Policy Optimization with a CGE Model
Martín Cicowiez (CEDLAS-Universidad Nacional de La Plata), Bernard Decaluwé (Université
Laval) and Mustapha Nabli
this version: May 9, 2016
VERY PRELIMINARY DRAFT; do not cite
1. Introduction
Generally speaking, with CGE models, policy analysis is mostly carried on as “shock
analysis”. That is, changing the values of selected policy variables and computing the
corresponding model results. However, today’s computer and software developments
allow us to perform optimal policy exercises, even for relatively large models. That is, for
the specification of an objective function and the computation of the corresponding
optimal values for selected policy variables, and where the CGE model operates as the
constraint of the optimization exercise.1 In formal terms, the problem can be stated as
 
max u J  g x*
s.t. F x, u, z,  
where
x = vector of endogenous variables
x* = vector of policy variables; subset of x
z = vector of exogenous variables
 = vector of parameters
1
In Mercado et al. (1998) an approach similar to the one proposed here is applied in the context of a small
macroeconomic model.
-1-
u = vector of policy variables, whose value is endogenously determined as the
result of the optimization problem
Moreover, parameter uncertainty may also be taken into account in a sophisticated way
when performing optimal policy exercises, something with a long tradition in the realm of
empirical macroeconomics, and to which CGE modeling may perhaps begin to converge.
The CGE literature is not abundant in this sort of applications. In Böhringer and Rutherford
(2002) a static multi-country CGE model is used to determine optimal environmental tax,
whereas Bovenberg and Goulder (1996) performed a similar analysis applied to the case of
the United States.2 In turn, Kim (2004) uses a CGE linear model in the context of a
stochastic control problem that incorporates the uncertainty about the value of certain
parameters of the model.
In this paper, however, we propose to solve a more general problem where the function
to be optimized is a loss function that can incorporate various objectives. In fact, we will
allow the use of different policy instruments, not only tax rates. To illustrate the potential
of our approach, we develop an exercise with real data from Argentina, a developing
country with a relatively large agri-food sector.
2. The Model
In this paper we ask the CGE model what would be the best policy mix, given an objective
function for the policy maker. In practical terms, we will start by using the small open
economy CGE model known as PEP-1-1 (Decaluwé et al., 2012) as a constraint to an
optimization problem. Specifically, we implement a loss function that the policy maker
minimizes. Mathematically,
u

x

min L   i  *i  1    j  *j  1
u

i
j
 xi

 j

2
2
2
The two articles can be framed within the theory of optimal taxation (see Myles (1995), Stiglitz (1987),
Auerbach and Hines (2002)).
-2-
s.t. F x, u, z,  
where
L = loss function
xi = endogenous variables
u j = policy instruments available in the model (e.g., tax rates)
*
*
In addition, xi and ui represent values reached by xi and u j , respectively, in the
reference scenario. As an alternative, xi could represent a given policy objective. In the
implementation below, we ran the static version of the model. Thus, departures of policy
instruments from their target (initial) values are penalized.
PEP-1-1-OPT Model: Mathematical Statement
As said before, as a first step, we extended the PEP-1-1 model (Decaluwé et al., 2012) in
order to incorporate endogenous unemployment – through a wage curve -- and a loss
function for the policy maker.3 In the model, the loss function is written as
3
In Appendix A we provide additional details on the extensions introduced to PEP-1-1.
-3-
 RGDPFC

