Computable General Equilibrium
Models and Impact Evaluation
Pasquale Lucio Scandizzo
University of Rome «Tor Vergata» and The World Bank
The three problems of impact evaluation
(Heckman, 2010)
• P1. Evaluating the impact of historical interventions on outcomes
including their impact in terms of welfare.
• P2. Forecasting the impacts (constructing counterfactual states) of
interventions implemented in one environment in other environments,
including their impacts in terms of welfare.
• P3. Forecasting the impacts of interventions (constructing
counterfactual states associated with interventions) never historically
experienced to various environments,including their impacts in terms
of welfare.
The general framework
• Assume a well defined set of individuals ω ∈ Ω and a
universe of counterfactuals or hypotheticals for each agent
Y(s,ω), s ∈ S. Different policies p ∈ P give different incentives
by assignment mechanism a to agents who are allocated to
treatment by a rule τ ∈ T .
• No well defined rules for constructing counterfactual or
hypothetical states or constructing the assignment to
treatment rules. Economic theories provide algorithms for
generating the universe of internally consistent, theoryconsistent counterfactual states.
The Policy Invariance Goal
• According to Marschak’s Maxim, the goal of explicitly formulated and
quantified economic models is to identify policy-invariant or
intervention-invariant parameters that can be used to answer classes
of policy evaluation questions.
• Policy invariant economic parameters may or may not be
interpretable economic parameters.
• The treatment-effect literature also seeks to identify interventioninvariant parameters for a class of interventions. In this sense the
structural and treatment effect literatures share common objectives.
CGE as a Causal Model
• Three distinct tasks arising in the analysis of causal models
• Defining the set of hypotheticals or counterfactuals A scientific
theory
• Identifying parameters (causal or otherwise) from hypothetical
population data : Mathematical analysis of point or set identification
• Identifying parameters from real data Estimation and testing theory
Definitions of Counterfactuals
• • Identification of causal models from idealized data of population
distributions (infinite samples without any sampling variation). The
hypothetical populations may be subject to selection bias, attrition
and the like. However, all issues of sampling variability are irrelevant
for this problem.
• • Identification of causal models from actual data, where sampling
variability is an issue. This analysis recognizes the difference between
empirical distributions based on sampled data and population
distributions generating the data.
A generalized Roy Model (1)
• Suppose that there are S states associated with different levels outcome such as
production, consumption, or choice of technology. witheach choice s is a
valuation of the outcome of the choice R(s), where R is the valuation function and
s is the state.
• Define Z as individual variables that affect choices. Each state may be
characterized by a bundle of attributes, characteristics or qualities Q(s)that fully
characterize the state. If Q(s) fully describes the state, R(s) = R(Q(s)). Assume that
the Z is observed and that additive separability is applicable. Let ν denote
unobserved components as perceived by the econometrician:
R(s) = μR(s,Z) + η(s,Z, ν),
where μR(s,Z) is the deterministic component of the utility function expressed in
terms of observed variables Z and η(s, Z, ν) represents unobservables from the
point of view of the econometrician .
A generalized Roy Model (2)
• Associated with each choice is outcome Y(s) which may be vector valued. These
outcomes can depend on X. The outcome model is thus:
Y(s) = μY (s,X) + U(s,X, ε)
• The set of possible treatments S is {1, . . . , ￣S }, the set of state labels. The set of
counterfactual outcomes is {Y(s,X)} s∈S. The treatment assignment mechanism is
produced by utility maximization:
D(j ) = 1 if argmax R(s) = j
s ∈S
• Thus agents self select into treatment (other selection rules can also be specified)
and the probabilities of selection which are defined at the individual level are
either zero or one for each agent (agents choose outcomes with certainty).
• Policies can operate to change Z,X, and the distributions η(s, Z, ν), U(s,X, ε).
Figure 1 : The Basic Economic Model
The general equilibrium economic model as a
policy variant parameter system
Productive Capacity
Consumption
Production
Employment
Income
Factor Prices
Product Prices
Prod.Capacities produttiva
Consumi
Production
Employment
Incomes
Factor Demand
Factor Prices
Factor Supply
Product Supply
Final Demand
Capital Stock Changes
Product Prices
A generalized SAM –CGE Model (Primary
Equations under Policy Invariant Parameters)
 A 0 Cy   X   X 

