Systems are
being used in
heterogeneous
populations
(ω)
Opportunity cost, system
choice and adoption
Opportunity cost  = v1 – v2
follows distribution ()
v1 = returns to system 1
V2 = returns to system 2
System 1:  > 0
(non-adopters)
System 2:  < 0
(adopters)
0
 opportunity cost
Map of a
heterogeneous
region
Adoption, Outcome Distributions and
Impact Indicators
• Outcome distributions are associated with system choice
– Farms select themselves into “non-adopter” and “adopter” subpopulations, generating corresponding outcome distributions for
these sub-populations
• Impact indicators are based on system choice and
outcome distributions
– TOA-MD produces mean indicators and threshold-based
indicators
• Analysis shows that impacts depend on the correlations
between adoption (opportunity cost) and outcomes
– Many impact assessments ignore correlations
– Yet these correlations are often important for accurate impact
assessment!
Adoption and outcome distributions
(z|1)
System 1 before adoption:
25% > threshold 
r(1,a)% nonadopters
Outcome z

r(2,a)% adopters
(z|1,a)
System 1: 20% > 
(z|2,a)
(z|a)
System 2: 90% > 
Entire Population with
adoption: 55% > 
Components of TOA-MD Analysis
Design
Population (Strata)
System characterization
Impact indicator design
Data
Opportunity cost distribution
Outcome distributions
Simulation
Adoption rate
Indicators and
Tradeoffs
An Example: Integrated Agriculture-Aquaculture
• Based on Dey et al (2010) Agricultural Economics: economic analysis of IAA
• stratified survey of farms, without and with IAA
• Design of TOA-MD analysis
• population: farm households in southern Malawi where aquaculture is
feasible
• strata: 5 southern districts
• systems:
• Subsistence crops
• Crops + aquaculture, low or high integration
Subsistence
crops
Aquaculture
Irrigated
vegetables
Adoption Rate and Opportunity Cost of Adopting IAA in Southern
Malawi – Predicted Adoption Rate is Point Where Curves Cross the
Horizontal Axis
800
600
400
Opportunity Cost
200
0
0
10
20
30
40
50
60
70
-200
-400
-600
-800
-1000
Adoption Rate (%)
Zomba
Mwanza
Mulanje
Thyolo
Mangochi
80
90
100
Poverty Rate and Adoption Rate of IAA, Southern Malawi
100
95
90
Poverty Rate (%)
85
80
75
70
65
60
0
10
20
30
40
50
60
70
Adoption Rate (%)
Zomba
Mwanza
Mulanje
Thyolo
Mangochi
80
90
100
Mean Monthly Protein Consumption and Adoption of IAA,
Southern Malawi
Mean Monthly Protein Consumption per person (kg)
2.5
2
1.5
1
Note most improvement occurs for
those districts with lowest protein
consumption
0.5
0
0
10
20
30
40
50
60
70
Adoption Rate (%)
Zomba
Mwanza
Mulanje
Thyolo
Mangochi
80
90
100
Relationship between adoption and Protein Consumption,
Non-adopters and Adopters of IAA, Mulanje Dist., Malawi
Slope of relationship between
indicator and adoption rate has
same sign as the correlation
between opp cost and the outcome
variable (negative in this case)
Adopter sub-population and
entire population are equal at
100% adoption
Non-adopter sub-population
and entire population are equal
at 0% adoption
Relationship between adoption and Mean Returns per Farm, NonAdopters and Adopters of IAA, Mulanje District, Malawi
800
600
400
200
Opportunity Cost
Economic outcomes that are
positively related to net returns
have a maximum in the entire
population at the predicted
adoption rate (41% in this
example)
0
0
10
20
30
40
50
60
70
-200
-400
-600
-800
-1000
Adoption Rate (%)
Zomba
Mwanza
Mulanje
Thyolo
Mangochi
80
90
100
The various “treatment effects” discussed in the experimental
and non-experimental statistical literatures are either equivalent
to or closely related to the mean indicators generated by the
TOA-MD model:
• AveTreatment Effect = mean population indicator
• Marginal Treatment Effect = change in mean indicator
• Treatment on Treated = related to mean indicator of adopters
• Treatment on Untreated = related to mean indicator of nonadopters
• Policy relevant treatment effect = derived from mean
indicators
1
Summary: Impacts of IAA Adoption on Farm Population
and IAA Adopters
Ave. farm income ($/year)
Adoption
rate (%)
% Change
on
population
54.60%
%
Change
on
adopters
135.62%
Mean Monthly Protein Consumption
(kg/person)
Poverty rate (%)
base (no
adoption)
87.50
% Change
on
population
-15.81%
%
Change
on
adopters
-42.48%
base (no
adoption)
1.41
% Change
on
population
12.86%
%
Change
on
adopters
38.95%
ZOMBA
49.22
base (no
adoption)
112.47
MWANZA
49.40
89.01
50.77%
137.61%
99.16
-16.01%
-51.88%
1.94
0.30%
10.64%
MULANJE
40.81
81.01
54.46%
179.51%
84.30
-11.38%
-44.26%
0.65
53.10%
191.35%
THYOLO
41.92
170.85
41.85%
116.92%
95.93
-16.48%
-56.11%
1.75
-0.49%
28.63%
MANGOCHI
37.95
188.62
30.77%
116.63%
72.24
-10.53%
-53.66%
0.77
56.42%
178.33%
REGION
44.49
123.90
45.23%
132.70%
87.11
-11.25%
-30.45%
1.29
15.32%
59.00%
Strata
Conclusions
• TOA-MD is a unique simulation tool for multi-dimensional
impact assessment of agricultural systems
• The Malawi case study illustrates how it can be used with
available data to simulate:
• the adoption rate of a new technology
• the economic, environmental or social impacts of the new technology
• The model can also be used for analysis of ecosystem services,
and impacts of climate change and other environmental change
• Training in use of the model, and the model software are
available from the TOA Team.
• More info is available at : http://tradeoffs.oregonstate.edu