LOSS  wtrgdpfc
 1
*
 RGDPFC

 UR

 wtur  *  1
UR


2
2
 RSG

 wtrsg 
 1
*
 RSG

2
 CAB

 wtcab 
 1
*
 CAB

2
 TTDHADJ

 wttdh 
 1
*
 TTDHADJ

 TTXADJ

 wttx 
 1
*
 TTXADJ

2
2
 CGADJ

 wtgovcon 
 1
*
CGADJ


2
and the wage curve is written as

W
WO
 UR 


PINDEX  URO  PINDEXO
where
UR = unemployment rate; URO refers to the initial unemployment rate
RSG = real government savings
RGDPFC = real GDP at factor cost
TTDHADJ = scaling/adjustment factor for direct tax rates
TTXADJ = scaling/adjustment factor for indirect tax rates
CGADJ = scaling/adjustment factor for government consumption
wtopt = weight of the opt argument in the loss function; certainly, not all weights in
the loss function will be simultaneously different from zero
W = wage
PINDEX = consumer price index
-4-
 = wage curve elasticity
and the variables with a star represent the policy objectives.
3. Illustrative Application
In this section, we show three example applications of the proposed approach,
implemented over the PEP-1-1 model. As will be shown, the proposed approach can be
applied for three different purposes: optimal policy response to a negative shock, optimal
selection of macro closure rule, and policy optimization – in the last case, starting from
the base scenario.
Social Accounting Matrix and Other Data
For illustrative purposes, we will implement our extension of the PEP-1-1 CGE model using
Argentina data. Like other CGE models, our CGE model uses a base-year SAM (in this case
for 2012), to define base-year values for the bulk of the model parameters, including
production technologies, sources of commodity supplies (domestic output or imports),
demand patterns (for household and government consumption, investment and exports),
transfers between different institutions, and tax rates. The disaggregation of the
Argentina SAM coincides with that of the rest of the model database. As shown in Table
3.1, it is disaggregated into 17 sectors (activities and commodities) – 1 in agriculture, 2 in
mining, 7 in manufacturing, and 7 in services – with each activity producing one or more
commodities. The factors are split into labor, capital, and natural resources (5 types:
agricultural land, forestry land, fishing resources, and two natural resources used in
extractive industries). The institutions are split into households, enterprises, government,
and the rest of world. A set of tax accounts cover the different tax instruments. A stylized
(Macro-)SAM for Argentina is provided in Table 3.2. Argentina GDP reached 2,766 million
pesos in 2012. In 2012, the government current account surplus was around 0.9 percent
-5-
of GDP and government current consumption was 15.1 of GDP. In 2013, exports and
imports were 15.5 and 13.7 percent of GDP, respectively.
Table 3.1: disaggregation of Argentina PEP-1-1-OPT and SAM
Category - #
Primary (3)
Sectors
(activities
and comm)
(17)
Manufact (7)
Services (7)
Item
Agriculture, forest and fish
Other mining
Petroleum and gas
Food
Textiles and apparel
Petroleum products
Chemicals, rubber and plast
Metals, mach and equip
Vehicles
Other manufacturing
Elect, gas and water
Construction
Trade
Transport and comm
Other services
Public administration
Education and health
Source: Authors’ elaboration.
-6-
Category - # Item
Factors (4) Labor
Capital
Land
Natural resources
Taxes (4)
Taxes on sales
Tariffs
Taxes on exports
Taxes on income
Institutions Households
(4)
Enterprises
Government
Rest of the world
SavingsSavings
Investment Investment, private
(4)
Investment, gov
Stock change
Table 3.2: Macro-SAM for Argentina 2012
act
com
f-lab
f-cap
tax-vat
tax-com
tax-imp
tax-exp
cssoc
tax-dir
hhd
ent
gov
row
sav
invng
invg
dstk
total
159.2
73.4
47.1
38.7
66.1
15.1 15.5
0.0
0.4
14.8
2.3
14.8
2.3
-0.1
8.1 76.8 35.7 31.6 16.8 17.0 14.8
2.3
6.9
4.5
0.6
2.2
6.5
3.1
40.6
13.7
35.4
1.2
0.0 2.5
0.0
159.2 187.1 47.1 39.1
6.9
6.9
4.5
4.5
0.6
0.6
2.2
2.2
6.5
6.5
8.1
1.3
0.2
6.1
5.0
20.8 15.3
0.2
0.3
9.6
0.0
0.9
0.1
0.1
0.3
0.4
to
ta
l
ds
tk
g
in
v
ng
in
v
sa
v
ro
w
go
v
en
t
ir
hh
d
ta
xd
om
ta
xim
p
ta
xex
p
cs
so
c
at
ta
xc
ta
xv
ap
f-c
ab
f-l
co
m
ac
t
(percent of GDP)
159.2
-0.1 187.1
47.1
39.1
6.9
4.5
0.6
2.2
6.5
8.1
76.8
35.7
31.6
16.8
17.0
14.8
2.3
-0.1
-0.1
where act = activities, com = commodities, f-lab = labor, tax-vat = value added tax, taxcom = sales tax, tax = tariffs, tax-exp = export tax, cssoc = social security contributions, taxdir = direct tax, hhd = households, ent = enterprises, gov = government, row = rest of the
world, sav = savings, invng = non-government investment, invg = government investment,
dstk = changes in stocks.
Source: Authors’ calculations based on Argentina SAM.
On the basis of SAM data, Table 3.3 summarizes the sectoral structure of Argentina’s
economy in 2012: sectoral shares in value-added, production, employment, exports and
imports, as well as the split of domestic sectoral supplies between exports and domestic
sales, and domestic sectoral demands between imports and domestic output. For