    
Q   F 0 0   Z  Z  
   
 0 Rzy R yy  Y  Y 
A generalized SAM –CGE Model (Dual
Equations under Policy Invariant Parameters)
 A F  0   P   P 






Q    0 0 Rzy    Pf    Pf 
C y 0 Ryy   Py   Py 
A differential Version (Policy Variant
Parameters)
I  Qd  dQ  
I  Qd  dQ  
(9)
Endogenous and exogenous components
d  d  dˆ

ˆ
d  d  d

dQ  dQ  dQˆ

(11)
(12)
Policy transaction matrix definition (Policy
Variant Parameters)
T  dQ   Qd




CGE Implicit Solution
T


 Q   d

 1
 Q  dQ


From the transaction definition it follws that.

 
dQ  T  Q d     

ˆ
I  Q dˆ  dQ    I  Q d

∆ is a divergence matrix


1
1
At least one
exogenous
sector
because of
Walras Law
 B11
B  
 B21
B12  ˆ1   




B22    2 


dˆ1  d  B   B12d

1
1
11

2

CGE
as a
gen
erali
zed
SAM
Product
Factor
Factor
Institutio
Facto
ITs
NTs
Exchan
Previo
s= dX
employme
Income
ns’
r
Domes
Domesti
ge
us
nt= dZ
s= dV
income=
price
tic
c
rate=
Shocks
dY
s=
Prices
Prices=
de
=
𝑑𝑃1
dPf
𝑑𝑃2
dYt 1
dX
A
0
0

0
0

0
dZ
F
0
0
0
0
0
0
0
dV
0
P 
0
0
Z 
0
0
0
dY
0
0

T
0
0
0
0
𝑑𝑃𝑓1
0
0
0
0
0

0
0
0
𝑑𝑃𝑓2
−1
𝐺Π
(𝐺𝑠
0
0
0
0
0
0
0
−1
𝐺Π
𝐺𝑡
0
0
0
0
0
0
P1*
0
0
0
0
0
0
f
− 𝐺𝑑 )
dP1
dP2
0
0
𝐹2′
𝑈21
𝐴′22
Explicit Solution with parameter change rules
 
*
ˆ
ˆ
dQ    Qdˆ  d Q   d   d
dˆ  I      I  Q    d   d 
1

CGE Explicit Solution

ˆ
dˆ  d   d  d

Generalized supply
function

 I       
1 1

 dˆ 

I     

d

1
ˆ




I



  