instance, while (primary) agriculture represents a significant share of exports (around 16
percent), its shares of value added (VA) and production are much smaller (in the range of
6.2 percent). The share of its output that is exported is around 16.8 percent while only
some 1.4 percent of domestic demands are met via imports.
-7-
Table 3.3: sectoral structure of Argentina’s economy in 2012
(percent)
Sector
Agriculture, forest and fish
Other mining
Petroleum and gas
Food
Textiles and apparel
Petroleum products
Chemicals, rubber and plast
Metals, mach and equip
Vehicles
Other manufacturing
Elect, gas and water
Construction
Trade
Transport and comm
Other services
Public administration
Education and health
Total
VAshr PRDshr
6.2
6.2
1.4
1.1
1.9
2.0
4.7
9.8
1.4
1.9
0.6
2.3
3.3
5.3
3.3
5.0
0.7
1.8
1.7
2.1
3.3
2.9
6.2
6.8
11.6
9.0
5.9
6.8
27.8
22.8
7.6
5.8
12.3
8.3
100.0
100.0
EXPIMPEXPshr OUTshr IMPshr DEMshr
16.1
16.8
0.8
1.4
5.0
40.0
1.4
15.2
2.8
6.2
4.8
18.0
28.1
15.4
1.7
1.8
2.9
9.9
3.1
14.2
4.3
7.9
5.0
17.2
8.8
12.2
17.6
25.6
5.8
9.3
29.0
36.6
10.3
40.8
14.7
55.1
1.0
3.7
3.0
12.1
0.2
0.5
0.5
1.4
0.1
0.1
0.2
0.2
0.0
0.0
0.0
0.0
3.3
4.7
4.5
5.6
11.2
4.8
13.7
5.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
100.0
6.9
100.0
9.5
where VAshr = value-added share (%); PRDshr = production share (%); EMPshr = share in
total employment (%); EXPshr = sector share in total exports (%); EXP-OUTshr = exports as
share in sector output (%); IMPshr = sector share in total imports (%); IMP-DEMshr =
imports as share of domestic demand (%).
Source: Authors’ calculations based on Argentina SAM and employment data.
Table 3.4 shows the factor shares in total sectoral value added. For example, the table
shows that agriculture is relatively intensive in the use of capital and land. On the other
hand government services and education and health are relatively intensive in the use
-8-
(salaried) labor.4 Of course, this information will be useful to analyze the results from the
CGE simulations.
Table 3.4: sectoral factor intensity in 2012
(percent)
Sector
Agriculture, forest and fish
Other mining
Petroleum and gas
Food
Textiles and apparel
Petroleum products
Chemicals, rubber and plast
Metals, mach and equip
Vehicles
Other manufacturing
Elect, gas and water
Construction
Trade
Transport and comm
Other services
Public administration
Education and health
Total
Labor
31.6
21.1
21.1
45.0
45.0
45.0
45.0
45.0
45.0
45.0
26.4
42.1
43.2
56.4
41.0
100.0
69.6
48.8
Capital
32.9
78.8
78.8
48.4
48.4
48.4
48.4
48.4
48.4
48.4
73.6
45.7
42.5
38.4
53.2
0.0
26.5
42.7
Land
35.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2.4
Total
100.0
99.9
99.9
93.4
93.4
93.4
93.4
93.4
93.4
93.4
100.0
87.7
85.7
94.8
94.2
100.0
96.0
93.9
Source: Authors’ calculations based on Argentina SAM.
In addition to the SAM, our CGE model also requires (a) base-year estimates for sectoral
employment levels and unemployment estimates for the different labor types, and (b) a
set of elasticities (for production, consumption and trade). In order to estimate sectoral
employment we combined population data with estimates for sectoral employment
shares in broad sectoral categories from the Encuesta Permanente de Hogares (EPH), the
4
As shown in the table, due to the lack of reliable data, we to assumed that factor shares in all
manufacturing sectors are the same.
-9-
main household survey in Argentina. In turn, elasticities were given a value based on the
available evidence for comparable countries. For elasticities, the following values were
used: (a) the elasticity of substitution among factors is in the 0.2–1.15 range, relatively low
for primary sectors and relatively high for manufactures and services (see Narayanan et al.
2015); (b) the expenditure elasticities for household consumption were obtained from
Seale et al. (2003); and (c) trade elasticities are 2 for both Armington and CET elasticities.
Given the uncertainty with respect to our elasticity values, in Appendix B we conduct a
systematic sensitivity analysis of our simulation results with respect to their values.
Optimal Policy Response to a Negative Shock
In this case, we compute the optimal policy response to a negative shock, imposing a loss
function with different weights. Firstly, we simulate a 25% decrease in all (immobile)
sectoral capital stocks, without computing the optimal policy response. The macro closure
for this scenario is the following: the government balance clears through endogenous
savings, exogenous/fixed saving rates for households with endogenous real investment,
and fixed current account balance (in foreign currency) with flexible real exchange rate.
The results of this scenario are shown under column non-opt (i.e., no policy optimization)
in Table 3.2. As expected, unemployment increases -- from 16.5 to 25.6 percent-- at the
same time that (real) government savings decrease – from 0.9 to -3.8 percent of GDP.
Secondly, we solve a variant of the following optimization problem with different sets of
weights in the loss function:
2
 UR

 RSG

min LOSS  wtUR 
 1  wt RSG 
 1
0
0
 UR

 RSG

2
s.t.
all equations in the CGE model, including CGi  CGi0 CGADJ
and using government consumption as the policy instrument; i.e., in this set of simulations
the variable CGADJ is endogenous. So, we have one policy variable and two objectives.
where
-10-
wtUR = weight of (percent deviation in) the unemployment in the loss function
wt RSG = weight of (percent deviation in) the real government savings in the loss
function
UR = unemployment rate
RSG = real government savings
UR 0 = base year unemployment rate
RSG 0 = base year real government savings
CGi = base year government consumption
CGi0 = base year government consumption
CGADJ = adjustment factor government consumption
Of course, restriction on the policy instrument could have been introduced. For example,
CGADJ0*0.90 <= CGADJ <= CGADJ0*1.1
In fact, one can solve the same optimization problem with the government using more
than one (constrained) policy instrument.
In practice, in order to solve the above problem it is useful to normalize the different
policy objectives so that their values lie between zero and one. To that end, we start by
computing the so-called pay-off matrix by solving two optimization problems. Firstly, we
solve
 
min LOSS  wtUR  UR
2
where  UR  UR UR0  1
subject to all the equations in the CGE model and considering government as the
decision/policy variable.
-11-
From solving this problem we obtain (a) the minimum attainable value for the percentage
UR
deviation of the unemployment rate (  min
), and, given the conflict that exist between both
policy objectives, (b) the maximum value for the percentage deviation of the real
RSG
government savings (  max
). Secondly, we solve


min LOSS  wtUR  RSG  1
2
where  RSG  RSG RSG 0  1
subject to all the equations in the CGE model and considering government as the
decision/policy variable.
From solving this problem we obtain (a) the minimum attainable value for the percentage
RSG
deviation of the real government savings (  min
), and (b) the maximum value for the
UR
percentage deviation of the unemployment rate (  max
).
In Table 3.1 we show the pay-off matrix for this particular exercise. In the second row, the
results from solving the first problem show that, after the negative shock, it is possible to
obtain an unemployment rate of 22 percent with negative government savings of -376.9.
Similarly, the results from solving the second problem show that it is possible to obtain
real government savings of $25.7 (i.e., no change relative to the base) together with an
unemployment rate of 30.2 percent. In other words, the values in the main diagonal of
Table 3.1 show the best attainable results when only one policy objective is considered.
Table 3.1: pay-off matrix; unemployment versus government savings; 25% decrease in all
the sectoral capital stocks
Scenario
base
min δ_UR
min δ_RSG
UR
16.5
22.0
30.2
-12-
RSG
25.7
-376.9
25.7
From Table 3.1, we compute the ideal and anti-ideal values for the policy objectives in the
loss function; i.e.,
RSG
RSG
UR
UR
 min
 0% ,  max
 1,566.8% ,  min
 33.2% ,  max
 82.8%
Next, we re-define our loss function as
2
UR
RSG
  UR   min