Explicit solution with parameter
variations rules
  1    I  Q    d   d  


1


d  d
  I     I   

1 1
An Example: The Impact of
Investment in the Ocean
Economy in Mauritius
Key messages
1. An investment strategy based on boosting the ocean economy beyond its traditional
boundary appears to be a smart choice for Mauritius to achieve balanced and
sustained growth over the next ten years.
2. With a cumulative investment of $5.8 billion over ten years, the ocean economy would
almost double by the end of the simulation period, account for 20% of GDP, and be
20% more diversified
3.
Investing those funds in Ocean economy would be better than in a plausible
alternative scenario: it would generate an additional 20% payoff on investment,
generate 36% more jobs, make the poor better off, and reduce (slightly) the debt/ GDP
ratio
4.
To achieve this potential it is essential to create attractive conditions for private sector
investment, invest in human capital, and conserve environmental quality
Approach: O2 and CF scenarios
 The economic model used in the simulations is based on the statistics provided
by Statistics Mauritius(SM) and on a Social Accounting Matrix developed in
collaboration with specialists from SM and the Ministry of Ocean Economy.
 The model was calibrated to reproduce Mauritius historical experience and fits
well the past production and consumption time series.
 The model was used to simulate two alternative scenarios: one based on the
investment on the Ocean Economy (named ) O2, and one with the same historical
structure of investment, representing a viable alternative (named counterfactual
or CF).
The model fits well Mauritius past growth
The treatment effect: OE2 Scenario
outperforms the Counterfactual (CF)
The OE2 scenario appears to outperform the CF in all the macro indicators
considered, with differences tending to increase over time.
The average contribution to growth of the OE2 scenario is significantly higher
(3.17 percent) than the CF scenario (2.93 percent).
The cumulative return, as measured by the ratio of the present value of
additional GDP and investment is more than twice as much in OE2 (49 percent)
versus CF (23 percent).
 Its effect on factor incomes (value added) and job creation is also larger than the
CF scenario However, the OE2 scenario shows an increase in the capital income
component of GDP, and its environmental costs (and the implicit investment costs
to neutralize them) are much higher for OE2 than for CF.
However, because of its reliance on ocean resources, even though its pressure on
the small land basis of Mauritius is low, the OE2 strategy is likely to result in
sizable environmental costs.
Treatment effect: Doubling the Ocean Economy Offers More Job Creation
(Job creation in comparison with the counterfactual (CF)
Number of Jobs created
OE2
CF
Labor Qualification
Year 1- 10
Year 1- 10
Primary Education
2388
Secondary Education <SC
2936
Secondary Education SC and above
1215
Tertiary Education
2694
3032
1649
981
2271
Own Account
Total
1390
9,324
3492
12,726
Policy Invariance? No: OE2 would change
sector structure and response parameters
Sector Production as % of OE Production
Year 1
Year 10
Fishery and Sea food
proc
18%
22%
Sea Transport and
Related Services
10%
13%
Marine ICT
7%
8%
Tourism
64%
55%
Sewage and Water
Treatment
2%
2%
Total
100%
100%
Probabilitic Impact: The OE2 scenario creates more
value and improves the income distribution
OE2 investment-CF scenario, percent increases in valueadded components
Income distribution effects of OE2, percent
OE2 changes versus CF baseline
)
Impact of Ocean Economy appears robust under stress (Performance of
the counterfactual scenario =100)
Performance Metric
Base case (no A. Unfavorable
constraints)
international
finance
B: A plus
constrained
skilled labor
supply
C: B plus
natural
resource
constraints
Average Contribution to
Growth
NPV (5%)GDP GROWTH
108.19
190.60
107.27
95.26
127.66
121.58
122.06
103.75
NPV GDP/NPV INV
121.14
121.10
121.69
104.13
..but key constraints must be overcome
• Boost productivity. In order to achieve a desirable 5% rate of growth, the country
will need to significantly increase its average rate of total factor productivity growth,
by about 1.8 percent under the OE2 strategy, which is a relatively large amount, even
though less than the 2.7 percent under the CF strategy.
• Strengthen the fiscal stance. Some fiscal consolidation, with somewhat higher saving
rates, lower government expenditure, and higher reliance on private domestic
investment, appears to be necessary to secure a firmer base for growth.
• Invest in education and training. While OE2 promises a high degree of job creation,
its reliance on new and technologically more sophisticated sectors requires focusing
on improving the school system and reforming vocational education. The private
sector can help by facilitating re-training and special skill transfers through privately
financed programs.
but key constraints must be overcome
• Conserve and improve natural resources. Even though the OE2 strategy
lessens some of the pressure on land-based activities that rely on natural
resources, the simulations show that its end use of ocean and internal
waters turns out to be much more intensive than the counterfactual.
• Moreover, much of the country’s natural resources are now being exploited
at no charge, maintenance and renewal activities are low, and pollution
and other forms of degradation appear to be rampant.
• Thus, investments in ocean environmental goods are essential. This means
replacing the current model of rent exploitation with significant investment
in the conservation and improvement of natural resources. Possible
solutions include marine spatial planning and lagoon rehabilitation,
improved sanitation and water treatment, and scaling up appropriate
environmental regulations.
The way forward
Mauritius could update and extend the CGE model to evaluate different
scenarios as the OE strategy and other government policies are deployed.
Mauritius’understanding of the relationships between key parameters, e.g.
between investment and income distribution, could be improved under the
feedback provided by new data and analyses of impact and cost benefit of
specific projects.
The model can also be used for training to further empower the government’s
statisticians and economists, who have already produced an exemplary set of
methodologies, national statistics, and economic accounts.
The model could be used in the nest stages of the implementation of the Ocean
Development strategy, by providing a consistent framework to define GDP and
employment creation targets, to analyze trade-offs in allocating investment
resources between Ocean/ Non Ocean sectors; and among Ocean sectors.