  RSG   min




LOSS  wtUR  d

wt
RSG  RSG
d 
RSG 
  max   min 
  max   min 
2
Thus, this normalization eliminates any units of measurement, and the weights wt in the
above formula are easier to interpret.
In this case, five alternative weighting schemes in the loss function are considered, as
shown in columns (3)-(7) of Table 3.2. As can be seen (see variable CGADJ), a trade-off
exists between both policy objectives: compensating for the negative impacts of the shock
implies (a) decreasing government consumption when wtUR  0 (see column [3]), and (b)
increasing government consumption when wtRSG  0 (see column [7]). In other words,
comparison of columns (3) and (7) shows the degree of conflict between the two policy
objectives considered in the loss function. Of course, results in columns (3) and (7) of
Table 3.2 are consistent with the pay-off matrix in Table 3.1.
Not surprisingly, reductions in unemployment relative to the non-opt (i.e., no policy
optimization) scenario cannot be attained without further decreasing in (real) government
savings (compare columns [2] and [7]). In fact, note that under wtUR  1 and wtRSG  0
real gross fixed capital formation is zero (again, see column [7]), meaning that the
government has exhausted the funds available to finance its deficit; in other words, the
crowding out effect is 100 percent.
-13-
Table 3.2: simulation results; optimal policy response to a negative shock; 25% decrease in
all the sectoral capital stocks
Item
UR
RSG
CGADJ
RGFCF
CAB
REXR
LOSS
Units
(%)
($)
(index)
($)
(FCU)
(index)
base
(1)
16.5
25.7
1.000
473.5
-11.3
1.000
N.A.
nonopt
(2)
27.7
-115.5
1.000
273.0
-11.3
0.985
N.A.
weights in loss fn
UR=0 UR=0.25
RSG=1 RSG=0.75
(3)
(4)
30.2
28.5
25.7
-69.2
0.694
0.901
392.8
313.3
-11.3
-11.3
1.003
0.990
0.000
0.201
UR=0.5 UR=0.75
RSG=0.5 RSG=0.25
(5)
(6)
26.4
24.0
-183.1
-298.4
1.142
1.380
211.5
95.8
-11.3
-11.3
0.977
0.966
0.278
0.205
UR=1
RSG=0
(7)
22.0
-376.9
1.542
0.0
-11.3
0.963
0.000
where UR = unemployment rate, RSG = real gov savings, CGADJ = scaling factor gov
consumption, RGFCF = real gross fixed capital formation, CAB = current account balance,
REXR = real exchange rate, and FCU = foreign currency units.
Source: Authors’ calculations.
Optimal Selection of Macro Closure Rule
Usually, a CGE application entails the selection of a macroeconomic closure rule. In
contrast, our approach allows the “optimal selection” of the macro closure rule. As an
example, we first simulate a 25% increase in government consumption assuming, as
before, that government budget clears through changes in government savings – for
savings-investment and rest of the world we also keep the same assumptions as before
(see column non-opt in Table 3.3). Then, we simulate the same increase in government
consumption but assuming that the government optimally selects the mix between
government savings and foreign savings used to finance the increase in government
consumption (see columns (3)-(7) in Table 3.3). Analytically, the optimal selection of the
(government) closure rule implies solving the mathematical program
2
 RSG

 CAB

min LOSS  wt RSG 
 1  wtUR 
 1
0
0
 RSG

 CAB

-14-
2
s.t.
all equations in the CGE model, including CGi  CGi0 CGADJ
and optimally selecting RSG and CAB in order to finance the increase in CGi brought
about by the simulated 25% increase in CG0.
where
wt RSG = weight of (percent deviation in) the real government savings in the loss
function
wtCAB = weight of (percent deviation in) the current account balance in the loss
function
RSG = real government savings
CAB = current account balance expressed in foreign currency
Table 3.3: simulation results; optimal selection of macro closure rule; 25% increase in
government consumption
Item
UR
RSG
CGADJ
RGFCF
CAB
REXR
LOSS
Units
(%)
($)
(index)
($)
(FCU)
(index)
base
(1)
16.5
25.7
1.000
473.5
-11.3
1.000
N.A.
nonopt
(2)
14.9
-98.7
1.250
365.7
-11.3
0.986
N.A.
weights in loss fn
CAB=0 CAB=0.25
RSG=1 RSG=0.75
(3)
(4)
2.7
4.5
-9.7
-31.0
1.250
1.250
1,199.1 1,073.6
-1,914.5 -1,350.9
0.343
0.448
0.000
0.167
CAB=0.5 CAB=0.75
RSG=0.5 RSG=0.25
(5)
(6)
6.3
9.4
-48.5
-73.3
1.250
1.250
964.5
778.8
-1,007.9
-591.2
0.540
0.693
0.232
0.197
CAB=1
RSG=0
(7)
14.9
-98.7
1.250
365.7
-11.3
0.986
0.000
where UR = unemployment rate, RSG = real gov savings, CGADJ = scaling factor gov
consumption, RGFCF = real gross fixed capital formation, CAB = current account balance,
REXR = real exchange rate, and FCU = foreign currency units.
Source: Authors’ calculations.
-15-
By construction, the case where wtRSG  0 and wtCAB  1 is equivalent to the non-optimal
selection of closure rule; i.e., columns (2) and (3) are equivalent. In addition, we see that
the higher (lower) the weight on RSG (CAB), the larger the decrease in CAB (RSG). Not
surprisingly, the decrease in CAB brings about a real exchange rate appreciation.
Thus, our proposed approach can be used to simulate increases in government spending
that are financed with more than one source of resources, whose mix is optimally selected
given an objective function for the policy maker.
Policy Optimization
In this set of simulations, we compute the optimal change in government consumption to
reduce unemployment by (ideally) 95% (i.e., from 16.5 to 0.8 percent), given a loss
function that also penalizes changes in government savings. Thus, in this case, all non-base
simulations are run under the policy optimization assumption. Analytically, we solve the
problem
2
 UR

 RSG

min LOSS  wtUR  *  1  wt RSG 
 1
*
 UR

 RSG

2
s.t.
UR*  0.05UR0  0.008
RSG *  RSG 0
all equations in the CGE model, including CGi  CGi0 CGADJ
and using government consumption as the policy instrument; i.e., in this set of simulations
the variable CGADJ is endogenous. So, we have one policy variable and two policy
objectives: decrease unemployment by increasing government consumption financed with
domestic resources, but taking into account the negative impact on government savings.
The results are shown in column (2)-(6) of Table 3.4.
-16-
Table 3.4: simulation results; optimal change in government consumption to reduce
unemployment
Item
UR
RSG
CGADJ
RGFCF
CAB
REXR
LOSS
Units
(%)
($)
(index)
($)
(FCU)
(index)
base
(1)
16.5
25.7
1.000
473.5
-11.3
1.000
N.A.
weights in loss fn
UR=0 UR=0.25
RSG=1 RSG=0.75
(2)
(3)
16.5
15.1
25.7
-86.8
1.000
1.222
473.5
376.3
-11.3
-11.3
1.000
0.987
0.000
0.196
UR=0.5 UR=0.75
RSG=0.5 RSG=0.25
(4)
(5)
13.5
11.8
-211.7
-339.7
1.461
1.697
260.6
127.8
-11.3
-11.3
0.974
0.962
0.267
0.200
UR=1
RSG=0
(6)
10.2
-440.0
1.878
0.0
-11.3
0.957
0.000
where UR = unemployment rate, RSG = real gov savings, CGADJ = scaling factor gov
consumption, RGFCF = real gross fixed capital formation, CAB = current account balance,
REXR = real exchange rate, and FCU = foreign currency units.
Source: Authors’ calculations.
By construction, there are no changes in the first non-base simulation (see column [2]), as
wtUR  0 and wt RSG  1 (i.e., only deviations of RSG from its base year are penalized). The
other columns show the trade-off between increased government consumption/decrease
in unemployment and decrease in government savings.
Source: Authors’ calculations.
NOTES:
Certainly, we could have selected more than one policy instrument in each simulation. For
example, taxes could also be optimally selected. In the optimization exercise, we can
restrict the tax rates to vary less than 5% with respect to their benchmark values (taxrat0);
-17-
that is, the following constraints could be imposed to the model: 0.95 taxrat0 <= taxrat <=
1.05 taxrat0.
As shown in the last set of experiments, there is no need to assume that policy targets in
the loss function correspond to base year values.
4. Concluding Remarks
In this paper, we have embedded a computable general equilibrium model within a
programming problem for policy simulation. In other words, policy design is seen as a
decision problem with multiple conflicting objectives.
Certainly, we could have selected more than one policy instrument in each simulation

for example, taxes could also be optimally selected

can restrict the tax rates to vary by less than 5% with respect to their benchmark
values
Next, we plan to
(a) apply the approach to a relevant policy issue in Argentina and/or elsewhere, and
(b) implement dynamic version of the approach, over a recursive dynamic CGE model and
assuming that the government is a forward-looking agent.
-18-
Appendix A: Extensions to PEP-1-1
In this appendix we present the modifications introduced to the single-country static PEP
model PEP-1-1 v2.1.
Exports
In the PEP 1-1 Standard Model, the world demand for exports of product i is
(62)
 e.PWX i
EXDi  EXDOi 
FOB
 PEi



 iXD
In case  iXD   , equation (64) simplifies to
(62’)
e.PWX i  PEiFOB
which represents the “pure” form of the small-country hypothesis; producers can always
sell as much as they want on the world market at the (exogenous) current price, PWX i .
To simulate a change in the world export demand of a given commodity exported by a
given industry keeping the small country assumption (see scenario edem-txt), we
introduce the following changes to the model: (1) again, replace equation (62) by (62’),
and (2) replace equation (61) (i.e., the relative supply of exports and local commodity) by
equation (61’) for the selected commodity and industry pair(s). In addition, we drop the
first order condition of the CET function that determines domestic and export sales.
(61’)
EX j ,i  EXO j ,i
Current Account BoP
Equation (RW1) defines the current account balance in foreign currency. Equations (RW2)
and (RW3) define the index for domestic producer prices and the real exchange rate,
respectively. As we be shown, variables CAB_FCU and REXR are used to select the
macroeconomic closure rule for the model.
(RW1) CAB FCU 
CAB
e
-19-
(RW2) DPI   dwtsi PLi
i
(RW3) REXR 
e
DPI
where
CAB_FCUO = current account balance in foreign currency units
DPI = index for domestic producer prices (PL-based)
REXR = real exchange rate
dwts(i) = domestic sales price weights
Government
In the PEP Standard Model, government consumption of commodity i is determined by
the following equation (see equation (55) in Decaluwé et al. (2010)).
(55)
PCi CGi   iGVT G
with G (i.e., current government expenditures on goods and services) fixed and equal to
its initial value (i.e., G  GO ). As an alternative, we modified the government behavior
assuming that the real government spending can be exogenous (i.e., all the CGi variables)
while G is endogenous. Specifically, we dropped equation (55) from the model and
added equations (55’) and (55’’),
(56’)
CGi  cgbari CGADJ
(56’’) G   PCi CGi
i
where
CGADJ = adjustment factor for CG
cgbar(i) = base-year CG(i)
Equation (G1) defines real government savings, as the ratio between nominal government
savings and the GDP deflator.
-20-
(G1)
SG REAL 
SG
PIBGDP
where
SG_REAL = real government savings
Tax Rates
(T1)
TTDH1h  ttdh1hTTDHADJ
(T1)
TTICi  ttic hTTICADJ
where
TTDHADJ = adjustment factor for TTDH
TTICADJ = adjustment factor for TTIC
ttdh1bar(h) = base-year TTDH1
tticbar(i) = base-year TTI
Household Savings
Equation (S1) defines the marginal propensity to save of households. Its structure is the
same as that of equations (T1) and (T2) for tax rates and (56’) for government
consumption. (43). In fact, whether MPSADJ is flexible depends on the closure rule for the
savings-investment balance.
(S1)
sh1h  sh1h MPSADJ
where
MPSADJ = savings rate scaling factor
sh1h = base-year sh1h
-21-
Calibration using Employment by Sector
In PEP-1-1 it is assumed that all sectors pay the same wage. In the extended PEP-1-1, the
analyst can complement the SAM with data on number of workers by sectors. To do so,
the remuneration to labor type l paid by the activity j is computed as
Wl wdist l , j 1 ttiwl , j 
where wdist l , j is a “distortion” factor applied to for labor type l in industry j that allows
modeling cases in which the factor remuneration differs across activities. In other words,
each activity pays an activity-specific wage that is the product of the economy-wide wage
and an activity-specific wage (distortion) term. To calibrate wdist l , j , the model dataset
must provide physical labor quantities. In implementing this extension, the following
equations of the original model were modified.
(11)
YHL h   Wh,lL Wl wdist l , j LDl , j
l
(37)
j
TIWl , j  ttiwl , jWl wdist l , j LDl , j
YROW  e PWM i IM i
 
(44)
k
i
RK
row, k
R
k, j
KDk , j
j
  WrowL ,l  Wl wdist l , j LDk , j
l
j
  TRrow, agd
agd
(70)
WTI l , j  Wl wdist l , j 1 ttiwl , j 
(92)
GDP _ IB  Wl wdist l , j LDl , j   RK k , j KDl , j  TPRODN  TPRCTS
l, j
k, j
Wage Curve
The PEP Standard Model assumes full employment of the labor force. As explained above,
we introduced endogenous unemployment by means of a wage curve. Specifically, we add
to the model equation (WC) and the endogenous variable UERAT (unemployment rate).
-22-
The value of the phillips parameter (i.e., the wage curve elasticity) was set at -0.1 based on
international evidence documented in Blanchflower and Oswald (2005). Of course, the
equilibrium condition for labor market was adjusted accordingly (see equation 85).
(WC)
 UERATl
Wl
WOl


PIXCON PIXCONO  UERATOl
(85)
LS l 1  UERATl    LDl , j



phillipsl
j
where
UERAT(l) = unemployment rate for type l labor
phillips(l) = elasticity of real wage with respect to unemployment rate
Policy Optimization
In its general form, the loss function for the policy maker is written as
 GDPBP, REAL

LOSS  wtGDPBP , REAL 
 1
*
 GDPBP, REAL

 UERATl


  wtUERATl 

1
*
UERAT
l
l


 SG

 wt SGREAL  REAL
 1
*
 SGREAL

2
2
2
 CABFCU

 wtCABFCU 
 1
*
 CABFCU

2
 TTDHADJ

 wtTTDHADJ 
 1
*
 TTDHADJ

 TTICADJ

 wtTTICADJ 
 1
*
 TTICADJ

 CGADJ

 wtTTICADJ 
 1
*
 CGADJ

2
2
2
where
-23-
wt(iopt) = weights in the policy optimization objective function
gdp_bp_realstar = GDP BP REAL in optimization objective function
ueratstar(l) = UERAT in optimization objective function
sg_realstar = SG_REAL in optimization objective function
cab_fcustar = CAB_FCU in optimization objective function
ttdhadjstar = TTDHADJ in optimization objective function
tticadjstar = TTICADJ in optimization objective function
cgadjstar = CGADJ in optimization objective function
-24-
Appendix B: Sensitivity Analysis
As usual, the results from the PEP-1-1-OPT model are a function of (i) the model structure
(e.g., functional forms used to model production and consumption decisions,
macroeconomic closure rule, among other elements); (ii) the base year data used for
model calibration (i.e., the SAM), and; (iii) the values assigned to the model elasticities or,
more generally, to the model’s free parameters.
Certainly, the elasticities used in this study implicitly carry an estimation error, as in any
similar model. Consequently, we have performed a systematic sensitivity analysis of the
results with respect to the value assigned to the model elasticities. Hence, if the
conclusions of the analysis are robust to changes in the set of elasticities used for model
calibration, we will have greater confidence in the results presented above.
In order to perform the systematic sensitivity analysis, it is assumed that each of the
model elasticities is uniformly distributed around the central value used to obtain the
results. The range of variation allowed for each elasticity is +/- 80%; that is, a wide range
of variation for each model elasticity is considered. Then, a variant of the method
originally proposed by Harrison and Vinod (1992) is implemented, which allows for
performing a systematic sensitivity analysis. In short, the aim is to solve the model
iteratively with different sets of elasticities. Thus, a distribution of results is obtained to
build confidence intervals for each of the model results. The steps for implementing the
systematic sensitivity analysis are as follows.
Step 1. In the first step, the distribution (i.e., lower and upper bound) for each of the
model parameter that will be modified as part of the systematic sensitivity analysis is
computed: elasticities of substitution between primary factor of production, trade-related
elasticities, expenditure elasticities, and unemployment elasticities for the wage curves.
Step 2. In the second step, the model is solved repeatedly, each time employing a
different set of elasticities; it is, therefore, a Monte Carlo type of simulation. First, the
value for each model elasticity is randomly selected. Second, the model is calibrated using
the selected elasticities. Third, the same counterfactual scenarios as previously described
-25-
are conducted. Then, the preceding steps are repeated several times, 500 in this case,
with sampling with replacement for the value assigned to the elasticities.
Table B.1 shows the percentage change in private consumption estimated (i) under the
central elasticities, and; (ii) as the average of the 500 observations generated by the
sensitivity analysis. For the second case, the upper and lower bounds under the normality
assumption were also computed; notice that all runs from the Monte Carlo experiment
receive the same weight. As can be seen, the results reported above are significant, while
estimates presented in Tables 1-3 are within the confidence intervals reported in Table
B.1. For example, there is virtual certainty that the pwefood scenario has a negative effect
on private consumption in Argentina.
Table B.2: sensitivity analysis; real private consumption percent deviation from base
95% confidence interval under normality assumption
Source: Authors’ elaboration.
Figure B.2 shows non-parametric estimates of the density function for the percentage
change in private consumption in the pwefood scenario. Again, the sign of the results (i.e.,
positive) is not changed when model elasticities are allowed to differ in +/- 80% of their
“central” value.
Figure B.1: sensitivity analysis, real private consumption deviation from base in 2030
-26-
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